A-1

APPENDIX A1. LITERATURE REVIEW

Appendix A1: FLECHT Low Flooding Rate Cosine Test Series 

Dates When Tests Were Performed: 1974 - 1975 

References:

R1 Rosal, E. R. et al, AFLECHT Low Flooding Rate Cosine Test Series Data Report,@

WCAP-8651, Dec 1975. 

R2 Lilly, G.P.,Yeh, H. C.,Hochreiter, L. E., and N. Yamaguchi, APWR FLECHT Cosine Low 

Flooding rate Test Series Evaluation Report,@ WCAP-8838, March 1977. 

Availability of Data: 

Plots of selected data exist in the data report in R1. The raw data and reduced and analyzed 

data exists at Westinghouse on CDC 6600 and 7600 Magnetic tapes. This data has been in 

storage at the Westinghouse facilities. Microfiche of the raw data and analyzed data exist at the 

Westinghouse Engineering offices in Monroeville, PA. It is not clear if any of this data was put 

on the INEL data bank. 

Test Facility Description, Types of Tests 

The FLECHT Low Flooding Rate Cosine Test Series was a continuation of the FLECHT reflood 

heat transfer program started in the late 1960's and focused on low forced flooding rates tests at 

low pressures to provide a broader data range for the Appendix K licensing basis during the 

reflood period. The overall objective of the test program was to obtain data that would be useful 

for calculating the reflood behavior of PWRs following a postulated Loss Of Coolant Accident. 

The tests were performed using a 10x10 rod bundle with 91 active electrical heater rods and 

nine guide tube thimbles in which instrumentation was placed. The rod bundle was placed 

inside a thick walled 19.05 mm (0.75 in square housing which was heated externally for the 

tests. There was excess flow area around the bundle such that the housing had to be heated to 

preserve the correct power-to-flow area of a PWR fuel assembly. The heater rods were 10.72 

mm (0.422 in) in diameter and were arranged on a square pitch of 14.3 mm (0.563 in) and had a 

heated length of 3.66 m (12 ft). The electrical heater rods used a 1.66 cosine power distribution 

which was approximated by different pitch heating coils. The facility layout is shown in Figure 

A1.1 and the bundle geometry is given in Figure A1.2 from R2. A radial power distribution was 

used in these experiments to simulate or bound the rod-to-rod power distribution in a PWR fuel 

assembly. One feature which was unique in this test series is that there were a large number of 

variable inlet flooding rates tests performed to better simulate the gravity reflood behavior of the 

PWR. There were also low initial clad temperature test performed to simulate lower power 

regions in the core that could have quenched during blowdown or during Upper Head Injection 

which was a newer high-pressure accumulator installed on PWRs which had Ice Condenser 

Containment. 
A-2

The ranges of conditions include: 

Constant Flooding Rates 10.16 - 38.1 mm/s (0.4 - 1.5 in/s) 

Upper Plenum Pressure 172.37 - 413.685 kPa (25 - 60 psia) 

Initial Clad Temperature 148.88 - 871.11 degrees C (300 - 1600 degrees F) 

(At Peak Location) 

Initial Peak Power 1.673 - 3.1167 kW/m (0.51 - 0.95 kW/ft) 

(At Peak Location) 

Inlet Subcooling 11.11 - 100 degrees C (20 180 degrees F) 

Variable Inlet Flooding Rate Ranged from 0.3048 m/s (12 in/s) for 5 s and 20.32 mm/s 

(0.8 in/s) onward, to 50.8 mm/s (2 in/s) for 20 s and 25.4 

mm/s (1 in/s) onward 

Continuously Variable Flooding There were two tests which simulated the average variable 

flooding rate from the FLECHT-SEASET Phase B systems 

tests. 

Housing Temperature Tests Housing initial temperature varied from 140 - 371.11 

degrees C (284 - 700 degrees F) 

FLECHT Repeat Tests There were six repeat tests of previously performed 

FLECHT reflood tests. 

Bundle and Housing Three different housing temperatures were used 

Stored Energy Tests 

Supplemental Entrainment These were entrainment tests with several disconnected 

heater rods and failed rods over a range of flooding rates 

and pressures to provide additional data. 

Instrumentation and Data From Tests 

The heater rods were instrumented with several thermocouples to measure the inside cladding 

surface temperature. The heat flux from the cladding surface was calculated form the 

thermocouple response using an inverse conduction computer program called DATAR. This 

program should still exist at Westinghouse and has been replaced by an improved version 

called DATARH. The thimbles shown in Figure A2.2 were unheated tubes which receive radiant 

heat from the heater rods. The temperatures of the thimbles were measured using 

thermocouples welded to the inside of the tubes. Housing temperatures were measured along 

the length of the housing to characterize its heat release as the bundle quenched. The inlet flow 

and water temperature were measured as well as the pressure in the exit or upper plenum. 

There were separators and collection tanks at the exit of the test section such that the existing 

steam and water flows could be separated and individually measured. There were also 

sensitive differential pressure cells every two feet along the housing to measure the bundle 
A-3

mass storage. The spacing is too sparse to obtain an accurate indication of local void fraction, 

however, the cells will indicate the mass stored in the bundle. 

One of the more important pieces of data is the steam probe measurements at the 2.1366, 

3.048 and 3.81 m (7, 10 and 12.5 ft) elevations. These were shielded aspirating thermocouples 

which could measure the vapor superheat until the quench front would approach and fill the 

probe with water. The steam probes indicated the high degree of superheat in the dispersed 

two-phase flow above the quench front. 

This FLECHT Test Series was the first to perform a mass and energy balance down the test 

section to determine the local quality conditions and the split of the heat transfer between 

radiation to drops, vapor and housing, and steam convection with entrained droplets. There are 

calculated values of the real quality for seven tests which span the matrix at different times in 

the transient. The analysis indicated, for the first time, that the convection is enhanced when 

droplets are entrained. The analysis also indicated the importance of the radiation heat transfer. 

The Appendix A in Reference 1 gives the details of the calculational method. 

Conclusions 

The FLECHT Low Flooding Rate Cosine tests do have some data which would be of interest for 

improved reflood modeling. In addition to the heater rod temperatures, the measurement of the 

vapor temperature at the 2.1366, 3.048 and 3.81 m (7, 10 and 12.5 ft) elevations are of value 

since these data indicate the degree of non-equilibrium within the flow. The pressure drop 

measurements are too coarse to be used as an indicator of the void fraction within the bundle. 

However, these measurements can be used to indicate the mass rate of accumulation within the 

bundle such that a complete mass balance can be calculated from the data for the tests. 

The conditions which were simulated are also useful from a code analysis and validation effort 

since a large range of conditions were simulated, in particular a variable inlet flooding rate and a 

continuously variable inlet flooding rate which simulates gravity reflooding. These experiments 

would be useful to assess the code performance. 

This is not sufficient data to make code model changes without the potential for compensating 

error. More detailed data is needed which identify code calculated parameters such as vapor 

superheat, convective enhancement, radiation to drops, rods, vapor and housing, droplet sizes 

and velocities along the bundle, and the void distribution in the froth region. These types of 

measurements are missing such that the code can only be compared to the cladding 

temperatures, quench front, and the overall mass balance. 

Therefore while these tests are useful in determining the overall reflood heat transfer, they 

provide very limited data which can be used to assess the reflood phenomena which was 

identified in the PIRT. Therefore, limited effort should be spent modeling these tests. 
Figure A1.1 FLECHT Low Flooding Rate Test Configuration. 

A-4
Figure A1.2 Rod Bundle Instrumentation for FLECHT Low Flooding Rate Tests.

A-5
 A-6

APPENDIX A2. LITERATURE REVIEW

Appendix A2: FLECHT Low Flooding Rate Skewed Test Series 

Dates When Tests Were Performed: 1976-1977 

References:

R3 Rosal, E. R. et al, “FLECHT Low Flooding Rate Skewed Test Series Data Report,” 

WCAP-9108, May 1977. 

R4 Lilly, G. P., Yeh, H. C., Dodge, C. E., and S. Wong, “PWR FLECHT Skewed Profile Low 

Flooding Rate Test Series Evaluation Report,” WCAP-9183, Nov. 1997. 

 

Availability of Data:

Plots and tables of selected data are given in R3 for the different tests. Some of the basic 

quantities which were measured and calculated from the bundle mass and energy balance 

(given in R4) such as the local non-equilibrium quality, portion of the rod energy which is due to 

radiation and convective film boiling, and energy absorbed by the drops above the quench front. 

Two skewed power tests and one low flooding rate cosine test were analyzed in detail, which 

can be used for computer code comparison purposes. A heat transfer correlation was also 

developed which was a function of the distance above the quench front and is given in 

Reference R4. The skewed profile data was also compared to the cosine power shape data for 

the same test conditions. 

The raw test data and the analyzed test data are available at Westinghouse on CDC 7600 

magnetic tapes. Some selected tests have been brought forward to the new UNIX system at 

Westinghouse. Microfiche exist for the measured data as well as the analyzed test data at 

Westinghouse Engineering Offices in Monroeville, PA. It is believed that some of the transient 

temperature data were placed in the NRC data bank at INEL. 

 

Test Facility Description, Types of Tests

The FLECHT Low Flooding Rate Skewed Tests were a continuation of the FLECHT Low 

Flooding Rate Cosine Tests which were performed in the 1975 time frame. The rod diameter 

used was 10.719 mm (0.422 in) on a square pitch of 14.33 mm (0.563 in). These tests were 

intended to provide data for supporting the Appendix K reflood heat transfer models for different 

possible axial power shapes for analysis of the Loss Of Coolant Accident. 

There were two unique differences in the skewed tests as compared to the earlier cosine tests. 

The axial power shape was skewed to the top of the bundle with a peak of 1.35 at 3.048 m (10 

ft), and a low mass circular housing was used for the first time in the FLECHT program. 

The test facility is shown in Figure A2.1 and is similar to that for the low flooding rate cosine 

tests. The power shape is shown in Figure A2.2 and the bundle cross section is given in Figure 

A2.3. The bundle contained 105 electrical heater rods, six guide tube thimbles, eight metal filler 

rods and the ANC liquid level probe. The use of the filler rods permitted the square pitch rod 

array to fit into the circular housing with a minimum of excess flow area. There was additional 
 A-7

instrumentation added to the skewed test facility as compared to the low flooding rate cosine 

tests. There was more extensive thermocouple instrumentation within the bundle, there were 

differential pressure cells every foot instead of every two feet, close coupled tanks were 

attached to the upper plenum to collect and separate the liquid entrainment, and a more reliable 

exit flow measurement was used to measure the exiting steam flow from the bundle. 

There was a radial power profile which was similar to the low flooding rate cosine bundle as 

seen in Figure A2.3. There were instrumented control rod guide tubes and aspirating steam 

probes in the rod bundle. The steam probes were at 2.1336, 3.048 and 3.3528 m (7, 10 and 11 

ft). Selected guide tube thimbles were also instrumented with wall thermocouples. 

The range of conditions which were investigated were similar to the low flooding rate cosine 

tests and included: 

Constant Flooding Rate 17.78 - 152.4 mm/s (0.7 - 6.0 in/s) 

Upper Plenum Pressure 137.896 - 413.685 kPa (20 - 60 psia) 

Initial Clad Temperature 263.89 - 871.11 degrees C (507 - 1600 degrees F) 

(At Peak Location) 

Initial Peak Power 1.4764 - 3.3808 kW/m (0.45 - 1.0 kW/ft) 

(At Peak Location) 

Inlet Subcooling 4.44 - 55.55 degrees C (8 - 100 degrees F) 

Variable Inlet Flooding Rate Ranged from 152.4 mm/s (6 in/s) for 5 seconds 

 to 20.32 mm/s (0.8 in/s), to 38.1 mm/s (1.5 in/s) for 100 s 

 to 12.7 mm/s (0.5 in/s) onward 

Cosine Overlap Tests Tests were performed to overlap Cosine and 

 Skewed test conditions 

Hot and Cold Channel Tests Tests were performed with portions of the bundle 

 hot and the remainder cold 

Transient Pressure and Tests were performed in which the inlet flow, system 

Subcooling Tests pressure, and the inlet subcooling varied with time 

There were also repeat tests which were performed to insure that the bundle geometry was not 

distorted. There were a total of 75 powered experiments. Very early on in the program, two 

heater rods failed at the beginning of testing. As the number of thermal cycles increased in the 

test bundle, additional heater rods failed later. 

Instrumentation and Data From Tests

The electrical heater rods were instrumented with several thermocouples at the different 

elevation which gave good coverage for the length of the bundle. However, there were no 

thermocouples placed around the spacer grids which would indicate a spacer grid effect on the 

two-phase flow. The liquid carried out of the test section was measured as well as the exiting 
 A-8

steam vapor. The mass storage within the test section was also measured using delta P cells at 

one-foot intervals along the length of the housing. From these measurements, a transient mass 

balance could be performed on the test to help validate the data. Typically the mass balances 

were within five percent. 

There were three aspirating steam probes at the 2.1336, 3.048 and 3.3528 m (7, 10 and 11 ft) 

elevations, as well as the exit pipe of the test section, to verify that the steam flow measurement 

was single phase. Using the flow measurements at the bundle exit, the actual steam nonequilibrium temperature, and the integrated wall heat flux between the steam probe locations; 

an energy balance can be performed to obtain the local quality and therefore the local steam 

and liquid flow. The change in the calculated quality indicates how much of the rod bundle 

surface heat flux goes into evaporating the entrained liquid droplets. The calculation was 

carried to the quench front where the vapor temperature was assumed to be the average of the 

rod temperature and the saturation temperature. 

A simple radiation network was developed to separate the radiation heat transfer component 

from the total measured wall heat flux on the heater rods. Knowing the total wall heat flux, and 

subtracting the radiation heat flux, the convective wall heat flux can be determined. In the 

dispersed flow film boiling, this is the heat flux to the superheated vapor which contains 

entrained liquid droplets. The Nusselt number for the convective flux was calculated and 

compared to the Nusselt number that typical single-phase correlations would predict. It was 

observed that the convective Nusselt number calculated from the test data lied significantly 

above the limits calculated with conventional single phase convective correlations. Also, since 

the flow was superheated steam at low pressure, the calculated vapor Reynolds number was 

quite small, from 1500 to 10,000. These data and that of the low flooding rate cosine tests 

indicated that the presence of entrained liquid droplets could enhance the convective nature of 

the single phase vapor significantly at low vapor Reynolds numbers. 

Conclusions

The FLECHT Low Flooding Rate Skewed Power Tests do have data which would be of interest 

for improved computer code modeling for the reflood heat transfer process. In particular, the 

different axial power shape used in these tests is very useful for assessing computer codes 

which may have been “tuned” to a cosine power shape. The pressure drop measurements are 

improved in the skewed bundle tests such that a more local void fraction (one-foot increments), 

can be determined and used to assess the local heat transfer. The void fractions and overall 

pressure drop are also used in the test bundle mass balances along with the inlet flows and exit 

flows. Typically the mass balances were within five percent. 

There were a large number of experiments which were performed over a wide range of 

conditions, some of which specifically over-lapped with the low flooding rate cosine tests. 

These overlap experiments are particularly useful for code validation purposes, since the 

accuracy of the computer code predictions for different axial power shapes can be assessed. A 

Best-Estimate computer code must be able to calculate a range of different axial power shapes 

to determine the most limiting shape. 

While the data from the skewed series of experiments as well as the data analysis of these tests 

was improved over the low flooding rate cosine tests; there was still the lack of sufficient vapor 

temperature distribution and information in the test bundle such that the axial distribution of the 

local qualities could be more accurately determined. The data was analyzed to determine the 
 A-9

heat flux split between radiation heat transfer and convective-dispersed flow film boiling heat 

transfer using a simplified radiation network approach. When the resulting convective-film 

boiling heat transfer (from the data) was compared to calculated single phase heat transfer 

correlation at the same vapor Reynolds number, the calculated data convective-film boiling 

transfer was significantly higher. Since the single phase correlation used the measured vapor 

temperature and the calculated vapor flow rate from the quality and energy balance, it is 

believed that the improved heat transfer is due to the presence of the entrained droplets which 

can add to the turbulence level in the flow at the low vapor Reynolds numbers. This 

phenomenon of enhanced convective-dispersed flow film boiling was identified in this report as 

well as in the low flooding rate report. 

Therefore, the Low Flooding Rate Skewed Power reflood tests are useful in determining the 

overall heat transfer processes and some of individual models and phenomena which 

compromise the reflood heat transfer process. 
Figure A2.1 FLECHT Low Flooding Rate Test Facility Schematic.

A-10
Figure A2.2 FLECHT Low Flooding Rate Test Power Shape. 

A-11
Figure A2.3 FLECHT Low Flooding Rate Test Rod Bundle Cross Section. 

A-12
 A-13

APPENDIX A3. LITERATURE REVIEW

Test Facility Name: Westinghouse FLECHT-SEASET 21-Rod Bundle Test Facility. 

Dates When Tests Were Performed: 1977-1982 

References:

R5 M. J. Loftus, et. al., APWR FLECHT SEASET 21-Rod Bundle Flow Blockage Task Data 

and Analysis Report,@ NUREG/CR-2444, EPRI NP-2014, ECAP-992, Vol. 1 and Vol. 2, 

September 1982. 

Availability of Data: 

Volume 1 contains data and limited analysis from the 21-Rod Bundle FLECHT-SEASET 

Program. Volume 2 contains sampling of data tables and plots collected for the unblocked 

bundle (Configuration A) and five blocked bundle configurations, (B, C, D, E and F). All the 

valid measured data are available in the NRC data bank. 

Test Facility Description, Types of Tests

Low forced flooding rate, gravity reflood, and single phase flow tests were performed in the 21-

Rod bundle FLECHT-SEASET Test Facility. The overall objectives of these tests were to 

determine effects of various flow blockages of reflooding behavior and to aid in 

development/assessment of computational models in predicting reflooding behavior of flow 

blockage configurations for the 163-Rod flow blockage bundle test. 

The tests were performed using a 5x5 rod bundle array typical of a 17x17 power fuel assembly. 

The bundle contained 21 active electrical heater rods and four triangular shaped filler strips 

placed at the corners in order to minimize excess flow areas due to the circular low mass flow 

housing as shown in Figure A3.1. The heater rods were 0.0095 m (0.374 in) in diameter and 

3.24 m in length. The electrical heater rods used a 1.66 peak to average axial power 

distribution with a chopped cosine shape, which was approximately simulated by different pitch 

coils in the electrical heating element. The heater rod bundle had a uniform radial power profile. 

Spacer grids were of a simple egg-crate style installed 0.533 m (21 in) apart. The tests were 

conducted in a heavily instrumented facility as indicated in the reference Reports. 

Four types of tests were conducted: hydraulic characteristics tests, steam cooling tests, forced 

reflood tests, and gravity reflood tests. The hydraulic characteristics tests were performed to 

determine the pressure losses associated with rod friction, grids, and blockage sleeves. The 

steam cooling tests were performed to measure single-phase heat transfer effects of unblocked 

and blocked configurations. Forced reflood tests were performed to measure the two-phase 

flow heat transfer effects of unblocked configurations. The gravity reflood tests were performed 

to measure heat transfer effects during the PWR-simulated gravity reflood injection for 

unblocked and blocked configurations. 
Figure A3.1 Schematic of the Test Bundle. 

The range of conditions included: 

Constant Flooding Rates: 10.2 - 152 mm/s (0.4 - 6.0 in/s) 

Upper Plenum Pressure: 0.14 - 0.28 MPa (20 - 40 psia) 

Initial Clad Temperature: 260 - 871 degrees C ( 500 - 1600 degrees F) 

(At Peak Location) 

Inlet Subcooling: 3 - 78 degrees C (5 - 140 degrees F) 

Variable Steps in Flooding Rates: 20 - 152 mm/s (0.8 - 6.8 in/s) 

Injection Gravity Reflood: 0.09 - 0.82 kg/s (0.2 - 1.8 lb/s) 

(Variable Steps) 

Housing Temperature Tests: 222 - 546 degrees C (431 - 1015 degrees F 

(At Peak Location) 

Repeat Tests: There were 2 repeat tests of the Unblocked 

 Configuration (A) 

Conclusions 

Comparisons of calculated and measured temperatures generally showed good agreement. 

Nusselt numbers calculated from the steam cooling data were compared with the Dittus-Boelter 

heat transfer correlation as a function of Reynolds number. The results showed that, in general, 

the Dittus-Boelter correlation under predicts the heat transfer coefficient for Reynolds numbers 

less than 2500 and is in agreement for values about Reynolds numbers greater than 10,000. 

Comparisons of the FLECHT-SEASET 21-Rod Bundle tests with the Rod Bundle PIRT are 

given in Tables A3.1 to A3.4. 

 A-14
A-15

Figure A3.2 21-Rod Bundle Flow Blockage Task Instrumentation Schematic Diagram
A-16

Table A3.1 Assessment of FLECHT-SEASET Unblocked 21-Rod Bundle Test to RBHT PIRT: Disperse

Core Component 
A-17

Table A3.2 Assessment of FLECHT-SEASET Unblocked 21-Rod Bundle Test to RBHT PIRT: Top Dow

Components

Process/Phenomena Ranking Basis FLECHT-SEA

De-entrainment of film flow Sputtering droplet size and velocity Fuel rod/heater rod properties for stored energy: ρ, cp and k. 

Gap heat transfer 

L1

L 

L1L1

The film flow is the heat sink needed to quench the heater rod. This has high uncertainty. The droplets are sputtered off at the quench front and are then re-entrained upward. Since the sputtering front is above the PCT location, no impact. The entrained sputtered drops do not affect the total liquid entrainment into the reactor system, as well as the steam production, in the steam generators. These properties are important since they determine the heat release into the coolant. However, since this occurs above the PCT level, no impact. Affects the rate of energy release from the fuel/heater rod. 

Top down quensome tests. Details at top qmeasured. Ontransfer was meHeater rod propNo gap in heate

Note: Some of these individual items can be ranked as High (H) within the top down quenching process; howevranked as low (L) for a PWR/BWR since it occurs downstream of the PCT location. 
A-18

Table A3.3 Assessment of FLECHT-SEASET Unblocked 21-Rod Bundle Test to RBHT P

Preliminary PIRT for Gravity Reflood Systems Effects Tests

Process/Phenomena Ranking Basis FLECHT-SEASE

Upper PlenumEntrainment/Deentrainment Hot leg - Entrainment, de-entrainment. Pressurizer Steam Generators Reactor Coolant Pumps Cold leg accumulator injection Cold leg pumped injection 

M 

L L 

H H H H 

The plenum will fill to a given void fraction after which the remaining flow will be entrained into the hot leg, large uncertainty. The hot legs have a small volume and any liquid swept with the hot leg will be entrained into the steam generator plenums, medium uncertainty. Pressurizer is filled with steam and is not an active component, small uncertainty. The generators evaporate entrained droplets and superheat the steam releases (particularly at low pressures). The result is a higher steam flow downstream of the generators. High uncertainty since a good model is needed. FLECHT-SEASET data exists for reflood. This is the largest resistance in the reactor coolant system which directly affects the core flooding ratelow uncertainty. Initial ECC flow into the bundle. Pumped injection maintains the core cooling for the majority of the reflood transient. 

Not measured. Not measured. Not measured. Not measured. Not measured. Not measured. Variabsimulated to model acinjections, also continuflooding rate tests werNot measured, variablto model accumulator also continuous by vartests were performed. Low pressure (20 psia
A-19

Table A3.3 Assessment of FLECHT-SEASET Unblocked 21-Rod Bundle Test to RBHT P

Preliminary PIRT for Gravity Reflood Systems Effects Tests (Continued)

Process/Phenomena Ranking Basis FLECHT-SEASE

Pressure Injection Subcooling Downcomer Wall Heat Transfer Lower Plenum Wall Heat Transfer Break 

H 

M/H 

H 

M 

L 

Low pressure (20 psia) significantly impacts the increased vapor volume flow rate, which decreases the bundle flooding rate. Lower subcooling will result in boiling below quench front such that there is additional vapor to vent. The heat transfer from the downcomer walls can raise the ECC fluid temprature as it enters the core, resulting in more steam generation. Source effect as downcomer but less severe. Excess ECC injection spills, but break ΔP helps pressurize reactor system. 

Low pressure (20 psiaLow subcooling simulaNot measured. Not measured. Not measured. 
A-20

Table A3.4 Assessment of FLECHT- SEASET Unblocked 21-Rod Bundle Test to RBHT PIRT: High R

Phenomena

Process/Phenomena Basis FLECHT-SEASET 

Core Film Boiling Upper Tie Plate CCFL Channel-Bypass Leakage Steam Cooling Dryout Natural Circulation Flow Flow Regime Fluid Mixing Fuel Rod Quench Front Decay Heat Interfacial Shear Rewet: Bottom Reflood 

PCT is determined in film boiling period. Hot assembly is in co-current flow above CCFL limit. Flow bypass will help quench the BWR fuel assembly core. A portion of the dispersed flow film boiling heat transfer. Transition from nucleate boiling and film boiling. Flow into the core and system pressure drops. Determines the nature and details of the heat transfer in the core. Determines the liquid temperature in the upper plenum for CCFL break down. Heat release from the quench front will determine entrainment to the upper region of the bundle. Energy source for heat transfer. Affects the void fraction and the resulting droplet and liquid velocity in the entrained flow. BWR hot assembly refloods like PWR. 

Total heat transfer is meNot applicable. Not applicable. Steam cooling heat transdata. Quench front is measureNot measured. Not measured. Not measured. Quench front data existsMeasured as initial/bounNot measured. Total reflood heat transfe
A-21

Table A3.4 Assessment of FLECHT- SEASET Unblocked 21-Rod Bundle Test to RBHT PIRT: High R

Phenomena (Continued)

Process/Phenomena Basis FLECHT-SEASET 

Rewet Temperature Top Down Rewet Void Distribution Two-Phase Level 

Determines the quench front point on the fuel rod. Top of the hot assembly fuel will rewet in a similar manner as PWR. Gives the liquid distribution in the bundle. Similar to quench front location, indicates the location of nucleate and film boiling. 

Quench temperature meTop down rewet quench Not measured. Measured by rod TC’s. measured, two phase levcells. 
A-22

APPENDIX A4. LITERATURE REVIEW 

Appendix A4: FLECHT-SEASET 161-Rod Unblocked Bundle Tests 

Dates When Tests Were Performed: 1981-1982 

References: 

R6 Loftus, M. J., et al,@ PWR FLECHT-SEASET Unblocked Bundle Forced and Gravity 

Reflood Task Data Report,@ NUREG/CR-1532, September 1981. 

R7 Lee, N. ,Wong, S., Yeh, H.C., and Hochreiter, L.E., APWR FLECHT-SEASET Unblocked 

Bundle Forced and Gravity Task, Data Evaluation and Analysis Report,@ NUREG/CR2256, February 1982. 

R8 Wong, S. and Hochreiter, L.E., APWR FLECHT-SEASET Analysis of Unblocked Bundle 

Steam-Cooling and Boil-off Tests,@ NUREG/CR-1533, May 1981. 

Availability of Data: 

Plots and tables of selected data are given in R6 for each of the tests. These tests are similar to 

the Low Flooding Rate Cosine Tests excepting that the rod array used in the FLECHT-SEASET 

tests used the newer 17x17 array while the Low Flooding Rate Cosine and Skewed Power 

Tests used the older 15x15 rod array. There are selected tests which were analyzed in detail in 

Reference 2, particularly Test 31504 which is a 40 psia, 1 in/s constant reflood test. There was 

additional instrumentation on the test bundle which permitted more accurate mass and energy 

balances for the two-phase dispersed flow region of the bundle. There were also several highspeed movies of the different tests taken at the three, six and nine-foot windows. The drop 

diameter and droplet velocities were obtained and are given in R7. A heat transfer correlation 

was developed as a function of the distance from the quench front for both the 15x15 and 17x17 

rod bundle geometry. 

The raw data in engineering units is available from the NRC Data Bank for selected tests. All 

the data exists at Westinghouse on Microfiche, including the analyzed data. The analyzed data 

and the row data in engineering units also exists at Westinghouse in storage on older computer 

tapes. It is not clear at this time if the data can be assessed. 

Test Facility Description, Types of Tests 

The FLECHT-SEASET Unblocked Bundle tests were the first publicly available reflood 

experiments on the newer 17x17 fuel array which was adopted by the utilities in the 1980's. 

This fuel array used fuel rod of approximately 9.5 mm (0.374 in) on a square pitch of 12.60 mm 

(0.496 in). 

The experiments used a 1.66 chopped cosine power shape which was the same as the 

FLECHT Low Flooding Rate Cosine Tests. The tests were used to help confirm the 

conservatism in the Appendix K rule as well as to be used for reflood safety analysis computer 

code assessment. Two of the experiments were also used as US Standard Problem 9 in which 
A-23

different parties predicted two FLECHT-SEASET unblocked bundle reflood transients. The 

unblocked bundle tests were also used as a basis for determining the effects of flow blockage 

within the rod bundle which simulated the ballooning and bursting of the Zircaloy cladding. 

The majority of the tests were separate effects constant and or variable reflood tests. There 

were also limited gravity reflood scoping experiments as well. In addition, there were boil-off 

and steam cooling tests performed as well as given in R8. 

The 161-rod bundle unblocked bundle did have problems with the electrical heater rod. The 

new smaller diameter rods, with smaller inside wall thermocouples, proved to be less reliable 

then the previous larger 10.719 mm (0.422 in) diameter rods. Several of the heater rod 

thermocouples failed in the initial transient tests such that the bundle instrumentation became 

degraded. Consequently, the 161-rod bundle was rebuilt by replacing heater rods 

approximately one-half way into the testing program. Those individuals using the test data must 

verify the proper channel and rod location since new rods were used in several different 

locations. The full channel list for all tests is given in R6. 

The 161-rod bundle also used the thin wall circular housing so as to minimize the housing 

radiation heat sink effects as well as the housing heat release effects. Figure A4.1 shows the 

cross-section of the rod bundle and Figure A4.2 shows the facility flow diagram. The majority of 

these tests were conducted with a uniform radial power profile for ease of analysis, as well as 

obtaining a statistical distribution for the hot spot temperatures and heat transfer coefficient. 

The 161-rod bundle was much more heavily instrumented as compared to the previous 

FLECHT test bundles. Most of the heater rods were instrumented and would have eight 

thermocouples per rod. Rods were located in symmetric positions such that complete coverage 

over the bundle length was achieved. The differential pressure cells were located one foot apart 

as in the skewed bundle tests and the data was used to determine the mass balance as well as 

for the average void fraction over the given cell span. There was no specific thermocouple 

placement relative to the grids, and the spacer grids were not instrumented; however, the axial 

placement was sufficiently fine that the data does indicate the heat transfer improvements 

caused by the spacer grids. The FLECHT egg-crate spacer grids were used and are the same 

as those used in previous FLECHT tests. One of the objectives of the 161 rod bundle tests was 

to provide improved data for the development and validation of safety analysis computer codes. 

To this end, there were additional aspirating steam probes added to the guide tube thimbles. 

Some of the steam probes aspirated the flow out the bottom of the bundle while other probes 

aspirated out the top of the bundle. It was discovered that the bottom probes would not indicate 

the true steam temperature since they were more easily wetted during the transient. The 

probes which are regarded as unreliable are given in R6. 

The range of conditions which were examined was similar to the Low Flooding Rate FLECHT 

tests and included: 

Constant Flooding Rates 11.43 - 154.94 mm/s (0.45 - 6.1 in/s) 

Upper Plenum Pressure 137.895 - 413.685 kPa (20 - 60 psia) 

Initial Clad Temperature 256.66 - 1118.33 degrees C (494 - 2045 degrees F) 

(At Peak Location) 
A-24

Initial Peak Power 1.312 - 3.2808 kW/m (0.40 - 1.0 kW/ft) 

(At Peak Location) 

Radial Power Distribution Uniform - FLECHT 

Similar to FLECHT Tests 

Inlet Liquid Temperature 51.11 - 125 degrees C (124 - 257 degrees F) 

Variable Flooding Rate Tests 161.544 mm/s (6.36 in/s) for 5 s; 

20.828 mm/s (0.82 in/s) onward; 

165.862 mm/s (6.53 in/s) for 5 s; 

24.892 mm/s (0.98 in/s) for 25 s; 

15.748 mm/s (6.36 in/s) onward 

Gravity Injection Tests 147.32 mm/s (5.8 in/s) for 15 s; 

19.94 mm/s (0.785 in/s) onward 

There were other tests performed such as hot and cold channel tests to examine the effects of 

liquid entrainment, repeat tests to verify that the bundle was performing in a repeatable manner 

overlap tests with the previously performed 15x15 cosine experiments and steam cooling tests. 

The steam cooling tests are given in Reference 3 and investigated the steam cooling in the 

bundle over a Reynolds number range of approximately 1500 to 25000. The test matrix for this 

test series is given as Table A4.1, along with the measured peak cladding temperatures. 

There was a significant number of power cycles performed on the test bundle which led to 

heater rod distortion at the end of the test program. An analysis was performed to determine 

when the effects of distortion became evident in the data. This analysis is given in Reference 1 

and should be consulted when modeling the tests from this program such that only valid data is 

used. 

High-speed movies were taken for a number of tests at the three, six, and nine-foot windows 

with camera speeds up to 2000 frames/sec. The movie data was reduced and analyzed to 

obtain droplet size and velocity data which was then compared to values from the literature as 

well as calculations. It was found that a log-normal distribution fit the droplet diameter data 

reasonably well while there was no real correlation of the droplet velocity with the droplet 

diameter or any other parameter. 

An empirical reflood heat transfer correlation was developed from the 161-rod bundle 

experiments. The heat transfer correlation was a function of the distance above the quench 

front as well as the bundle initial conditions of power, pressure, flooding rate, inlet subcooling, 

and initial power. This correlation was used to predict the heat transfer above the quench. In 

addition, a quench front correlation was also developed such that given a set of system 

conditions; the dispersed flow film boiling heat transfer above the quench front in the PCT 

region could be predicted. The correlation was also used the older 15x15 FLECHT Low 

Flooding Rate Cosine and Skewed Power test data for developing the correlation. 

The unique area that the 161-rod bundle tests addressed was the analysis of the test data 

above the quench front in the film boiling region. The analysis methods which were first 

developed as part of the FLECHT Low Flooding Rate Test Series were expanded upon in the 
A-25

FLECHT-SEASET program. There was increased instrumentation for axial vapor temperature 

measurements along the test bundle which could then be used with the exit flow measurements 

to calculate the local actual quality in the test bundle, from an energy balance, such that the 

local liquid and vapor velocities could be determined. From the calculations of the vapor flows, 

velocities, and temperatures, the local vapor Reynolds number could be calculated such that a 

convective heat transfer could be predicted from different single-phase correlations. The effects 

of the vapor superheat on the calculated Reynolds number were significant since superheated 

steam flows at 15.24 m/s (50 ft/s) could result in a Reynolds number in the laminar regime. The 

results from the energy balance were also used with the high-speed movie from the analysis of 

the droplet data to calculate the void fraction in the flow. The measured void fraction from the 

differential pressure cells is not as accurate in the highly dispersed flow regime when the flow 

has very little liquid content. 

The wall heat flux was also decomposed using a six node radiation heat transfer network such 

that the radiation heat transfer from the inner hot rods, outer cold rods, guide tube thimbles, 

housing, droplets, and vapor could be calculated. Once the radiation component of the hot rods 

was calculated, the convective-dispersed flow film boiling portion of the rod heat transfer could 

be determined by subtracting the calculated radiation heat transfer from the measured total heat 

transfer which was calculated from an inverse conduction calculation using the heater rod 

thermocouple and local power. The convective-dispersed flow film boiling heat transfer was 

also compared to the single phase heat transfer one would predict using the same vapor 

Reynolds number, wall temperature and vapor temperature conditions. As with the FLECHT 

tests, the convective dispersed flow heat transfer data gave much higher values of the Nusselt 

number when compared to the Nusselt number calculated form the same conditions for a 

single-phase vapor. The interpretation of this difference is that the droplets are acting to 

enhance the heat transfer in the flow by acting as additional turbulence promoters, as well as 

temperature sinks which change the local bulk temperature profile. The comparisons indicate 

that the droplet effects are the greatest at the lowest vapor Reynolds numbers where the natural 

turbulence in the flow is the smallest. Therefore, the drops could be promoting increased 

turbulence in the flow which provides for increased heat transfer. It was also observed that as 

the liquid content of the flow increased, the difference between the convective dispersed flow 

film boiling heat transfer and the predicted single phase heat transfer also increased. 

The 161-rod bundle tests also clearly showed that two different two-phase regions exist above 

the quench front. A lower void fraction, liquid rich froth or transition region, exists at and just 

above the quench front for the forced flooding tests. The length of this region depends on the 

flooding rate value relative to the quench velocity. The larger the flooding rates relative to the 

quench velocity (which is conduction controlled), the longer the froth region. The froth region 

was observed and appears as liquid ligaments which are sheared into increasingly smaller 

droplets from the steam flow generated at the quench front and the higher wall temperature in 

the quench front region. The vapor shearing effects generate the entrained droplets which then 

provide cooling at the upper elevations of the test bundle in the non-equilibrium dispersed flow 

film-boiling regime. 

Conclusions

The FLECHT-SEASET 161-rod unblocked bundle experiments represent the best reflood 

experiments which were performed. It was recognized in the test planning that data was 
A-26

needed for advanced reflood computer code development such that an effort was made to 

obtain additional local heat transfer and fluid flow data in addition to the total heater rod heat 

transfer data for an empirical correlation. The mass balances on the tests were generally very 

good such that the data can be used with confidence, however, one must be careful of the 

vapor measurements as indicated earlier since some of the steam probes did not function as 

desired. Also because of heater rod problems, the bundle was rebuilt so that channel 

designation relative to specific heater rods may have changed. These changes are 

documented in the reports such that the user can correctly obtain the data for a given test. 

The analysis for the test data is the most complete of all the FLECHT test series. Test 31504 

was analyzed in detail with several plots given in the reports which can be used for computer 

code validation. There is also an amount of very good droplet size and velocity information 

which can also be used for computer code validation. If all the data is used for the validation, 

not just the heater rod temperatures, one can more realistically assess a computer code reflood 

heat transfer model since the test measurements include the rod surface temperature, vapor 

temperature, drop size, drop velocity as well as the local quality, void fraction, and heat flux split 

between radiation heat transfer and convective dispersed flow film boiling heat transfer. 

Two of the FLECHT-SEASET tests were used as US Standard Problem 9 for the purposes of 

code validation. It is strongly recommended that these data be used for validating the NRC 

merged code. 
A-27

Figure A4.1 FLECHT-SEASET Rod Bundle Cross Section. 
Figure A4.2 FLECHT-SEASET Facility Flow Diagram. 

A-28
A-29

Table A4.1 FLECHT-SEASET Unblocked Bundle Reflood Test Data Summary 
Table A4.1 FLECHT-SEASET Unblocked Bundle Reflood Test Data Summary (Continu

A-30
Table A4.1 FLECHT-SEASET Unblocked Bundle Reflood Test Data Summary (Continu

A-31
A-32

Table A4.1 FLECHT-SEASET Unblocked Bundle Reflood Test Data Summary (Continu
A-33

Table A4.1 FLECHT-SEASET Unblocked Bundle Reflood Test Data Summary (Continu
A-34

Table A4.1 FLECHT-SEASET Unblocked Bundle Reflood Test Data Summary (Continu
A-35

APPENDIX A5. LITERATURE REVIEW 

Test Facility Name: FEBA - Flooding Experiments with Blocked Arrays. 

Dates When Tests Were Performed: 1977 

References:

R9 P. Ihle, K. Rust, “FEBA - Flooding Experiments with Blocked Arrays Evaluation Report,” 

KfK 3657, March 1984. 

R10 P. Ihle, K. Rust, “FEBA - Flooding Experiments with Blocked Arrays Data Report 1, 

Test Series I through IV,” KfK 3658, March 1984. 

R11 P. Ihle, K. Rust, “FEBA - Flooding Experiments with Blocked Arrays Data Report 2, 

Test Series V through VIII,” KfK 3659, March 1984. 

Availability of Data:

Reduced instrument responses are presented in References R9 to R11 in a variable versus 

time plot format. Tables and figures describing instrument locations are provided. Results are 

presented in ‘almost SI’ units. A listing of computer channel numbers and of data identification 

are available on tapes or in the USNRC/RSR Data Bank. 

Test Facility Description, Types of Tests

The test facility is designed for a separate effect test program involving a constant flooding rate 

and a constant back pressure to allow investigation of the influence of coolant channel 

blockages independently of system effect. 

Figure A5.1 shows a scheme of the test facility. The coolant water is stored in tank and during 

operation the flow is forced into the bundle with a back pressure control system. A 1x5 as well 

as 5x5 rod array are placed in a full length stainless steel housing which have a wall thickness 

of 1/4 in. The heater rods were 10.75 mm (0.423 in) in diameter and were arranged on a 

square pitch of 14.3 mm (0.563 in) and had a heated length of 3.90 m (12.8 ft) for the 5x5 rod 

bundle tests and 2.9 m (9.5 ft) for the 1x5 rod bundle tests. The axial power profile is shown in 

Figure A5.2. Top-down quenching was prevented in the experiments by using a particular 

upper plenum design (Figure A5.3). 

The ranges of conditions include: 

Constant Mass Flow Rate 2.0 - 9.5 cm/s (0.8 - 3.7 in/s) 

Pressure 2.0 - 6.2 bar (29.4 - 91.1 psia) 

Initial Clad Temperature 368 - 794 degrees C (694 - 1461 degrees F) 

Power Axial Peak Factor 1.19 
A-36

Initial Average Power 120 percent ANS: 40s after Reactor Trip 

Inlet Temperature 40 - 125 degrees C (104 - 257 degrees F) 

Initial Housing Temperature 275 - 760 degrees C (527 - 1400 degrees F) 

Flow Blockage Ratio 0, 62, 90 and 90+62 percent 

Flow Blockage Geometry Various 

The FEBA 5x5 rod bundle program consisted of eight test series with different grid spacer and 

sleeve blockage arrays within the bundle (Figure A5.4). Series I tests are baseline tests with 

undisturbed bundle geometry. Series II tests investigate the grid spacer effect on the axial 

temperature profile at bundle mid-plane. Series III and IV tests consider 90 and 62 percent 

blockage at bundle midplane respectively. Series V tests consider both the blockage and the 

grid spacer effects while Series VI tests have double blockage and investigate on the possibility 

of a hot region between the two blockages. Finally Series VII and VIII tests investigate on 

cooling enhancement downstream the blockages. 

Instrumentation and Data From Tests

Thermocouples (Chromel-Alumel) are imbedded in each of the rods as shown in Figure A5.5 

and A5.6. They are used to measure cladding, sleeve, grid spacers and housing temperatures 

at different locations (Figure A5.7). Fluid temperatures were measured with three different 

thermocouples (Figure A5.8) and probes in order to provide information about two separate 

phases. The signals of all three fluid thermocouples indicated roughly same temperature during 

most part of reflood. Radiation effect for the unshielded thermocouple was not detected 

however shielding let to earlier quenching of the shielded thermocouples. Pressure and 

pressure differences were measured with pressure transducers. In addition to inlet and outlet 

pressure, the pressure differences along the midplane as well as along both the lower and 

upper portion of the bundle were measured. The flooding rate was measured with a turbine flow 

meter. The amount of water carry over was measured continuously by a pressure transducer 

on the water collecting tank. All data were digitally recorded with a scan frequency of 10 Hz. 

The water level rising in the lower plenum at the onset of reflood was detected by 

thermocouples. In some tests high-frequency probes were used to detect the presence of water 

in the flow channel. 

Conclusions

The FEBA experiments provide very good information concerning the separate effect of grids 

and blocked bundle regions on the heat transfer during reflood. Separate tests were run with 

the same boundary conditions with and without grids, with and without blockage to address this 

effect. On the other hand, very little effort has been dedicated to investigating the single 

thermal-hydraulic process involved in the heat transfer during reflood (droplets behavior, 

entrainment, etc.). This does not provide sufficient data to develop and validate mechanistic 

models to be used in best-estimate code. 
A-37

Figure A5.1 FEBA Test Facility. 
A-38

Figure A5.2 Axial Power Profile. 

Figure A5.3 Upper Bundle End and Upper Plenum.
A-39

Figure A5.4 5x5 Rod Bundle, Test Matrix for Series I Through VIII. 
A-40

Figure A5.5 Rod Geometry and Location of Thermocouple. 
A-41

Figure A5.6 Radial and Axial Location of Cladding, Fluid and Housing 

T/C’s for Test Series I.
A-42

Figure A5.7 Axial Locations of Various Thermocouples in 5x5 Rod Bundle. 
A-43

Figure A5.8 5-Rod Row: Comparison of Different Fluid Temperature Measuring Device
A-44

Table A5.1 Assessment of FEBA Test to RBHT PIRT: Single Phase Liquid Convective Heat Tra

Core Component During Reflood Below the Quench Front
A-45

Table A5.2 Assessment of FEBA Test to RBHT PIRT: Subcooled and Saturated Boiling i

Core Component Below the Quench Front 
A-46

Table A5.3 Assessment of FEBA Tests to RBHT PIRT: Quench Front Behavior in the Core Co
A-47

Table A5.3 Assessment of FEBA Tests to RBHT PIRT: Quench Front Behavior in the Core Compon
A-48

Table A5.4 Assessment of FEBA Tests to RBHT PIRT: Froth Region for the Core Compo
A-49

Table A5.5 Assessment of FEBA Tests to RBHT PIRT: Dispersed Flow Region for the Core C

Process/Phenomena Ranking Basis F

Radiation Heat Transfer to: - Surfaces - Vapor - Droplets Gap Heat Transfer Cladding Material Reaction Rate Fuel Clad Swelling/Ballooning 

M/H M/H M/H 

L L 

M 

L 

This is important at higher bundle elevations (H) where the convective heat transfer is small since the vapor is highly superheated. Very important for BWR reflood with spays and colder surrounding can. Large uncertainty. Controlling thermal resistance is the dispersed flow film boiling heat transfer resistance. The large gap heat transfer uncertainties can be accepted, but fuel centerline temperature will be impacted. Cladding material use din the tests is Inconel which has the same thermal conductivity as zircaloy. Nearly the same temperature drop will occur. Inconel will not react while zircaloy will react and create a secondary heat source at very high PCTs. Zirc reaction can be significant. Ballooning can divert flow from the PCT location above the ballooning region. The ballooned cladding usually is not the PCT location. Large uncertainty. 

Radiation heat tranconsidered in data A 0.5 mm gap is prsleeve in the blockeexperiments. Rod temperature were mUsed Ni-Cr 80-20 cNot present. The effect of clad bextensively investigmain issue of FEBA campaign. Large aavailable. 
A-50

Table A5.6 Assessment of FEBA Tests to RBHT PIRT: Top Down Quench in Core Compo

Process/Phenomena Ranking Basis 

De-Entrainment of Film Flow Sputtering Droplet Size and Velocity Fuel Rod/Heater Rod Properties for Stored Energy: r, cp, k. 

Gap Heat Transfer 

L1

L 

L1L1

The film flow is the heat sink needed to quench the heater rod. This has high uncertainty. The droplets are sputtered off at the quench front and are then re-entrained upward. Since the sputtering front is above the PCT location, no impact. The entrained sputtered drops do affect the total liquid entrainment into the reactor system, as well as the steam production in the steam generators. These properties are important since they determine the heat release into the coolant. However, since this occurs above PCT level, no impact. Affects the rate of energy releases from the fuel/heater rod. 

Top down quprevented in Not applicablquenching waNot applicablquenching waNot applicablquenching wa

Note: Some of these individual items can be ranked as high (H) within the top down quenching process; however, the entir

for a PWR/BWR since it occurs downstream of the PCT location. 
A-51

Table A5.7 Assessment of FEBA Tests to RBHT Preliminary PIRT for Gravity Reflood Systems E

Process/Phenomena Ranking Basis 

Upper PlenumEntrainment/De-Entrainment Hot Leg - Entrainment, De-Entrainment. Pressurizer Steam Generators Reactor Coolant Pumps Cold Leg Accumulator Injection Cold Leg Pumped Injection Pressure Injection Subcooling Downcomer Wall Heat Transfer Lower Plenum Wall Heat Transfer Break 

M 

L L 

H H H H H 

M/H 

H 

M 

L 

The plenum will fill to a given void fraction after which the remaining flow will be entrained into the hot leg, large uncertainty. The hot legs have a small volume and any liquid swept with the hot leg will be entrained into the steam generator plenums, medium uncertainty. Pressurizer is filled with steam and is not an active component, small uncertainty. The generators evaporate entrained droplets and superheat the steam releases (particularly at low pressures). The result is a higher steam flow downstream of the generators. High uncertainty since a good model is needed. FLECHT-SEASET data exists for reflood. This is the largest resistance in the reactor coolant system which directly affects the core flooding rate- low uncertainty. Initial ECC flow into the bundle. Pumped injection maintains the core cooling for the majority of the reflood 

transient. Low pressure (20 psia) significantly impacts the increased vapor volume flow rate, which decreases the bundle flooding rate. Lower subcooling will result in boiling below quench front such that there is additional vapor to vent. The heat transfer from the downcomer walls can raise the ECC fluid temprature as it enters the core, resulting in more steam generation. Source effect as downcomer but less severe. Excess ECC injection spills, but break ΔP helps pressurize reactor system. 
A-52

Table A5.8 Assessment of FEBA Tests to RBHT PIRT for High Ranked BWR Core Pheno

Process/Phenomena Basis FEB

Core Film Boiling Upper Tie Plate CCFL Channel-Bypass Leakage Steam Cooling Dryout Natural Circulation Flow Flow Regime Fluid Mixing Fuel Rod Quench Front Decay Heat Interfacial Shear Rewet: Bottom Reflood Rewet Temperature Top Down Rewet 

PCT is determined in film boiling period. Hot assembly is in co-current flow above CCFL limit. Flow bypass will help quench the BWR fuel assembly core. A portion of the dispersed flow film boiling heat transfer. Transition from nucleate boiling and film boiling. Flow into the core and system pressure drops. Determines the nature and details of the heat transfer in the core. Determines the liquid temperature in the upper plenum for CCFL break down. Heat release from the quench front will determine entrainment to the upper region of the bundle. Energy source for heat transfer. Effects the void fraction and the resulting droplet and liquid velocity in the entrained flow. BWR hot assembly refloods like PWR. Determines the quench front point on the fuel rod. Top of the hot assembly fuel will rewet in a similar manner as PWR. 

Total heat transfer is meNot applicable. Not applicable. Steam cooling heat transdata. Quench front is measureNot applicable. Movies exist to determinNot applicable. Quench front data existsMeasured as initial/bounNot measured. Total reflood heat transfeQuench temperature meTop down rewet quench 
A-53

Table A5.8 Assessment of FEBA Tests to RBHT PIRT for High Ranked BWR Core Phenomena 

Process/Phenomena Basis FEB

Void Distribution Two-Phase Level 

Gives the liquid distribution in the bundle. Similar to quench front location, indicates the location of nucleate and film boiling. 

Not measured. Measured by rod TC’s. measured, two-phase lecells. 
A-54

APPENDIX A6. LITERATURE REVIEW 

Test Facility Name: Oak Ridge National Laboratory Thermal-Hydraulic Test Facility (THTF). 

Dates when tests were performed: 1980 - 1982. 

References: 

R12 Mullins, C. B., et al., AORNL Rod Bundle Heat Transfer Test Data,@ NUREG/CR - 2525, 

Vol. 1 to Vol. 5, 1982. 

R13 Yoder, G. L., et al., ADispersed Flow Film Boiling in Rod Bundle Geometry - Steady State 

Heat Transfer Data and Correlations Comparisons,@ NUREG/CR - 24351, 1982. 

Availability of Data: 

Reduced instrument responses are presented in Reference R12 for transient film boiling in 

upflow. Microfiche of the reduced data in graphical form exist along with three types of tables to 

assist the reader in using the data. The first table lists instrumentation in terms of instrument 

function, type and location. The second table lists instruments in the order they appear 

graphically in the microfiche. The third table lists instruments alphabetically in terms of the 

instrument application number (IAN). In addition to the transient data, steady state data exist in 

Reference R13 for dispersed flow film boiling. The data are presented in two separate sets of 

tables, one in SI units and the other in English units, listing fluid conditions, surface conditions 

and correlation - predicted versus experimentally determined heat transfer coefficients. 

Test Facility Description, Types of Tests 

Both the transient and steady state experiments were performed in the Thermal-Hydraulic Test 

Facility (THTF), as shown in Figure A6.1. The THTF was a heavily instrumented non-nuclear 

pressurized water loop containing 64 full-length rods arranged in an 8x8 bundle; 60 of the rods 

were electrically heated (see Figure A6.2). The rod diameter was 0.0095 m (0.374 in) and the 

rod pitch was 0.0127 m (0.501 in) on a square lattice, typical of PWRs with 17xl7 fuel rod 

assemblies. Figure A6.3 shows a simplified cross section of a typical fuel rod simulator. The 

axial and radial power profile was flat. The heated length of the bundle was 3.66 m (12 ft) and 

there were eight spacer grids in the heated length, as shown in Figure A6.4. The spacer grids 

were of the egg crate type installed 0.61 m (2 ft) apart. 

Two types of tests were performed, one transient and the other steady state. The transient 

tests were initiated by breaking the outlet rupture disk assembly. Although the THTF had a 

rupture disk assembly at the inlet, it was not employed to assure a unidirectional flow up through 

the test section. At the same time the outlet rupture disk was broken, the pump was tripped and 
A-55

Figure A6.1. THTF System with Instrumented Spool Pieces Labeled. 
A-56

 

Figure A6.2. Identification of THTF Heater Rods, Subchannel Location, 

and Inactive Rods in THTF Heater Bundle. 

Figure A6.3. Cross-Section of a Typical Fuel Rod Simulator. 
A-57

Figure A6.4. Axial Locations of Spacer Grid and Thermocouples. 
A-58

bundle power was ramped up to about 6-8 MW. After the initial power ramped up, the bundle 

power remained at this high level until most of the sheath temperatures at level G in the bundle 

reached 811 degrees K (1000 degrees F). The bundle power was then ramped down to 

maintain high rod sheath temperatures in the upper bundle without reaching the safety limit of 

1116 degrees K (1550 degrees F). All test series including test 3.03.6AR, test 3.06.6B and test 

3.08.6C were conducted under reactor accident-type conditions to obtain transient film boiling 

data. The ranges of conditions are given are given below: 

Test 3.03.6AR 

Mass Velocity 136 B 502 kg/m2

s (1x105 to 3.7x105 lbm/hr - ft2) 

Quality 23 B 100 percent 

Pressure 5 B 10 MPa (700 B 1500 psi) 

Heat Flux 158 B 1000 kW/m2

 (5x104 to 3.2x105 Btu/hr - ft2) 

Test 3.06.6B 

Mass Velocity 136 B 610 kg/m2

s (1x105 to 4.5x105 lbm/hr - ft2) 

Quality 5 B 100 percent 

Pressure 6 B 13 MPa (875 B 1900 psi) 

Heat Flux 158 B 630 kW/m2

 (5x104 to 2x105 Btu/hr - ft2) 

Test 3.08.6C 

Mass Velocity 330 B 1090 kg/m2

s (2.4x105 to 8x105 lbm/hr - ft2) 

Quality 35 B 100 percent 

Pressure 6.6 B 11.7 MPa (950 B 1700 psi) 

Heat Flux 160 B 1100 kW/m2

 (5x104 to 3.5x105 Btu/hr-ft2) 

In the steady state tests, the working fluid flowed from the pump through two control values, 

past the inlet rupture disk assembly and through a vertical spool piece before it entered the 

external downcomer. The working fluid then flowed through two spool pieced in the downcomer 

and entered the test section. The fluid was heated as it flowed along the rods within the test 

section. It then left the test section from the upper plenum, past through the three outlet spool 

pieces and the heat exchangers, and returned to the pump. During the run, the loop was 

adjusted to provide the desired inlet fluid temperature and inlet pressure. The bundle power 

was then increased until the dryout point was at the desired position in the bundle. The steady 

state operating conditions were assumed to have been reached when the operating pressure 

and rod surface temperatures stabilized. A total of 22 steady-state tests were performed. The 

ranges of conditions were: 

Mass Velocity 226 B 806 kg/m2

s (1.66x105 to 5.94x105 lbm/hr - ft2) 

Quality 0 B 100 percent 

Pressure 4.4 B 13.4 MPa (635 B 1938 psi) 

Heat Flux 320 B 940 kW/m2

 (1x105 to 3x105 Btu/hr - ft2) 
A-59

Instrumentation and Data from Tests 

The bundle was fully instrumented with thermocouples at various axial locations (i.e., at A, B, C, 

D, E, F and G levels) to measure the rod temperatures and in-bundle fluid temperatures. At 

each axial location where a rod had thermocouples, there were three individual thermocouples 

spaced azimuthally around the rod. In-bundle fluid temperatures were measured using 

thermocouples extending a short distance from the rod surface into the fluid as well as 

thermocouples mounted on the spacer grids. Rods 36 and 46 also contained gamma 

densitometer instrumentation for measuring in-bundle fluid density. Two flow measurement 

sites were positioned at each end of the test section containing the rod bundle. Differential 

pressure and pressure instrumentation was made at various locations along the heated bundle. 

In addition, there was instrumentation located in the entire piping system including the outlet 

nozzle, vertical outlet and external downcomer spool pieces. 

In the transient tests, local bundle fluid conditions were calculated with the homogeneous twophase flow and thermodynamic equilibrium thermal-hydraulics code RLPSFLUX. The transient 

data were compared to six existing film boiling correlations. Results of the comparisons were 

presented in Reference R12. In the steady state tests, mass and energy conservation 

relationship were used to calculate equilibrium fluid conditions within the rod bundle. These 

fluid conditions, along with calculated rod surface temperatures, were used to evaluate the six 

film boiling correlations as well as single-phase vapor correlation. Results of the comparisons 

were presented in Reference R13. In addition to the dispersed flow film boiling data, results 

were also obtained for the spacer grid effects, which had beneficial influence on the heat 

transfer due to a boundary layer breakup-rebuild process at the grids. 

Conclusions 

The ONRL/THTF tests provide both transient and steady state film boiling heat transfer data in 

rod bundle geometry. In general, the steady state results support the conclusions reached in 

the analysis of the transient results. The experimentally determined heat transfer coefficients 

may be useful as they have been compared to various existing heat transfer correlations. It is 

found that the Dougall-Rohsenow correlation often overpredicts the heat transfer coefficient 

whereas the Groeneveld-Delorme correlation tends to underpredict the heat fluxes near dryout 

but improves as distance from dryout increases. On the other hand, the Groeneveld 5.7, 

Groeneveld 5.9 and Condie-Bengston IV correlations give better agreement with the 

experimental data. 

It should be noted that although the steady state and the transient data appear to be consistent 

with each other, the bundle fluid conditions in both cases are determined from mass and energy 

conservation consideration based on the assumption of thermodynamic equilibrium. However, 

non-equilibrium conditions probably exist within the bundle. Thus, a more sophisticated 

calculational method accounting for the effect of non-equilibrium is needed to determine the 

actual bundle fluid conditions. Non-equilibrium also implies that liquid droplets can be present in 

the flow when equilibrium qualities are calculated to be larger than unity. 
A-60

The ORNL/THTF tests have been focused on the case of dispersed flow film boiling in upflow 

under high-pressure high-temperature conditions. The data may provide some relevant 

information in the dispersed flow region for core component in the RBHT PIRT Table 5. 

However, the results are not applicable to single phase liquid corrective heat transfer in the core 

component during reflood below the quench front (RBHT PIRT Table 1), subcooled and 

saturated boiling in the core component below the quench front (RBHT PIRT Table 2), quench 

front behavior in the core component (RBHT PIRT Table 3), froth region for the core component 

(RBHT PIRT Table 4), top down quench in core component (RBHT PIRT Table 6), and gravity 

reflood system effects (RBHT PIRT Table 7). 

Even in the dispersed flow region, the ORNL/THFT data must be used with caution. This is 

because the pressure range of 4.4 - 13.4 MPa (635 - 1938 psi) explored in the THTF tests is 

very high, more characteristic of a PWR or BWR blowdown situation. Thus the results may not 

be directly applicable to transient stage of reflood heat transfer in rod bundles. 
A-61

Table A6.1 Assessment of ORNL/THTF Data to RBHT PIRT: Dispersed Flow Region for 

Component
A-62

Table A6.1 Assessment of ORNL/THTF Data to RBHT PIRT: Dispersed Flow Region for 

Component (Continued)
A-63

APPENDIX A7. LITERATURE REVIEW 

Test Facility Name: FRIGG-2 36-Rod Loop (Sweden) 

Dates When Tests Were Performed: 1965-1968 

References: 

R14 Becker, K. M., Flinta, J., and Nylund, O., ADynamic and Static Burnout Studies for the 

Full Scale 36-Rod Marviken Fuel Element in the 8 MW Loop FRIGG,@ Paper presented 

at the Symposium on Two-Phase Flow Dynamics, Eindhoven, September 1967. 

R15 Nylund, O., et al., AMeasurements of Hydrodynamic Characteristics, Instability 

Thresholds, and Burnout Limits for 6-Rod Clusters in Natural and Forced Circulation,@

ASEA and AB Atomenergi Report FRIGG-1, 1967. 

R16 Nylund, O., Becker, K. M., Eklund, R., Gelius, O., Haga, I., Herngorg, G., Rouhani, Z., 

and Akerhielm, F., AHydrodynamic and Heat Transfer Measurements on a Full Scale 

Simulated 36-Rod Marviken Fuel Element with Uniform Heat Flux Distribution,@ ASEA 

and AB Atomenergi Report FRIGG-2, 1968. 

Availability of Data: 

The experimental investigation simulates the fuel element of a Swedish heavy water cooled 

Marviken BVRR with 35 uniformly heated heater rods and a unheated (but larger in diameter) 

center rod simulating the control rod. Experimental data available from the FRIGG-2 tests, all 

under pressures up to 50 bar (711 psi), are single- and two-phase pressure drops; burnout (or 

critical heat flux) in natural and forced circulation; natural circulation mass velocity as a function 

of total power and inlet subcooling; the stability limit; as well as the details about the system 

during transient conditions. Additionally, a unique output of the FRIGG-2 tests is the axial and 

radial void distributions measured by the Cobalt-60 gamma-ray densitometer system. The 

results have been compared to data obtained from in the previous six-rod tests (R15, FRIGG- 1) 

and to predictions with existing correlations and models. All pressure drop data are consistently 

agreeable between FRIGG-2, FRIGG-1, and actual Marviken conditions. The natural circulation 

burnout value is very close to that of forced circulation, but both are about 20 percent low 

compared to predictions by the Becker correlation. This is believed to be due to the unfavorable 

conditions in the inner subchannels of the uniformly heated bundle. The results of natural 

circulation mass velocity, stability limit, and transient behavior at different power levels agree 

well with the calculation. Calculations indicate that the conditions in a real Marviken boiling 

channel are somewhat more favorable than in the FRIGG-2 experiment. This suggests that 

sufficient margins against burnout and hydrodynamic instability are present in the Marviken 

reactor. 
A-64

Test Facility Description, Types of Tests

The primary purpose of FRIGG-2 tests was to obtain the burnout values of the 36-rod bundle at 

different mass fluxes and inlet subcoolings to simulate the core conditions of a Marviken BWR. 

The geometric features of the test section are: 

 

Number of heated rods: 35 Rod diameter: 13.8 mm (0.5433 in) 

Number of unheated rods: 1 Unheated rod dia.: 20 mm (0.7874 in) 

Circular housing diameter: 160 mm (6.30 in) Number of spacers: 8 

Average hydraulic dia.: 26.9 mm (1.06 in) Heated hydraulic dia.: 36.6 mm (1.44 in) 

Heated length (uniform): 4375 mm (172 in) No. of burnout T/C's: 4 

Tests were run with 35 rods electrically heated and one center rod unheated. Both the axial and 

radial power profiles are uniform. A cross-sectional view of the test section is shown in Figure 

A7.1, indicating the placement pattern of the unheated center rod and 35 heated rods in three 

orbital rows. The flow diagram of the FRIGG-2 loop is shown in Figure A7.2. For burnout tests 

FRIGG-2 requires a significant DC electrical power: 80 MW, 80 kA, and DC voltage regulation 

from 0 to 200 V. The heater rods were of a type with coaxial feeder rod eliminating the 

electromagnetic forces between the rods. Most of the heat is produced in the 0.8 mm stainless 

steel canning of the rod, which is isolated from the center copper conductor. This means that 

the reactor fuel time constant (or heat capacity) is not correctly simulated. There are four 

electrically isolated burnout detectors (or thermocouples) measuring temperatures at different 

elevations and there wires running axially along the inside surface of the stainless steel canning. 

If a burnout event is detected by any of the burnout detectors in the bundle, the DC power 

applied to the bundled would be immediately reduced by 20 percent within 0.1 s and the 

histories of all important fluid and thermal parameters are recorded. These burnout conditions 

are the primary objective of the FRIGG-2 tests. 

A secondary but important test of FRIGG-2 is the void fraction measurement in both the axial 

and radial directions of the bundle. The measurement system comprises one gamma source, 

Co-60, and four scintillation detectors with adjustable collimators. The pulses from the detectors 

are amplified, analyzed and counted in separate scalars built into the data collection system. 

The penetration paths of the four gamma beams can be changed between three prefixed radial 

positions within the bundle. The void at a certain level is thus evaluated from the twelve 

measurements covering different parts of the bundle. This gives a rather good cross sectional 

mean value of the void and also information about the radial void distribution. The void 

measurement system is moved up and down the test section by means of an electric elevator 

that allows for axial void distribution measurement. 

Other instrumentation includes: Chromel-alumel thermocouples for fluid temperature 

distribution measurement; fast response differential pressure (DP) cells with venturi units and 

turbine flow meters for mass velocity measurement; and impedance void gauge to measure the 

outlet quality. Standard single and two-phase pressure drops at all test conditions are also 

measured using differential and absolute pressure sensors. 
A-65

 

Figure A7.1. 36-Rod Bundle of the FRIGG-2. 
A-66

 

Figure A7.2. Flow Diagram of the FRIGG-2 Loop.
A-67

The ranges of test conditions include: 

Single-Phase (Cold) Mass Flux 840 - 3195 kg/m2

-s (0.618 B 2.35x106 lbm/ft2-hr) 

Two-Phase Mass Flux 366 - 1492 kg/m2

-s (0.269 B 1.098x106 lbm/ft2-hr) 

Pressure 50 bar (711 psi) 

Rod Temperature measured with thermocouples serving as burnout 

 detectors 

Average Heat Flux 8.1 - 103 W/cm2

 (0.0257 B 0.326x106 Btu/ft2-hr) 

Exit Quality 2.2 - 51.5 percent 

)Tsub 2.4 - 29.4 degrees C 

Flow Regimes Liquid 1-N, bubbly, transition, annular (typical of BWR). 

Void Fraction 0 - 100 percent 

Instrumentation and Data from Tests 

Each of the heater rods was instrumented with four thermocouples. These thermocouples are 

primarily for burnout detectors and thus calibration is not necessary. Neither was any 

visualization view port provided, such that the identification of flow regimes was based on 

empirical correlations from the state of local quality. Heat transfer information were mainly 

derived from the voltage and current parameters of the DC power system, thus only global heat 

flux (rather than local heat flux) were obtained. Although the heater rods were pushed to the 

burnout limits in order to obtain the critical heat flux (CHF), the normal BWR operating mass flux 

range was maintained. Therefore the post-LOCA reflood (or blowdown) scenarios were not 

addressed, neither were the radiation heat transfer and dispersed flow film boiling phenomena 

as normally encountered in a uncovered core during reflood. However, the FRIGG-2 gammaray densitometer experiments provided valuable information on the axial and radial distribution 

of void faction. It could facilitate the physical correlation between void fraction, local quality, and 

interfacial slip. 

Extensive single and two-phase flow pressure drop data were obtained in the FRIGG-2 tests. 

These pressure drop data are specific to the Marviken reactor core condition, but have 

compared favorably with the Martinelli-Nelson and Becker correlations. 

 The only complete natural circulation curve was also obtained at conditions close to the 

Marviken reactor's. However, by far, the most important data obtained from the FRIGG-2 tests 

are the CHF data for the particular fuel type and grid spacer pattern, as well as the void fraction 

distribution of the 36-rod bundle. 

Conclusions 

For the burnout experiments in FRIGG-2, all independent parameters (mass flux, inlet 

subcooling, pressure, and power to the bundle) have been carefully and independently 

controlled. Due to the uniform axial and radial power profiles of FRIGG-2, which resulted in a 

less favorable heat transfer condition in FRIGG-2 as compared to the actual Marviken core, the 
A-68

measured burnout data were approximately 20 percent lower than those predicted. This points 

out the major deficiency of the uniform power profiles of FRIGG-2. Follow-up tests using the 

actual Marviken reactor's power profiles have been suggested and recognized. 

The natural circulation mass flow rate in Marviken is 10-15 percent above the experimental 

values of FRIGG-2 in the power range of interest, while there is a close agreement between the 

calculated and measured FRIGG-2 flows. The differences are attributed to the Marviken's 

coolant (heavy water); larger radial heat loss of Marviken channel; and distributed power profiles 

of Marviken fuel assembly. 

Although the FRIGG-2 facility has improved our understanding of the burnout limits and natural 

circulation flows of a simulated Marviken core, it did not address the heat transfer phenomena 

associated with post-LOCA reflood conditions, in which the quench front progression, froth 

region propagation, and dispersed flow film boiling are of major interest. However, the relevant 

heat transfer information of FRIGG-2 is assessed against the RBHT PIRT in the following 

Tables A7.1 through A7.3: 
A-69

Table A7.1 Assessment of FRIGG-2 36-Rod Bundle Test to RBHT PIRT: Single Phase L

Convective Heat Transfer in the Core Component During Reflood Below the Quench Fr
A-70

Table A7.2 Assessment of FRIGG-2 36-Rod Bundle Test to RBHT PIRT: Subcooled an

Saturated Boiling in the Core Component During Reflood Below the Quench Front 
A-71

Table A7.3 Assessment of FRIGG-2 36-Rod Bundle Test to RBHT PIRT for 

High Ranked BWR Core Phenomena 
A-72

APPENDIX A8. LITERATURE REVIEW 

Test Facility Name: General Electric 9-Rod Bundle Facility 

Dates When Tests Were Performed: 1968-1970 

References: 

R17 Lahey, R. T., and Schraub, F. A., AMixing, Flow Regimes, and Void Fraction for TwoPhase Flow in Rod Bundles,@ Two-Phase Flow and Heat Transfer in Rod Bundles, 

ASME, Nov. 1969. 

R18 Lahey, R. T., Shiralkar, B. S., and Radcliff, D. W., ATwo-Phase Flow and Heat Transfer 

in Multirod Geometries: Subchannel and Pressure Drop Measurements in a Nine-rod 

Bundle for Diabatic and Adiabatic Conditions,@ GEAP-13049, AEC, 1968. 

Availability of Data: 

In the 3x3 9-rod bundle configuration for typical BWR operating conditions, there are three types 

of geometrical subchannels: comer, side, and center subchannels. Subchannels are also 

classified into hot (locally heated), cold (unheated), and uniform (uniformly heated) 

subchannels. Data for all test points are available in tabulated form for all types of subchannel. 

Bundle average mass flux, bundle average exit quality, measured subchannel mass flux, and 

subchannel quality are tabulated against the test points in Refereces R17 and R18. Substantial 

differential pressure drop data for both single- and two-phase flows are available in the same 

references. Other reduced or analyzed data are also available in graphic format that include: 

subchannel quality-vs-average quality; subchannel energy flux-vs-subchannel mass flux; 

subchannel quality-vs-subchannel type; subchannel mass flux-vs-subchannel type; etc. Singlephase friction factors are graphed against the Reynolds number, while two-phase friction 

multipliers are graphed against flow quality and favorably compared with the Martinelli-Nelson 

correlation. 

Test Facility Description, Types of Tests 

The primary purpose of this investigation was to obtain the mass flux and enthalpy distribution in 

a simulated rod bundle for a BWR. The geometric features of the test section are: 

Number of rods 9 Rod diameter 14.48 mm (0.570 in) 

Radius of channel corner 10.16 mm (0.400 in) Rod-rod clearance 4.287 mm (0.168 in) 

Rod-wall clearance 3.429 mm (0.135 in) Hydraulic diameter 12.04 mm (0.474 in) 

Heated length 1.83 m (72 in) 
A-73

Tests were run with all nine rods electrically heated. The radial local peaking was either uniform 

or a peaking pattern typical of BWR conditions. A cross-sectional view of the test section is 

shown in Figure A8.1, indicating the corner, side, and center subchannels. One of the unique 

features of the facility is that provisions are made for bringing static and differential pressure 

lines at the same axial location but for different subchannels. To measure the flow in any given 

subchannel, that subchannel is isolated at some point from the rest of the channel. The 

subchannel flow, also referred as sample flow as shown in Figure A8.2, can then be taken 

through special ducting to another point outside the test section, where both the flow rate and 

enthalpy can be measured. Flow splinters made of thin metal sheets are used to separate and 

isolate flow of a subchannel at the end of the heated length. Such an isolated flow is guided 

through a tube before passing out the test section flange and entering a heat exchanger 

(calorimeter) as shown in Figure A8.2. The condensed flow is monitored by a turbine flow meter 

for subchannel flow measurement. 

The sample enthalpy was determined by a heat balance on the calorimeter. For this purpose, 

the cooling water flow and temperature rise are carefully measured to provide as accurate 

energy information as possible. The outlet thermocouples are inserted beyond a right- angle 

bend in the piping to ensure good mixing in the water. Pressure drop measurements were also 

made during both single- and two-phase tests. All pressure drop measurements were 

corrected-for the hydrostatic head in the pressure tap lines based on the average density of 

water between the relevant pressure taps. 

The ranges of test conditions include: 

Single-Phase (Cold) Mass Flux 422.67 - 3089.21 kg/m2

-sec (0.311 - 2.273x106 lbm/ft2-hr) 

Two-Phase Mass Flux 505.58 - 1603.72 kg/m2

-sec (0.372 - 1.180x106 lbm/ft2-hr) 

Pressure 75.84 - 82.74 bar (1100 - 1200 psi) 

Rod Temperature not measured 

Average Heat Flux 690.63 - 2513.4 kW/m2

-K (0.219 - 0.797x106 Btu/ft2-hr) 

Exit Quality 3.1 - 44.4 percent 

)hsub 674.54 - 1239.76 kJ/kg (290 - 533 Btu/lbm) 

Flow Regimes Liquid 1-N, bubbly, transition, annular 

Instrumentation and Data from Tests 

The heater rods were not instrumented with thermocouples. Thus, little local heat transfer 

information could be obtained. Neither was any visualization view port provided, such that the 

identification of flow regimes was based on empirical correlations from the state of local quality. 

Since the heater rods were sufficiently cooled under the normal BWR operating conditions and 

the issues of DNB and LOCA/reflood were not addressed, radiation heat transfer was not a 

important factor. However, flow and enthalpy distributions among the subchannels that are 

unique to BWR conditions were carefully measured and addressed. The tests were able to 

measure flow, enthalpy, and derive local quality in each individual subchannel. Thus the facility 

can yield some significant information on the heterogeneous flow core, of which the cross flow 

phenomenon is of importance. 
A-74

Figure A8.1 Positions of Pressure Taps for Setting Isokinetic Conditions. 

Figure A8.2 Schematic of Loop Showing Sampling Circuit. 
A-75

While the heater rods were uniformly heated in the axial direction, the radial power distribution 

was controlled by peaking the individual transformers. Thus the flow, enthalpy, and quality 

distributions across the subchannels due to radial power peaking were also unique output of the 

facility. 

Pressure drop data for single (cold) and two-phase flow tests were obtained for frictional loss 

correlation. At the same axial locations, cross-flow phenomenon (between subchannels) was 

interpreted from the pressure differential between subchannels (non-isokinetic cases). 

Conclusions 

Subchannel test data were taken for a 9-rod bundle in typical BWR operating conditions. In 

general the following observations are made: 

1. The corner subchannel runs a mass flux and quality below the bundle average values. 

2. The side subchannel has mass flux and quality approximately equal to or slightly less than 

the bundle average. 

3. The center subchannel has both mass flux and quality above the bundle average values. 

4. There is an observable, though somewhat inconsistent, tendency for the subchannels to 

approach bundle average condition in the regions of slug-annular flow-regime transition. 

5. The effect of heat flux on subchannel enthalpy distribution was small for low flows, but 

showed a strong effect at the high flows. 

6. The effect of the bundle average mass flux on subchannel mass flux distribution was to 

increase the mass flux in the comer and center subchannels, and decrease the mass flux in 

the side subchannels, as the bundle average mass flux was increased. 

7. The effect of heat flux on subchannel mass flux distribution was to decrease the mass flux in 

the comer subchannel but leave the mass flux in other subchannels relatively unchanged. 

8. The adiabatic single-phase friction factor for the clean 9-rod bundle under consideration was 

slightly higher than the smooth-tube friction factor, for all Reynolds numbers. 

9. The two-phase friction drop multiplier showed only a very minor flow effect, and the data 

was well correlated by the classical Martinelli-Nelson curve. 

Although this facility and work improved our understanding of subchannel flow and energy 

diversions in typical BWR conditions, it did not address the heat transfer phenomena associated 

with post-LOCA reflood conditions, in which the quench front progression, froth region 

propagation, and dispersed flow film boiling are of major interest. However, the relevant heat 

transfer information is assessed against the RBHT PIRT in the following Tables A8.1 and A8.2: 
A-76

Table A8.1 Assessment of General Electric 9-Rod Bundle Tests to RBHT PIRT: 

Subcooled and Saturated Boiling in the Core Component Below the Quench Front 
A-77

Table A8.2 Assessment of General Electric 9-Rod Bundle Tests to RBHT PIRT 

for High Ranked BWR Core Phenomena 
A-78

APPENDIX A9. LITERATURE REVIEW

Test Facility Name: PNL LOCA Simulation Program at NRU Reactor, Chalk River, Canada 

Dates When Tests Were Performed: October 1980 - November 1981 

References: 

R19 C. L. Mohr, et. al., AData Report for Thermal-Hydraulic Experiment 2 (TH-2)@, 

NUREC/CR-2526, PNL-4164, November 1982. 

R20 C. L. Mohr, et. al., AData Report for Thermal-Hydraulic Experiment 3 (TH-3)@, 

NUREC/CR-2527, PNL-4165, March 1983. 

Availability of Data: 

Graphical data demonstrating fuel cladding temperature control using the preset reflood flow 

and temperature feedback. Photographs of guard and test fuel used are shown. Data in 

graphical form on the test assembly temperatures, cooling flow and the neutronic environment 

are also presented. Data is available in both SI and British units. Microfiche of the entire report 

is available with NTIS. 

Test Facility Description, Types of Tests 

The TH-2 included 14 tests. A schematic of the test train used is depicted in Figure A9.1. The 

fuel assembly consists of a 6x6 segment of a 17x17 PWR fuel assembly with four corner rods 

removed, providing a basic fuel array of 32 rods. The 20 guard rods in the outer row reduced 

the heat net heat transfer from the inner test rods during the test. All the inner 12 test fuel rods 

were arranged in cruciform pattern. All the 32 unpressurized fuel rods were filled with helium. 

The core configuration is shown in Figure A9.2. 

The following table gives the test fuel rod design variables: 

Cladding Material Zircaloy-4 

Cladding Outside Diameter (OD) 0.963 cm (0.379 in) 

Cladding Inside Diameter (ID) 0.841 cm (0.331 in) 

Pitch (Rod to Rod) 1.275 cm (0.502 in) 

Fuel Pellet OD 0.826 cm (0.325 in) 

Fuel Pellet Length 0.953 cm (0.375 in) 

Active Fuel Length 3.66 m (12 ft) 

The TH-2 experiment included a preconditioning phase and 14 successive tests, each having a 

pre-transient and transient phase. The average test assembly fuel rod power during 

preconditioning was ~18.7 kW/m (5.7 kW/ft) with the U-2 loop providing water cooling; this was 

also used for the TH-3 experiment. System loop pressure was held at 8.63 MPa (1250 psia). 

The pre-transient stage for the TH-3 tests was conducted with the steam cooling provided by 

the U-1 loop at a mass flow rate of ~0.379 kg/s (~3000 lbm/hr) and a reactor power of ~7.4 MW. 
A-79

Figure A9.1 Schematic of NRU Loss-of-Coolant Accident Test Train. 

This enabled the total assembly power to remain constant, even though the peak cladding 

temperature varied from test to test. The transient phase of TH-3 commenced when the steam 

coolant flow was reduced from ~3000 lbm/hr to 0, with the reactor power being maintained at 

about 7.4 MW. No preconditioning operation was conducted for the TH-3 experiment. 

The test conditions measured during the TH-2 and TH-3 experiments are described in Tables 

A9.1 and A9.2, respectively. 

Instrumentation and Data from Tests

The instrumentation for the TH-2 experiment included: 24 self-powered neutron detectors 

(SPNDs), 115 fuel rod thermocouples, 18 steam probe thermocouples and four closure head 

thermocouples. The instrumentation was located at 21 elevations along the test train assembly. 

These are shown in Figure A9.3. 
A-80

Figure A9.2 NRU Reactor Core Configuration. 

The instrumentation for the TH-3 experiment included: 24 SPNDs, 69 fuel rods thermocouples, 

four hanger thermocouples and four closure head thermocouples. The instrumentation was 

located at 22 elevations along the test train assembly. These are shown in the Figure A9.4. 

Thermal-hydraulic data was obtained by turbine flowmeters and thermocouples. Local coolant 

temperatures were measured with steam probe thermocouples that protruded into the coolant 

channel and with thermocouples attached to the shroud. Azimuthal temperature variations 

were measured by thermocouples located at the fuel centerline and attached to the inside of the 

cladding surface. The cladding temperature was monitored by cladding thermocouples that 

were spot welded to the interior cladding surface. 
A-81

Figure A9.3 Instrumentation Levels in the TH-2 Test Assembly. 

The SPNDs provided neutron flux measurements within the fuel bundle. These measurements 

were made at opposite corners of the stainless steel shroud at several elevations, ranging from 

13.3 - 139.3 in above the bottom of the fuel column. The SPNDs provide a measure of the 

radial neutron flux gradient and neutron flux distribution over the vertical axis of the test 

assembly. These could also detect the coolant density variations (through flux changes) 

associated with the quench front that passed each SPND during the reflood phase of the 

transient. The instrument signals were monitored on a real-time basis with the DACS (Data 

Acquisition and Control System). The recorded data characterized the coolant flow rates, 

temperature neutron flux and operating history. 

The reflood flow measurement system included a Fisher-Porter turbine flowmeter in the high 

flow rate and a series connected Barton and Fisher-Porter turbine flowmeters in the parallel low 

flow rate line. Steam probe temperature history provided independent measurements of the 

reflood coolant level in the test assembly. 
A-82

Figure A9.4 Instrumentation Levels in the TH-3 Test Assembly. 

Conclusions

These tests give the average fuel rod cladding temperatures during pre-conditioning, pretransient and transient phases. Also available are the test coolant and shroud temperatures. 

However, these tests do not have enough data to make code model changes without the 

potential for compensating errors. Many of the heat transfer phenomena such as droplet to 

vapor interfacial heat transfer, dry wall contact are not simulated, though overall wall heat 

transfer is measured. Therefore, while these tests are useful in simulating the overall reflood 

heat transfer, they provide limited data which can be used to assess the reflood phenomena 

which was identified in the PIRT table for the RBHT Program. 
A-83

Table A9.1 Measured Conditions for the TH-2 Experiment(1)
A-84

Table A9.1 Measured Conditions for the TH-2 Experiment (Continued) 
A-85

Table A9.2 Measured Conditions for the TH-3 Experiment
A-86

Table A9.3 Assessment of NRU Inpile Reflood Data to RBHT PIRT: Dispersed Flow Region for Co
A-87

Table A9.3 Assessment of NRU Inpile Reflood Data to RBHT PIRT: Dispersed Flow Region for Co

(Continued) 
A-88

Table A9.4 Assessment of NRU Inpile Reflood Data to RBHT PIRT: High Ranked BWR Core P

Process/Phenomena Basis NRU Inpile R

Core Film Boiling Upper Tie Plate CCFL Channel-Bypass Leakage Steam Cooling Dryout Natural Circulation Flow Flow Regime Fluid Mixing Fuel Rod Quench Front Decay Heat Interfacial Shear Rewet: Bottom Reflood Rewet Temperature 

PCT is determined in film boiling period. Hot assembly is in co-current flow above CCFL limit. Flow bypass will help quench the BWR fuel assembly core. A portion of the dispersed flow film boiling heat transfer. Transition from nucleate boiling and film boiling. Flow into the core and system pressure drops. Determines the nature and details of the heat transfer in the core. Determines the liquid temperature in the upper plenum for CCFL break down. Heat release from the quench front will determine entrainment to the 

upper region of the bundle. Energy source for heat transfer. Affects the void fraction and the resulting droplet and liquid velocity in the entrained flow. BWR hot assembly refloods like PWR. Determines the quench front point on the fuel rod. 

PCT is determined in Not simulated. Not simulated. Simulated but overall measured. Quench front location Not applicable. Dispersed flow film boNot applicable. Simulated with nucleaSimulated. Not measured. Measured. Measured. 
A-89

Table A9.4 Assessment of NRU Inpile Reflood Data to RBHT PIRT: High Ranked BWR Core Phenom

Process/Phenomena Basis NRU Inpile R

Top Down Rewet Void Distribution Two-Phase Level 

Top of the hot assembly fuel will rewet in a similar manner as PWR. Gives the liquid distribution in the bundle. Similar to quench front location, indicates the location of nucleate and film boiling. 

Not measured. Not measured. Measured. 
A-90

APPENDIX A10. LITERATURE REVIEW 

Appendix A10: ACHILLES Reflood Heat Transfer Tests 

Dates when Tests Were Performed: 1989 - 1991 

References: 

R21 Denham, M. K., Jowitt, D., and K. G. Pearson, AACHILLES Unballooned Cluster 

Experiments, Part 1: Description of the ACHILLES Rig, Test Section, and Experimental 

Procedures,@ AEEW-R2336, Winfrith Technology Centre (Commercial in Confidence), 

November 1989. 

R22 Denham, M. K., and K. G. Pearson, AACHILLES Unballooned Cluster Experiments, Part 

2: Single Phase Flow Experiments,@ AEEW-R2337, Winfrith Technology Centre 

(Commercial in Confidence), May 1989. 

R23 K.G. Pearson and M. K. Denham, A ACHILLES Unballooned Cluster Experiments, Part 

3: Low Flooding Rate Reflood Experiments,@ AEEW-R2338, Winfrith Technology Centre 

(Commercial in Confidence), June 1989. 

R24 K.G. Pearson and M.K. Denham, AACHILLES Unballooned Cluster Experiments, Part 4: 

Low Pressure Level Swell Experiments,@ AEEW-R2339, Winfrith Technology Centre 

(Commercial in Confidence), July 1989. 

R25 Dore, P and M.K. Denham, AACHILLES Unballooned Cluster Experiments, Part 5: Best 

Estimate Experiments,@ AEEW-R2412, Winfrith Technology Centre, (Commercial in 

confidence), July 1990. 

R26 Dore, P. and D.S. Dhuga, AACHILLES Unballooned Cluster Experiments, Part 6: Flow 

Distribution Experiments,@ AEA-RS-1064, Winfrith Technology Centre (Commercial in 

Confidence), December 1991. 

Availability of Data: 

The ACHILLES experiments were performed as part of the safety case for PWRs in the United 

Kingdom. The ACHILLES tests were funded by the Central Electricity Generating Board 

(CEGB) and were performed by the United Kingdom Atomic Energy Authority (UKAEA) at the 

Winfrith Laboratories. The data does have some release restrictions and is not unlimitedly 

available to the general public. However, more recently, data has been released to interested 

parties and governments as part of cooperative data exchange. Some of the data was used for 

an International Standard Problem. Westinghouse has been able to obtain some of the data 

directly from the CEGB provided that reference was given to the CEGB in the reports prepared 

by Westinghouse. Therefore, the data should be available to the Nuclear Regulatory 

Commission. 
A-91

Test Facility Description, Types of Tests

The ACHILLES tests were specifically conducted to support the PWR (Sizewell) safety case in 

the United Kingdom in the late 1980's and early 1990's. Since these tests were performed after 

the FLECHT-SEASET tests, the authors had made some improvements which are of value for 

the current Rod Bundle Heat Transfer Program. The testing consisted of specific test series 

which were used to examine specific safety issues and safety analysis issues. Specifically, 

experiments were performed to examine: 

• Low reflooding rate behavior similar to FLECHT-SEASET and FLECHT, 

• Best-Estimate Reflood tests were performed to assess a realistic LOCA transient, 

• Single-phase flow distribution tests were performed to examine the flow uniformity and 

single-phase heat transfer within the rod bundle, and 

• Low-pressure level swell experiments were also performed to validate drift flux/void 

fraction relationships. 

There were also gravity feed reflood tests with loop resistance simulated, and variable injection 

reflood tests which simulated evaluation model type system response. There were also 

oscillating inlet flow injection tests. 

One of the purposes of the ACHILLES test program was to examine the heat transfer 

performance of a fuel assembly with high blockages caused by the swelling of the zirc cladding 

(sausage ballooning problem). This issue had been resolved in the U.S. but it still remained as 

an open item in the United Kingdom safety case for the PWR. The reports given in the review 

only discuss the unblocked or unballooned configuration of the test program. There is a 

continuation of the ACHILLES test program which specifically examines flow blockages of up to 

80 percent to address the clad swelling issues during a LOCA. These tests will not be 

discussed here. 

The ACHILLES bundle is shown in Figure A10.1 and contains a total of 69 heater rods of 9.5 

mm (0.374 in) in diameter on a square pitch of 12.6 mm (0.496 in) and have 3.66 m (12 ft) of 

heated length. ACHILLES used production Inconel mixing vane grids supplied by 

Westinghouse. All rods were heated in ACHILLES such that there was no simulation of the 

guide tube thimbles in the bundle such as in the FLECHT-SEASET experiments. However, 

experiments were performed in ACHILLES to examine the effects of increased surface-tosurface radiation heat transfer by performing tests with selective unpowered heater rods. 

Figure A10.2 indicates the flow loop schematic for the ACHILLES facility. There was ample 

flexibility built into the test facility such that both single phase, two-phase, forced reflood 

injections could be performed, as well as oscillatory injection and gravity injection tests with little 

facility modifications. The test bundle was contained within a circular shroud of wall thickness of 

6.5 mm (0.26 in) and a pressure capability of 6 bars (approximately 90 psia). There were no 

filler rods in the test bundle design which resulted in excess flow area for the square array of 

rods within the circular housing. To compensate for the excess flow area and to better simulate 

an infinite array of fuel rods, the ACHILLES housing was heated with zonal heaters which had a 
A-92

Figure A10.1 Cross Section of ACHILLES 69-Rod Bundle. 

total power of 46 kW. These heaters provided a similar axial temperature distribution as the 

heater rods. 

The heater rods were manufactured by RAMA corporation, the same company that made the 

FLECHT-SEASET heater rods. A chopped cosine power shape with a peak-to-average of 1.4 

was used. These rods used Inconel cladding, and could have up to six thermocouples per rod 

installed. The axial distribution of the heater rod thermocouples and the other instrumentation is 

shown in Figure A10.3. One unique feature of the ACHILLES bundle is that the instrumentation 

plan was developed with the idea of examining the heat transfer effects of the spacer grids both 

upstream and downstream of the grids. 
A-93

Figure A10.2 Schematic of ACHILLES Flow Loop. 

The grids used were Inconel production 17x17 spacer grids with mixing vanes. These grids 

were instrumented with 0.5 mm (0.20 in) thermocouples which were attached to the grids using 

Inconel shim stock which was spot-welded to the spacer. The attachment method was 

designed to minimize the flow disturbance and the effects of the thermocouple lead leading to 

early grid rewet. Each grid had two thermocouples attached to the spacer at the top and lower 

edges at different radial positions. The data indicates that this installation method worked well 

and only one-grid thermocouples failed. 

The vapor temperature was measured in the rod bundle at different axial location, up steam and 

down stream of spacer grids using 1 mm (0.040 in) thermocouples which were swagged to a tip 

size of 0.5 mm (0.020 in). There is an uncertainly analysis given in the report which indicates 

that f or the conditions used in the ACHILLES tests, the vapor temperature uncertainty is only 

13 degrees C (23.4 degrees F) which is consistent with the uncertainty which was derived in the 

FLECHT-SEASET program. It is mentioned in Reference R22 that the vapor temperature 

measurements did have an effect on the entrained droplets with the probe causing additional 
A-94

Figure A10.3 Axial Locations in Test Section. 

droplet breakup and slowing down of larger droplets. There is insufficient data presented to 

draw an independent conclusion of these effects. 

There were additional pressure taps placed along the shroud such that the pressure drops 

across the spacer grids were obtained as well as the frictional pressure drop in the rod bundle 

section. The pressure drop information was used to infer void fraction; however, there was no 

frictional or acceleration pressure drop corrections to the data such that the void fractions given 

for ACHILLES are lower then those expected. 
A-95

The shroud had windows at the mid-plane for photographic purposes with the view being 

through specific rows of heater rods. The windows were very small such that they could be 

heated by the rods during heat-up before each test. The windows were set back from the inside 

edge to avoid direct droplet impact which would have caused the window to wet. From the 

report, it appears that the windows would stay dry until the quench front was within the grid span 

where the windows were located. One could interpret this as having the top of the froth front 

approaching the window before the window wetted. 

Tests were performed using a four-cylinder piston pump which superimposed an oscillating flow 

on the forced flooding rate. The period and magnitude of the flow and oscillation frequency 

could be adjusted for different sensitivity tests. The bi-directional flow probe showed reverse 

flow, but is not clear if Areal@ reverse flow occurred. One significant observation is that with 

oscillatory flow, the grids quickly rewet as compared to constant forced injection flow. The same 

situation occurred for initially high injection flows. 

An improved photographic droplet diameter and velocity measuring technique was developed 

as part of the ACHILLES program in which a pulse of green light was shined into the open 

camera shutter, followed by a pulse of red light. The duration of each pulse was short and there 

was a fixed time between the two pulses. This approach produced two images of a droplet 

which were of different color such that the drop size and velocity could be inferred from the 

prints. The filming rate was 100 frames/s; clips of shots were taken during a given test. Two 

cameras were also able to focus on different subchannels such that a reasonable droplet 

distribution across the bundle could be determined. It was observed that the droplet flow was 

not uniform with more liquid in the outermost channel near the wall. The outermost channel has 

the larger hydraulic diameter and hence the greater steam flows as compared to the inner 

regions of the bundle which could explain the observed trend. The report included droplet 

distribution plots for selected tests. 

The test matrix for the low flooding rate tests is given in Table A10.1. One parameter to note is 

that they purposely controlled the power such that very high heater rod temperatures never 

occurred and the maximum temperatures were very similar. Details of the reference test and 

the effects for the different sensitivity tests are given in Reference R23. The temperature rise 

values were different. Table A10.2 gives the test numbers for the droplet distribution 

experiments. Table A10.3 gives the conditions for the single-phase air flow distribution 

experiments and for the voidage distribution experiments. Each series of tests is discussed in 

Reference R22. The test matrix for the best-estimate or realistic Reflood tests is given in Table 

A10.4 from Reference R25. 

The authors did perform a similar analysis as in the FLECHT and FLECHT-SEASET tests in 

which the actual quality was calculated at the bundle cross sections where vapor measurements 

existed. The same or similar exit flow measurements were made in the ACHILLES tests as in 

the FLECHT and FLECHT-SEASET tests such that a bundle heat and mass balance could be 

determined. However, the authors did not attempt to separate the radiation component from the 

total measured heat transfer such that their estimates of the convective dispersed flow film 

boiling heat transfer results in higher heat transfer coefficients then would be the case in the 

FLECHT and FLECHT-SEASET experiments. However, very similar trends were observed, 

with very low vapor Reynolds number flows and enhancement of the dispersed flow film boiling 

heat transfer above the single phase convection heat transfer limit for the same fluid conditions. 
A-96

The effects of the spacer grids were analyzed and a correlation was suggested for the 

convective enhancement of the local heat transfer downstream of the grid. There were also 

some very informative plots of the vapor temperatures and the spacer grid temperatures which 

showed that when the grid quenches, the vapor temperature downstream of the grid decreases. 

The axial distribution of the heater rod thermocouples gave an excellent indication of the quench 

front along the bundle. These authors did display their data more as axial plots for different time 

periods such that additional information good be obtained with fewer figures. Variable reflood 

rates, oscillatory flooding rates, and stepped flooding rates would easily quench the spacer grids 

and they remained wetted throughout the transient. The very high flooding rates also quenched 

the miniature thermocouples used to measure the vapor temperature. Some of these 

thermocouples could dry out later in the tests and would indicate the presence of superheated 

vapor. 

The best-estimate tests had more favorable test initial conditions such that the heat transfer was 

higher and the bundle would quench more easily. The same or similar phenomenon was 

observed in these tests excepting that the transients were shorter and the temperatures were 

lower. 

Single-phase heat transfer and flow tests were also conducted using air as the fluid. A specially 

constructed hot film probe was used for the air velocity distribution which confirmed that a 

bypass effect was occurring in the ACHILLES bundle due to the large excess flow area located 

on the outside edge of the bundle between the heater rods and the shroud. Single-phase 

effects of the spacer grids were also determined and compared to a previous correlation. We 

need to verify the axial distribution of the thermocouples in the RBHT test to make sure that we 

can detect the decaying heat transfer trend downstream of the spacer grids. 

One of the more unique data obtained in the ACHILLES program is the droplet or liquid 

distribution across the bundle using the photographic technique. Again, this distribution is 

distorted and shows more liquid at the edge of the bundle where the steam mass flow is higher 

due to the increased bypass flow at this location. The opposite would be expected in an infinite 

bundle since the center rods would be hotter creating a thermal syphon which should result in 

increased entrainment. 

Conclusions 

The ACHILLES Reflood experiments potentially represent some of the best reflood data 

available for computer code validation. However, a two-channel model which includes 

crossflow should be used to represent the inner region of the bundle which has the correct flow 

are per rod, while an outer channel would represent the outer region of the bundle where there 

is excess flow area. Also, the computer code would have to model the housing or shroud which 

also supplies energy to the fluid. Computer codes such as the TRAC- P series, and COBRA-TF 

and COBRA-TRAC have the ability to model these effects. However, the flow diversion, excess 

flow area, and housing heat release effects must be assessed as test distortions. Also, if they 

are first order effects, it will be difficult to determine what models in the candidate code need 

improving since the test distortions could mask the model requirements resulting in 

compensating error being introduced into the code. 
A-97

There is some unique data from the ACHILLES tests which are not available from other tests 

such as the subchannel droplet distribution data, spacer grid loss coefficient data, 

instrumentated spacer grid and local fluid temperature data, along with very finely spaced 

heater rod thermocouple data which shows the heat transfer effects of the spacer grids and 

quench front. The differential pressure data was taken using small spans both between grids 

and across spacer grids. This data needs to be corrected for frictional pressure drop and 

acceleration pressure drop in order to be used for inferring the local void fraction. Once this is 

performed, the local heat transfer can then be correlated with the void fraction. 

The tests cover a wide range of conditions which are equally applicable to evaluation of model 

calculations as well as best-estimate reflood conditions such that an ample set of data is 

available. Also the tests include oscillating inlet flow, stepped forced flooding rate tests, and 

gravity reflood tests. 

It is strongly recommended that these data be screened and selected ACHILLES tests be 

obtained from CEGB and added to the NRC data bank and analyzed with the TRAC-M code 

and COBRA-TF. These tests can also be used for comparison purposes with the Rod Bundle 

Heat Transfer Tests. 
A-98

Table A10.1 Summary of Low Flooding Rate Reflood Experiments 
A-99

Table A10.2 Droplet Distribution Experiments 
A-100

Table A10.3 Airflow and Voidage Distribution Experiments 
A-101

Table 10A.4 Summary of Best Estimate Reflood Experiments 
A-102

APPENDIX A11. LITERATURE REVIEW 

Appendix A11: Lehigh 9-Rod Bundle Tests

Dates When Tests Were Performed: 1982 - 1986 

References: 

R27 Tuzla, K., Unal, C., Badr, O., Neti, S., Chen, J.C., AThermodynamic Nonequilibrium in 

Post-Critical-Heat-Flux Boiling in a Rod Bundle,@ NUREG-CR 5095, Vol. 1-4, June 1998. 

R28 Unal C., Tuzla, K., Badr, O., Neti, S., Chen, J.C., AConvective Boiling in a Rod Bundle: 

Traverse Variation of Vapor Superheat Temperature Under Stabilized post-CHF 

Conditions,@ Int. J. Heat and Mass Transfer, Vol. 34, No. 7, pp. 1695-1706, 1991. 

Availability of Data: 

The data for these experiments is contained in Volumes 2 - 4 of Reference R27. Raw data are 

not available from the original source. 

Test Facility Description, Types of Tests 

The rods were 9.5 mm (0.374 in) in diameter and were arranged in a square pitch of 12.6 mm 

(0.496 in) as shown in Figure A11.1. The actual test section of the facility was 1.22 m (4 ft) long 

with one spacer grid located at 0.762 m (30 in) from the bottom as shown in Figure A11.2. The 

rods had a linear power profile to provide a constant heat flux over the length of the test section. 

Each subchannel had the same wetted perimeter and this resulted in about 39 percent of 

excess flow area in the bundle. The excess flow area was to account for the housing effect. 

Coolant Mass Flow Rate 6.6x10-4 - 0.1694 kg/s (3x10-4 - 0.077 lbm/s) 

Inlet Subcooling 40 - 0.55 degrees C (72 - 1 degrees F) 

Pressure 102.042 - 119.97 kPa (14.8 - 17.4 psi) 

Initial Shroud Temperature 301.67 - 398.89 degrees C (575 - 750 degrees F) 

Initial Rod Temperature 593.33 degrees C (1100 degrees F) 

Heat Flux 5 - 4312 kW/m2 

Linear Heat Generation 1.3123 to 11.483 kW/m (0.4 to 3.5 kW/ft) 

(Constant Over the Length) 

Constant Flooding Rates 1.016 to 4.064 mm/s (0.04 to 0.16 in/s) 
A-103

Figure A11.1 Cross-Sectional View of Test Bundle. 

Figure A11.2 Schematic of Test Section Support System. 
A-104

Instrumentation and Data From Tests 

There were eight thermocouples imbedded in each of the nine heater rods at 152.4 mm (6 in) 

intervals. Due to limitations of the data collection system, only 80 channels could be monitored 

for any given test. The arrangement of thermocouple elevations has one disturbing 

shortcoming. There are no thermocouples located at identical elevations and angles to allow for 

checking of the symmetry of the test section. The pressure cells were spaced too far apart to 

be able to make a calculation of the void fraction. Two aspirating steam probes were located at 

609.6 mm (24 in) and 965.2 mm (38 in), respectively. These probes were traversed through the 

bundle in several experiments to measure the traverse variation of vapor superheat. The vapor 

temperature difference was reduced from 120 to 40 degrees C superheat when the inlet quality 

was increased from 0.04 to 0.40. Effects of dispersed droplet cooling were evident after the grid 

as well. 

The data presented in Figures A11.3 to A11.7 and Tables A11.1 to A11.4 shows a pronounced 

effect caused by the spacer grid located at the 762 mm (30 in) elevation. This information might 

be used in evaluating the effects of spacer grids in two-phase-dispersed droplet flow. The data 

also showed a small error caused by the steam probes. 

Conclusions 

This series of tests is of limited use to the RBHT Program. The information gathered using a 

traversing steam probe is the most significant contribution. 

Figure A11.3 Sample Plot of Temperature and Steam Quality Data for the 

Stabilized Quench Front Experiments. 
A-105

Figure A11.4 Sample Plot of Heat Flux and Steam Quality Data for the 

Advancing Quench Front Experiments. 

Figure A11.5 Sample Plot of Rod and Steam Temperature Data for the 

Advancing Quench Front Experiments. 
A-106

Figure A11.6 Typical Transverse Vapor Temperature Profiles for Various Vapor Qualities. 

Figure A11.7 Typical Transverse Vapor Temperature Profiles Downstream 

of the Grid Spacer. 
A-107

Table A11.1 Sample Tabulation of a Stabilized Quench Front Data Point 

(See Table A11.2 for Nomenclature) 
A-108

Table A11.2 Definition of Parameters Used in Table A11.1 

QRS = shroud heat flux (local) 

TR 1 = surface temperature of test rod number 1 

TR 3 = surface temperature of test rod number 3 

TR 4 = surface temperature of test rod number 4 

TR 5 = surface temperature of test rod number 5 

TR 6 = surface temperature of test rod number 6 

TR 7 = surface temperature of test rod number 7 

TR 8 = surface temperature of test rod number 8 

TR 9 = surface temperature of test rod number 9 

TS = shroud surface temperature 

TV 1 = vapor temperature obtained from first probe 

TV 2 = vapor temperature obtained from second probe 

XA 1 = actual quality at the first vapor probe location 

XA 2 = actual quality at the second vapor probe location 

XE = equilibrium quality 

XE 1 = equilibrium quality at the first vapor probe location 

XE 2 = equilibrium quality at the second vapor probe location 

ZS = shroud axial location (reference to hot-patch inlet) 

ZT = Test section axial location (reference to hot-patch inlet) 
A-109

Table A11.3 Sample Tabulation of an Advancing Quench Front Data Point 

(See Table A11.4 for Nomenclature) 
A-110

Table A11.4 Definition of Parameters Used in Table A11.3 

DEV = device 

DIS = distance 

QRS = shroud=s heat flux (local value) 

QUAL = equilibrium quality 

R1 = test rod #1 

R3 = test rod #3 

R4 = test rod #4 

R6 = test rod #6 

R7 = test rod #7 

R8 = test rod #8 

SH = shroud 

TR 1 = surface temperature of test rod number #1 

TR 3 = surface temperature of test rod number #3 

TR 4 = surface temperature of test rod number #4 

TR 6 = surface temperature of test rod number #6 

TR 7 = surface temperature of test rod number #7 

TR 8 = surface temperature of test rod number #8 

TS = surface temperature of the shroud 

TV1 = vapor temperature of first vapor probe elevation 

TV2 = vapor temperature of second vapor probe elevation 

XA 1 = actual quality at the first vapor probe location 

XA 2 = actual quality at the second vapor probe location 

XE = equilibrium quality 

XE 1 = equilibrium quality at the first vapor probe location 

XE 2 = equilibrium quality at the second vapor probe location 

ZS = shroud axial location (reference to hot-patch outlet) 

ZT = test section axial location (reference to hot-patch outlet) 
APPENDIX B1. RADIATION HEAT TRANSFER NETWORK AND 

CALCULATION OF PI GROUPS 

Description of the Radiation Network

In order to calculate the radiative heat transfer from the rods to the surfaces and the housing, a 

six node radiation network (Figure 6.3) has been developed which includes radiation heat 

transfer to droplets and vapor. The network resistances discussed in Section 7 (Refs. 7-2, 7-3 

and 7-4) are defined as follows: 

i

w A

Rii w ε

ε

1− = 1

( )( ) ijivl

ij

FA

R

11 −−= εε

1

( ) ivl

il

A

R

1−= εε

1

( ) ilv

iv

A

R

1 −= εε

1 

∑=

=

4

1

1

i

ivl

lv

A

R

εε

where 

Ai radiating area per unit length for the i-th radiating wall surface 

Fij view factor from node >i= to node >j=

εw wall emissivity 

εl, εv drop and vapor emissivity 

The view factors are calculated by summing up single rod-to-rod, rod-to-housing and rod-tosurfaces view factors which are calculated with the VIEWFAC subroutine of MOXY computer 

program (Ref. 7-1): 

, 49

1

49

1

12 ∑

∑

∑

=

= = j

i

i

i

iji

A

FA

F where and 

CR = jj CR ≠ ji ( are the cold rods indices) CR j

B-1
, 49

1

49

1

13 ∑

∑

∑

=

= = j

i

i

i

iji

A

FA

F where and 

S = jj CRS ≠ , jji ( are surfaces indices: 1,7,43,49) Sj

∑

∑

=

= = 49

1

49

1

14

i

i

i

iNi

A

FA

F , where CRS ≠ , jji

, 49

1

49

1

23 ∑

∑

∑

=

= = j

i

i

i

iji

A

FA

F where S = jj and CR = ji

 

∑

∑

=

= = 49

1

49

1

24

i

i

i

iNi

A

FA

F , where CR = ji

+++ AAAA 494371

7711 4343 4949

34

FAFAFAFA F N N ++ N + N =

 

Assuming that the droplet and vapor media are optically thin, the drop and vapor emissivities εl

and εv are calculated with the following formula: 

La ml

l e− ε 1−=

La mv

v e− ε 1−=

where the beam length Lm is defined as follows for rod bundle geometry: 

m = 85.0 DL h

Assuming the droplets in the geometric scattering regime, the liquid absorption coefficient is 

calculated by the following formula which is based on Reference 7-4 with the additional 

assumption of considering a single drop size group (Sauter mean diameter): 

 l d a nd

2 = π.0185

B-2
where d is the drop Sauter mean drop diameter (m) while the number of droplet per unit volume 

nd is calculated from the void fraction: 

3 .

)1(6

d

nd

π

−α =

where the Sauter mean diameter and the void fractions are inputs in the program. The vapor 

absorption coefficient av is calculated with the following formula: 

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

− ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ ⋅= −

2 4

5 555 555 66.181084.9

w w

v TT

a P

 

where P is the pressure (kPa) and Tw is the wall temperature (K). 

Solution of the Radiation Network

Kirchhoff Law is applied to nodes 1, 2, 3 and 4: 

0.0 . . .

1

4

1

1

4

1

13

41

13

31

12

21

11

4

1 = − + − + − + − + − + −

v

v

l

hr l

R

TJ

R

TJ

R

JJ

R

JJ

R

JJ

R

σ TJ σ σ

0.0 . . .

2

4

2

2

4

2

24

42

23

32

12

12

22

4

2 = − + − + − + − + − + −

v

v

l

cr l

R

TJ

R

TJ

R

JJ

R

JJ

R

JJ

R

σ TJ σ σ

 0.0 . . .

3

4

3

3

4

3

34

43

23

23

13

13

33

4

3 = − + − + − + − + − + −

v

v

l

s l

R

TJ

R

TJ

R

JJ

R

JJ

R

JJ

R

σ TJ σ σ

0.0 . . .

4

4

4

4

4

4

34

34

24

24

14

14

44

4

4 = − + − + − + − + − + −

v

v

l

h l

R

TJ

R

TJ

R

JJ

R

JJ

R

JJ

R

σ TJ σ σ

where are the radiosities in the network nodes. i J

For a given temperature field (Thr, Tcr, Ts, Th, Tl and Tv), the equations are solved for the 

unknowns (J1, J2, J3 and J4). Then the heat rate across each resistance in the network can be 

calculated as: 

ij

ij

ij R

JJ

Q − =

B-3
The previous procedure has been implemented in the Fortran program called RADNET 

attached in Appendix B5. 

Another input to the RADNET computer program is how hot versus cold rods are lumped 

together in the bundle. It can be recognized that for given boundary conditions, the result is 

dependent on how hot and cold rods are lumped together in the model. Sensitivity studies have 

carried out where the hot rods sub-array has been assumed to be the central rod, the inner 3x3 

array or the inner 5x5 array. For example, the Pi group π30 (see later) calculated with the three 

different lumping approaches is: 

π ,30 cr = 567.0

π x33,30 = 388.0

π x55,30 = 345.0

It is important to note that this is the group affected most while the effect of different lumping 

approach on the other groups is less important. Results from the detailed rod-to-rod model 

calculations discussed in Section 7 show that the temperature is practically uniform in the inner 

3x3 array while the temperature drops in the periphery due to the effect of the housing. Thus, 

the inner 3x3 hot rods lumping approach is the most appropriate and was chosen in the 

dimensionless groups calculation. 

B-4
B-5

APPENDIX B2. ROD GRID RADIATION NETWORK FOR RBHT 

Inputs 

H grid 1.5 in 0.0381 m

N grids 6

rod diameter 0.374 in 0.0094996 m

rods pitch 0.496062992 in 0.0126 m

rod power 5.6 kW

pressure 40 psia 272.1088435 kPa

liquid temperature 267 F 403.6955556 K

vapor temperature 1177 F 909.2511111 K

rod temperature 1650 F 1172.028889 K

grid temperature 1376 F 1019.806667 K

void fraction 0.995

droplets Sauter mean diameter 0.001 m

wall emissivity 0.8 

Calculation 

bundle hydraulic diameter 0.011789932 m

droplet density 9554140.127 Ndrp/m3

liquid absorption coefficient 5.55 m-1

beam length 0.010021442 m

liquid emissivity 0.054100549 

vapor absorption coefficient 0.182435145 m-1

vapor emissivity 0.000542019 

rod area (based on Hgrid) Ar 1.76154 in2 0.001136475 m2

grid area (per rod) Ag 2.976 in2 0.001919996 m2

1/R11 0.004545901 

1/R22 0.007679985 

1/R12 0.001074409 

1/R1L 6.14506E-05 

1/R1V 5.82665E-07 

1/R2L 0.000103817 

1/R2V 9.84373E-07 

1/RLV 8.96264E-08 

A11 0.005682342 

A22 0.008859194 

A12=A21 -8.96264E-08 

C1 486.4733384 

C2 471.1878606 
B-6

APPENDIX B3. ROD GRID RADIATION NETWORK FOR PWR 

Inputs 

H grid 1.5 in 0.0381 m 

N grids 6 

rod diameter 0.374 in 0.0094996 m 

rods pitch 0.496063 in 0.0126 m 

rod power 5.6 kW 

pressure 40 psia 272.10884 kPa 

liquid temperature 267 F 403.69556 K 

vapor temperature 1177 F 909.25111 K 

rod temperature 1650 F 1172.0289 K 

grid temperature 1376 F 1019.8067 K 

void fraction 0.995 

droplets Sauter mean diameter 0.001 m 

wall emissivity 0.9 

Calculation 

bundle hydraulic diameter 0.0117899 m 

droplet density 9554140.1 Ndrp/m3

liquid absorption coefficient 5.55 m-1

beam length 0.0100214 m 

liquid emissivity 0.0541005 

vapor absorption coefficient 0.1824351 m-1

vapor emissivity 0.000542 

rod area (based on Hgrid) Ar 1.76154 in2 0.0011365 m2

grid area (per rod) Ag 2.976 in2 0.00192 m2

1/R11 0.0102283 

1/R22 0.01728 

1/R12 0.0010744 

1/R1L 6.145E-05 

1/R1V 5.827E-07 

1/R2L 0.0001038 

1/R2V 9.844E-07 

1/RLV 8.963E-08 

A11 0.0113647 

A22 0.0184592 

A12=A21 -8.963E-08 

C1 1094.4211 

C2 1059.9296 
B-7

APPENDIX B4. ROD GRID RADIATION NETWORK FOR BWR 

Inputs 

H grid 1.5 in 0.0381 m

N grids 6

rod diameter 0.4830709 in 0.01227 m

rods pitch 0.6377953 in 0.0162 m

rod power 5.6 kW

pressure 40 psia 272.10884 kPa

liquid temperature 267 F 403.69556 K

vapor temperature 1177 F 909.25111 K

rod temperature 1650 F 1172.0289 K

grid temperature 1376 F 1019.8067 K

void fraction 0.995

droplets Sauter mean diameter 0.001 m

wall emissivity 0.9 

Calculation 

bundle hydraulic diameter 0.0149768 m

droplet density 9554140.1 Ndrp/m3

liquid absorption coefficient 5.55 m-1

beam length 0.0127303 m

liquid emissivity 0.068215 

vapor absorption coefficient 0.1824351 m-1

vapor emissivity 0.000868 

rod area (based on Hgrid) Ar 2.2752638 in2 0.0014679 m2

grid area (per rod) Ag 2.976 in2 0.00192 m2

1/R11 0.0132112 

1/R22 0.01728 

1/R12 0.0013666 

1/R1L 0.0001 

1/R1V 1.187E-06 

1/R2L 0.0001309 

1/R2V 1.553E-06 

1/RLV 2.006E-07 

A11 0.014679 

A22 0.018779 

A12=A21 -2.006E-07 

C1 1413.6388 

C2 1059.9923 
B-8

APPENDIX B5. FORTRAN PROGRAM RADNET 

program radnet 

c 

 dimension f(50,50),area(50) 

 dimension pir(50) 

 dimension ir(50) 

c 

 common/cgauss/ a(10,10),b(10),c(10),na 

 common/temp/t(10),eb(10),tl,tv,ebl,ebv,q(10) 

 common/resist/ r(10,10) 

c 

 data sig/5.67E-08/ 

 data pi/3.141592654/ 

c 

c......input values 

 nhot=9 

 trmed=1650.0 

 thr=2100.0 

 ts=800.0 

 th=800.0 

 tl=267.0 

 tv=1650.0 

 hqch=4.0 

 qrod=2296.6 

c 

 hcore=12.0 

 qtot=qrod*45.0 

 qhr=qrod*float(nhot) 

 nsurf=4 

 nrod=49 

 ncold=nrod-nhot-nsurf 

 n=nrod+1 

 drod=0.0095 

 dh=0.01178 

 dtemp=155.0 

 if (nhot.eq.9) dtemp=161.0 

 if (nhot.eq.25) dtemp=170.0 

 if (thr.eq.0.0) thr=trmed+ncold*dtemp/float(ncold+nhot) 

 tcr=thr-dtemp 

 write(6,*) thr,tcr 

c 

c......pressure in psia 

 press=40.0 

 alp=0.995 

 dd=0.001 

 ew=0.8 

 timax=500.0 

c 

c......end of inputs 

c 

 do 301 i=1,49 

 ir(i)=2 

 301 continue 
B-9

 if (nhot.eq.1) then 

 ir(25)=1 

 endif 

 if (nhot.eq.9) then 

 ir(17)=1 

 ir(18)=1 

 ir(19)=1 

 ir(24)=1 

 ir(26)=1 

 ir(31)=1 

 ir(32)=1 

 ir(33)=1 

 endif 

 if (nhot.eq.25) then 

 ir(9)=1 

 ir(10)=1 

 ir(11)=1 

 ir(12)=1 

 ir(13)=1 

 ir(16)=1 

 ir(20)=1 

 ir(23)=1 

 ir(27)=1 

 ir(27)=1 

 ir(30)=1 

 ir(34)=1 

 ir(37)=1 

 ir(38)=1 

 ir(39)=1 

 ir(40)=1 

 ir(41)=1 

 endif 

c 

 ir(1)=3 

 ir(7)=3 

 ir(43)=3 

 ir(49)=3 

c 

 shrod=float(nhot)*pi*drod 

 scrod=float(ncold)*pi*drod 

 ssrf=float(nsurf)*pi*drod 

 shou=0.3607 

 nd=6.0*(1.0-alp)/(pi*dd**3.0) 

 al=0.185*nd*pi*dd**2.0 

 press=press*100.0/14.7 

c 

c......calculate global view factors with inner hot rods array considered 

c 

 do 11 i=1,n 

 do 12 j=1,n 

 read(9,*) ni,nj,f(i,j) 

 12 continue 

 read(9,*) area(i) 

 11 continue 

c 
B-10

 fhrcr=0.0 

 do 101 j=1,nrod 

 fsum=0.0 

 asum=0.0 

 if (ir(j).ne.2) goto 101 

 do 102 i=1,nrod 

 if (ir(i).ne.1) goto 102 

 fsum=fsum+area(i)*f(i,j) 

 asum=asum+area(i) 

 102 continue 

 fhrcr=fhrcr+fsum/asum 

 101 continue 

c 

 fsum=0.0 

 asum=0.0 

 fhrh=0.0 

 do 202 i=1,nrod 

 if (ir(i).ne.1) goto 202 

 fsum=fsum+area(i)*f(i,n) 

 asum=asum+area(i) 

 202 continue 

 fhrh=fsum/asum 

c 

 fsum=0.0 

 asum=0.0 

 fcrh=0.0 

 do 302 i=1,nrod 

 if (ir(i).ne.2) goto 302 

 fsum=fsum+area(i)*f(i,n) 

 asum=asum+area(i) 

 302 continue 

 fcrh=fsum/asum 

c 

 fhrs=0.0 

 do 401 j=1,nrod 

 fsum=0.0 

 asum=0.0 

 if (ir(j).ne.3) goto 401 

 do 402 i=1,nrod 

 if (ir(i).ne.1) goto 402 

 fsum=fsum+area(i)*f(i,j) 

 asum=asum+area(i) 

 402 continue 

 fhrs=fhrs+fsum/asum 

 401 continue 

c 

 fcrs=0.0 

 do 501 j=1,nrod 

 fsum=0.0 

 asum=0.0 

 if (ir(j).ne.3) goto 501 

 do 502 i=1,nrod 

 if (ir(i).ne.2) goto 502 

 fsum=fsum+area(i)*f(i,j) 

 asum=asum+area(i) 
B-11

 502 continue 

 fcrs=fcrs+fsum/asum 

 501 continue 

c 

 asum=area(1)+area(7)+area(43)+area(49) 

 fs1=area(1)*f(1,n) 

 fs2=area(7)*f(7,n) 

 fs3=area(43)*f(43,n) 

 fs4=area(49)*f(49,n) 

 fsh=(fs1+fs2+fs3+fs4)/asum 

c 

c......calculate network resistances 

c 

 ebl=sig*tl**4.0 

 ebv=sig*tv**4.0 

 av=9.84e-5*press*(18.66*(555.0/tv)**2.0 - (555.0/tv)**4.0) 

 xlm=0.85*dh 

 el=1.0-exp(-al*xlm) 

 ev=1.0-exp(-av*xlm) 

 r(1,1)=(1.0-ew)/(ew*shrod) 

 r(1,2)=1.0/((1.0-el)*(1.0-ev)*shrod*fhrcr) 

 r(1,3)=1.0/((1.0-el)*(1.0-ev)*shrod*fhrs) 

 r(1,4)=1.0/((1.0-el)*(1.0-ev)*shrod*fhrh) 

 r(1,5)=1.0/(el*(1.0-ev)*shrod) 

 r(1,6)=1.0/(ev*(1.0-el)*shrod) 

c 

 r(2,1)=r(1,2) 

 r(2,2)=(1.0-ew)/(ew*scrod) 

 r(2,3)=1.0/((1.0-el)*(1.0-ev)*scrod*fcrs) 

 r(2,4)=1.0/((1.0-el)*(1.0-ev)*scrod*fcrh) 

 r(2,5)=1.0/(el*(1.0-ev)*scrod) 

 r(2,6)=1.0/(ev*(1.0-el)*scrod) 

c 

 r(3,1)=r(1,3) 

 r(3,2)=r(2,3) 

 r(3,3)=(1.0-ew)/(ew*ssrf) 

 r(3,4)=1.0/((1.0-el)*(1.0-ev)*ssrf*fsh) 

 r(3,5)=1.0/(el*(1.0-ev)*ssrf) 

 r(3,6)=1.0/(ev*(1.0-el)*ssrf) 

c 

 r(4,1)=r(1,4) 

 r(4,2)=r(2,4) 

 r(4,3)=r(3,4) 

 r(4,4)=(1.0-ew)/(ew*shou) 

 r(4,5)=1.0/(el*(1.0-ev)*shou) 

 r(4,6)=1.0/(ev*(1.0-el)*shou) 

c 

 r(5,1)=r(1,5) 

 r(5,2)=r(2,5) 

 r(5,3)=r(3,5) 

 r(5,4)=r(4,5) 

 r(5,5)=0.0 

 r(5,6)=1.0/(ev*el*(shrod+scrod+ssrf+shou)) 

c 

 r(6,1)=r(1,6) 
B-12

 r(6,2)=r(2,6) 

 r(6,3)=r(3,6) 

 r(6,4)=r(4,6) 

 r(6,5)=r(5,6) 

 r(6,6)=0.0 

c 

 na=4 

c 

 t(1)=273.14+(thr-32.0)/1.8 

 t(2)=273.14+(tcr-32.0)/1.8 

 t(3)=273.14+(ts-32.0)/1.8 

 t(4)=273.14+(th-32.0)/1.8 

 t(5)=273.14+(tl-32.0)/1.8 

 t(6)=273.14+(tv-32.0)/1.8 

 do 10 i=1,6 

 eb(i)=sig*t(i)**4.0 

 10 continue 

c 

 call matrix 

 call gauss 

c 

 do 351 i=1,na 

 q(i)=(c(i)-eb(i))/r(i,i) 

 351 continue 

 q(5)=0.0 

 q(6)=0.0 

 do 352 i=1,na 

 q(5)=q(5)+(c(i)-eb(5))/r(i,5) 

 q(6)=q(6)+(c(i)-eb(6))/r(i,6) 

 352 continue 

 qvl=(eb(6)-eb(5))/r(5,6) 

 q(5)=q(5)+qvl 

 q(6)=q(6)-qvl 

c 

 q12=(c(1)-c(2))/r(1,2) 

 q13=(c(1)-c(3))/r(1,3) 

 q23=(c(2)-c(3))/r(2,3) 

 q14=(c(1)-c(4))/r(1,4) 

 q24=(c(2)-c(4))/r(2,4) 

 q1l=(c(1)-eb(5))/r(1,5) 

 q1v=(c(1)-eb(6))/r(1,6) 

 q2l=(c(2)-eb(5))/r(2,5) 

 q2v=(c(2)-eb(6))/r(2,6) 

 q3l=(c(3)-eb(5))/r(3,5) 

 q3v=(c(3)-eb(6))/r(3,6) 

 q4l=(c(4)-eb(5))/r(4,5) 

 q4v=(c(4)-eb(6))/r(4,6) 

c 

c......pi groups in the flow energy equation 

 pir(1)=(q1v+q2v)/qtot 

 pir(2)=(q1l+q2l)/qtot 

 pir(3)=q4v/qtot 

 pir(4)=q4l/qtot 

 pir(5)=q3v/qtot 

 pir(6)=q3l/qtot 
B-13

pir(7)=qvl/qtot 

c 

c......pi groups in the rod energy equation 

 pir(8)=q13/qhr 

 pir(9)=q14/qhr 

 pir(10)=q12/qhr 

 pir(11)=q1l/qhr 

 pir(12)=q1v/qhr 

c 

c......correction to account for the above quench length 

 corf=(hcore-hqch)/hcore 

 do 701 i=1,7 

 pir(i)=pir(i)*corf 

 701 continue 

c 

 write(6,*) 'RV = ', pir(1) 

 write(6,*) 'RL = ', pir(2) 

 write(6,*) 'HV = ', pir(3) 

 write(6,*) 'HL = ', pir(4) 

 write(6,*) 'SV = ', pir(5) 

 write(6,*) 'SL = ', pir(6) 

 write(6,*) 'VL = ', pir(7) 

 write(6,*) 

 write(6,*) 'RS = ', pir(8) 

 write(6,*) 'RH = ', pir(9) 

 write(6,*) 'RR = ', pir(10) 

 write(6,*) 'RL = ', pir(11) 

 write(6,*) 'RV = ', pir(12) 

c 

 stop 

 end 

c 

c 

 subroutine matrix 

c 

 common/cgauss/ a(10,10),b(10),c(10),na 

 common/temp/t(10),eb(10),tl,tv,ebl,ebv,q(10) 

 common/resist/ r(10,10) 

c 

 do 10 i=1,na 

 b(i)=0.0 

 do 10 j=1,na 

 a(i,j)=0.0 

 10 continue 

c 

 do 101 i=1,na 

 b(i)=eb(i)/r(i,i)+ebl/r(i,5)+ebv/r(i,6) 

 do 102 j=1,na 

 if (i.ne.j) then 

 a(i,j)=-1.0/r(i,j) 

 else 

 do 103 k=1,6 

 a(i,i)=a(i,i)+1.0/r(i,k) 

 103 continue 

 endif 
B-14

 102 continue 

 101 continue 

c 

 return 

 end 

c 

c 

 subroutine gauss 

c 

 common/cgauss/ a(10,10),b(10),c(10),na 

c 

 k=1 

 20 temp = 1.0/a(k,k) 

 j=k 

 30 a(k,j) = a(k,j)*temp 

 if (j.eq.na) goto 40 

 j=j+1 

 goto 30 

 40 b(k) = b(k)*temp 

 j=k+1 

 50 temp = a(j,k) 

 l=k 

 60 a(j,l) = a(j,l)-a(k,l)*temp 

 if (l.eq.na) goto 70 

 l=l+1 

 goto 60 

 70 b(j) = b(j)-b(k)*temp 

 if (j.eq.na) goto 80 

 j=j+1 

 goto 50 

 80 if (k.eq.na-1) goto 90 

 k=k+1 

 goto 20 

 90 continue 

 c(na) = b(na)/a(na,na) 

 i=1 

 120 sum = 0.0 

 j=na-i+1 

 100 sum = sum+a(na-i,j)*c(j) 

 if (j.eq.na) goto 110 

 j=j+1 

 goto 100 

 110 c(na-i) = b(na-i)-sum 

 if (i.eq.na-1) goto 130 

 i=i+1 

 goto 120 

 130 continue 

c 

 return 

 end 

c 
APPENDIX C1. BUNDLE MODEL DESCRIPTION 

A full model of a square lattice rod bundle was developed to calculate the cross section 

temperature distribution during the reflood transient. The model includes the rod-to-rod and rodto-housing thermal radiation heat transfer as well as the radial heat conduction in the rods and 

the housing. The convection heat transfer between rods and fluid as well as housing and fluid is 

simulated by inputting a convective heat transfer coefficient time history. The fluid temperature 

is another input value and it is kept constant during the transient. 

The view factor matrix is calculated with the VUEFAC subroutine of MOXY computer program 

(Ref. 7-1). The conduction heat transfer is computed in each of the fuel rods, subject to the 

transient heat flux boundary condition of combined convection and radiation heat transfer. The 

radiative heat transfer computations are based on assumptions of gray and diffuse surfaces. 

The model neglects absorption, emission, or scattering of radiation by steam and droplets 

contained between surfaces. The radiation heat transfer between the surfaces and vapor was 

taken into account in the lumped model described in Section 6 (RADNET computer program). 

Conductive Heat Transfer 

The heat conduction in fuel rods, solid inactive rods and housing is computed by numerical 

integration of the one-dimensional Fourier heat conduction equation: 

1

r r

kr T

r

q c

T

t p

∂

∂

∂

∂ ρ

∂

∂

⎛

⎝

⎜ ⎞

⎠

⎟ + = "'

where q’’’ is zero for the inactive rods. The equation is discretized as follows: 

( ) ρ

π

c V

t

T TQ k p n n T T n n ,1 1

1

1

11 1

2 1 2

Δ 2

+ − =+

⎡ −

⎣

⎢

⎢

⎤

⎦

⎥

⎥

( ) ρ

π

c V

t

T T Q kr

dr T T

dr

k r

dr T T

dr

pi i

i

n

i

n

i ii

i i

n

i

n

i

i i

i i

n

i

n

i

,

Δ

+ +

−

− −

−

− =+ +

⎛

⎝

⎜ ⎞

⎠

⎟

⎛ −

⎝

⎜

⎜

⎞

⎠

⎟

⎟ − − ⎛

⎝

⎜ ⎞

⎠

⎟

⎛ −

⎝

⎜

⎜

⎞

⎠

⎟

⎟

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

1 1

1

1 1

1

2

2 2

C-1
( ) [ ] ( ) ρ

π π

c V

t

T TQ kr

dr T T

dr r q hT T pN N

N

n

N

n

N NN

N N

n

N

n

N

N rod

n

N

n

f

,

Δ

+

−

− −

−

−=− − ⎛

⎝

⎜ ⎞

⎠

⎟

⎛ −

⎝

⎜

⎜

⎞

⎠

⎟

⎟

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

− +− 1

1

1 1

1

2

2

2

where 

V r dr dr ( ) dr dr

i ii i

i i = ++

⎡ −

⎣

⎢

⎢

⎤

⎦

⎥

⎥ − − π 1

2

1

2

4

The equation for the heat conduction in the housing is: 

∂

∂

∂

∂ ρ

∂

x ∂

k T

x

q c

T

t p

⎛

⎝

⎜ ⎞

⎠

⎟ + = "'

Again, this is solved numerically with the following equations: 

( ) ( ) ρc dx

t

T Tk

T T

dx

hTT p n n n n

loss

n

out

,1

1

1

1 1

2 1

1 Δ

+ − = ⎛ −

⎝

⎜

⎜

⎞

⎠

⎟

⎟ − −

( ) ρc dx

t

T Tk

T T

dx

k

T T

dx

p i

i

n in ii

n

i

n

i

i

n

i

n ,

Δ

+ + − − − = ⎛ −

⎝

⎜

⎜

⎞

⎠

⎟

⎟ − ⎛ −

⎝

⎜

⎜

⎞

⎠

⎟

⎟ 1 1

1

1

( ) ( ) ρc dx

t

TT k

T T

dx hT T q p N

N

n Nn NN

n

N

n

N

n f ra

, n

Δ

+ − − − =− ⎛ −

⎝

⎜

⎜

⎞

⎠

⎟

⎟ − −− 1

1

1

d

E i ε

Once the radiative heat rate is calculated from the radiation transport equations, the 

previous equations are solved for the temperature field at time tn+1.

n qrad

Radiative Heat Transfer 

The equations governing the radiative heat transfer are the following: 

 (i = 1, 2, ... N) J F ( ) J i ij

j

N

1 j ib

1

−− = 1

=

ε ∑ ,

where 

Ji radiosity of the ith surface 

Eb,i blackbody emissive power of the ith surface 

Fij view factor matrix 

Ei emissivity of the ith surface 

Once the temperature field is known by solving the conduction equation at time tn the emissive 

power Eb,i can be calculated. Then the previous system is solved for the radiosities Ji and the 

radiative heat fluxes at time tn are calculated from the following equation: 

C-2
)( 1 1, , iib

i

n i

rad q − JE − = ε

ε

The radiative heat fluxes are applied as the wall boundary condition for the conduction equation 

which is used to evaluate the temperature field at time tn+1. 

The program herein presented can operate also in a steady state mode. In this case the 

conduction equation is not solved while the temperature field is calculated iteratively. The 

source list of the Fortran program called BUNDLE is attached in Appendix C2. 

C-3
C-4

APPENDIX C2. FORTRAN PROGRAM BUNDLE 

program bundle 

c 

 implicit double precision (a-h,o-z) 

 dimension d(1000),pwf(1000) 

 dimension a(1001,1001),b(1001) 

c 

 common /vf/ f(1001,1001),area(1001) 

 common/heat/q(1001),qrad(1001),qconv(1001),temp(1001), 

 + emiss(1001),bs(1001),qold(1001) 

 common/heat1/tfad,tenvad,h,hout,hmin,qct,qrt,qt 

 common/geoint/nrod,n,nl 

 common/geo/vrod(1000) 

 common/temp/told(1001) 

 common/converg/alfa 

 common/printc/tpcv,nprt1,nprt2,imod 

c 

 common/trans1/regsze(4),ql(1000),qr(1000),tr(1000,100),th(100) 

 common/trans2/ndreg,ndx,ndr,npc,np1,ntab,ntab2,ifrad,inuc 

 common/trans3/dt,tmax,time,tft,s,tenv,hloss,qavg,htrs,trst, 

 + tdst,thst,tmin,fdcy,hgap 

 common/trans4/tme(100),hft(100),tmep(100),pdcy(100),tmix(100) 

c 

 data pi/3.141592654/ 

 data sig/5.67D-08/ 

c 

 open(unit=8,file='bd.inp') 

 open(unit=11,file='bd.out') 

 open(unit=12,file='bd.dmp') 

 open(unit=13,file='bd.flx') 

c 

 write(11,800) 

 write(12,600) 

 write(13,700) 

 read(8,*) nl 

 write(11,812) nl,nl 

 read(8,*) inuc 

 read(8,*) dd,p,drh 

 write(11,801) dd 

 write(11,802) p 

 write(11,803) drh 

 read(8,*) pwavg 

 write(11,804) pwavg 

 read(8,*) emirod,emihs 

 write(11,805) emirod 

 write(11,806) emihs 

 read(8,*) hf,tf,tmin 

 write(11,807) hf 

 write(11,808) tf 

 hf=hf*5.679 

 tf=(tf-32.0)*5.0/9.0 + 273.14 
C-5

 tmin=(tmin-32.0)*5.0/9.0 + 273.14 

read(8,*) hloss,tenv 

 write(11,809) hloss 

 write(11,810) tenv 

 hloss=hloss*5.679 

 tenv=(tenv-32.0)*5.0/9.0 + 273.14 

 read(8,*) s 

 write(11,813) s 

 s=s*0.0254 

c 

 hmin=0.2 

c 

 write(11,811) 

 nrod=nl*nl 

 n=nrod+1 

 k1=1 

 k2=k1+nl-1 

 do 500 i=1,nl 

 read(8,*) (pwf(k),k=k1,k2) 

 write(11,903) (pwf(k),k=k1,k2) 

 k1=k1+nl 

 k2=k2+nl 

 500 continue 

c 

 read(8,*) err 

 read(8,*) imod,ifrad 

c 

 if (imod.eq.0) goto 510 

c 

c.....read transient data 

 read(8,*) dt,tmax,nprt1,nprt2 

 read(8,*) (regsze(i),i=1,4) 

 do 505 i=1,4 

 regsze(i)=regsze(i)*0.0254 

 rsum=rsum+regsze(i) 

 vrod(i)=(rsum**2.0-(rsum-regsze(i))**2.0)*pi 

 505 continue 

 read(8,*) hgap 

 hgap=hgap*5.679 

 read(8,*) ndreg,ndx 

c read(8,*) tft 

c tft=(tft-32.0)*5.0/9.0 + 273.14 

 read(8,*) ntab 

 do 507 i=1,ntab 

 read(8,*) tme(i),hft(i),tmix(i) 

 hft(i)=hft(i)*5.679 

 tmix(i)=(tmix(i)-32.0)*5.0/9.0 + 273.14 

 507 continue 

 read(8,*) ntab2 

 do 508 i=1,ntab2 

 read(8,*) tmep(i),pdcy(i) 

 508 continue 

 read(8,*) trst,tdst,thst 

 trst=(trst-32.0)*5.0/9.0 + 273.14 
C-6

 tdst=(tdst-32.0)*5.0/9.0 + 273.14 

 thst=(thst-32.0)*5.0/9.0 + 273.14 

c 

c 

c....'pwavg' is the radial average power in kW/ft 

c 

 510 feet=0.3048 

 pwl=pwavg*1000./feet 

 tpcv=tf+pwl/(hf*pi*dd*0.0254) 

c 

 call vufac(nl,dd,p,drh) 

c 

 do 301 i=1,n 

 do 302 j=1,n 

 302 continue 

 area(i)=area(i)*0.0254 

 301 continue 

c 

 do 401 i=1,nrod 

 d(i)=dd*0.0254 

 ql(i)=pwf(i)*pwl 

 emiss(i)=emirod 

 401 continue 

 emiss(n)=emihs 

 qavg=pwl/(pi*d(1)) 

c 

 if (imod.eq.1) goto 2000 

c 

c.....Set dimensionless variables 

c 

 tfad=(sig*tf**4.0d0/qavg)**0.25d0 

 tenvad=(sig*tenv**4.0d0/qavg)**0.25d0 

 tguess=tfad 

 h=hf/(qavg**0.75d0 * sig**0.25d0) 

 hout=hloss/(qavg**0.75d0 * sig**0.25d0) 

 do 501 i=1,nrod 

 q(i)=pwf(i) 

 501 continue 

 q(n)=0.0 

c 

c.....Start Iteration loop 

c 

 if (h.lt.hmin) then 

 alfa=1.0 

 nitmax=1000 

 goto 150 

 endif 

c 

 write(6,*) 'ALFA = ?' 

 read (6,*) alfa 

 write(6,*) 'NITER = ?' 

 read (6,*) nitmax 

c 

 150 niter=0 
C-7

c 

c.....Initial guess for temperature 

c 

 do 201 i=1,n 

 temp(i)=tfad 

 201 continue 

c 

1001 niter=niter+1 

c 

 call rads 

 call conv 

c 

c.....check for convergence 

 eps=0.0 

 elast=0.0 

 do 240 i=1,n 

 tnew=temp(i) 

 eps=abs(tnew-told(i)) 

 eps=max(elast,eps) 

 elast=eps 

 told(i)=tnew 

 240 continue 

 write(6,*) niter,eps 

 if (niter.gt.nitmax) goto 1002 

 if (eps.gt.err) goto 1001 

1002 continue 

 goto 2100 

c 

c.....transient calculation 

c 

2000 call trans 

 goto 9001 

c 

c.....print results steady state 

c 

2100 call print 

c 

c 

 600 format(5x,'TIME',4x,'TCR-1',4x,'TCR-N',4x,'TWR-N',4x,'T0R-N', 

 + 4x,'THO-1',4x,'THO-N',4x,'TN3x3',4x,'TN5x5',4x,'TN7x7',/) 

 700 format(5x,'TIME',3x,'Q-RtoH',3x,'Q-RtoF',3x,'Q-HtoF',3x, 

 + 'Q-LOSS',3x,'T-RODS',3x,'T-SURF',3x,'T-HOUS',//) 

 800 format(/,40x,'CALCULATION RBHT', 

 + //,3x,'INPUT DATA') 

 801 format(3x,'Rod Diameter (in) = ',F8.3) 

 802 format(3x,'Rods Array Pitch (in) = ',F8.3) 

 803 format(3x,'Distance Rods-to-Housing (in) = ',F8.3) 

 804 format(3x,'Rod Average Power (kW) = ',F8.3) 

 805 format(3x,'Rod Surface Emissivity (-) = ',F8.3) 

 806 format(3x,'Housing Surface Emissivity (-) = ',F8.3) 

 807 format(3x,'Bundle Covection H.T.C. (Btu/hr-F-ft2)= ',F8.3) 

 808 format(3x,'Fluid Temperature (F) = ',F8.3) 

 
C-8

809 format(3x,'Housing Heat Losses H.T.C. (Btu/hr-F-ft2)= ',F8.3) 

 810 format(3x,'Enviroment Temperature (F) = ',F8.3) 

 811 format(//,3x,'RODS POWER FACTOR',///) 

 812 format(//,3x,'Bundle Array Size (-) = ',3x, 

 + I2,'x',I2) 

 813 format(3x,'Housing Thickness (in) = ',F8.3) 

 903 format(20(1x,F7.2)) 

c 

9001 stop 

 end 

c 

c***************************************************************** 

c 

 subroutine trans 

c 

 implicit double precision (a-h,o-z) 

c 

 common/trans1/regsze(4),ql(1000),qr(1000),tr(1000,100),th(100) 

 common/trans2/ndreg,ndx,ndr,npc,np1,ntab,ntab2,ifrad,inuc 

 common/trans3/dt,tmax,time,tft,s,tenv,hloss,qavg,htrs,trst, 

 + tdst,thst,tmin,fdcy,hgap 

 common/trans4/tme(100),hft(100),tmep(100),pdcy(100),tmix(100) 

 common/heat/q(1001),qrad(1001),qconv(1001),temp(1001), 

 + emiss(1001),bs(1001),qold(1001) 

 common/geoint/nrod,n,nl 

 common /vf/ f(1001,1001),area(1001) 

 common/printc/tpcv,nprt1,nprt2,imod 

c 

 dimension trf(1000,100),thf(100) 

c 

 data pi/3.141592654/ 

 data sig/5.67D-08/ 

c 

 ndr=4*ndreg 

 npc=ndr+1 

 ndt1=0 

 ndt2=0 

 ic=(nl**2.0+1)/2.0 

 iw=ic-(nl-1)/2.0 

c 

c.....initial condition 

c 

 do 10 j=1,nrod 

 qr(j)=0.0 

 do 10 i=1,npc 

 tr(j,i)=trst 

 if (ql(j).eq.0.0) tr(j,i)=tdst 

 10 continue 

 do 11 i=1,ndx+1 

 th(i)=thst 

11 continue 

 qr(n)=0.0 

c 

 100 call interp(tme,hft,time,htrs,ntab) 
C-9

 if (tr(ic,npc).lt.tmin) htrs=5600.0 

 call interp(tme,tmix,time,tft,ntab) 

 call interp(tmep,pdcy,time,fdcy,ntab2) 

 call trod 

 call thous 

c 

 qrf=0.0 

 do 102 i=1,nrod 

 tw=tr(i,npc) 

 temp(i)=(sig*tw**4.0d0/qavg)**0.25d0 

 qrf=qrf+htrs*area(i)*(tw-tft) 

 102 continue 

 temp(n)=(sig*th(np1)**4.0d0/qavg)**0.25d0 

 qhf=htrs*area(n)*(th(ndx+1)-tft) 

 qloss=hloss*area(n)*(th(1)-tenv) 

c 

 if(ifrad.eq.0) goto 210 

c 

c.....turn off radiation after quench 

 if(htrs.ge.5600.0) then 

 qrh=0.0 

 do 141 i=1,n 

 qr(i)=0.0 

 141 continue 

 goto 210 

 endif 

c 

 call rads 

c 

c.....calculate new radiation fluxes qrad 

c 

 do 201 i=1,n 

 qr(i)=(temp(i)**4.0d0 - bs(i))*qavg*emiss(i)/(1.0d0-emiss(i)) 

 201 continue 

 qrh=-qr(n)*area(n) 

c 

 210 time=time+dt 

 ndt1=ndt1+1 

 ndt2=ndt2+1 

 if(ndt1.eq.nprt1) then 

 write(6,*) time,htrs,tr(ic,npc) 

 do 301 i=1,nrod 

 do 302 j=1,npc 

 trf(i,j)=(tr(i,j)-273.14)*9.0/5.0 + 32.0 

 302 continue 

 301 continue 

 do 303 i=1,np1 

 thf(i)=(th(i)-273.14)*9.0/5.0 + 32.0 

 303 continue 

c 

c.....3x3 Taverage 

 tsum=0.0 

 is3=ic-nl-1 

 do 402 k=1,3 
C-10

 do 401 i=is3,is3+2 

 tsum=tsum+trf(i,npc) 

 401 continue 

 is3=is3+nl 

 402 continue 

 t33=tsum/9.0 

c 

c.....5x5 Taverage 

 tsum=0.0 

 is5=ic-2*nl-2 

 do 404 k=1,5 

 do 403 i=is5,is5+4 

 tsum=tsum+trf(i,npc) 

 403 continue 

 is5=is5+nl 

 404 continue 

 t55=tsum/25.0 

c 

c.....7x7 Taverage 

 tsum=0.0 

 n7=0 

 is7=ic-3*nl-3 

 do 406 k=1,7 

 do 405 i=is7,is7+6 

 if (ql(i).eq.0.0) goto 405 

 tsum=tsum+trf(i,npc) 

 n7=n7+1 

 405 continue 

 is7=is7+nl 

 406 continue 

 t77=tsum/n7 

c 

c.....Hot-Rods Taverage 

 tsum1=0.0 

 tsum2=0.0 

 ndum=0 

 do 407 i=1,nrod 

 if (ql(i).eq.0.0) then 

 tsum2=tsum2+trf(i,npc) 

 ndum=ndum+1 

 goto 407 

 endif 

 tsum1=tsum1+trf(i,npc) 

 407 continue 

 thot=tsum1/float(nrod-ndum) 

 tcold=tsum2/float(ndum) 

c 

 write(12,601) time,trf(ic,1),trf(ic,npc),trf(22,npc), 

 + trf(1,npc),thf(1),thf(np1),t33,t55,t77 

 write(13,701) time,qrh,qrf,qhf,qloss,thot,tcold,thf(np1) 

 ndt1=0 

 endif 

 if(ndt2.eq.nprt2) then 

 call print 
C-11

 ndt2=0 

 endif 

c 

 if(time.lt.tmax) goto 100 

c 

 return 

c 

 601 format(10(1x,F8.2)) 

 701 format(8(1x,F9.0)) 

c 

 end 

c 

c***************************************************************** 

c 

 subroutine rads 

c 

 implicit double precision (a-h,o-z) 

c 

 common /vf/ f(1001,1001),area(1001) 

 common/heat/q(1001),qrad(1001),qconv(1001),temp(1001), 

 + emiss(1001),bs(1001),qold(1001) 

 common/geoint/nrod,n,nl 

c 

 dimension a(1001,1001),b(1001),c(1001) 

c 

 do 205 i=1,n 

 do 204 j=1,n 

 204 a(i,j) =-f(i,j)*(1.0d0-emiss(i)) 

 a(i,i)=a(i,i)+1.0 

 205 continue 

 do 206 i=1,n 

 b(i)=emiss(i)*temp(i)**4.0d0 

 206 continue 

c 

 call gauss(a,n,b,bs) 

c 

 return 

 end 

c 

c***************************************************************** 

c 

 subroutine conv 

c 

 implicit double precision (a-h,o-z) 

c 

 common /vf/ f(1001,1001),area(1001) 

 common/heat/q(1001),qrad(1001),qconv(1001),temp(1001), 

 + emiss(1001),bs(1001),qold(1001) 

 common/heat1/tfad,tenvad,h,hout,hmin,qct,qrt,qt 

 common/geoint/nrod,n,nl 

 common/temp/told(1001) 

 common/converg/alfa 

c 

 data sig/5.67D-08/ 
C-12

c 

 qct=0.0 

 qrt=0.0 

 qt=0.0 

c 

 do 102 i=1,n 

 sumbs=0.0d0 

 do 101 j=1,n 

 sumbs=sumbs+f(i,j)*bs(j) 

 101 continue 

c 

c.....special case: radiation dominated cases 

 if (h.lt.hmin) then 

 eb=q(i)*(1.0d0-emiss(i))/emiss(i) + bs(i) 

 temp(i)=eb**0.25d0 

 goto 102 

 endif 

c 

 temp(i)=tfad + (q(i)-bs(i)+sumbs)/h 

 102 continue 

 c1=(h*tfad+hout*tout)/(h+hout) 

 c2=1.0d0/(h+hout) 

 temp(n)=c1+c2*(sumbs-bs(n)) 

c 

c.....underrelaxation 

 do 103 i=1,n 

 temp(i)=(1.0d0-alfa)*told(i) + alfa*temp(i) 

 103 continue 

c 

 do 105 i=1,n 

 qconv(i)=h*(temp(i)-tfad) 

 qrad(i)=q(i)-qconv(i) 

 qrt=qrt+qrad(i)*area(i) 

 qt=qt+q(i)*area(i) 

 qct=qct+qconv(i)*area(i) 

 105 continue 

 if (h.lt.hmin) temp(n)=tenvad+qt/(hout*area(n)) 

c 

 return 

 end 

c 

c***************************************************************** 

c 

 subroutine gauss(a,na,b,c) 

c 

 implicit double precision (a-h,o-z) 

 dimension a(1001,1001),b(1001),c(1001) 

c 

 k=1 

 20 tmp = 1.d0/a(k,k) 

 j=k 

 30 a(k,j) = a(k,j)*tmp 

 if (j.eq.na) goto 40 

 j=j+1 
C-13

 goto 30 

 40 b(k) = b(k)*tmp 

 j=k+1 

 50 tmp = a(j,k) 

 l=k 

 60 a(j,l) = a(j,l)-a(k,l)*tmp 

 if (l.eq.na) goto 70 

 l=l+1 

 goto 60 

 70 b(j) = b(j)-b(k)*tmp 

 if (j.eq.na) goto 80 

 j=j+1 

 goto 50 

 80 if (k.eq.na-1) goto 90 

 k=k+1 

 goto 20 

 90 continue 

 c(na) = b(na)/a(na,na) 

 i=1 

 120 sum = 0.0 

 j=na-i+1 

 100 sum = sum+a(na-i,j)*c(j) 

 if (j.eq.na) goto 110 

 j=j+1 

 goto 100 

 110 c(na-i) = b(na-i)-sum 

 if (i.eq.na-1) goto 130 

 i=i+1 

 goto 120 

 130 continue 

c 

 return 

 end 

c 

c***************************************************************** 

c 

 subroutine trod 

c 

 implicit double precision (a-h,o-z) 

c 

 common/trans1/regsze(4),ql(1000),qr(1000),tr(1000,100),th(100) 

 common/trans2/ndreg,ndx,ndr,npc,np1,ntab,ntab2,ifrad,inuc 

 common/trans3/dt,tmax,time,tft,s,tenv,hloss,qavg,htrs,trst, 

 + tdst,thst,tmin,fdcy,hgap 

 common/trans4/tme(100),hft(100),tmep(100),pdcy(100),tmix(100) 

 common/heat/q(1001),qrad(1001),qconv(1001),temp(1001), 

 + emiss(1001),bs(1001),qold(1001) 

 common/geoint/nrod,n,nl 

 common/geo/vrod(1000) 

c 

 dimension cd(100),cp(100),t(100),qh(100),ddr(100) 

c 

 data pi/3.141592654/ 

c 
C-14

 do 201 j=1,nrod 

c 

 do 10 i=1,npc 

 t(i)=tr(j,i) 

 qh(i)=0.0 

 10 continue 

 i1=ndreg+2 

 i2=ndreg*2 

 do 20 i=i1,i2 

 qh(i)=ql(j)*fdcy/float(ndreg-1) 

 20 continue 

 qvnuc=0.0 

 if (inuc.ne.0) qvnuc=fdcy*ql(j)/(vrod(1)+vrod(2)+vrod(3)) 

 

c 

c.....calculation properties 

c 

 ireg=1 

 jr=1 

 do 50 i=1,ndr 

 ddr(i)=regsze(ireg)/float(ndreg) 

 tn=t(i) 

 call prop(tn,ireg,cnd,cpm,inuc) 

 if (ql(j).eq.0.0) call prop(tn,4,cnd,cpm,inuc) 

 if (i.eq.(ndreg*3+1).and.hgap.ne.0) 

 + cnd=cnd*hgap*ddr(i)/(cnd+hgap*ddr(i)) 

 cd(i)=cnd 

 cp(i)=cpm 

 if (jr.eq.ndreg) then 

 jr=0 

 ireg=ireg+1 

 endif 

 jr=jr+1 

 50 continue 

c 

c.....calculation conduction in rod 

c.....centerline, inner regions, clad surface 

c 

 r=0.0 

c 

 dr=ddr(1) 

 vol=0.25*pi*dr**2.0 

 a=cd(1)*0.5*(t(2)-t(1)) 

 c=dt/(cp(1)*vol) 

 if (inuc.ne.0) qh(1)=qvnuc*vol 

 t(1)=t(1)+(qh(1)+2.0*pi*a)*c 

c 

 r=ddr(1) 

 do 101 i=2,ndr 

 drm1=ddr(i-1) 

 dr=ddr(i) 

 vol=pi*(r*(drm1+dr) + (dr**2.0-drm1**2.0)/4.0) 

 vol2=pi*(r*drm1-(drm1**2.0)/4.0) 

 if (inuc.ne.0) then 
C-15

 qh(i)=qvnuc*vol 

 if (i.gt.ndreg*3) qh(i)=qvnuc*vol2 

 if (i.gt.ndreg*3+1) qh(i)=0.0 

 endif 

 a=cd(i)*(r+dr/2.0)*(t(i+1)-t(i))/dr 

 b=cd(i-1)*(r-drm1/2.0)*(t(i)-t(i-1))/drm1 

 c=dt/(cp(i)*vol) 

 t(i)=t(i)+(qh(i)+2.0*pi*(a-b))*c 

 r=r+dr 

 101 continue 

c 

 vol=pi*(r*dr - 0.25*dr**2.0) 

 a=-cd(ndr)*(r-dr/2.0)*(t(npc)-t(npc-1))/dr 

 b=r*(qr(j) + htrs*(t(npc)-tft)) 

 c=dt/(cp(ndr)*vol) 

 t(npc)=t(npc)+(qh(npc)+2.0*pi*(a-b))*c 

c 

 do 151 i=1,npc 

 tr(j,i)=t(i) 

 151 continue 

c 

 201 continue 

c 

 return 

 end 

c 

c***************************************************************** 

c 

 subroutine thous 

c 

 implicit double precision (a-h,o-z) 

c 

 common/trans1/regsze(4),ql(1000),qr(1000),tr(1000,100),th(100) 

 common/trans2/ndreg,ndx,ndr,npc,np1,ntab,ntab2,ifrad,inuc 

 common/trans3/dt,tmax,time,tft,s,tenv,hloss,qavg,htrs,trst, 

 + tdst,thst,tmin,fdcy,hgap 

 common/trans4/tme(100),hft(100),tmep(100),pdcy(100),tmix(100) 

 common/heat/q(1001),qrad(1001),qconv(1001),temp(1001), 

 + emiss(1001),bs(1001),qold(1001) 

 common/geoint/nrod,n,nl 

c 

 dimension cd(100),cp(100),t(100) 

c 

 data pi/3.141592654/ 

c 

 dx=s/float(ndx) 

 np1=ndx+1 

c 

c.....calculation properties 

c 

 ireg=4 

 do 50 i=1,ndx 

 tt=th(i) 

 call prop(tt,ireg,cnd,cpm,inuc) 
C-16

 cd(i)=cnd 

 cp(i)=cpm 

 50 continue 

c 

c.....calculation conduction in the housing wall 

c 

 a=2.0*cd(1)*(th(2)-th(1))/dx 

 b=hloss*(th(1)-tenv) 

 c=dt/(cp(1)*dx) 

 th(1)=th(1)+(a-b)*c 

c 

 do 101 i=2,ndx 

 a=2.0*cd(i)*(th(i+1)-th(i))/dx 

 b=2.0*cd(i-1)*(th(i)-th(i-1))/dx 

 c=dt/(cp(i)*dx) 

 th(i)=th(i)+(a-b)*c 

 r=r+dr 

 101 continue 

c 

 a=-2.0*cd(ndx)*(th(np1)-th(np1-1))/dx 

 b=htrs*(th(np1)-tft) 

 c=dt/(cp(ndx)*dx) 

 th(np1)=th(np1)+(a-b-qr(n))*c 

c 

 return 

 end 

c 

c***************************************************************** 

c 

 subroutine prop(tk,ireg,cnd,cpm,inuc) 

c 

 implicit double precision (a-h,o-z) 

c 

 t=tk-273.14 

c 

c.....nuclear rod 

c 

 if (inuc.eq.0) goto 100 

 if (ireg.eq.4) goto 110 

c 

c.....uranium dioxide 

 rho=9649.0 

 cnd=2.45 

 cpm=333.0*rho 

 return 

c 

c.....zircalloy 

 110 rho=6560.0 

 a=1.461e-2 

 b=12.092 

 cnd=a*t+b 

 cpm=347.0*rho 

 return 

c 
C-17

c.....region 1 and 3 - BN 

c 

 100 if (ireg.ne.3.and.ireg.ne.1) goto 101 

 rho=1910.0 

 a=-0.061356 

 b=122.734 

 cnd=a*t + b 

 cpm=1500*rho 

 return 

c 

c.....region 2 - Heater 

 101 if (ireg.ne.2) goto 102 

 rho=8470.0 

 a=4.7742e-10 

 b=-1.1151e-6 

 c=5.2571e-4 

 d=4.0755e-1 

 cpm=1000.0*(a*t**3.0+b*t**2.0+c*t+d)*rho 

 a=2.8263e-2 

 b=17.583 

 cnd=a*t+b 

 return 

c 

c.....region 4 - Clad - Inconel 600 

c 

 102 rho=8270.0 

 a=4.7427e-4 

 b=4.1430e-1 

 cpm=1000.0*(a*t+b)*rho 

 a=1.6972e-2 

 b=14.599 

 cnd=a*t+b 

 cnd=15.0 

 return 

c 

 end 

c 

c 

c*********************************************************** 

c 

 subroutine print 

c 

 implicit double precision (a-h,o-z) 

c 

 common/heat/q(1001),qrad(1001),qconv(1001),temp(1001), 

 + emiss(1001),bs(1001),qold(1001) 

 common/trans3/dt,tmax,time,tft,s,tenv,hloss,qavg,htrs,trst, 

 + tdst,thst,tmin,fdcy,hgap 

 common/trans4/tme(100),hft(100),tmep(100),pdcy(100),tmix(100) 

 common/printc/tpcv,nprt1,nprt2,imod 

 

common/geoint/nrod,n,nl 

c 

 data sig/5.67D-08/ 
C-18

c 

c.....print results 

 if (imod.eq.0) write(11,900) 

 if (imod.eq.1) write(11,904) time 

 do 250 i=1,n 

 temp(i)=temp(i)/(sig/qavg)**0.25d0 

c 

c.....conversion to british units 

 temp(i)=(temp(i)-273.14)*9.0/5.0 + 32.0 

c 

 250 continue 

c 

 k1=1 

 k2=k1+nl-1 

 do 600 i=1,nl 

 write(11,903) (temp(k),k=k1,k2) 

 k1=k1+nl 

 k2=k2+nl 

 600 continue 

 write(11,901) temp(n) 

 tpcv=(tpcv-273.14)*9.0/5.0 + 32.0 

 if (imod.eq.0) write(11,902) tpcv 

c 

 return 

c 

 900 format(///,3x,'RESULTS STEADY STATE', 

 + //,3x,'RODS SURFACE TEMPERATURE (F)',//) 

 904 format(///,'***********************************************', 

 + /,3x,'RESULTS AT TIME (sec) = ',F7.2, 

 + //,3x,'RODS SURFACE TEMPERATURE (F)',//) 

 901 format(/,3x,'HOUSING TEMPERATURE (INSIDE WALL) (F) = ',F7.2) 

 902 format(//,3x,'Rod Surf. Temp. for infinite array at SS (F) = ', 

 + F7.2) 

 903 format(20(1x,F7.2)) 

c 

 end 

c 

c 

c***************************************************************** 

c 

 subroutine vufac(nmx,dd,p,drh) 

C 

c the subroutine is based 

C VUFAC 12/06/78 D.R.EVANS 

c and modified by C. Frepoli 3/10/98 

c the symmentry logic (MIRRIM, ISWAP etc.) is deleted 

c 

 implicit double precision (a-h,o-z) 

C 

c DIMENSION AREA(226),R0(225) 

 dimension r0(1000) 
C-19

 COMMON /VF/ F(1001,1001),area(1001) 

 COMMON /RI/ RIJ(1001,1001) 

c 

 data nf,npt,n,na/1001,200,37,37/ 

 data pi/3.14159265358979323846/ 

 

c 

 xlh=p*float(nmx-1)+dd+2.0*drh 

c 

 nlim=nmx 

 n2=nmx*nmx +1 

 nl=nmx 

 nl=8 

 nl1=nmx 

 ahs=xlh*4.0 

c 

 NP=N2-1 

 

 TWOPI=2.*PI 

 

 DO 1700 I=1,NP 

 

 r0(i)=dd/2.0 

 AREA(I)=TWOPI*R0(I) 

 

1700 CONTINUE 

 

 AREA(N2)=ahs 

c 

 CALL VFAC(F,AREA,AEA,SCALFC,BB,R0,IROW,JCOL,MIRRIM,P,PI,N, 

 1NF,NLIM,N2,NA,NSYM,NL,NL1,NPT) 

 

c 

 do 998 i=1,n2 

 do 997 j=1,n2 

 write(9,*) i,j,f(i,j) 

 997 continue 

 write(9,*) area(i) 

 998 continue 

c 

 return 

 END 

 

c 

C****** FIJ 12/12/78 D.R.EVANS 

 SUBROUTINE FIJ(F,R,P,PI,M,NPT,L,SOURCE,IX,IY,L1,L2,IRC,IA) 

 implicit double precision (a-h,o-z) 

 DIMENSION F(M,1),R(1),XA(2,100),YA(2,100),RA(2,100) 

 COMMON /RI/ RIJ(1001,1001) 

INTEGER SOURCE,TARGET,UPPER(14),LOWER(14) 

 

 LOGICAL SKIP 

 

 DATA XA(1,1),YA(1,1)/2*0.D0/ 
C-20

 DATA SKIP/.FALSE./ 

 IF(SKIP) GO TO 10 

 SKIP=.TRUE. 

 RNPT=1.D0/NPT 

 DELTA=2.D0*PI*RNPT 

 

 RDELT=1.D0/DELTA 

 

 PIO2=.5D0*PI 

 

10 CONTINUE 

 

 IF(IRC-2) 12,16,20 

 

12 CONTINUE 

 

C ROWS 

 

 IF(IA.EQ.2) GO TO 14 

 

C ADJACENT ROW 

 

 IXY=IX 

 

 K2=L 

 

 K3=1 

 

 GO TO 24 

 

 14 CONTINUE 

 

C ROWS BEYOND ADJACENT ROW 

 

 IXY=IY 

 

 IYX=IX 

 I3=1 

 

 K2=0 

 

 K3=L 

 GO TO 24 

 16 CONTINUE 

C HIGHER-NUMBERED COLUMNS 

 IF(IA.EQ.2) GO TO 18 

C ADJACENT COLUMN 

 

 K2=1 

 GO TO 22 

 18 CONTINUE 

C COLUMNS BEYOND ADJACENT COLUMN 

 IXY=IX 

 IYX=IY 

 
C-21

 I3=L 

 K2=0 

 K3=1 

 GO TO 24 

 20 CONTINUE 

C LOWER-NUMBERED COLUMNS 

 K2=-1 

 22 CONTINUE 

 IXY=IY 

 K3=L 

 24 CONTINUE 

C COMPUTE SHADOWING ROD NUMBERS 

 

 KMI=L2-IXY 

 

 IF(KMI.LT.0) KMI=L1-IXY 

 KMIABS=IABS(KMI) 

 TARGET=SOURCE+K2+K3*KMI 

 I2=K3*ISIGN(1,KMI) 

 IF(IA.EQ.2) GO TO 30 

C ADJACENT ROW AND COLUMNS 

 K4=KMIABS 

 GO TO 40 

 30 CONTINUE 

 

C ROWS AND COLUMNS BEYOND ADJACENT 

 

 K4=KMIABS-1 

 UPPER(1)=0 

 LOWER(KMIABS)=0 

 K5=0 

 40 CONTINUE 

 DO 70 I=1,K4 

 LOWER(I)=SOURCE+I2*I 

 

 IF(IA.EQ.2) GO TO 60 

 

 UPPER(I)=TARGET-I2*(KMIABS-I+1) 

 GO TO 70 

 60 CONTINUE 

 UPPER(I+1)=LOWER(I)+I3 

 IF(IYX.EQ.L) UPPER(I+1)=0 

70 CONTINUE 

 

 K=KMIABS+1 

 

C SET RADII AND COORDINATES OF SOURCE,TARGET, AND ALL POTENTIAL 

C SHADOWING RODS 

 

 R1=R(SOURCE) 

 

 RA(1,1)=R1 

 RA(2,K)=R(TARGET) 

C XA(2,1)=0.D0 

 XA(2,1)=0.E0 
C-22

 YA(2,1)=P 

 DO 230 I=1,KMIABS 

 FI=I 

 PTFI=P*FI 

 

 IP1=I+1 

 

 XA(1,IP1)=PTFI 

C YA(1,IP1)=0.D0 

 YA(1,IP1)=0.E0 

 XA(2,IP1)=PTFI 

 YA(2,IP1)=P 

 IF(LOWER(I).EQ.0) GO TO 200 

 RA(1,IP1)=R(LOWER(I)) 

 GO TO 210 

 200 CONTINUE 

C RA(1,IP1)=0.D0 

 RA(1,IP1)=0.E0 

 

 210 CONTINUE 

 IF(UPPER(I).EQ.0) GO TO 220 

 

 RA(2,I)=R(UPPER(I)) 

 GO TO 230 

 

 220 CONTINUE 

 

C RA(2,I)=0.D0 

 RA(2,I)=0.E0 

 230 CONTINUE 

 DO 700 K1=L1,L2 

 KMI=K1-IXY 

 KMIABS=IABS(KMI) 

 TARGET=SOURCE+K2+K3*KMI 

 K=KMIABS+1 

 IF(IA.EQ.2) GO TO 235 

 Y1=YA(2,K) 

 R2=RA(2,K) 

 K4=KMIABS 

 GO TO 238 

 235 CONTINUE 

 IF(R(SOURCE).LE.R(LOWER(1)).AND. 

 * R(LOWER(KMIABS-1)).GE.R(TARGET)) GO TO 700 

 

C Y1=0.D0 

 

 Y1=0.E0 

 

 R2=R(TARGET) 

 K4=KMIABS-1 

 238 CONTINUE 

 X1=XA(2,K) 

 FKMI=KMIABS-1 

C DIAG=FKMI**2+1.D0 

 DIAG=FKMI**2+1.E0 
C-23

C RR12=1.D0/(P*DSQRT(DIAG)) 

 RR12=1.E0/(P* SQRT(DIAG)) 

 

 TEMP=P*SQRT((FLOAT(KMIABS))**2+1.) 

 

 RIJ(SOURCE,TARGET)=TEMP-0.5*(R(SOURCE)+R(TARGET)) 

C I1=RDELT*(PI-DARCOS((R1+R2)*RR12)-DATAN2(1.D0,FKMI)) 

 I1=RDELT*(PI- ACOS((R1+R2)*RR12)- ATAN2(1.E0,FKMI)) 

 240 CONTINUE 

C COMPUTE VIEW FACTOR 

 VIEWFC=0. 

 DO 500 IPT=I1,NPT 

 XIPT = IPT - 1 

 THETA = DELTA * XIPT 

C XV=-R1*DCOS(THETA) 

 XV=-R1* COS(THETA) 

C YV=R1*DSIN(THETA) 

 YV=R1* SIN(THETA) 

C DETERMINE IF (XV,YV) CAN SEE THE TARGET ROD 

 

 IF(XV*X1+YV*Y1.LE.R1*(R1-R2)) GO TO 500 

 

C TS IS THE TANGENT TO THE SOURCE ROD AT (XV,YV) 

C TS=DATAN2(-XV,YV) 

 TS= ATAN2(-XV,YV) 

C COMPUTE TANGENTS TO TARGET ROD 

C T1 IS THE LOWER TANGENT TO THE TARGET ROD 

C T2 IS THE UPPER TANGENT TO THE TARGET ROD 

 X1MXP=X1-XV 

 Y1MYP=Y1-YV 

 RSQ=X1MXP**2+Y1MYP**2 

 

C S=DSQRT(RSQ-R2**2) 

 

 S= SQRT(RSQ-R2**2) 

C RRSQ=1.D0/RSQ 

 RRSQ=1.E0/RSQ 

 SORSQ=S*RRSQ 

 R1ORSQ=R2*RRSQ 

 

 A=SORSQ*X1MXP 

 

 B=R1ORSQ*Y1MYP 

 C=SORSQ*Y1MYP 

 D=R1ORSQ*X1MXP 

 XTAMXP=S*(A-B) 

 YTAMYP=S*(C+D) 

 

 XTBMXP=S*(A+B) 

 

 YTBMYP=S*(C-D) 

 

C T2=DATAN2(YTAMYP,XTAMXP) 

 T2= ATAN2(YTAMYP,XTAMXP) 

C T1=DATAN2(YTBMYP,XTBMXP) 
C-24

 T1= ATAN2(YTBMYP,XTBMXP) 

 

C COMPUTE TANGENTS THROUGH (XV,YV) TO SHADOWING RODS 

 

C FIND MINIMUM UPPER SHADOWING AND MAXIMUM LOWER SHADOWING 

 DO 300 J=1,2 

 

 DO 300 I=1,K4 

 

 RB=RA(J,I+2-J) 

 IF(RB.EQ.0.) GO TO 300 

 XB=XA(J,I+2-J) 

 YB=YA(J,I+2-J) 

 X1MXP=XB-XV 

 Y1MYP=YB-YV 

 RSQ=X1MXP**2+Y1MYP**2 

C S=DSQRT(RSQ-RB**2) 

 

 S= SQRT(RSQ-RB**2) 

 

 IF(S.EQ.0.) GO TO 260 

C RRSQ=1.D0/RSQ 

 RRSQ=1.E0/RSQ 

 SORSQ=S*RRSQ 

 R1ORSQ=RB*RRSQ 

 A=SORSQ*X1MXP 

 B=R1ORSQ*Y1MYP 

 C=SORSQ*Y1MYP 

 D=R1ORSQ*X1MXP 

 

 IF(J.EQ.2) GO TO 250 

 

C UPPER TANGENTS TO LOWER SHADOWING RODS 

 XTAMXP=S*(A-B) 

 YTAMYP=S*(C+D) 

 TA=DATAN2(YTAMYP,XTAMXP) 

c TA= ATAN2(YTAMYP,XTAMXP) 

 T1=DMAX1(TA,T1) 

c T1=AMAX1(TA,T1) 

 GO TO 300 

 

 250 CONTINUE 

C LOWER TANGENTS TO UPPER SHADOWING RODS 

 XTBMXP=S*(A+B) 

 YTBMYP=S*(C-D) 

 TB=DATAN2(YTBMYP,XTBMXP) 

c TB= ATAN2(YTBMYP,XTBMXP) 

 T2=DMIN1(TB,T2) 

c T2=AMIN1(TB,T2) 

 GO TO 300 

260 CONTINUE 

 

 IF(J.EQ.2) GO TO 270 

 

 T1=DMAX1(PIO2,T1) 
C-25

c T1=AMAX1(PIO2,T1) 

 GO TO 300 

 270 CONTINUE 

 T2=DMIN1(0.D0,T2) 

c T2=AMIN1(0.E0,T2) 

 300 CONTINUE 

 IF (T1 .GE. T2) GO TO 490 

 IF (T1 .LT. TS .OR. T1 .GE. TS + PI) GO TO 320 

 PHI1 = T1 - TS 

 GO TO 350 

 320 CONTINUE 

 PHI1 = 0. 

 IF (T1 .GE. TS) PHI1 = PI 

 350 CONTINUE 

 IF (T2 .LT. TS .OR. T2 .GE. TS + PI) GO TO 370 

 

 PHI2 = T2 - TS 

 

 GO TO 380 

 370 CONTINUE 

 PHI2 = 0. 

 IF (T2 .GE. TS) PHI2 = PI 

 380 CONTINUE 

C CONFIG=.5D0*(DCOS(PHI1)-DCOS(PHI2)) 

 CONFIG=.5E0*( COS(PHI1)- COS(PHI2)) 

 VIEWFC=VIEWFC+CONFIG 

 GO TO 500 

 490 CONTINUE 

 IF(VIEWFC.NE.0.) GO TO 510 

 500 CONTINUE 

 510 CONTINUE 

 IF(IA.EQ.1) GO TO 550 

 IF(K5.EQ.1) GO TO 540 

 FSAVE=VIEWFC 

 K5=K5+1 

 DO 530 I=1,K4 

 IF(IYX.EQ.1) GO TO 520 

 UPPER(I+1)=LOWER(I)-I3 

 RA(2,I+1)=R(UPPER(I+1)) 

 GO TO 530 

 520 CONTINUE 

C RA(2,I+1)=0.D0 

 RA(2,I+1)=0.E0 

 

530 CONTINUE 

 

 GO TO 240 

 540 CONTINUE 

 VIEWFC=VIEWFC+FSAVE 

 K5=0 

 DO 545 I=1,K4 

 IF(IYX.EQ.L) GO TO 542 

 UPPER(I+1)=LOWER(I)+I3 

 RA(2,I+1)=R(UPPER(I+1)) 

 GO TO 545 
C-26

 542 CONTINUE 

C RA(2,I+1)=0.D0 

 RA(2,I+1)=0.E0 

 545 CONTINUE 

 550 CONTINUE 

 F(SOURCE,TARGET)=VIEWFC*RNPT 

 700 CONTINUE 

 RETURN 

 END 

c 

C****** PATHLEN 12/14/78 D.R.EVANS 

 

 SUBROUTINE PATHLEN(R,DELTAX,P,N2,L) 

 

 implicit double precision (a-h,o-z) 

 DIMENSION F(15),R(1) 

 

 COMMON /RI/ RIJ(1001,1001) 

 

 INTEGER SOURCE 

 REAL L1,L2,L3,L4 

 

 DATA F/0.5,0.086740,0.013966,0.001517,0.000424,0.000172, 

 

 1 0.000088,0.000048,0.000034,6*0./ 

C COMPUTE PATH LENGTHS FROM RODS TO CANISTER 

 DO 100 IX=1,L 

 DO 100 IY=1,L 

 SOURCE=IY+(IX-1)*L 

 HALFR1=0.5*R(SOURCE) 

C PATH OND 

 L1=P*FLOAT(IX-1)+DELTAX-HALFR1 

C PATH TWO 

 L2=P*FLOAT(L-IX)+DELTAX-HALFR1 

C PATH THREE 

 L3=P*FLOAT(IY-1)+DELTAX-HALFR1 

C PATH FOUR 

 

 L4=P*FLOAT(L-IY)+DELTAX-HALFR1 

 

C PATH LENGTH IS THE VIEW-FACTOR-WEIGHTED MEAN OF FOUR 

C CONTRIBUTIONS 

 RIJ(SOURCE,N2)=(L1*F(IX) 

 1 +L2*F(L-IX+1) 

 2 +L3*F(IY) 

 3 +L4*F(L-IY+1)) / 

 4 (F(IX) 

 5 +F(L-IX+1) 

 6 +F(IY) 

 7 +F(L-IY+1)) 

100 CONTINUE 

 

 RETURN 

 

 END 
C-27

c 

C****** STRING 12/12/78 D.R.EVANS 

 

 SUBROUTINE STRING(F,R,P,PI,M,L,SOURCE,IX,IY) 

 

 implicit double precision (a-h,o-z) 

 DIMENSION F(M,1),R(1) 

 COMMON /RI/ RIJ(1001,1001) 

 DIMENSION TIN(1000,4),THET(1000,4),TEX(1000,2),ALPH(1000,2) 

 INTEGER SOURCE,TARGET 

 LOGICAL SKIP 

 DATA SKIP/.FALSE./,PP/0./ 

 IF(SKIP) GO TO 10 

 SKIP=.TRUE. 

C RPI=1.D0/PI 

 RPI=1.E0/PI 

C PIO2=.5D0*PI 

 PIO2=.5E0*PI 

C PIO4=.5D0*PIO2 

 PIO4=.5E0*PIO2 

 10 CONTINUE 

 IF(PP.EQ.P) GO TO 20 

 PP=P 

 PSQ=P**2 

C R13SQ=2.D0*PSQ 

 R13SQ=2.E0*PSQ 

C RR13=1.D0/DSQRT(R13SQ) 

 RR13=1.E0/ SQRT(R13SQ) 

C RP=1.D0/P 

 

 RP=1.E0/P 

 

 20 CONTINUE 

 

C COMPUTE TANGENT LENGTHS AND ANGLES FOR CROSSED STRING METHOD 

 

 IF(IX.GT.1.OR.IY.EQ.L) GO TO 145 

 

 J1=SOURCE 

 J2=SOURCE+L-2 

 DO 140 I=J1,J2 

 R1=R(I) 

 R2=R(I+1) 

 R3=R(I+1+L) 

 R4=R(I+L) 

 R2MR3=R2-R3 

 

 R4MR3=R4-R3 

 

C TIN13=DSQRT(R13SQ-(R1+R3)**2) 

 

 TIN13= SQRT(R13SQ-(R1+R3)**2) 

C TIN23=DSQRT(PSQ-(R2+R3)**2) 

 TIN23= SQRT(PSQ-(R2+R3)**2) 

C TIN34=DSQRT(PSQ-(R3+R4)**2) 
C-28

 TIN34= SQRT(PSQ-(R3+R4)**2) 

C TIN24=DSQRT(R13SQ-(R2+R4)**2) 

 TIN24= SQRT(R13SQ-(R2+R4)**2) 

 TIN(I,2)=TIN13 

 TIN(I+1,3)=TIN23 

 TIN(I+L,1)=TIN34 

 TIN(I+1,4)=TIN24 

C THET(I,2)=DARSIN(TIN13*RR13) 

 THET(I,2)= ASIN(TIN13*RR13) 

C THET(I+1,3)=DARSIN(TIN23*RP) 

 THET(I+1,3)= ASIN(TIN23*RP) 

C THET(I+L,1)=DARSIN(TIN34*RP) 

 THET(I+L,1)= ASIN(TIN34*RP) 

C THET(I+1,4)=DARSIN(TIN24*RR13) 

 THET(I+1,4)= ASIN(TIN24*RR13) 

 IF(R2MR3.EQ.0.) GO TO 100 

C ALPH(I+1,2)=DARCOS(R2MR3*RP) 

 

 ALPH(I+1,2)= ACOS(R2MR3*RP) 

 

C TEX(I+1,2)=DSQRT(PSQ-R2MR3**2) 

 TEX(I+1,2)= SQRT(PSQ-R2MR3**2) 

 GO TO 105 

 100 CONTINUE 

 ALPH(I+1,2)=PIO2 

 TEX(I+1,2)=P 

 105 CONTINUE 

 IF(R4MR3.EQ.0.) GO TO 110 

C ALPH(I+L,1)=DARCOS(R4MR3*RP) 

 ALPH(I+L,1)= ACOS(R4MR3*RP) 

C TEX(I+L,1)=DSQRT(PSQ-R4MR3**2) 

 TEX(I+L,1)= SQRT(PSQ-R4MR3**2) 

 GO TO 115 

 110 CONTINUE 

 ALPH(I+L,1)=PIO2 

 TEX(I+L,1)=P 

 115 CONTINUE 

 IF(I.GT.J1) GO TO 130 

 R1MR4=R1-R4 

C TIN14=DSQRT(PSQ-(R1+R4)**2) 

 TIN14= SQRT(PSQ-(R1+R4)**2) 

 TIN(I,3)=TIN14 

C THET(I,3)=DARSIN(TIN14*RP) 

 THET(I,3)= ASIN(TIN14*RP) 

 IF(R1MR4.EQ.0.) GO TO 120 

 

C ALPH(I,2)=DARCOS(R1MR4*RP) 

 

 ALPH(I,2)= ACOS(R1MR4*RP) 

C TEX(I,2)=DSQRT(PSQ-R1MR4**2) 

 TEX(I,2)= SQRT(PSQ-R1MR4**2) 

 GO TO 125 

 120 CONTINUE 

 ALPH(I,2)=PIO2 

 TEX(I,2)=P 
 125 CONTINUE 

 130 CONTINUE 

 IF(IY.GT.1) GO TO 140 

 R1MR2=R1-R2 

C TIN12=DSQRT(PSQ-(R1+R2)**2) 

 TIN12= SQRT(PSQ-(R1+R2)**2) 

 TIN(I,1)=TIN12 

C THET(I,1)=DARSIN(TIN12*RP) 

 THET(I,1)= ASIN(TIN12*RP) 

 IF(R1MR2.EQ.0.) GO TO 135 

C ALPH(I,1)=DARCOS(R1MR2*RP) 

 ALPH(I,1)= ACOS(R1MR2*RP) 

C TEX(I,1)=DSQRT(PSQ-R1MR2**2) 

 TEX(I,1)= SQRT(PSQ-R1MR2**2) 

 GO TO 140 

 135 CONTINUE 

 ALPH(I,1)=PIO2 

 TEX(I,1)=P 

 

 140 CONTINUE 

 

 145 CONTINUE 

C COMPUTE ADJACENT AND DIAGONAL ROD VIEW FACTORS 

C USING CROSSED STRING METHOD 

C COMPUTE ADJACENT ROD VIEW FACTORS 

 R1=R(SOURCE) 

 DO 150 I=1,2 

 IF(IX.EQ.L.AND.I.EQ.1) GO TO 150 

 IF(IY.EQ.L.AND.I.EQ.2) GO TO 150 

 TARGET=SOURCE+L**(I-1) 

 R2=R(TARGET) 

 CROLEN=TIN(SOURCE,2**I-1)+R1*ALPH(SOURCE,I) 

D +R2*(PI-ALPH(SOURCE,I))-(R1+R2)*THET(SOURCE,2**I-1) 

 

 CROMUN=CROLEN-TEX(SOURCE,I) 

 

C F(SOURCE,TARGET)=.5D0*RPI*CROMUN/R1 

 F(SOURCE,TARGET)=.5E0*RPI*CROMUN/R1 

 RIJ(SOURCE,TARGET)=P-0.5*(R1+R2) 

 IF(IY.NE.IX) GO TO 150 

 

 F(SOURCE,SOURCE+L)=F(SOURCE,TARGET) 

 

 RIJ(SOURCE,SOURCE+L)=RIJ(SOURCE,TARGET) 

 GO TO 152 

 150 CONTINUE 

 

 152 CONTINUE 

 IF(IY.EQ.L) GO TO 190 

C COMPUTE DIAGONAL ROD VIEW FACTORS 

 DO 185 I=1,2 

 IF(IX.EQ.1.AND.I.EQ.1) GO TO 185 

 IF(IX.EQ.L.AND.I.EQ.2) GO TO 185 

 MORP1=(-1)**I 

C-29

 M1ORZ=I-2 
C-30

 TARGET=SOURCE+L+MORP1 

 R2=R(SOURCE+MORP1) 

 R3=R(TARGET) 

 R4=R(SOURCE+L) 

 TIN12=TIN(SOURCE+M1ORZ,1) 

 THET12=THET(SOURCE+M1ORZ,1) 

 TIN13=TIN(SOURCE,2**(3-I)) 

 THET13=THET(SOURCE,2**(3-I)) 

 TIN14=TIN(SOURCE,3) 

 THET14=THET(SOURCE,3) 

 TIN23=TIN(SOURCE+MORP1,3) 

 THET23=THET(SOURCE+MORP1,3) 

 TIN34=TIN(SOURCE+L+M1ORZ,1) 

 THET34=THET(SOURCE+L+M1ORZ,1) 

 PSI2=PIO2-THET12-THET23 

 PSI4=PIO2-THET14-THET34 

 IF(PSI2.GT.0.) GO TO 155 

 

 R1MR3=R1-R3 

C ALPH31=DARCOS(R1MR3*RR13) 

 ALPH31= ACOS(R1MR3*RR13) 

 PSI312=ALPH31-THET13 

 PSI132=PI-ALPH31-THET13 

C TIN12=DSQRT(R13SQ-R1MR3**2) 

 TIN12= SQRT(R13SQ-R1MR3**2) 

C TIN23=0.D0 

 TIN23=0.E0 

C PSI2=0.D0 

 PSI2=0.E0 

 GO TO 160 

 155 CONTINUE 

 PSI312=PIO4+THET12-THET13 

 PSI132=PIO4+THET23-THET13 

160 CONTINUE 

 

 IF(PSI4.GT.0.) GO TO 175 

 

 IF(PSI2.LE.0.) GO TO 165 

 R1MR3=R1-R3 

C ALPH31=DARCOS(R1MR3*RR13) 

 ALPH31= ACOS(R1MR3*RR13) 

 PSI314=ALPH31-THET13 

 PSI134=PI-ALPH31-THET13 

C TIN14=DSQRT(R13SQ-R1MR3**2) 

 TIN14= SQRT(R13SQ-R1MR3**2) 

 GO TO 170 

 

 165 CONTINUE 

 PSI314=PSI312 

 PSI134=PSI132 

 TIN14=TIN12 

 170 CONTINUE 

C TIN34=0.D0 

 TIN34=0.E0 

C PSI4=0.D0 
C-31

 PSI4=0.E0 

 GO TO 180 

 175 CONTINUE 

 PSI314=PIO4+THET14-THET13 

 

 PSI134=PIO4+THET34-THET13 

 

 180 CONTINUE 

C CROLEN=2.D0*TIN13+R1*(PSI312+PSI314)+R3*(PSI132+PSI134) 

 CROLEN=2.E0*TIN13+R1*(PSI312+PSI314)+R3*(PSI132+PSI134) 

 UNCLEN=TIN12+TIN23+TIN34+TIN14+R2*PSI2+R4*PSI4 

 CROMUN=CROLEN-UNCLEN 

C F(SOURCE,TARGET)=.25D0*RPI*CROMUN/R1 

 F(SOURCE,TARGET)=.25E0*RPI*CROMUN/R1 

 RIJ(SOURCE,TARGET)=SQRT(R13SQ)-0.5*(R1+R3) 

 185 CONTINUE 

 190 CONTINUE 

 RETURN 

 END 

c 

C****** VFAC 12/12/78 D.R.EVANS 

 

 SUBROUTINE VFAC(F,AREA,E,SCALFC,B,R0,IROW,JCOL,MIRRIM,P,PI,N, 

1 M,L,N2,NA,NSYM,NL,NL1,NPT) 

 

 implicit double precision (a-h,o-z) 

 DIMENSION F(M,1),AREA(1),E(1),SCALFC(1),B(NA,1),IROW(1), 

 1 JCOL(1),MIRRIM(20,1),R0(1) 

 COMMON /RI/ RIJ(1001,1001) 

 INTEGER ROD,TARGET 

 

 NP=N2-1 

 SL=0.25*AREA(N2) 

 

C SL IS THE DISTANCE BETWEEN OPPOSITE SIDES OF THE CANISTER 

 

 DELTAX=0.5*(SL-P*FLOAT(L-1)) 

 

C DELTAX IS THE DISTANCE FROM THE CENTER OF AN EDGE ROD TO 

 

C THE ADJACENT FACE OF THE CANISTER 

 

C CALCULATE THE PATH LENGTH FROM ROD TO CANISTER 

 

 CALL PATHLEN(R0,DELTAX,P,N2,L) 

 

C 

C GENERATE UPPER DIAGONAL PORTION OF VIEW FACTOR MATRIX 

 

 DO 50 IY=1,L 

 

 IYP2=IY+2 

 

 IYP1=IY+1 

 
C-32

 DO 45 IX=1,L 

 

 IYMIX=IY-IX 

 

 IXP2=IX+2 

 

 ROD=IX+L*(IY-1) 

 

C ZERO OUT MATRIX 

 

 DO 10 KK=ROD,NP 

 F(ROD,KK)=0. 

 RIJ(ROD,KK)=0. 

 10 CONTINUE 

 

C ADJACENT AND DIAGONAL ROD VIEW FACTORS BY CROSSED STRING 

 

C METHOD 

 

 CALL STRING(F,R0,P,PI,M,L,ROD,IX,IY) 

 

 IF(IY.EQ.L) GO TO 40 

 

C MORE-DISTANT VIEW FACTORS BY MODIFIED VIEWPIN METHOD 

C HIGHER-NUMBERED ROWS 

C ADJACENT ROW 

 K1=IX-NL 

 IF(K1.LE.0) K1=1 

 IXM2=IX-2 

 IF(IXM2.LT.K1) GO TO 12 

 CALL FIJ(F,R0,P,PI,M,NPT,L,ROD,IX,IY,K1,IXM2,1,1) 

 12 CONTINUE 

 K2=IX+NL 

 IF(K2.GT.L) K2=L 

 IF(K2.LT.IXP2) GO TO 14 

 

 CALL FIJ(F,R0,P,PI,M,NPT,L,ROD,IX,IY,IXP2,K2,1,1) 

 

 14 CONTINUE 

 IF(IYMIX.NE.0) GO TO 20 

 DO 15 KK=K1,K2 

 IF(KK.LT.IX.OR.KK.EQ.IYP1) GO TO 15 

 TARGET=KK+L*IY 

 ITARG2=IYP1+(KK-1)*L 

 RIJ(ROD,ITARG2)=RIJ(ROD,TARGET) 

 F(ROD,ITARG2)=F(ROD,TARGET) 

 15 CONTINUE 

 20 CONTINUE 

 IF(IYP1.GE.L) GO TO 40 

C ROWS BEYOND ADJACENT ROW 

 K2=IY+NL1 

 IF(K2.GT.L) K2=L 

 

 IF(K2.LT.IYP2) GO TO 24 

 
C-33

 CALL FIJ(F,R0,P,PI,M,NPT,L,ROD,IX,IY,IYP2,K2,1,2) 

 IF(IYMIX.NE.0) GO TO 24 

 DO 21 KK=IYP2,K2 

 TARGET=ROD+(KK-IY)*L 

 ITARG2=ROD+KK-IY 

 F(ROD,ITARG2)=F(ROD,TARGET) 

 21 CONTINUE 

 24 CONTINUE 

 IF(IX.EQ.1) GO TO 34 

C LOWER-NUMBERED ADJACENT COLUMN 

 K2=IY+NL 

 IF(K2.GT.L) K2=L 

 

 IF(K2.LT.IYP2) GO TO 40 

 

 CALL FIJ(F,R0,P,PI,M,NPT,L,ROD,IX,IY,IYP2,K2,3,1) 

 34 CONTINUE 

 IF(IYMIX.EQ.0) GO TO 45 

 IF(IX.EQ.L) GO TO 45 

C HIGHER-NUMBERED COLUMNS 

C ADJACENT COLUMN 

 CALL FIJ(F,R0,P,PI,M,NPT,L,ROD,IX,IY,IYP2,K2,2,1) 

40 CONTINUE 

 

 IF(IX.EQ.L-1) GO TO 45 

 

C COLUMNS BEYOND ADJACENT COLUMN 

 K2=IX+NL1 

 IF(K2.GT.L) K2=L 

 IF(K2.LT.IXP2) GO TO 44 

 CALL FIJ(F,R0,P,PI,M,NPT,L,ROD,IX,IY,IXP2,K2,2,2) 

 44 CONTINUE 

 45 CONTINUE 

 

 50 CONTINUE 

c 

C FILL VIEW FACTOR MATRIX 

 

 DO 225 I=1,NP 

 DO 225 J=I,NP 

 RIJ(J,I)=RIJ(I,J) 

 225 F(J,I)=F(I,J)*AREA(I)/AREA(J) 

 SUMA=1. 

 DO 230 I=1,NP 

 SUM=1. 

 DO 235 J=1,NP 

 235 SUM=SUM-F(I,J) 

 F(I,N2)=SUM 

 RIJ(N2,I)=RIJ(I,N2) 

 

 F(N2,I)=F(I,N2)*AREA(I)/AREA(N2) 

 

 230 SUMA=SUMA-F(N2,I) 

 F(N2,N2)=SUMA 

 RIJ(N2,N2)=0.25*SL 
C-34

c 

 RETURN 

 

 END 

c 

c 

c************************************************ 

c 

 SUBROUTINE INTERP(X,Y,X1,Y1,N) 

c 

 implicit double precision (a-h,o-z) 

c 

 dimension x(100),y(100) 

c 

 DO 100 I=1,n 

 I1=I 

 IF(X(I1)-X1) 100,100,200 

 100 CONTINUE 

 200 Y1=Y(I1-1)+((X1-X(I1-1))/(X(I1)-X(I1-1)))*(Y(I1)-Y(I1-1)) 

 RETURN 

 END 

 
D-1

APPENDIX D1. COBRA-TF LISTINGS 

Introduction

Appendix D2 contains an input listing from the two-channel model of COBRA-TF and associated 

input processing as well as the output for time zero. A full listing of the sub-channel model is 

not given because the listing is too large because the file is too large, instead only the input file 

is given here. 

Appendix D3 contains the input deck for the sub-channel model. 
D-2

APPENDIX D2. TWO-CHANNEL MODEL LISTING 

1********************************* input file listing *********************************  12345678901234567890123456789012345678901234567890123456789012345678901234567890  1 0  2 0 0.0  3 .001 10 40  4 1   RBHT Bundle 7x7 Rods ** **  5 1 1  6 40.0 1170. 0.0 0.466 124. 0.0 .9999 1.0  7 air .0001  8 2 5  9 144.8671.74 0 7.22  10 27.22071.74  11 32.17918.79  12 45.04052.95  13 550.2471.74 7.22 0  14 3 1  15 1 3 41.952 1.38 2.0 0.0 0 0 1.0 0 0  16 16. 0.0  17 0  18 4 4 1 0  19 1 1 2 4.0  20 1 2 1  21 2 1 1 5.75  22 2 3 4 1  23 3 2 22 2.51 10  24 2 2.51 3 7.72 4 7.72 5 7.72 6 6.85  25 20 6.85 21 6.85 22 6.85 22 6.85 23 6.85  26 3 5 2  27 4 5 2  28 4 1 3 4.0  29 5 5 3 4  30 2  12345678901234567890123456789012345678901234567890123456789012345678901234567890  31 50  32 7 8 1 1 1 1 1 0 0 0 
D-3

 33 1.2 2 2 3  34 1.2 5 2 3  35 1.2 8 2 3  36 1.2 11 2 3  37 1.2 14 2 3  38 1.2 17 2 3  39 1.2 20 2 3  40 1.2 23 2 3  41 1 8 2 1 1.4 .2952 1.5 1.984  42 2 5 8 11 14 17 20 23  43 3 16. 1 1  44 4 33. 2 1  45 8 3 1 2 2 0 0 0 1  46 1 1 1 2 0.05 16. 1.0 5000. 1 

 47 3 1.0  48 2 1 1 2 0.05 29.0 1.0 5000. 1  49 4 1.0  50 3 2 0 2 0.05 4. 0.0 5000. 1  51 4 1.0  52 1 3 14.20 14.20 1.0 4 0. 90.0  53 1 2 0 4  54 1 2  55 13.75 521.0 121.75 1563. 157.75 502.0 169.76 502.0  56 2 1 1 2  57 3  58 -1  59 13.75 521.0 169.0 521.  60 9 3  12345678901234567890123456789012345678901234567890123456789012345678901234567890  61 1 hrod .374 0.0 4 0  62 1 2.0685 0.0 1 3 .044 1.0 3 2.0545 0.0 3 1 .02 0.0  63 2 tube .374 .209 1 0  64 3 1.0825 0.0  65 3 wall 14.20 .250 1 0  66 3 1 .250  67 10 3  68 1 17 516.7  69 32. .1010 8.1400 70. .1030 8.340  70 212. .1110 9.090 392. .1210 10.04 
D-4

 71 500. .1270 10.60 572. 0.131 10.98  72 752. .1410 11.93 932. 0.151 12.88  73 1000. 0.158 13.23 1112. 0.166 13.82  74 1292. 0.178 14.77 1472. 0.191 15.72  75 1500. 0.193 15.86 1652. 0.204 16.66  76 1832. 0.216 17.61 2012. 0.229 18.56  77 2192. 0.241 19.50  78 2 14 119.  79 212. .16587 67.37 392. .22014 63.827  80 572. .26263 60.28 752. .29590 56.737  81 932. .32194 53.19 1112. .34233 49.646  82 1292. .35829 46.10 1472. .37078 42.555  83 1652. .38056 39.01 1832. .38822 35.464  84 2012. .39421 31.92 2192. .39891 28.375  85 2372. .40259 24.83 2552. .40546 21.284  86 3 10 528.8  87 70.0 .10000 10.083 200. 0.107 11.333  88 400. .11400 13.00 600. 0.117 14.833  89 800. .120 16.50 1000. 0.125 18.333  90 1200. .132 20.00 1400. 0.141 21.833  12345678901234567890123456789012345678901234567890123456789012345678901234567890  91 1600. 0.157 23.50 1800. 0.186 25.167  92 11 1 25  93 1 5  94 13.75 0.5 121.75 1.50 157.75 0.5 157.76 0.0  95 168.0 0.0  96 0.0 1. 17.5 .921 35.0 .8704 52.5 .8326  97 70. .803 87.5 .7755 105.0 .7512 122.5 .7302  98 140. .714 157.5 .6973 175.0 .6837 192.5 .6710  99 220. .652 255.0 .6332 290.0 .6167 325.0 .6017  100 360. .588 395.0 .5769 430.0 .5656 465.0 .5562  101 500. .547 535.0 .5444 570.0 .5304 605.0 .5243  102 1000. .002  103 13 2 0 2 0 0  104 3 3  105 0.0 0.0 0.1 .801500. .80  106 0.0 1.0 0.2 1.01500. 1.0  107 1 1 2 1 0 .260 92.05 40.0  108 124. 1.0.9999.0001 
D-5

 109  110 5 5 1 0 0 40.0 1170.0 40.0  111 124. 1.0.9999.0001  112  113 14 5 0 0 0 0 1 2  114 0  115 0  116  117 500 0 0  118 .0002 .015 500. 1.0 99999.  119 5. 1. 800. 800.  120 -.001 .005 5.0 1.0 200.  12345678901234567890123456789012345678901234567890123456789012345678901234567890  121 10. 10. 500. 500.  122  123  124  125  126  127  128  129 1  cobra_tf date 19980803 time 00:00:00 1 main control parameters are:  restart time step . . . . . . . . . . . 0  simulation start time . . . . . . . . . .000  outer iteration convergence limit . . . .0010000  maximum number of inner iterations . . 40  maximum number of outer iterations . . 10  1 1 0 0 0 0 0 0 0 0 0  2 5 0 0 0 0 0 0 0 0 0  3 1 0 0 0 0 0 0 0 0 0  4 4 1 0 0 0 0 0 0 0 0  7 8 1 1 1 1 1 0 0 0 0  8 3 1 2 2 0 0 0 1 0 0  9 3 0 0 0 0 0 0 0 0 0 
D-6

 10 3 0 0 0 0 0 0 0 0 0  11 1 25 0 0 0 0 0 0 0 0  13 2 0 2 0 0 0 0 0 0 0  14 5 0 0 0 0 1 2 0 0 0  0 0 0 0 0 0 0 0 0 0 0 1 input summary    Test 31504 Bundle Rod 7x7 ** **  general information  ******************* 0 initial system operating pressure (psi) . . . 40.00000  initial system steam/water enthalpy . . . . .1170.00000  initial noncondensable gas enthalpy . . . . . 124.00000  initial liquid volume fraction . . . . . .00000  mass flux for initialization (lb/ft**2-sec) . . .00000  average linear heat rate (kw/ft) . . . . . . . .46600  total axial length (inches). . . . . . . . . . 174.71997  total no. of axial nodes . . . . . . . . . . . 28 1  initial volume fractions of vapor and noncondensable gases 1  100.00000 percent of the total system volume is initially filled with vapor and/or noncondensable gases. the fracti of this gas volume occupied by water vapor and each noncondensable gas is as follows:  steam .9999 air .00010 1  subchannel data  nominal wetted momentum momentum axial variation tables  subchannel channel area perimeter area area continuity momentum wetted  id. no. (in**2) (in.) (bottom) (top) area area perimeter  ---------------------------------------------------------------------------------------------------- 
D-7

 1 44.8600 71.740 44.8600 7.2200 0 0 0  2 7.2200 71.740 7.2200 7.2200 0 0 0  3 2.1790 18.790 2.1790 2.1790 0 0 0  4 5.0400 52.950 5.0400 5.0400 0 0 0  5 50.2400 71.740 7.2200 50.2400 0 0 0 0 1 ************************************************************************************************************************  grid spacer data  model selection grid quench front heat transfer to fluid 1  (0=off,1=on) drop breakup at grid spacer 1  grid enhancement of single phase vapor convection 1  grid type 1 material type index, 1  grid length [in] 1.500  grid perimeter [in] 1.984  fraction of channel blocked .295  loss coefficient multiplier 1.400  axial levels containing grid type 1  2 5 8 11 14 17 20 23  grid located no. of grids fuel rod - surface index pairs surrounding grid  in channel in channel  ------------ ------------ ------------------------------------------------------------------  3 16.000 1 - 1 0 - 0 0 - 0 0 - 0 0 - 0 0 - 0  4 33.000 2 - 1 0 - 0 0 - 0 0 - 0 0 - 0 0 - 0 0 0 data for lateral momentum convected by axial velocities at section boundries  channel node gap gap area node gap gap area node gap gap area node gap gap ar no. no. below above no. below above no. below above no. below above 
D-8

0  ***************************************************************************************************************************** channel thermal connection input data  -------------------------------------  channel no. fuel rod - surface index pairs heat slab indices  ----------- ------------------------------------------------------------ ----------------------------------------  3 1 - 1 0 - 0 0 - 0 0 - 0 0 - 0 0 - 0 0 0 0 0 0 0 0 0  4 2 - 1 3 - 1 0 - 0 0 - 0 0 - 0 0 - 0 -1 0 0 0 0 0 0 0  ***************************************************************************************************************************** 0  gap data  gap gap centroid loss frict. gap gap sign gaps which face this gap variation  no. ik jk width distance coeff. flag below above modifier ii side jj side table  1 3 4 1.952 1.380 2.000 .00 0 0 1.000 0 0 0 0 0 0 0 1  channel splitting data - axial level 1 of 4  number no. of cell length  of channels nodes (nominal)  1 2 .3333  channel channels above channels below  ---------------------------- ----------------------------  1 2 0 0 0 0 0 1 0 0 0 0 0 1  channel splitting data - axial level 2 of 4 
D-9

 number no. of cell length  of channels nodes (nominal)  1 1 .4792  channel channels above channels below  ---------------------------- ----------------------------  2 3 4 0 0 0 0 1 0 0 0 0 0  variable axial noding  ---------------------  node length node length node length node length node length  no. (ft) no. (ft) no. (ft) no. (ft) no. (ft)  ---- ------ ---- ------ ---- ------ ---- ------ ---- ------  2 .4792 1  channel splitting data - axial level 3 of 4  number no. of cell length  of channels nodes (nominal)  2 22 .5643  channel channels above channels below  ---------------------------- ----------------------------  3 5 0 0 0 0 0 2 0 0 0 0 0  4 5 0 0 0 0 0 2 0 0 0 0 0  variable axial noding  ---------------------  node length node length node length node length node length  no. (ft) no. (ft) no. (ft) no. (ft) no. (ft)  ---- ------ ---- ------ ---- ------ ---- ------ ---- ------  2 .2092 3 .6433 4 .6433 5 .6433 6 .5708  7 .5708 8 .5708 9 .5708 10 .5708 11 .5708  12 .5708 13 .5708 14 .5708 15 .5708 16 .5708  17 .5708 18 .5708 19 .5708 20 .5708 21 .5708 
D-10

 22 .5708 23 .5708 1  channel splitting data - axial level 4 of 4  number no. of cell length  of channels nodes (nominal)  1 3 .3333  channel channels above channels below  ---------------------------- ----------------------------  5 5 0 0 0 0 0 3 4 0 0 0 0  variable axial noding  ---------------------  node length node length node length node length node length  no. (ft) no. (ft) no. (ft) no. (ft) no. (ft)  ---- ------ ---- ------ ---- ------ ---- ------ ---- ------  2 .3333 3 .3333 4 .3333  simultaneous solution group information  no. of last cell number in each group  groups  1 50 1  *****************************************************************************************************************************  fuel rod and heat slab model input  no. of fuel rods = 3 no. of fuel rod surfaces = 3  no. of heat slabs = 1  *****************************************************************************************************************************  fuel rod model input 
D-11

 fuel rod axial location geometry conductor radial power axial power renoding minimum r index (in.) - ( in.) type type factor profile flag node size multiplier  -------- ------------ -- -------- --------- ------------ ----------- -------- --------- ----------  1 13.75 - 162.72 hrod 1 1.000 1 2 .0500 16.000  2 13.75 - 162.72 hrod 1 1.000 1 2 .0500 29.000  3 13.75 - 162.72 tube 2 .000 0 2 .0500 4.000  heat slab model input  heat slab ch annel connection - heated perimeter geometry conductor slab  index inside outside type type multiplier  --------- ------------ ------------- -------- --------- ----------  1 4 - 14.20 0 - 14.20 wall 3 1.000  ----------------------------------------------------------------------------------------------------------------------------- 

 conductor geometry description 

 no. of geometry types = 3  -----------------------------------------------------------------------------------------------------------------------------  type 1 - hrod cylindrical heater rod ----------------------------------------------------------------------------  rod diameter .3740 (in.)  inside diameter .0000 (in.)  no. of nodes (total) 8  material index (oxide) 0  radial noding information  node material radial node boundaries power  no. index location (inside) (outside) fraction  ---- -------- -------- -------- --------- --------  1 2 .0484 .0000 .0685 .00000  2 3 .0931 .0685 .1125 1.00000 
D-12

 3 2 .1219 .1125 .1307 .00000  4 2 .1400 .1307 .1488 .00000  5 2 .1582 .1488 .1670 .00000  6 1 .1710 .1670 .1750 .00000  7 1 .1790 .1750 .1830 .00000  8 1 .1870 .1830 .1870 .00000  type 2 - tube tube conductor geometry --------------------------------------------------------------------------- 

 outside diameter .3740 (in.)  inside diameter .2090 (in.)  no. of nodes (total) 3  material index (inside) 0  material index (outside) 0  radial noding information  node material radial node boundaries power  no. index location (inside) (outside) fraction  ---- -------- -------- -------- --------- --------  1 1 .1045 .1045 .1251 .00000  2 1 .1472 .1251 .1664 .00000  3 1 .1870 .1664 .1870 .00000  type 3 - wall flat plate conductor geometry ---------------------------------------------------------------------  wall perimeter 14.2000 (in.)  wall thickness .2500 (in.)  no. of nodes (total) 3  material index (inside) 0  material index(outside) 0  radial noding information  node material radial node boundaries power  no. index location (inside) (outside) fraction  ---- -------- -------- -------- --------- --------  1 1 .0000 .0000 .0625 .00000  2 1 .1250 .0625 .1875 .00000 
D-13

 3 1 .2500 .1875 .2500 .00000  ------------------------------------------------------------------------------------------------------------------------  material property tables  ------------------------  material type - 1 cold state density = 516.700 (lbm/ft3)  temperature (f) specific heat (btu/lbm-f) conductivity (btu/hr-ft-f)  32.0 .10100 8.140  70.0 .10300 8.340  212.0 .11100 9.090  392.0 .12100 10.040  500.0 .12700 10.600  572.0 .13100 10.980  752.0 .14100 11.930  932.0 .15100 12.880  1000.0 .15800 13.230  1112.0 .16600 13.820  212.0 .16587 67.370  392.0 .22014 63.827  572.0 .26263 60.280  752.0 .29590 56.737  932.0 .32194 53.190  1112.0 .34233 49.646  1292.0 .35829 46.100  material type - 2 cold state density = 119.000 (lbm/ft3)  temperature (f) specific heat (btu/lbm-f) conductivity (btu/hr-ft-f)  212.0 .16587 67.370  392.0 .22014 63.827  572.0 .26263 60.280  752.0 .29590 56.737  932.0 .32194 53.190 
D-14

 1112.0 .34233 49.646  1292.0 .35829 46.100  1472.0 .37078 42.555  1652.0 .38056 39.010  1832.0 .38822 35.464  70.0 .10000 10.083  200.0 .10700 11.333  400.0 .11400 13.000  600.0 .11700 14.833  material type - 3 cold state density = 528.800 (lbm/ft3)  temperature (f) specific heat (btu/lbm-f) conductivity (btu/hr-ft-f)  70.0 .10000 10.083  200.0 .10700 11.333  400.0 .11400 13.000  600.0 .11700 14.833  800.0 .12000 16.500  1000.0 .12500 18.333  1200.0 .13200 20.000  1400.0 .14100 21.833  1600.0 .15700 23.500  1800.0 .18600 25.167  ------------------------------------------------------------------------------------------------------------------------  axial power profile tables  --------------------------  axial profile no. 1 - used by rod nos. = 1 2  rod node no. axial location (in.) fluid node no. axial power factor  ------------ -------------------- -------------- ------------------  1 13.75 5 .5029  2 15.01 5 .5145  3 20.12 6 .5590  4 27.84 7 .6305  5 35.56 8 .7019 
D-15

 6 42.84 9 .7694  7 49.69 10 .8328  8 56.54 11 .8962  9 63.39 12 .9597  10 70.24 13 1.0231  11 77.09 14 1.0865  12 83.94 15 1.1500  13 90.79 16 1.2134  14 97.64 17 1.2768  15 104.49 18 1.3402  16 111.34 19 1.4037  17 118.19 20 1.4671  18 125.04 21 1.4084  19 131.89 22 1.2182  20 138.74 23 1.0279  21 145.59 24 .8376  22 152.44 25 .6474  23 159.29 26 .1930  24 162.72 26 .0000  this table integrates to .9689 over a heated length of 148.97 (in.)  ------------------------------------------------------------------------------------------------------------------------  power forcing function table  ----------------------------  transient time (secs) power factor  --------------------- ------------  .0000 1.0000  17.5000 .9210  35.0000 .8704  52.5000 .8326  70.0000 .8030  87.5000 .7755  105.0000 .7512  122.5000 .7302  140.0000 .7140  157.5000 .6973  175.0000 .6837 
D-16

 192.5000 .6710  220.0000 .6520  255.0000 .6332  290.0000 .6167  325.0000 .6017  360.0000 .5880  395.0000 .5769  430.0000 .5656  465.0000 .5562  500.0000 .5470  535.0000 .5444  570.0000 .5304  605.0000 .5243  1000.0000 .0020  ------------------------------------------------------------------------------------------------------------------------ 1 forcing function tables 0 table 1  time forcing time forcing time forcing time forcing time forcing  coord. factor coord. factor coord. factor coord. factor coord. factor  .000 .000 .100 .800 1500.000 .800 0 table 2  time forcing time forcing time forcing time forcing time forcing  coord. factor coord. factor coord. factor coord. factor coord. factor  .000 1.000 .200 1.000 1500.000 1.000 1 axial and/or injection boundary conditions  boundary type property specification  -------------------------------- ----------------------  1= pressure and enthalpy (axial) . . . . . . . pressure  2= flow and ehthalpy (axial) . . . . . . . . . mass flow 
D-17

 3= zero axial flow . . . . . . . . . . . . . . zero  4= injected flow and enthalpy . . . . . . . . injected flow  5= pressure sink and enthalpy . . . . . . . . sink pressure  boundary specified  channel axial type property  index node (see above) (see above) enthalpy  1 1 2 .26 92.05  5 5 1 40.00 1170.00 0  zero crossflow boundary conditions  gap axial  index node  5 channels will be printed  1 2 3 4 5 0 3 rods will be printed  1 2 3 0 1 gaps will be printed  1 0 ***** graphics dump data ******************************************************************************************  initial run  maximum number of graphics (check against dimension of indcmp array --  dumps . . . . . . . . . . . . . . 500 must not exceed it.)  normal vessel dump selected 1 trac major edit  time = 0.000E+00 seconds delt = 0.000E+00 seconds time steps = 0 oitno= 0 
D-18

 last minimum number of inner iterations was 0 at step 0  current convergence limits and limitation counts  delamx delemx delrmx delvmx delcmx delpmx  0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00  0 0 0 0 0 0  cptime = 0.000E+00 0 channel results date 19980803 time 00:00:00   Test 31504 Bundle Rod 7x7 ** **  ******************************************************************************************************************************** simulation time = .00000 seconds fluid properties for channel 1  node dist. pressure velocity void fraction flow rate flow heat added gama 

 no. (ft.) (psi) (ft/sec) (lbm/s) reg. (btu/s) (lbm/s)  liquid vapor entr. liquid vapor entr. liquid vapor entr. liquid vapor  3 .67 40.009 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 2 .33 40.010 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 1 .00 40.010 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 node dist. enthalpy density net  no. (ft.) (btu/lbm) (lbm/ft3) entrain  -------------------------------------------------------------------------- -------------------------------  vapor hg vapor-hg liquid hf liq. - hf mixture liquid vapor mixture  3 .67 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09446 .0945 . 2 .33 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09446 .0945 . 1 .00 1170.00 1169.77 .23 236.13 236.15 -.02 1169.25 58.29915 .09446 .0945 . * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  node dist. mixture mixture -- relative velocities -- area vap./liq. vap./drop -------- grid spacers --------  no. flow rate velocity vap. - liq. vap. - entr. interfacial interfacial grid temperature percent  drag drag type degf quenched  3 .67 .00 .00 .00 .00 .0501 .0010 .0010 0 .00 .000  2 .33 .00 .00 .00 .00 .3115 .0010 .0010 0 .00 .000  1 .00 .00 .00 .00 .00 .3115 .0010 .0010 0 .00 .000  * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  node dist. hashl hascl hashv hascv drop ai ai source sent sdent qradd qradv snkld gams
D-19

 3 .67 347.3965 34.7397 3.4740 34.7397 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E

.0000E+00  2 .33 347.3965 34.7397 3.4740 34.7397 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  1 .00 347.3965 34.7397 3.4740 34.7397 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00 0 -------------------------------- gas volumetric analysis --------------------------------  hmgas rmgas steam air diam-ld diam-sd flow-sd veloc-sd gamsd  3 .67 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .00

 2 .33 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .00 1 .00 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .00 ********************************************************************************************************************************0 channel results date 19980803 time 00:00:00   Test 31504 Bundle Rod 7x7 ** **  ******************************************************************************************************************************** simulation time = .00000 seconds fluid properties for channel 2  node dist. pressure velocity void fraction flow rate flow heat added gama 

 no. (ft.) (psi) (ft/sec) (lbm/s) reg. (btu/s) (lbm/s)  liquid vapor entr. liquid vapor entr. liquid vapor entr. liquid vapor  2 1.15 40.009 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 1 .67 40.009 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 node dist. enthalpy density net  no. (ft.) (btu/lbm) (lbm/ft3) entrain  -------------------------------------------------------------------------- -------------------------------  vapor hg vapor-hg liquid hf liq. - hf mixture liquid vapor mixture  2 1.15 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09446 .0945  1 .67 1170.00 1169.77 .23 236.13 236.14 -.01 1169.22 58.29915 .09446 .0945 . * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  node dist. mixture mixture -- relative velocities -- area vap./liq. vap./drop -------- grid spacers --------  no. flow rate velocity vap. - liq. vap. - entr. interfacial interfacial grid temperature percent  drag drag type degf quenched  2 1.15 .00 .00 .00 .00 .0501 .0010 .0010 0 .00 .000  1 .67 .00 .00 .00 .00 .0501 .0010 .0010 0 .00 .000 
D-20

 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  node dist. hashl hascl hashv hascv drop ai ai source sent sdent qradd qradv snkld gams 2 1.15 80.3732 8.0373 .8037 8.0373 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00  1 .67 80.3732 8.0373 .8037 8.0373 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+0.0000E+00 0 -------------------------------- gas volumetric analysis --------------------------------  hmgas rmgas steam air diam-ld diam-sd flow-sd veloc-sd gamsd  2 1.15 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 1 .67 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .00 ********************************************************************************************************************************0 channel results date 19980803 time 00:00:00   Test 31504 Bundle Rod 7x7 ** **  ******************************************************************************************************************************** simulation time = .00000 seconds fluid properties for channel 3  node dist. pressure velocity void fraction flow rate flow heat added gama 

 no. (ft.) (psi) (ft/sec) (lbm/s) reg. (btu/s) (lbm/s)  liquid vapor entr. liquid vapor entr. liquid vapor entr. liquid vapor  23 13.56 40.001 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 22 12.99 40.001 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 21 12.42 40.002 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 20 11.85 40.002 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 19 11.28 40.003 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 18 10.71 40.003 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 17 10.13 40.003 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 16 9.56 40.004 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 15 8.99 40.004 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 14 8.42 40.004 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 13 7.85 40.005 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 12 7.28 40.005 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 11 6.71 40.006 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 10 6.14 40.006 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 9 5.57 40.006 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 8 5.00 40.007 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 7 4.43 40.007 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 6 3.86 40.007 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 5 3.28 40.008 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0
D-21

 4 2.64 40.008 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 3 2.00 40.009 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 2 1.36 40.009 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 1 1.15 40.009 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 node dist. enthalpy density net  no. (ft.) (btu/lbm) (lbm/ft3) entrain  -------------------------------------------------------------------------- -------------------------------  vapor hg vapor-hg liquid hf liq. - hf mixture liquid vapor mixture  23 13.56 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09444 .0945  22 12.99 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09444 .0945  21 12.42 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09444 .0945  20 11.85 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09444 .0945  19 11.28 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09444 .0945  18 10.71 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09444 .0945  17 10.13 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09444 .0945  16 9.56 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09444 .0945  15 8.99 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09444 .0945  14 8.42 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09444 .0945  13 7.85 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  12 7.28 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  11 6.71 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  10 6.14 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  9 5.57 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  8 5.00 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  7 4.43 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  6 3.86 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  5 3.28 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  4 2.64 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  3 2.00 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  2 1.36 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09446 .0945  1 1.15 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09446 .0945  * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  node dist. mixture mixture -- relative velocities -- area vap./liq. vap./drop -------- grid spacers --------  no. flow rate velocity vap. - liq. vap. - entr. interfacial interfacial grid temperature percent  drag drag type degf quenched 
D-22

 23 13.56 .00 .00 .00 .00 .0151 .0010 .0010 1 .00 .000  22 12.99 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  21 12.42 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  20 11.85 .00 .00 .00 .00 .0151 .0010 .0010 1 502.00 .000  19 11.28 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  18 10.71 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  17 10.13 .00 .00 .00 .00 .0151 .0010 .0010 1 1062.12 .000  16 9.56 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  15 8.99 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  14 8.42 .00 .00 .00 .00 .0151 .0010 .0010 1 1528.70 .000  13 7.85 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  12 7.28 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  11 6.71 .00 .00 .00 .00 .0151 .0010 .0010 1 1330.43 .000  10 6.14 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  9 5.57 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  8 5.00 .00 .00 .00 .00 .0151 .0010 .0010 1 1132.16 .000  7 4.43 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  6 3.86 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  5 3.28 .00 .00 .00 .00 .0151 .0010 .0010 1 933.89 .000  4 2.64 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  3 2.00 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  2 1.36 .00 .00 .00 .00 .0151 .0010 .0010 1 731.43 .000  1 1.15 .00 .00 .00 .00 .0151 .0010 .0010 0 .00 .000  * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  node dist. hashl hascl hashv hascv drop ai ai source sent sdent qradd qradv snkld gams 23 13.56 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000.0000E+00  22 12.99 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000.0000E+00  21 12.42 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000.0000E+00  20 11.85 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000.0000E+00  19 11.28 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000.0000E+00 
D-23

 18 10.71 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000.0000E+00  17 10.13 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000.0000E+00  16 9.56 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000

.0000E+00  15 8.99 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000

.0000E+00  14 8.42 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000

.0000E+00  13 7.85 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000

.0000E+00  12 7.28 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000

.0000E+00  11 6.71 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000

.0000E+00  10 6.14 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000

.0000E+00  9 5.57 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  8 5.00 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  7 4.43 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  6 3.86 110.3287 11.0329 1.1033 11.0329 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  5 3.28 124.3412 12.4341 1.2434 12.4341 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  4 2.64 124.3412 12.4341 1.2434 12.4341 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  3 2.00 124.3412 12.4341 1.2434 12.4341 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  2 1.36 40.4270 4.0427 .4043 4.0427 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+

.0000E+00  1 1.15 40.4270 4.0427 .4043 4.0427 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00 0 -------------------------------- gas volumetric analysis --------------------------------  hmgas rmgas steam air diam-ld diam-sd flow-sd veloc-sd gamsd  23 13.56 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .
D-24

 22 12.99 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .

 21 12.42 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .

 20 11.85 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .

 19 11.28 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .

 18 10.71 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .

 17 10.13 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .

 16 9.56 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 15 8.99 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 14 8.42 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 13 7.85 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 12 7.28 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 11 6.71 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 10 6.14 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 9 5.57 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 8 5.00 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 7 4.43 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 6 3.86 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 5 3.28 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 4 2.64 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 3 2.00 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 2 1.36 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 1 1.15 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 ********************************************************************************************************************************0 channel results date 19980803 time 00:00:00   Test 31504 Bundle Rod 7x7 ** **  ******************************************************************************************************************************** simulation time = .00000 seconds fluid properties for channel 4  node dist. pressure velocity void fraction flow rate flow heat added gama 

 no. (ft.) (psi) (ft/sec) (lbm/s) reg. (btu/s) (lbm/s)  liquid vapor entr. liquid vapor entr. liquid vapor entr. liquid vapor  23 13.56 40.001 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 22 12.99 40.001 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 21 12.42 40.002 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 20 11.85 40.002 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 19 11.28 40.003 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 18 10.71 40.003 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 17 10.13 40.003 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 16 9.56 40.004 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+
D-25

 15 8.99 40.004 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 14 8.42 40.004 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 13 7.85 40.005 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 12 7.28 40.005 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 11 6.71 40.006 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 10 6.14 40.006 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 9 5.57 40.006 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 8 5.00 40.007 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 7 4.43 40.007 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 6 3.86 40.007 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 5 3.28 40.008 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 4 2.64 40.008 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 3 2.00 40.009 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 2 1.36 40.009 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 1 1.15 40.009 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+0 node dist. enthalpy density net  no. (ft.) (btu/lbm) (lbm/ft3) entrain  -------------------------------------------------------------------------- -------------------------------  vapor hg vapor-hg liquid hf liq. - hf mixture liquid vapor mixture  23 13.56 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09444 .0945  22 12.99 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09444 .0945  21 12.42 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09444 .0945  20 11.85 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09444 .0945  19 11.28 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09444 .0945  18 10.71 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09444 .0945  17 10.13 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09444 .0945  16 9.56 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09444 .0945  15 8.99 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09444 .0945  14 8.42 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09444 .0945  13 7.85 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  12 7.28 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  11 6.71 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  10 6.14 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  9 5.57 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  8 5.00 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  7 4.43 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  6 3.86 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945 
D-26

 5 3.28 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  4 2.64 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  3 2.00 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09445 .0945  2 1.36 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09446 .0945  1 1.15 1170.00 1169.77 .23 236.13 236.14 -.01 1169.25 58.29915 .09446 .0945 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * node dist. mixture mixture -- relative velocities -- area vap./liq. vap./drop -------- grid spacers --------  no. flow rate velocity vap. - liq. vap. - entr. interfacial interfacial grid temperature percent  drag drag type degf quenched  23 13.56 .00 .00 .00 .00 .0350 .0010 .0010 1 .00 .000  22 12.99 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  21 12.42 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  20 11.85 .00 .00 .00 .00 .0350 .0010 .0010 1 502.00 .000  19 11.28 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  18 10.71 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  17 10.13 .00 .00 .00 .00 .0350 .0010 .0010 1 1062.12 .000  16 9.56 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  15 8.99 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  14 8.42 .00 .00 .00 .00 .0350 .0010 .0010 1 1528.70 .000  13 7.85 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  12 7.28 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  11 6.71 .00 .00 .00 .00 .0350 .0010 .0010 1 1330.43 .000  10 6.14 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  9 5.57 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  8 5.00 .00 .00 .00 .00 .0350 .0010 .0010 1 1132.16 .000  7 4.43 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  6 3.86 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  5 3.28 .00 .00 .00 .00 .0350 .0010 .0010 1 933.89 .000  4 2.64 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  3 2.00 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  2 1.36 .00 .00 .00 .00 .0350 .0010 .0010 1 731.43 .000  1 1.15 .00 .00 .00 .00 .0350 .0010 .0010 0 .00 .000  * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * node dist. hashl hascl hashv hascv drop ai ai source sent sdent qradd qradv snkld gams
D-27

 23 13.56 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  22 12.99 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  21 12.42 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  20 11.85 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  19 11.28 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  18 10.71 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  17 10.13 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  16 9.56 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00  15 8.99 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00  14 8.42 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00  13 7.85 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00  12 7.28 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00  11 6.71 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00  10 6.14 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00  9 5.57 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00  8 5.00 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00  7 4.43 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00  6 3.86 90.5571 9.0557 .9056 9.0557 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00  5 3.28 102.0585 10.2059 1.0206 10.2059 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00 
D-28

 4 2.64 102.0585 10.2059 1.0206 10.2059 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  3 2.00 102.0585 10.2059 1.0206 10.2059 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E.0000E+00  2 1.36 33.1822 3.3182 .3318 3.3182 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00  1 1.15 33.1822 3.3182 .3318 3.3182 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000E+.0000E+00 0 -------------------------------- gas volumetric analysis --------------------------------  hmgas rmgas steam air diam-ld diam-sd flow-sd veloc-sd gamsd  23 13.56 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .

 22 12.99 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .

 21 12.42 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .

 20 11.85 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .

 19 11.28 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .

 18 10.71 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .

 17 10.13 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .

 16 9.56 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 15 8.99 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 14 8.42 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 13 7.85 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 12 7.28 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 11 6.71 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 10 6.14 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 9 5.57 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 8 5.00 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 7 4.43 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 6 3.86 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 5 3.28 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 4 2.64 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 3 2.00 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 2 1.36 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 1 1.15 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0 ********************************************************************************************************************************0 channel results date 19980803 time 00:00:00   Test 31504 Bundle Rod 7x7 ** **  ******************************************************************************************************************************** simulation time = .00000 seconds fluid properties for channel 5  node dist. pressure velocity void fraction flow rate flow heat added gama 
D-29

 no. (ft.) (psi) (ft/sec) (lbm/s) reg. (btu/s) (lbm/s)  liquid vapor entr. liquid vapor entr. liquid vapor entr. liquid vapor  4 14.56 40.000 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 3 14.23 40.000 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 2 13.89 40.001 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ 1 13.56 40.001 .00 .00 .00 .0000 1.0000 .0000 .00000 .00000 .00000 0 .000E+00 .000E+ node dist. enthalpy density net  no. (ft.) (btu/lbm) (lbm/ft3) entrain  -------------------------------------------------------------------------- -------------------------------  vapor hg vapor-hg liquid hf liq. - hf mixture liquid vapor mixture  4 14.56 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09443 .0945  3 14.23 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09444 .0945  2 13.89 1170.00 1169.77 .23 236.13 236.13 .00 1169.25 58.29915 .09444 .0945  1 13.56 1170.00 1169.77 .23 236.13 236.13 .00 1169.29 58.29915 .09444 .0945  * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  node dist. mixture mixture -- relative velocities -- area vap./liq. vap./drop -------- grid spacers --------  no. flow rate velocity vap. - liq. vap. - entr. interfacial interfacial grid temperature percent  drag drag type degf quenched  4 14.56 .00 .00 .00 .00 .3489 .0010 .0010 0 .00 .000  3 14.23 .00 .00 .00 .00 .3489 .0010 .0010 0 .00 .000  2 13.89 .00 .00 .00 .00 .3489 .0010 .0010 0 .00 .000  1 13.56 .00 .00 .00 .00 .0501 .0010 .0010 0 .00 .000  * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  node dist. hashl hascl hashv hascv drop ai ai source sent sdent qradd qradv snkld gams 4 14.56 389.0593 38.9059 3.8906 38.9059 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000

.0000E+00  3 14.23 389.0593 38.9059 3.8906 38.9059 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000

.0000E+00  2 13.89 389.0593 38.9059 3.8906 38.9059 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000

.0000E+00 
D-30

 1 13.56 389.0593 38.9059 3.8906 38.9059 .1000E-09 .0000E+00 .0000E+00 .0000E+00 .0000E+00 .0000

.0000E+00 0 -------------------------------- gas volumetric analysis --------------------------------  hmgas rmgas steam air diam-ld diam-sd flow-sd veloc-sd gamsd  4 14.56 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0

 3 14.23 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0

 2 13.89 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0

 1 13.56 124.00 .00001 99.990 .010 .000 .000 .000 .000 .0000 .00000 .0000E+00 .00 .0

 ********************************************************************************************************************************1 rod results date 1998 0803 time 00:0 0:00    Test 31504 Bundle Rod 7x7 ** **  ******************************************************************************************************************************** heater rod number 1 simulation time = .00 seconds  surface no. 1 of 1  -------------------- conducts heat to channels 3 0 0 0 0 0 geometry type = 1  and azimuthally to surfaces 1 and 1 no. of radial nodes = 8  ******************************************************************************************************************************** rod axial fluid temperatures surface heat heater rod temperatues,  node location (deg-f) heat flux transfer (deg-f)  no. (in.) liquid vapor (b/h-ft2) mode surface center  ---- -------- ------ ----- --------- -------- ------- ------  24 162.72 .0 .0 .0000E+00 502.00 502.00 .0000E+00  23 * 159.29 .0 .0 .0000E+00 502.00 502.00 .0000E+00  22 * 152.44 .0 .0 .0000E+00 658.35 658.35 .0000E+00  21 * 145.59 .0 .0 .0000E+00 860.24 860.24 .0000E+00  20 * 138.74 .0 .0 .0000E+00 1062.12 1062.12 .0000E+00  19 * 131.89 .0 .0 .0000E+00 1264.00 1264.00 .0000E+00  18 * 125.04 .0 .0 .0000E+00 1465.89 1465.89 .0000E+00  17 * 118.19 .0 .0 .0000E+00 1528.70 1528.70 .0000E+00  16 * 111.34 .0 .0 .0000E+00 1462.61 1462.61 .0000E+00  15 * 104.49 .0 .0 .0000E+00 1396.52 1396.52 .0000E+00  14 * 97.64 .0 .0 .0000E+00 1330.43 1330.43 .0000E+00  13 * 90.79 .0 .0 .0000E+00 1264.34 1264.34 .0000E+00 
D-31

 12 * 83.94 .0 .0 .0000E+00 1198.25 1198.25 .0000E+00  11 * 77.09 .0 .0 .0000E+00 1132.16 1132.16 .0000E+00  10 * 70.24 .0 .0 .0000E+00 1066.07 1066.07 .0000E+00  9 * 63.39 .0 .0 .0000E+00 999.98 999.98 .0000E+00  8 * 56.54 .0 .0 .0000E+00 933.89 933.89 .0000E+00  7 * 49.69 .0 .0 .0000E+00 867.80 867.80 .0000E+00  6 * 42.84 .0 .0 .0000E+00 801.71 801.71 .0000E+00  5 * 35.56 .0 .0 .0000E+00 731.43 731.43 .0000E+00  4 * 27.84 .0 .0 .0000E+00 656.94 656.94 .0000E+00  3 * 20.12 .0 .0 .0000E+00 582.46 582.46 .0000E+00  2 * 15.01 .0 .0 .0000E+00 533.11 533.11 .0000E+00  1 13.75 .0 .0 .0000E+00 521.00 521.00 .0000E+00  rod axial ---------------------------------rod temperatures (deg-f)---------------------------------  node location radii in inches  no. (in.) .0484 .0931 .1219 .1400 .1582 .1710 .1790 .1870  ---- -------- ------ ------ ------ ------ ------ ------ ------ ------ ------ ------  23 * 159.29 502.0 502.0 502.0 502.0 502.0 502.0 502.0 502.0  22 * 152.44 658.4 658.4 658.4 658.4 658.4 658.4 658.4 658.4  21 * 145.59 860.2 860.2 860.2 860.2 860.2 860.2 860.2 860.2  20 * 138.74 1062.1 1062.1 1062.1 1062.1 1062.1 1062.1 1062.1 1062.1  19 * 131.89 1264.0 1264.0 1264.0 1264.0 1264.0 1264.0 1264.0 1264.0  18 * 125.04 1465.9 1465.9 1465.9 1465.9 1465.9 1465.9 1465.9 1465.9  17 * 118.19 1528.7 1528.7 1528.7 1528.7 1528.7 1528.7 1528.7 1528.7  16 * 111.34 1462.6 1462.6 1462.6 1462.6 1462.6 1462.6 1462.6 1462.6  15 * 104.49 1396.5 1396.5 1396.5 1396.5 1396.5 1396.5 1396.5 1396.5  14 * 97.64 1330.4 1330.4 1330.4 1330.4 1330.4 1330.4 1330.4 1330.4  13 * 90.79 1264.3 1264.3 1264.3 1264.3 1264.3 1264.3 1264.3 1264.3  12 * 83.94 1198.3 1198.3 1198.3 1198.3 1198.3 1198.3 1198.3 1198.3  11 * 77.09 1132.2 1132.2 1132.2 1132.2 1132.2 1132.2 1132.2 1132.2  10 * 70.24 1066.1 1066.1 1066.1 1066.1 1066.1 1066.1 1066.1 1066.1  9 * 63.39 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0  8 * 56.54 933.9 933.9 933.9 933.9 933.9 933.9 933.9 933.9  7 * 49.69 867.8 867.8 867.8 867.8 867.8 867.8 867.8 867.8  6 * 42.84 801.7 801.7 801.7 801.7 801.7 801.7 801.7 801.7  5 * 35.56 731.4 731.4 731.4 731.4 731.4 731.4 731.4 731.4 
D-32

 4 * 27.84 656.9 656.9 656.9 656.9 656.9 656.9 656.9 656.9  3 * 20.12 582.5 582.5 582.5 582.5 582.5 582.5 582.5 582.5  2 * 15.01 533.1 533.1 533.1 533.1 533.1 533.1 533.1 533.1  ******************************************************************************************************************************** heater rod number 2 simulation time = .00 seconds  surface no. 1 of 1  -------------------- conducts heat to channels 4 0 0 0 0 0 geometry type = 1  and azimuthally to surfaces 1 and 1 no. of radial nodes = 8  ******************************************************************************************************************************** rod axial fluid temperatures surface heat heater rod temperatues,  node location (deg-f) heat flux transfer (deg-f)  no. (in.) liquid vapor (b/h-ft2) mode surface center  ---- -------- ------ ----- --------- -------- ------- ------  24 162.72 .0 .0 .0000E+00 502.00 502.00 .0000E+00  23 * 159.29 .0 .0 .0000E+00 502.00 502.00 .0000E+00  22 * 152.44 .0 .0 .0000E+00 658.35 658.35 .0000E+00  21 * 145.59 .0 .0 .0000E+00 860.24 860.24 .0000E+00  20 * 138.74 .0 .0 .0000E+00 1062.12 1062.12 .0000E+00  19 * 131.89 .0 .0 .0000E+00 1264.00 1264.00 .0000E+00  18 * 125.04 .0 .0 .0000E+00 1465.89 1465.89 .0000E+00  17 * 118.19 .0 .0 .0000E+00 1528.70 1528.70 .0000E+00  16 * 111.34 .0 .0 .0000E+00 1462.61 1462.61 .0000E+00  15 * 104.49 .0 .0 .0000E+00 1396.52 1396.52 .0000E+00  14 * 97.64 .0 .0 .0000E+00 1330.43 1330.43 .0000E+00  13 * 90.79 .0 .0 .0000E+00 1264.34 1264.34 .0000E+00  12 * 83.94 .0 .0 .0000E+00 1198.25 1198.25 .0000E+00  11 * 77.09 .0 .0 .0000E+00 1132.16 1132.16 .0000E+00  10 * 70.24 .0 .0 .0000E+00 1066.07 1066.07 .0000E+00  9 * 63.39 .0 .0 .0000E+00 999.98 999.98 .0000E+00  8 * 56.54 .0 .0 .0000E+00 933.89 933.89 .0000E+00  7 * 49.69 .0 .0 .0000E+00 867.80 867.80 .0000E+00  6 * 42.84 .0 .0 .0000E+00 801.71 801.71 .0000E+00  5 * 35.56 .0 .0 .0000E+00 731.43 731.43 .0000E+00  4 * 27.84 .0 .0 .0000E+00 656.94 656.94 .0000E+00 
D-33

 3 * 20.12 .0 .0 .0000E+00 582.46 582.46 .0000E+00  2 * 15.01 .0 .0 .0000E+00 533.11 533.11 .0000E+00  1 13.75 .0 .0 .0000E+00 521.00 521.00 .0000E+00  rod axial ---------------------------------rod temperatures (deg-f)---------------------------------  node location radii in inches  no. (in.) .0484 .0931 .1219 .1400 .1582 .1710 .1790 .1870  ---- -------- ------ ------ ------ ------ ------ ------ ------ ------ ------ ------  23 * 159.29 502.0 502.0 502.0 502.0 502.0 502.0 502.0 502.0  22 * 152.44 658.4 658.4 658.4 658.4 658.4 658.4 658.4 658.4  21 * 145.59 860.2 860.2 860.2 860.2 860.2 860.2 860.2 860.2  20 * 138.74 1062.1 1062.1 1062.1 1062.1 1062.1 1062.1 1062.1 1062.1  19 * 131.89 1264.0 1264.0 1264.0 1264.0 1264.0 1264.0 1264.0 1264.0  18 * 125.04 1465.9 1465.9 1465.9 1465.9 1465.9 1465.9 1465.9 1465.9  17 * 118.19 1528.7 1528.7 1528.7 1528.7 1528.7 1528.7 1528.7 1528.7  16 * 111.34 1462.6 1462.6 1462.6 1462.6 1462.6 1462.6 1462.6 1462.6  15 * 104.49 1396.5 1396.5 1396.5 1396.5 1396.5 1396.5 1396.5 1396.5  14 * 97.64 1330.4 1330.4 1330.4 1330.4 1330.4 1330.4 1330.4 1330.4  13 * 90.79 1264.3 1264.3 1264.3 1264.3 1264.3 1264.3 1264.3 1264.3  12 * 83.94 1198.3 1198.3 1198.3 1198.3 1198.3 1198.3 1198.3 1198.3  11 * 77.09 1132.2 1132.2 1132.2 1132.2 1132.2 1132.2 1132.2 1132.2  10 * 70.24 1066.1 1066.1 1066.1 1066.1 1066.1 1066.1 1066.1 1066.1  9 * 63.39 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0  8 * 56.54 933.9 933.9 933.9 933.9 933.9 933.9 933.9 933.9  7 * 49.69 867.8 867.8 867.8 867.8 867.8 867.8 867.8 867.8  6 * 42.84 801.7 801.7 801.7 801.7 801.7 801.7 801.7 801.7  5 * 35.56 731.4 731.4 731.4 731.4 731.4 731.4 731.4 731.4  4 * 27.84 656.9 656.9 656.9 656.9 656.9 656.9 656.9 656.9  3 * 20.12 582.5 582.5 582.5 582.5 582.5 582.5 582.5 582.5  2 * 15.01 533.1 533.1 533.1 533.1 533.1 533.1 533.1 533.1  ******************************************************************************************************************************** cylindrical tube rod no. 3 simulation time = .00 seconds  surface no. 1 of 1  ------------------------ conducts heat to channels 4 0 0 0 0 0 geometry type = 2  and azimuthally to surfaces 1 and 1 no. of radial nodes = 3 
D-34

 ******************************************************************************************************************************** rod axial *---------------- outside surface ----------------* *---------------- inside surface ----------------*  node location heat flux h.t. **** temperatures (deg-f)   ** ** temperatures (deg-f) **** h.t. heat flux 

 no. (in.) (b/h-ft2) mode wall vapor liquid liquid vapor wall mode (b/h-ftl)  ---- -------- --------- ---- ------- ------- ------- ------- ------- -------  24 162.72 .0000E+00 521.00 .00 .00 521.00 .0000E+00  23 * 159.29 .0000E+00 521.00 .00 .00 521.00 .0000E+00  22 * 152.44 .0000E+00 521.00 .00 .00 521.00 .0000E+00  21 * 145.59 .0000E+00 521.00 .00 .00 521.00 .0000E+00  20 * 138.74 .0000E+00 521.00 .00 .00 521.00 .0000E+00  19 * 131.89 .0000E+00 521.00 .00 .00 521.00 .0000E+00  18 * 125.04 .0000E+00 521.00 .00 .00 521.00 .0000E+00  17 * 118.19 .0000E+00 521.00 .00 .00 521.00 .0000E+00  16 * 111.34 .0000E+00 521.00 .00 .00 521.00 .0000E+00  15 * 104.49 .0000E+00 521.00 .00 .00 521.00 .0000E+00  14 * 97.64 .0000E+00 521.00 .00 .00 521.00 .0000E+00  13 * 90.79 .0000E+00 521.00 .00 .00 521.00 .0000E+00  12 * 83.94 .0000E+00 521.00 .00 .00 521.00 .0000E+00  11 * 77.09 .0000E+00 521.00 .00 .00 521.00 .0000E+00  10 * 70.24 .0000E+00 521.00 .00 .00 521.00 .0000E+00  9 * 63.39 .0000E+00 521.00 .00 .00 521.00 .0000E+00  8 * 56.54 .0000E+00 521.00 .00 .00 521.00 .0000E+00  7 * 49.69 .0000E+00 521.00 .00 .00 521.00 .0000E+00  6 * 42.84 .0000E+00 521.00 .00 .00 521.00 .0000E+00  5 * 35.56 .0000E+00 521.00 .00 .00 521.00 .0000E+00  4 * 27.84 .0000E+00 521.00 .00 .00 521.00 .0000E+00  3 * 20.12 .0000E+00 521.00 .00 .00 521.00 .0000E+00  2 * 15.01 .0000E+00 521.00 .00 .00 521.00 .0000E+00  1 13.75 .0000E+00 521.00 .00 .00 521.00 .0000E+00  ********************************************************************************************************************************1 heat slab results date 1998 0803 time 00:0 0:00    Test 31504 Bundle Rod 7x7 ** **  ********************************************************************************************************************************
D-35

 heat slab no. 1 (wall) simulation time = .00 seconds  fluid channel on inside surface = 4  fluid channel on outside surface = 0  geometry type = 3 

no. of nodes = 3 

 ******************************************************************************************************************************** rod axial *---------------- outside surface ----------------* *---------------- inside surface ----------------*  node location heat flux h.t. **** temperatures (deg-f)   ** ** temperatures (deg-f)   h.t. heat flux 

 no. (in.) (b/h-ft2) mode wall vapor liquid liquid vapor wall mode (b/h-ftl)  ---- -------- --------- ---- ------- ------- ------- ------- ------- -------  23 159.29 .0000E+00 521.00 .00 .00 521.00 .0000E+00  22 152.44 .0000E+00 521.00 .00 .00 521.00 .0000E+00  21 145.59 .0000E+00 521.00 .00 .00 521.00 .0000E+00  20 138.74 .0000E+00 521.00 .00 .00 521.00 .0000E+00  19 131.89 .0000E+00 521.00 .00 .00 521.00 .0000E+00  18 125.04 .0000E+00 521.00 .00 .00 521.00 .0000E+00  17 118.19 .0000E+00 521.00 .00 .00 521.00 .0000E+00  16 111.34 .0000E+00 521.00 .00 .00 521.00 .0000E+00  15 104.49 .0000E+00 521.00 .00 .00 521.00 .0000E+00  14 97.64 .0000E+00 521.00 .00 .00 521.00 .0000E+00  13 90.79 .0000E+00 521.00 .00 .00 521.00 .0000E+00  12 83.94 .0000E+00 521.00 .00 .00 521.00 .0000E+00  11 77.09 .0000E+00 521.00 .00 .00 521.00 .0000E+00  10 70.24 .0000E+00 521.00 .00 .00 521.00 .0000E+00  9 63.39 .0000E+00 521.00 .00 .00 521.00 .0000E+00  8 56.54 .0000E+00 521.00 .00 .00 521.00 .0000E+00  7 49.69 .0000E+00 521.00 .00 .00 521.00 .0000E+00  6 42.84 .0000E+00 521.00 .00 .00 521.00 .0000E+00  5 35.56 .0000E+00 521.00 .00 .00 521.00 .0000E+00  4 27.84 .0000E+00 521.00 .00 .00 521.00 .0000E+00  3 20.12 .0000E+00 521.00 .00 .00 521.00 .0000E+00  2 15.01 .0000E+00 521.00 .00 .00 521.00 .0000E+00  ** ******************************************************************************************************************************
D-36

1 lateral drift results date 1998 0803 time 00:0 0:00  case 0   Test 31504 Bundle Rod 7x7 ** **  ******************************************************************************************************************************** simulation time = .00000 seconds summary for gap 1 connecting channel 3 to channel 4  --- axial --- -------- crossflows -------- ------------ velocities ------------ pressure void fraction flow  range (lb/sec) diff. area  (in.) liquid vapor entrained liquid vapor entrained pii-pjj ii jj  13.8- 16.3 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .034  16.3- 24.0 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .105  24.0- 31.7 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .105  31.7- 39.4 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .105  39.4- 46.3 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  46.3- 53.1 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  53.1- 60.0 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  60.0- 66.8 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  66.8- 73.7 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  73.7- 80.5 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  80.5- 87.4 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  87.4- 94.2 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  94.2-101.1 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  101.1-107.9 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  107.9-114.8 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  114.8-121.6 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  121.6-128.5 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  128.5-135.3 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  135.3-142.2 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  142.2-149.0 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  149.0-155.9 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093  155.9-162.7 .00 .00 .00 .00 .00 .00 .000 1.0000 1.0000 .093 1 injection boundary conditions date 1998 0803 time 00:0 0:00  case 0   Test 31504 Bundle Rod 7x7 ** **  ******************************************************************************************************************************** simulation time = .00000 seconds 
D-37

 channel node wginjt wlinjt hginjt hlinjt  no. no. lbm/sec lbm/sec btu/lbm btu/lbm  *************************************************************************  * new time domain reached *  * minimum maximum time long short graphics dump *  * time time domain edit edit edit *  * step step end interval interval interval interval *  * *  * 2.000E-04 1.500E-02 5.000E+02 5.000E+00 8.000E+02 1.000E+00 8.000E+02 *  *************************************************************************  time step ratio = 1.000E+00  * * * * * saved graphics data at time .0000 * * * * * * * * * * *  * * * * * saved graphics data at time .9868 * * * * * * * * * * *  * * * * * saved graphics data at time 1.9918 * * * * * * * * * * *  * * * * * saved graphics data at time 2.9968 * * * * * * * * * * *  * * * * * saved graphics data at time 4.0018 * * * * * * * * * * * 
D-38

APPENDIX D3. SUB-CHANNEL MODEL INPUT DECK 

 0 

 0 0.0 

 .001 5 40 

 1 ****** Sub-Channel Model of RBHT 7x7 Bundle ****** 

 1 1 

 40.0 1169.77 0.0 .46667 124. 0.0 .9999 1.0 

air .0001 

 2 18 

 1.0681.5875 0.0 0.0 1 

 23 1 0 

 2.13621.175 0.0 0.0 3 

 23 1 0 23 2 0 23 3 0 

 3.0681.5875 0.0 0.0 2 

 23 2 0 23 4 0 

 4.13621.175 0.0 0.0 3 

 23 3 0 23 5 0 23 7 0 

 5.13621.175 0.0 0.0 4 

 23 4 0 23 5 0 23 6 0 23 8 0 

 6.0681.5875 0.0 0.0 2 

 23 6 0 23 9 0 

 7.08741.083 0.0 0.0 2 

 23 7 0 23 10 0 

 8.08741.083 0.0 0.0 3 

 23 8 0 23 10 0 23 11 0 

 9.08741.083 0.0 0.0 3 

 23 9 0 23 11 0 23 12 0 

 10.0275.4339 0.0 0.0 1 

 23 12 0 

 11.4920 1.01 0.0 0.0 1 

 3 13 0 

 12.6150 1.01 0.0 0.0 2 

 3 13 0 3 14 0 

 13.50941.775 0.0 0.0 1 

 3 14 0 

 14.27242.350 0.0 0.0 2 

 3 15 3 3 15 4 

 15.34052.938 0.0 0.0 5 

 3 15 3 3 15 4 3 16 7 3 16 8 3 16 9 

 16.28973.683 0.0 0.0 3 

 3 16 7 3 16 8 3 16 9 

 175.60710.69 0.0.9026 2 

 3 0 15 3 0 16 

 186.2803.5001.616 0.0 0 

 3 16 

 1 1 20.1220.496 0.5 0.0 0 0 1.0 1 3 

 1. 0.0 

 2 2 30.1220.496 0.5 0.0 0 0 1.0 0 4 

 1. 0.0 

 3 2 40.1220.496 0.5 0.0 0 0 1.0 1 7 

 1. 0.0 

 4 3 50.1220.496 0.5 0.0 0 0 1.0 2 8 
D-39

 1. 0.0 

 5 4 50.1220.496 0.5 0.0 0 0 1.0 0 6 

 1. 0.0 

 6 5 60.1220.496 0.5 0.0 0 0 1.0 5 9 

 1. 0.0 

 7 4 70.122.3915 0.5 0.0 0 0 1.0 3 -1 

 1. 0.0 

 8 5 80.122.3915 0.5 0.0 0 0 1.0 4 -1 

 1. 0.0 

 9 6 90.122.3915 0.5 0.0 0 0 1.0 6 -1 

 1. 0.0 

 10 7 80.1000.496 0.5 0.5 0 0 1.0 0 11 

 1. 0.0 

 11 8 90.1000.496 0.5 0.5 0 0 1.0 10 12 

 1. 0.0 

 12 9 100.100.3915 0.5 0.5 0 0 1.0 11 -1 

 1. 0.0 

 13 11 120.9920.744 0.0 0.0 0 0 1.0 0 14 

 1. 0.0 

 14 12 131.4880.496 0.0 0.0 0 0 1.0 13 0 

 1. 0.0 

 15 14 150.1220.744 0.5 0.0 0 0 1.0 0 16 

 2. 0.0 

 16 15 160.1220.496 0.5 0.0 0 0 1.0 15 0 

 3. 0.0 

 18 

 1 2 1 2 2 1 2 4 3 3 5 2 

 4 5 2 4 6 4 5 4 3 5 8 7 

 6 6 4 6 9 8 7 10 5 8 10 5 

 8 11 6 9 11 6 9 12 9 10 8 7 

 11 9 8 12 12 9 

 4 5 1 0 

 1 1 2 4.0 

 17 14 15 16 17 

 2 3 2 2.875 

 14 1 2 3 17 

 15 4 5 6 17 

 16 7 8 9 10 17 

 3 10 22 2.51 5 

 2 2.51 3 7.72 5 7.72 6 6.85 23 6.85 

 1 11 14 

 2 11 14 

 3 11 14 

 4 12 15 

 5 12 15 

 6 12 15 

 7 13 16 

 8 13 16 

 9 13 16 

 10 13 16 

 4 3 2 4.0 

 11 18 1 2 3 

 12 18 4 5 6 

 13 18 7 8 9 10 

 5 1 1 4.0 
D-40

 18 18 11 12 13 

 18 

 235 

 7 8 1 1 1 1 1 0 0 0 

 1.2 2 1 2 3 4 5 6 7 8 9 10 

 1.2 5 1 2 3 4 5 6 7 8 9 10 

 1.2 8 1 2 3 4 5 6 7 8 9 10 

 1.2 11 1 2 3 4 5 6 7 8 9 10 

 1.2 14 1 2 3 4 5 6 7 8 9 10 

 1.2 17 1 2 3 4 5 6 7 8 9 10 

 1.2 20 1 2 3 4 5 6 7 8 9 10 

 1.2 23 1 2 3 4 5 6 7 8 9 10 

 1 8 10 1 1.4 .2952 1.5 1.984 

 2 5 8 11 14 17 20 23 

 1 0.5 1 1 2 1 3 1 

 2 1.0 2 2 3 2 4 1 5 1 

 3 0.5 3 3 5 2 6 1 

 4 1.0 4 2 5 4 7 1 8 1 

 5 1.0 5 3 6 2 8 2 9 1 

 6 0.5 6 3 9 2 10 1 

 7 0.75 7 2 8 4 

 8 0.75 8 3 9 4 

 9 0.75 9 3 10 2 

 10 0.50 10 3 

 8 10 4 3 3 10 6 31 1 

 1 1 1 2 0.05 1. 1.0 0. 1 0. 

 1 .125 

 2 1 1 2 0.05 1. 1.0 0. 1 0. 

 1 .25 2 .25 

 3 1 1 2 0.05 1. 1.0 0. 1 0. 

 1 .125 2 .25 3 .125 

 4 1 1 2 0.05 1. 1.0 0. 1 0. 

 2 .25 4 .25 

 5 1 1 2 0.05 1. 1.0 0. 1 0. 

 2 .25 3 .25 5 .25 4 .25 

 6 1 1 2 0.05 1. 1.0 0. 1 0. 

 3 .125 5 .25 6 .125 

 7 1 1 2 0.05 1. 1.0 0. 1 0. 

 4 .25 7 .25 

 8 1 1 2 0.05 1. 1.0 0. 1 0. 

 4 .25 5 .25 8 .25 7 .25 

 9 1 1 2 0.05 1. 1.0 0. 1 0. 

 5 .25 6 .25 9 .25 8 .25 

 10 2 0 2 0.05 1. 0.0 0. 1 0. 

 6 .125 9 .25 10 .125 

 1 3 0.496 0.496 1.0 7 0. 90.0 

 2 3 0.496 0.496 1.0 8 0. 90.0 

 3 3 0.496 0.496 1.0 9 0. 90.0 

 4 3 0.537 0.287 1.0 10 0. 90.0 

 1 9 0 4 

 1 2 3 4 5 6 7 8 9 

 13.75 822.0 121.75 1600. 157.75 858.0 168.76 858.0 

 2 1 0 4 

 10 

 13.75 372.0 121.75 645.0 157.75 383.0 168.76 383.0 
D-41

 3 0 4 4 

 -1 -2 -3 -4 

 13.75 322.0 121.75 482.0 157.75 327.0 168.76 327.0 

 1 1 -1 20 0 1.0 1.0 1.0 1.0 1.0 

 1 2 4 2 1 2 4 2 1 2 4 2 3 5 9 7 

 3 7 9 5 

 2 2 -1 20 0 1.0 1.0 1.0 1.0 1.0 

 3 5 9 7 2 1 2 4 3 7 9 5 8 12 18 16 

 6 10 13 10 

 3 3 -1 20 0 1.0 1.0 1.0 1.0 1.0 

 6 10 13 10 5 3 7 9 5 9 7 3 11 14 22 19 

 11 19 22 14 

 4 4 2 19 0 1.0 1.0 1.0 1.0 1.0 

 8 12 18 16 7 3 5 9 8 16 18 12 17 21 -1 11 

 14 22 19 

 5 5 2 19 0 1.0 1.0 1.0 1.0 1.0 

 11 14 22 19 10 6 10 13 12 18 16 8 20 25 -2 15 

 23 26 23 

 6 6 3 18 0 1.0 1.0 1.0 1.0 1.0 

 15 23 26 23 14 11 19 22 14 22 19 11 24 27 -3 24 

 -3 27 

 7 7 4 13 0 1.0 1.0 1.0 1.0 1.0 

 17 21 -1 16 8 12 18 17 -1 21 20 25 -2 

 8 8 4 13 0 1.0 1.0 1.0 1.0 1.0 

 20 25 -2 19 11 14 22 21 -1 17 24 27 -3 

 9 9 5 12 0 1.0 1.0 1.0 1.0 1.0 

 24 27 -3 23 15 23 26 25 -2 20 28 -4 

 10 10 6 8 0 1.0 1.0 1.0 1.0 1.0 

 28 -4 27 24 -3 27 -3 24 

 -1 

 .374 .8 .374 .496 

 -2 

 .374 .8 .100 .496 0.0 0.0 .8 .374 

 -3 

 .374 .8 .100 .496 0.0 0.0 .8 .374 

 -4 

 .374 .8 .100 .496 0.0 .248 .8 .374 

 -5 

 .374 .8 .100 .496 0.0 .248 .8 .374 

 -6 

 .374 .8 .100 .496 0.0 .248 .8 .374 
D-42

 9 3 

 1 hrod .374 0.0 4 0 

 1 2.0675 0.0 1 3 .045 1.0 3 2.0465 0.0 3 1.0280 0.0 

 2 tube .375 .209 1 0 

 3 1 .083 0.0 

 3 wall .496 .250 1 0 0 

 3 1 .250 

 10 3 

 1 12 528.8 Inco 

 212. .111 9.09 392. .121 10.04 

 572. .131 10.98 752. .141 11.93 

 932. .151 12.88 1112. .166 13.82 

 1292. .178 14.77 1472. .191 15.72 

 1652. .204 16.66 1832. .216 17.61 

 2012. .229 18.56 2192 .241 19.50 

 2 14 119.2 BN 

 212. .16587 67.37 392. .22015 63.87 

 572. .26264 60.28 752. .29590 56.74 

 932. .32194 53.19 1112. .34233 49.65 

 1292. .35829 46.10 1472. .37078 42.56 

 1652. .38057 39.01 1832. .38822 35.47 

 2012. .39421 31.92 2192. .39891 28.37 

 2372. .40259 24.83 2552. .40546 21.28 

 3 10 528.8 Mon 

 70. .100 10.083 200. .107 11.333 

 400. .114 13.000 600. .117 14.833 

 800. .120 16.500 1000. .125 18.333 

 1200. .132 20.000 1400. .141 21.833 

 1600. .157 23.500 1800. .186 25.167 

 11 1 25 

 1 4 

 13.75 .5 121.75 1.5 157.75 .5 157.76 0.0 

 0.0 1. 17.5 .921 35.0 .8704 52.5 .8326 

 70. .803 87.5 .7755 105.0 .7512 122.5 .7302 

 140. .714 157.5 .6973 175.0 .6837 192.5 .6710 

 220. .652 255.0 .6332 290.0 .6167 325.0 .6017 

 360. .588 395.0 .5769 430.0 .5656 465.0 .5562 

 500. .547 535.0 .5444 570.0 .5304 605.0 .5243 

 1000. .002 

 13 2 0 1 0 0 

 3 3 

 0.0 0.0 0.1 1.01500. 1.0 

 17 1 2 1 0 .0321610 95.3047 40.0 

 124. 1.0.9999.0001 

 18 4 1 0 0 40. 1169.7685 40.0 

 124. 1.0.9999.0001 

 14 5 0 0 0 0 0 0 

 0 

 0 

 300 0 0 

 .00001 .00110 0.2 1.0 99000.0 
D-43

 .19 50.0 100.0 50.0 0 

 .00001 .00200 50.0 1.0 99000.0 

 25.0 50.0 100.0 5.0 0 

 -.00001 .00100 300.0 1.0 99000.0 

 5.0 5.0 100.0 5.0 0 

 -.001 
D-44