NUREG/IA-0236 

 International 

 Agreement Report

 

Analysis and Computational Predictions of 

CHF Position and Post-CHF Heat Transfer 

Prepared by: 

B. Belhouachi, S.P. Walker, G.F. Hewitt 

Nuclear Research Group 

Mechanical Engineering Department 

Imperial College 

London SW7 2BX 

UK 

 

A. Calvo, NRC Project Manager 

Office of Nuclear Regulatory Research 

U.S. Nuclear Regulatory Commission 

Washington, DC 20555-0001 

May 2010 

 

Prepared as part of 

The Agreement on Research Participation and Technical Exchange 

Under the Thermal-Hydraulic Code Applications and Maintenance Program (CAMP) 

Published by 

U.S. Nuclear Regulatory Commission
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iii 

ABSTRACT

The objective of the current study is to investigate the capability of the US NRC TRACE code to 

predict the Critical Heat Flux (CHF) position and temperature profiles for different axial heat flux 

distributions in the reflooding of a hot single tube. Measurements of each of Bennett, Keeys and 

Becker were used for this. 

Hydrodynamic and post-dryout heat transfer calculations were performed using TRACE Code. 

CHF and critical quality correlations (based on the ‘look-up’ tables of Groeneveld, the ‘local 

conditions’ hypothesis, and the boiling length/quality relationship) are usually implemented in 

system codes. Each of these has been used to analyze the experiments. These simulations 

showed that generally the CHF position was well predicted whereas the estimation of the wall 

temperature was not correct for particular ranges of mass and heat fluxes. This is investigated 

and possible causes, associated with ‘local conditions’ issues, are proposed. 
iv 
v 

FOREWORD

This document reports an investigation of the US NRC TRACE code in regards to the prediction 

of the Critical Heat Flux (CHF) position and temperature profiles for different axial heat flux 

distributions in the reflooding of a hot single tube. 

We outline strengths and deficiencies of the reflood module of the TRACE system code. In fact, 

we perform a simulation for a single tube where initial and boundary conditions are in the range 

of Large Break Loss-of-Coolant-Accident conditions. 

Conclusions imply a better modeling of the reflooding for both tubes, and by extension for rod 

bundles. 
vi 
vii 

CONTENTS

Page

Abstract ....................................................................................................................................... iii 

Foreword...................................................................................................................................... v 

List of Figures ........................................................................................................................... viii 

Executive Summary ................................................................................................................... ix 

Acknowledgement ...................................................................................................................... x 

Abbreviations ............................................................................................................................. xi 

1. Introduction ........................................................................................................................ 1-1 

2. Critical heat flux and post dryout heat transfer .............................................................. 2-1 

2.1 Critical Heat Flux (CHF) Prediction Methods .............................................................. 2-1 

2.2 Dispersed Flow Film Boiling (DFFB) .......................................................................... 2-2 

2.3 Experiments ................................................................................................................ 2-4 

3. Simulations ......................................................................................................................... 3-1 

3.1 TRACE ........................................................................................................................ 3-1 

3.2 Nodalization and Fine Mesh Technique ...................................................................... 3-1 

3.3 Simulations, results and comparisons ......................................................................... 3-2 

4. Conclusions .................................................................................................................. 4-1 

5. References .................................................................................................................... 5-1 
viii 

LIST OF FIGURES

Page

Fig. 1 Nodalization study ....................................................................................................... 3-1 

Fig. 2 CHF position and temperature predictions for a uniform heat flux ........................ 3-3 

Fig. 3 CHF position and temperature predictions for a non-uniform heat flux ................ 3-3 

Fig. 4 Effect of pressure on dryout position........................................................................ 3-4 

Fig. 5 Dryout position and temperature profiles ................................................................. 3-5 

Fig. 6 Comparison between calculated and experimental temperature profiles ............. 3-5 

Fig. 7 Effect of wall friction factor on temperature distribution ........................................ 3-6 

Fig. 8 Influence of the droplet drag on the temperature profile prediction ...................... 3-7 

Fig. 9 Comparison of different heat transfer correlations.................................................. 3-7 

Fig. 10 Assessment of a proposed model ............................................................................. 3-9 
ix 

EXECUTIVE SUMMARY

The analysis and the assessment of the TRACE codes demonstrate its ability to well predict the 

point of critical heat flux reasonably well. However, the temperature profile, and thus, the peak 

clad temperature, is not well predicted for the case of a non-uniform heat flux. For the case of 

uniform heat flux distributions, the combination of the so-called ‘Look-Up Tables’ and the Biasi 

critical quality provides results that match well with the Bennett experimental data. This is not 

true at high mass and heat fluxes. 

The study of the DFFB models usually implemented in thermal-hydraulics system code such as 

TRACE established the crucial character of the interfacial heat transfer. A key point would be to 

study the variations of the heat transfer coefficient and its sensitiveness to both the mentioned 

correlations and the interfacial area concentration (which has not been treated in this paper for 

simplicity). The droplet drag did not play an important role in the calculations performed here. 

The two-phase enhancement factor applied in the wall heat transfer correlation, namely, the 

Gnielinski correlation, had a little influence on the temperature predicted for the experiments 

simulated. The droplet diameter and the number density are important in the prediction of both 

the position of dryout and the temperature profile upstream from the quench front (precursory 

cooling effects). 
x 

ACKNOWLEDGEMENT 

The authors would like to acknowledge EPSRC for the funding under grant EP/C549465/1, the 

UK - HSE and the US NRC for making available the TRACE code. 
ABBREVIATIONS

AECL Atomic Energy of Canada Limited, Canada 

AFD Axial-heat Flux Distribution 

CHF Critical Heat Flux 

DFFB Dispersed Flow Film Boiling 

IPPE Institute of Power and Physics, Obninsk-Russia 

LWR Light Water Reactor 

NRC Nuclear Regulatory Commission, USA 

PCT Peak Clad Temperature 

NOMENCLATURE 

B 

cp 

CD

D 

DH 

F 

g 

G 

Gr 

k 

K 

LB 

Nu 

P 

Pr 

q′′

Re 

T 

V 

x 

Nomenclature 

Blowing factor 

Specific heat (J/kg-K) 

Drag coefficient 

Diameter 

Hydraulic diameter (m) 

Friction factor 

Gravitational acceleration (m/s2

) 

Mass flux (kg/m2-s) 

Grashof no. 

Conductivity 

Dummy factor 

Boiling Length (m) 

Nusselt no. 

Pressure (Pa) 

Prandt no. 

Heat flux (W/m3) 

Reynolds no. 

Temperature 

Velocity (m/s) 

Quality 

α

β

μ

ρ

Ψ2Φ

CHF

conv 

d 

FC 

g 

l 

lam 

rad 

sat 

turb 

v 

w 

Greek symbols 

Void fraction 

Exponent 

Viscosity 

density 

Two-Phase enhancement factor 

Subscripts 

Related to CHF 

Related to convection 

Related to droplet 

Related to forced convection 

Related to gas 

Related to liquid 

Related to laminar flow 

Related to radiation 

Related to saturation 

Related to turbulent flow 

Related to vapour 

Related to wall 

xi 
1-1 

1. INTRODUCTION

The integrity of the cladding of the nuclear fuel of Light Water Reactors (LWR) as first 

containment barrier is of high importance in nuclear safety. The cladding is intended to operate 

with a temperature less than 2200°F (~1477°K) to avoid both oxidation and radial expansion. 

The situations for which such a temperature can be reached are numerous. A typical description 

is the presence of a blanket of vapour surrounding the pin inducing a very sharp decrease in 

heat transfer and consequent temperature increase. 

While the design intent is generally to avoid this condition, predicting the Peak Clad 

Temperature (PCT) is important. Geometric factors and operating parameters (pressure, power 

profiles, mass flow rates, inlet sub-cooling to name a few) affecting the Critical Heat Flux (CHF), 

the maximum heat flux applied to a solid surface for which unstable vapour patches appear, 

have been investigated in the past [1-3] and resulted in many correlations. 

Hence, it has become increasingly difficult to select the correct CHF prediction methods that 

can be used for a variety of conditions and geometries. Additionally, a lack of knowledge of the 

undergoing heat transfer regimes encountered in the post-CHF region has limited the 

development of theoretical models. 

This present work intends to first provide a study of the main correlations implemented in 

system codes, (such as the 1995 Groeneveld look-up table [1], the Biasi and CISE-GE 

correlations). A focus will be on the quench front (CHF location with a wall superheat of about 

200°K [2]) and the temperature profiles in the Dispersed Flow Film Boiling (DFFB) region. The 

computer code used as a basis for these simulations is the thermal-hydraulics system code 

TRACE, developed by the US NRC. A feature of the TRACE code, the fine mesh technique, 

was used in order to gain in accuracy; we will investigate this issue. 

Along these same lines, the above-mentioned CHF prediction methods will be assessed in the 

case of uniform and cosine axial-heat flux distributions (AFD) for a range of pressures and mass 

fluxes in tubes. 

In a second part, we will discuss the modelling of the post-CHF heat transfer and the sensitivity 

of the code to the different correlations accounting for the interfacial droplet drag, the interfacial 

heat transfer and the wall heat transfer. 

Finally, we have performed some calculations with a selected set of post-dryout heat transfer 

correlations where a ‘Blowing’ factor accounting for the effect of the mass transfer upon the heat 

transfer was added to the interfacial droplet drag and the interfacial heat transfer. A two-phase 

enhancement factor, which represents the enhancement of the convective heat transfer in the 

expression of the wall-to-gas heat flux due to the presence of the dispersed droplets in the 

superheated vapour flow, is commonly implemented and tuned in system codes to fit data. In 

here, we will conserve its original form and study its influence on the de-superheating of the 

vapour phase. 
2-1

2. Critical Heat Flux and Post Dryout Heat Transfer 

2.1 Critical Heat Flux (CHF) prediction methods

As noted, the critical heat flux (CHF) is the heat flux for which a heated surface becomes 

vapour-blanketed with increasing heat flux inputs. The vapour patches/blanket resulting from 

this excess in heat flux leads to a deterioration of the convective heat transfer exchanges 

between the wall and the coolant. The superheat beyond the CHF point could significantly be of 

the order of 600°K. 

In general, three approaches are adopted in the prediction of the CHF: 

• The 1995 AECL1

-IPPE2 “look-up” tables [1], 

• Flux-quality relationships, and 

• Boiling length/quality relationships. 

The differences between the two latter relationships are reported in [3]. 

It is usually accepted that the Groeneveld look-up tables comply with the margin requirements 

imposed by both nuclear regulatory bodies and energy producers. However, the main 

assumption is that CHF can be determined on local conditions basis, i.e.: 

q K fn P G x D &CHF ′′ = ⋅ { , ,, H } (1) 

where is the critical heat flux, K is a product of factors accounting for the geometry, low 

flow conditions etc. P is the pressure, G the mass flux, x the quality and 

CHF q&′′

DH is the hydraulic 

diameter. From Eq. (1), it could be understood that the Groeneveld et al. tables [1] imply a 

specific relationship between CHF and local quality for a given mass flux and pressure. 

Nevertheless, the relationship between heat flux ( CHF q&′′ ) and quality (x) is not a universal one 

and this is amply proved by data for non-uniform heat flux, exemplified by some Refrigerant-114 

data from Shiralkar [4]. 

The two other approaches, namely the F-factor and the boiling length approaches, allow better 

results to be obtained. 

The F-factor method developed by Tong et al. [5] takes into account the influence of the nonuniformity of the heat flux upon the prediction of the CHF. The so-called F-factor is defined at a 

given enthalpy as the ratio of a uniform heat flux (CHF) to the non-uniform CHF. As this 

approach assumes the importance of the effect of the upstream heat flux profile on the local 

CHF, it has to be noted that at low qualities, the ‘memory effect’ is small, and thus the CHF is 

conditioned by the local heat flux. At high qualities, this same ‘memory effect’ is sizeable and 

the average heat flux fixes the CHF position. 

On the other hand, the boiling length/ critical quality ( CHF x ) relationship introduced by Bertoletti 

et al. [6] is expressed as: 

B

CHF i

B

A L x K

B L

⋅ = +

 (2) 

where is the boiling length, i.e. the distance from which the fluid reaches saturation, x=0; Ki

is a factor accounting for the radial peaking factor and, in the case of the Biasi correlation, 

LB

 

1 AECL: Atomic Energy of Canada Limited. 

2 IPPE: Institute of Power and Physics, Obninsk, Russia. 
2-2

accounting for the ratio between the heated perimeter to the wetted perimeter. ‘A’ and ‘B’ are 

two system-dependent functions, i.e.: A = fn P G { , } and B = fn P G D { , , H }. 

 

In the TRACE code, the CHF position is essentially determined by the 1995 look-up tables 

(notwithstanding the non-physical nature of the local condition hypothesis). The reason is that 

the overall average and the RMS errors associated with the adoption of this approach are 

0.38% and 8.17% respectively, which in practice, is difficult to better. In addition to this 

prediction method, the user can combine the prediction of the CHF with the CISE-GE [7] or 

Biasi [8] critical quality correlation. The critical quality value is only used as a transition criterion 

from pre to post-CHF while the CHF point ( CHF q&′′ TCH , ) remains determined by the Groeneveld 

et al. tables [9]. No attempt was made to modify the determination of the CHF point by other 

means than the look-up tables. 

F

In part 2, we present results of the effect of the different correlations described above on the 

temperature distribution. 

2.2 Dispersed Flow Film Boiling (DFFB)

The regimes present in the post-CHF region are the inverted annular flow and/or the dispersed 

flow film boiling (dispersed droplet mixture in a superheated continuous vapour phase). Here we 

discuss only the latter given the high void fractions α ≥ 0.80

,

 encountered above the dryout 

location. The modelling of DFFB heat transfer is, in computer codes, a three step process: wallvapour heat transfer, vapour-drop convection, and wall to drop heat transfer. 

2.2.1 Wall heat transfer 

The wall heat transfer is a combination of forced convection to the superheated vapour and 

thermal radiation to the liquid droplets. 

Therefore, the heat flux is expressed as follow: 

DFFB wg FC wg rad , , qqq ′′ ′′ ′′ wl rad wd = + + q q ′′ ′′ + (3) 

The wall temperature is often greater than the Leidenfrost temperature, the droplet-to-wall3

contact could be considered by an enhanced Forslund-Rohsenow correlation at high vapour 

Reynolds no. ( 4000 ): Rev ≥

0.25

0.6 2/3 0.00638( 4000) (1 ) ( )

v fg d v

dw v

w d gd

kh g h Re

TT D

ρ ρ

α

μ

⎡ ⎤ = −− ⎢ ⎥ ⎢⎣ − ⎥⎦

 (4) 

The convective wall-to-gas heat transfer ( wg FC , q′′ ) is usually calculated by making the key 

assumption that the heat transfer is similar to single-phase forced convection heat transfer. A 

correction factor ( ), which accounts for the two-phase heat transfer exchanges 

enhancement due to the presence of the dispersed droplets in the continuous vapour phase, is 

added to the Gnielinski

Ψ2Φ

4

 correlation [10]: 

 

3 In highly turbulent flows (and at high pressure), the droplet radial velocity increases, therefore, droplets-wall 

interactions should not be neglected since they participate to the rewetting hot walls. 

4 At the moderate Reynolds nos. entrance length effects can enhance the wall heat transfer but are neglected in this 

present study. 
2-3

, , 2 ( g

wg FC wg FC w l

H

k

q Nu T D Φ ′′ = ⋅ ⋅Ψ ⋅ −T ) (5) 

where: 

,

1/2 2/3

4,36

( 2)( 1000)

1 12.7 ( 2) ( 1)

lam

wg FC

turb

Nu

Nu f Re Pr Nu

f Pr

⎧ = ⎪ = ⎨ − ⋅ = ⎪

⎩ +⋅ ⋅ −

 (6) 

In Eq. (6) f is a friction factor, and: 

1/2

2 2

(1 ) 1

2

H

w gg

g D

f V

α ρ

ρ

Φ

⎡ − ⋅ ⋅Δ ⋅ ⎤

Ψ=+ ⎢ ⎥ ⋅⋅⋅ ⎢⎣ ⎥⎦

 (7) 

wf is the wall friction factor and Vg is the gas velocity. 

In general, the axial gradient of vapour superheat first increases and then, due to the precursory 

cooling effects, decreases with increasing axial distance downstream from the quench front. 

The effect of heat transfer on the vaporization of the liquid phase could be caused by either heat 

transfer from the superheated vapour to the entrained liquid or from heat transfer from the 

superheated wall to the liquid. 

Hence, the interfacial heat transfer between the vapour phase and the droplet mixture plays a 

key role in determining the maximum superheat of the vapour, which in turn limits the Peak Clad 

Temperature (PCT). We will discuss this point in the next section. 

2.2.2 Drop drag and interfacial heat transfer 

The modelling of the dispersed phase requires a particular attention in regard to the interfacial 

droplet drag and the interfacial heat transfer. A critique of the key assumptions in the modelling 

of DFFB regimes in multiphase flow system codes can be found in [11]. 

We will only mention the assumptions relevant to our analysis. 

First, for the calculation of both interfacial drag and heat transfer, it is assumed that the cloud of 

droplets of a range of sizes can be represented by a single representative5

 spherical (justified 

by small Eotvos no.) droplet with the same area to volume ratio as that of the entire population. 

The physical mechanisms that affect the droplet size distribution (impingement on the wall, 

evaporation, break-up, coalescence) are ignored. The droplet size is taken to depend only on 

local conditions, namely relative velocity and fluid properties and is calculated from the local 

critical Weber no. Thus, the number density of droplets generated at the locus of CHF varies in 

the computational domain whereas this transport of the droplet population should be historydependent and consistent. 

Droplet-to-droplet interactions are incorporated through empirical approximations. In TRACE, for 

example, this is accomplished through the evaluation of an empirical correlation based on the 

local flow conditions and is calculated using the correlation of Kataoka, Ishii and Mishima [12]. 

In some other computer codes, the recent trend of multi-field modelling intends to solve this 

problem [13]. 

Moreover, since the droplets are mainly generated at the quench front where the fluid properties 

are at saturation, the droplet temperature is expected to be at saturation (no 

 

5 This representation is limited, in fact, a same volume may produce different interfacial.
2-4

v

v

conduction/convection inside the drop). Only heat transfer exchanges on the vapour side are 

considered. Then, the interfacial heat transfer coefficient could be based either on the Lee and 

Ryley correlation developed at atmospheric pressure: 

 (8) 1/2 1/3 2 0.74Re Pr Nud = +

Or on the correlation suggested by Ranz and Marshall [14]: 

 (9) 1/2 1/3 2 0.60Re Pr Nud = +

The drag coefficient is expressed as: 

24 0.75 (1 0.1 ) D

d

C

Re

= ⋅+ ⋅ R d e (10) 

Studies on the sensitivity of the temperature distribution to different drag coefficients and 

interfacial heat transfer correlations are presented in the results section. The main modification 

is the addition of the so-called ‘Blowing factor’ accounting for the effect of mass transfer upon 

heat transfer in the expressions of drag coefficient and Nusselt no. 

2.3 Experiments

From the experimental studies available in the literature, we have selected the Bennett et al. 

[15] data set for uniformly heated tube. To investigate the effect of the axial heat flux 

distribution, we use the Keeys et al. [16] tests for which a cosine heat flux distribution was 

applied to a tube. Thirdly, the Becker et al. [17] study on the post dryout heat transfer which, for 

instance, reveals the importance of pressure on the dryout location, has been modelled. 

The objective of the Bennett experiment was essentially to obtain a measure of the wall surface 

temperature in the region beyond the dryout point. The dryout ‘interface’ between the heated 

wall and the dry regions was investigated and has led to the demonstration of the nonequilibrium effects associated with developing flows in heated tubes. The variables reported 

were the mass flux, system pressure, wall heat flux, inlet sub-cooling and quality. Systematic 

experiments in a 12.6 mm internal diameter tube were conducted at the constant pressure of 

6.89MPa. At a given mass flow rate, the heat flux was varied by an increment of ~1%, and the 

axial temperature profiles measured. 

In another UKAEA study, Keeys et al. in 1971 examined the post-CHF heat transfer in a 3.66m 

long tube with a cosine heat flux distribution (with a form factor of 1.4). The data set are 

summarized in table 1. These two experiments demonstrated the dependency of the local 

critical heat flux on the axial heat flux distribution. In fact, at the same dryout quality, the CHFs 

of the non-uniformly heated tube were noticeably lower than those measured on the uniformly 

heated tubes. Hence the necessity of modelling the post dryout heat transfer in a non-uniform 

heated tube by taking into account the flow history, in other terms: the boiling length. 

Becker et al. [17] conducted at the Royal Institute of Technology (RIT) in Stockholm post dryout 

experiments where the wall temperatures were measured on a set of 7 m long electrically 

heated tubes with inner diameters of 10, 14.9 and 24.7 mm. The tube was cooled by upwards 

flow of water with mass fluxes from 500 to 3000 kg/m2-s. However, in this present work, the 

cases selected covered pressures ranging from 3 to 14MPa, heat fluxes from 400 to 

1060kW/m2

 and inlet sub-cooling from 8.5 to 12K. 

Table 1: Experimental data 

Year Experiment P (MPa) G (Kg/m2

s) D (mm) L (m) X Q (MW/m2 )
2-5

1967 Bennett 6.9 393-5235 12.6 5.56 - 0.35-1.84 

1972 Keeys 6.9 700-4100 12.7 3.66 0.15-0.95 0.8-1.5 

1983 Becker 3-20 500-3000 14.9 7.0 0.03-1.60 0.1-1.25 
3-1

3. Simulations 

3.1 TRACE (TRAC-RELAP Advance Computational Engine)

TRACE is a thermal-hydraulics computational modelling code for nuclear power systems 

developed by the US Nuclear Regulatory Commission (US-NRC). TRACE is a code designed to 

analyze reactor transients and accidents up to the point of fuel failure. The partial differential 

equations that describe the two-phase flow and heat transfer are solved using the finite volume 

numerical methods. The heat-transfer equations are evaluated using a semi-implicit timedifferencing technique while the Navier-Stokes equations in the spatial one-dimensional (1D) 

and three-dimensional (3D) components use, by default, a multi-step time-differencing 

procedure that allows the material Courant-limit condition to be exceeded. In this present paper, 

all results presented arise from one dimensional modelling. 

3.2 Nodalization and Fine Mesh Technique

Nodalization studies with shorter test section cells show that decreasing the length from 0.30 m 

to 0.10 m did not noticeably increase the accuracy in predictions as illustrated in figure 1. CHF 

and temperature profile predictions require correct numerical and physical models. The 

approach adopted by developers is to improve the numerical techniques implemented in twofluid codes such as TRACE in order to track both the variations of the void fraction (level 

tracking methods) and the thermal gradient at the quench front (fine mesh rezoning techniques) 

[9]. 

500

550

600

650

700

750

800

850

900

01234567

Temperature (K)

Elevation (m)

TRACE V5 w/o Fine Mesh

TRACE V5 w/ Fine Mesh

Data Bennett RUN 5353

500.00

600.00

700.00

800.00

900.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 Elevation (m)

Temperature (K)

20 Cells

25 Cells

30 Cells

35 Cells

40 Cells

28 Cells- Non uniform

Data Bennett Run 5353-92kW G=380kg/m2-s

Figure 1. Nodalization study for the Bennett run 5353, on the left, the case was run with the fine 

mesh technique activated. On the right, the nodalization shows that a number of 20 cells is 

sufficient. 

With a fine mesh technique, the axial resolution of the axial gradient involves the insertion of 

transitory nodes whenever the difference between adjacent nodes exceeds a heat transfer 

regime dependent value ΔTmax, usually of the order of 25°C. The figure 2-c, modelling the 

Bennett run 5358, shows indeed a good agreement, the predictions fit perfectly the data at low 

mass fluxes and low heat fluxes while using the Biasi correlation. The analysis of the output 

reveals that even though the last part of the graph tends to be similar, the heat transfer regimes 

are different: we encounter the DFFB in the run performed with the fine mesh technique and 

single phase vapour heat transfer in the other. 

A maximum number of 1000 transitory nodes and a minimum distance of 1 mm between two 

adjacent nodes were imposed. These criteria suggest that the technique is consistent with the 

space-averaging theory on which is based the two-fluid formulation [18]. In the selected data, 

the regimes are liquid and vapour single phase, nucleate boiling, transition boiling and DFFB. 

With a drop size lower than 1 mm, we are assuming that the fine mesh technique is suitable for 
3-2

DFFB. According to this preliminary study, most of runs were performed using this fine mesh 

technique, generally used in transient and quasi-steady reflood-like situations. 

However, those calculations failed to predict well the position of the CHF and the temperature 

profile in the dryout region; at this stage, one could question the validity of the physical models 

implemented in system codes. The precursory cooling effects (due to slugs and droplets 

generated at the quench front) could be important beyond the CHF; this phenomenon controls 

the wall temperature by essentially cooling down the superheated vapour. Recent work in this 

area has been carried out by Andreani and Yadigaroglu [19-21] and contributed to a better 

understanding of the physics involved in the post-dryout region. 

Also, the wall-droplet interactions could be significant, but they are usually not modelled. In fact, 

the wall temperature in the DFFB regime is often above the temperature at which a droplet will 

wet the wall (the Leidenfrost point). The recent strategy to tackle this physical problem is to 

implement a multi-field model [22, 23] and to have a better treatment of the interfacial area by 

solving the interfacial area transport equation [24-26] coupled to a macroscopic k −ε model 

[27]. 

3.3 Simulations, results and comparisons

The code assessment process is based on the comparison between the computed predictions 

and experimental data in order to validate individual physical models. In this paper, we are 

interested in the prediction of the critical heat flux position but also in the interfacial droplet drag, 

interfacial heat transfer and wall heat transfer in the post dryout region. In the following results, 

we have added when necessary a Blowing factor B to account for the evaporation process. In 

fact, the drag dependency on the mass efflux (evaporation or condensation) is real and proved. 

In TRACE, the model of Renksizbulut and Yuen [28] is attended to re-transcribe the effect of 

mass transfer upon heat transfer. 

3.3.1 CHF and critical quality correlations 

The determination of the CHF location is crucial and determines the extent of the temperature 

rise in the post-CHF region. As mentioned earlier, we used here the different options available 

in the TRACE code: 

• AECL-IPPE (Look-Up Tables), 

• AECL-IPPE with the Biasi critical quality correlation, 

• AECL-IPPE with the CISE-GE critical quality correlation. 

The latter was developed for rod-bundle geometries and is not expected to provide the best fit to 

data. Moreover, the correlation is adequate only for mass fluxes in the range: 300

(kg/m2

-s). On the contrary, the Biasi correlation developed for tubes is stated to be valid for 

mass fluxes in the range: 100 (kg/m2

-s); we recall here that the Biasi correlation 

was corrected to account for the conversion from ATA to Bar units [29]. Again, using the 

Bennett run 5359, the comparison (Figure 2-d) establishes that both the look-up table method 

and the Biasi critical quality predict satisfactorily the data. However, the simulation of a Keeys 

test at high power and high mass flux shows that none of the correlation predicts the dryout 

point. The CISE-GE correlation is the best prediction for this particular run despite the fact that it 

was primarily developed for rod bundle geometries. 

≤ ≤ G 1400

≤ ≤ G 6000

As the Biasi critical correlation is based on the boiling length approach essentially accounting 

for the history of the flow upstream from the dryout point, it was used for our simulations. 

An important step in the code assessment process is to check whether TRACE is capable of 

estimating the dryout point for uniform and non uniform heat flux distributions. Figure 2 
3-3

380 / g ms

demonstrates that TRACE is able to predict well the CHF location and the temperature profile 

for a uniform heat flux at low mass flux (G k ) for different heat inputs. 2 =

(a)

500

550

600

650

700

750

800

850

900

01234567

Temperature (K)

Elevation (m)

TRACE V5 92kW G=380kg/m2-s

Data Bennett Run 5353

(b)

500

550

600

650

700

750

800

850

900

950

1000

01234567 Elevation (m)

Temperature (K)

TRACE V5 102kW G=380kg/m2-s

Data Bennet Run 5356

(c)

500

600

700

800

900

1000

1100

01234567

Elevation (m)

Temperature (K)

TRACE V5 113kW G=380kg/m2-s

Data Bennett Run 5358

(d)

500

600

700

800

900

1000

1100

1200

01234567 Elevation (m)

Temperature (K)

TRACE V5 120kW G=380kg/m2-s

Data Bennett Run 5359

Figure 2. CHF position and temperature predictions for a uniform heat flux (Bennett Data). 

In the case of non-uniform heat flux, the prediction is less good. Indeed, we notice on figure 3-b 

that the position of dryout is over-predicted by about 0.6m. 

(a)

500

550

600

650

700

750

800

850

0 0.5 1 1.5 2 2.5 3 3.5 4

Elevation (m)

Temperature (K)

TRACE V5 129.8kW G=720kg/m2-s

Data Keeys 129.8kW G=720kg/m2-s

(b)

500

550

600

650

700

750

800

850

900

950

1000

0 0.5 1 1.5 2 2.5 3 3.5 4 Elevation (m)

Temperature (K)

TRACE V5 191kW G=2000kg/m2-s

DATA Keeys 191kW G=2000kg/m2-s

Figure 3. CHF position and temperature predictions for a non-uniform heat flux (Keeys data). 

The pressure also influences the prediction of the dryout point and the consequent post dryout 

heat transfer exchanges. At constant mass flux and power input, an increasing pressure favours 

the occurrence of CHF; the predictions of the Becker tests confirm this behaviour (figure 4). 

Downstream from the dryout point, the temperatures appear to tend to an asymptotic value. 

This could be explained by the fact that in this region, only vapour exists and some sort of 

equilibrium homogenises the thermal exchanges. 
3-4

G=1500kg/m2-s

500

550

600

650

700

750

800

850

900

950

012345678

Temperature (K)

Elevation (m)

TRACE V5 RUN 147 P=14MPa

TRACE V5 RUN 232 P=10MPa

TRACE V5 RUN 264 P=7MPa

TRACE V5 RUN 320 P=3MPa

Figure 4. Effect of pressure on the dryout position at a constant mass flux of 1500kg/m2-s and at 

a constant heat flux of 760kW/m2

 (Becker data). 

 

RUN#136

600

700

800

900

1000

012345678

Temperature (K)

Elevation (m)

TRACE V5 w/o Fine Mesh

TRACE V5 w/ Fine Mesh

DATA RUN 136

Run#139

600

700

800

900

1000

1100

1200

1300

1400

01234567 Elevation (m)

Temperature (K)

8

TRACE V5 w/o Fine Mesh

TRACE V5 w/ Fine Mesh

DATA RUN 139

Run#147

600

700

800

900

1000

1100

1200

012345678 Elevation (m)

Temperature (K)

TRACE V5 w/o Fine Mesh

TRACE V5 w/ Fine Mesh

DATA RUN 147

Run#154

600

700

800

900

1000

1100

1200

012345678

Elevation (m)

Temperature (K)

TRACE V5 w/o Fine Mesh

TRACE V5 w/ Fine Mesh

Data RUN 154
3-5

Run#161

600

700

800

900

1000

1100

1200

012345678 Elevation (m)

Temperature (K)

TRACE V5 w/o Fine Mesh

TRACE V5 w/ Fine Mesh

Data RUN 161

Figure 5. Dryout position and temperature profiles for the calculations of the Becker tests at 

constant pressure (14MPa) and varying mass fluxes (from the top left corner to the right bottom 

corner: 1977, 1970, 1494, 1006, 503 kg/m2

-s). 

In short, these previous results demonstrate the ability of the code to predict the CHF location 

and post-dryout heat transfer reasonably well at low mass fluxes and low uniform heat fluxes 

using the Groeneveld et al. [1] ‘look-up tables’ with the Biasi critical quality correlation. Indeed, 

in Figure 5 and 6, one can notice that at high heat fluxes and high mass fluxes, the CHF is still 

well predicted but the distribution of temperatures is now less well predicted. Also, at a given 

heat flux and pressure, and for conditions of low mass velocities, the code fails to estimate 

either the CHF position and/or the temperature profile. It is worth noting that when the CHF 

position is forced by the authors to occur at a given elevation (Figure 6-b), the temperature 

distribution beyond the dryout point does not coincide with experimental data and the PCT is 

under-predicted. Indeed, two reasons could be suggested, (1) non-equilibrium effects become 

significant and hence the reduction in accuracy and (2) upstream history effects are 

predominant in the development of film boiling. 

Since the CHF point was, in most cases, well estimated; we decided to focus on the DFFB 

regime by implementing modified and/or new models into the thermal-hydraulics TRACE code. 

Bennett RUN#5379

500

550

600

650

700

750

800

850

900

950

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

Temperature (K)

Elevation (m)

Data Run 5379_377kW

TRACE V5 w/ Fine Mesh Technique

(b)

500

550

600

650

700

750

800

850

900

950

1000

0 0.5 1 1.5 2 2.5 3 3.5 4

Temperature (K)

Elevation (m)

TRACE V5 191kW G=2000kg/m2-s

DATA Keeys 191kW G=2000kg/m2-s

TRACE V5 CHF Position Fixed

Figure 6. Comparison between calculated temperature profiles and: (left) the Bennett 

experimental run 5379 (P=6.9MPa, G=3800kg/m2

-s and Power=377kW); (right) the Keeys data 

(P=6.9MPa, G=2000kg/m2

-s and Power=191kW) while the computed CHF position is fixed 

3.3.2 Two-phase enhancement factor 

In this section, the two-phase enhancement factor (Ψ2Φ ) is used in the following form: 
3-6

2

2 2

(1 ) 1

n

Reg

Φ Ψ

Gr K α Φ ⎡ − ⋅ ⎤

Ψ =+ ⋅⎢ ⎥ (11) 

⎢⎣ ⎥⎦

where is the Grashof no. ( Gr2Φ

3 3

2 ( ) Gr g D Φ = ⋅ ⋅Δ ⋅ ρ g ρ μ H g ), KΨ is a wall friction factor 

dependant coefficient ( ) and the exponent n takes either the value of 0.5 or 0.85 

depending on the droplet diameter considered. While 

2 100 ≤ ≤ KΨ

KΨ is too high, the two-phase 

enhancement factor becomes important in Eq. (5) causing a higher heat flux and then underpredicting the PCT. However, as it could be noticed in figure 7, the TRACE is not sensitive to a 

change of values for K . Ψ

Run#232

500

550

600

650

700

750

800

850

900

950

1000

01234567

Elevation (m)

Temperature (K)

8

Data RUN 232

TRACE V5 w/ Fine Mesh K-psi=25

TRACE V5 w/ Fine Mesh K-psi=100

Figure 7. Effect of different values on the temperature distribution for the Becker run 232 

(P=10MPa and G=1500kg/m2

-s) 

KΨ

3.3.3 Interfacial Droplet Drag 

As mentioned in part 2, the evaluation of droplet drag is crucial. This encouraged us to 

investigate the impact of different correlations on post-CHF regimes. For conditions of constant 

relative velocity, the droplet drag CD is related to the droplet Reynolds no. as follow: 

5

0 2 24 /

2 500 0.4 40 /

d D

d D

Re C Re

500 10 0.44

d

d

d D

Re C

Re C

<< =

≤ < =+

≤≤ =

Re (12) 

As an alternative to the expression of the droplet drag CD in Eq.(10), we used a drag law which 

has been obtained in the context of an accelerating cloud of droplets; Ingebo [30] has studied 

particle acceleration and has correlated a wide range of data by the expression: 

0.84

27 CD R d e = (13) 

Indeed, a model for accelerating cloud of droplets is likely better to represent the physics 

involved. Thermal gradients can cause the continuous vapour phase to be accelerated 

increasing the droplet mean velocity. 

In order to account for the effect of evaporation on the drag coefficient, a factor has been added 

to the previous expression: 
3-7

0.2

new D

D

C C = (1 ) + B (14) 

where the blowing factor B suggested by Renksizbulut and Yuen [28] is: 

, ( ) ( ) 1 P g g sat wd rad P g g sat c TT q q c TT

B

h qq h

⎛ ⎞ ⋅ − ⎛ ⎞ ′′ ′′ ⎛ ⎞ ⋅ − = ⋅ ⎜ ⎟ ⎜ ⎟ − + ≈ ⎜ ′′ ′′ ⎜

,

fg wg conv fg

⎟

⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠

 (15) 

From the calculations performed (figure 8), one can state that the droplet drag coefficient does 

not have a significant effect on the PCT. The addition of a blowing factor increases the PCT by 

no more than 5°K. 

Run#232

650

660

670

680

690

700

710

720

730

740

750

4 4.5 5 5.5 6 6.5 7 7.5

Temperature (K)

Elevation (m)

Data RUN 232

TRACE V5 Cd in equation 8

TRACE V5 Cd Ingebo

TRACE V5 Cd in equation 8+Blowing factor

Figure 8. Influence of the droplet drag on the temperature profile prediction for the Becker Run 

232 (P=10MPa and G=1500kg/m2

-s). 

3.3.4 Interfacial Heat Transfer 

Despite the minor effect of the blowing factor on the droplet drag coefficient (figure 8) and 

therefore on the temperature distribution; figure 9 reveals the central role of the single particle 

Nusselt no. in the temperature and CHF predictions. The Renksizbulut and Yuen correlation is 

the correlation implemented in the TRACE code. We have implemented few more correlations 

(Ranz-Marshall, Lee and Ryley and Beard and Pruppacher) to quantify their respective 

influences. 

Run#232

500

550

600

650

700

750

800

850

900

950

1000

2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 Elevation (m)

Temperature (K)

Data RUN 232

TRACE V5 Renksizbulut and Yuen

TRACE V5 Beard and Pruppacher

TRACE V5 BP Beta=2

TRACE V5 BP Beta=1.4

TRACE V5 BP Beta=1.1

TRACE V5 Lee-Ryley

Figure 9. Comparison of different interfacial heat transfer correlations in the DFFB region for the 

Becker Run 232 (P=10MPa and G=1500kg/m2

-s). 
3-8

 

The results obtained with the different correlations show that the best agreement was obtained 

with a modified version of the Beard and Pruppacher (BP) correlation[31] to account for the 

mass evaporation: 

1/2 1/3 1.56 0.616 d g

d (1 )

Re Pr

Nu β

+ = + B

0.07 2.79

 (16) 

where < < β . 

Eq. (16) determines the single-particle Nusselt no. In our calculations, a multi-particle Nusselt 

no. is used; this latter contains an additional factor dependant on the void fraction. 

The use of the Beard and Pruppacher correlation with a value of 1.1 for the exponent β does 

not predict the first temperature peak well; but, upstream from the quench front, the precursory 

cooling effects seem to be well estimated. It is worth noting that the validity of the above 

correlations can be discussed in the sense that most of them were obtained at atmospheric 

pressure and at relatively low Reynolds nos. 

3.3.5 A selected set of constitutive laws for heated single tubes 

In this section, we have chosen a set of correlations which (1) better suited the conditions of the 

Bennett, Keeys and Becker experiments and (2) accounted for more physical phenomena (3) 

enables us to over-predict the PCT (measure of safety). The graphs (figure 10) were obtained 

while expressing the interfacial droplet drag from a modified version of the Schiller-Naumann 

correlation accounting for the mass efflux: 

0.687

0.2

24 (1 0.15 ) 0 1000

(1 )

d

D

d

Re C

Re B

+ ⋅ = ⋅ ≤ ≤

+

R d e (17) 

However, we select the maximum value of the drag in between the latter, 0.44 and the Ingebo 

drag coefficient value. 

The interfacial heat transfer was based on the Beard and Pruppacher correlation: 

1/2 1/3

1.1

1.56 0.616

(1 )

d g

d

Re Pr

Nu

B

+ = +

 (18) 

and the two-phase enhancement factor considers a wall friction factor value for a smooth pipe 

of 0.005: 

1/2

2

2 2

(1 ) 1 100

g

Gr

Re

α Φ

Φ

⎡ − ⋅ ⎤

Ψ =+ ⋅⎢ ⎥ ⎢⎣ ⎥⎦

 (19) 

RUN#232

500

550

600

650

700

750

800

850

900

012345678

Elevation (m)

Temperature (K)

Data Run 232 P=10MPa, G=1500kg/m2-s

TRACE V5 NEW

TRACE V5

RUN#154

500

600

700

800

900

1000

1100

01234567

Elevation (m)

Temperature (K)

8

Data Run 154 P=14MPa G=1000kg/m2-s

TRACE V5 NEW

TRACE V5
3-9

Bennett RUN#5379

500

550

600

650

700

750

800

850

900

950

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

Elevation (m)

Temperature (K)

Data Run 5379_377kW

TRACE V5 w/ Fine Mesh Technique

TRACE V5 NEW

Figure 10. Assessment of the proposed model for the Becker Run 232 (top left) and 154 (top 

right): the over-prediction of the temperature is due to poor precursory cooling effects. In this 

model, there is too rapid evaporation of the droplets beyond the dryout point leading to single 

phase vapour convection, with the vapour not cooled further by the dispersed droplets. As for 

the Bennett run (bottom), the temperature is slightly higher but not high enough to fit the data. 

In our modelling, we do not account for the droplet-to-wall heat transfer or for radiation. This set 

of correlations (Eq.(17), (18),(19)) is supposed to better represent the physics involved such as 

the droplet mass evaporation, droplet drag coefficient derived from accelerating cloud of 

droplets etc. Nevertheless, some results (figure 10) exhibited large discrepancies right after the 

CHF point. The calculation of both the droplet diameter (at a critical Weber number value of 12) 

and the relative velocity might cause these differences. A too high relative velocity value 

induces an under-prediction of the temperature at low mass flux. 

Regarding the Blowing factor, the mass efflux from the droplet reduces the convective heat 

transfer from the superheated steam: the evaporation process increases the boundary layer 

thickness leading to a sharp decrease in heat transfer to the droplet surface, which in return 

reduces the rate at which additional mass can be added. This shielding effect is limited in our 

calculations and droplets completely evaporate. 
4-1 

4. Conclusion 

The analysis and the assessment of the TRACE codes demonstrate its ability to well predict the 

point of critical heat flux reasonably well. However, the temperature profile, and thus, the peak 

clad temperature, is not well predicted for the case of a non-uniform heat flux. For the case of 

uniform heat flux distributions, the combination of the so-called ‘Look-Up Tables’ and the Biasi 

critical quality provides results that match well with the Bennett experimental data. This is not 

true at high mass and heat fluxes. 

The study of the DFFB models usually implemented in thermal-hydraulics system code such as 

TRACE established the crucial character of the interfacial heat transfer. A key point would be to 

study the variations of the heat transfer coefficient and its sensitiveness to both the mentioned 

correlations and the interfacial area concentration (which has not been treated in this paper for 

simplicity). The droplet drag did not play an important role in the calculations performed here. 

The two-phase enhancement factor applied in the wall heat transfer correlation, namely, the 

Gnielinski correlation, had a little influence on the temperature predicted for the experiments 

simulated. The droplet diameter and the number density are important in the prediction of both 

the position of dryout and the temperature profile upstream from the quench front (precursory 

cooling effects). 
5-1 

5. REFERENCES

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Vinogradov, X.C. Huang, and E. Royer," The 1995 look-up table for critical heat flux in tubes", 

Nuclear Engineering and Design Vol. 163, No. 1-2, 1996, pp. 1-23. 

[2] Evans, D., S. Webb, and J.C. Chen," Axially varying vapor superheats in convective film 

boiling", ASME Journal of Heat Transfer Vol. 107, 1985, pp. Pages: 663-669. 

[3] Yang, J., D.C. Groeneveld, L.K.H. Leung, S.C. Cheng, and M.A.E. Nakla," An 

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[4] Shiralkar, B.S.," Analysis of non-uniform CHF data in simple geometries", Report NEDM13279, 1972. 

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[7] Borkowski, J.A., N.L. Wade, S.Z. Rouhani, R.W. Shumway, W.L. Weaver, W.H. Rettig, 

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[9] US-NRC, "TRACE V5.0 Theory Manual", 2007. 

[10] Gnielinski, V.," New equations for heat and mass transfer in turbulent pipe and channel 

flow", Int. Chem. Eng., 1976, pp. pp. 359–368. 

[11] Andreani, M., and G. Yadigaroglu, "Dispersed Flow Film Boiling", 1992. 

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annular two-phase flow", J. Fluids Eng. ; Vol/Issue: 105, 1983, pp. Pages: 230-238. 

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[14] Ranz, W.E., and W.R. Marshall," Evaporation from drops. Parts I & II", Chemical 

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exceeded", Technical report AERE-R5373, 1967. 

[16] Keeys, R.K.F., J.C. Ralph, and D.N. Roberts, "Post burnout heat transfer in high 

pressure steam water mixtures in a tube with cosine heat flux distribution", 1971, pp. Size: 

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[17] Becker, K.M., C.H. Ling, S. Hedberg, and G. Strand," An experimental investigation of 

post-dryout heat tansfer", Report KTH-NEL-33, Royal Institute of Technology, Stockholm, 

Sweden, 1983. 

[18] Pasamehmetoglu, K.O., and R.A. Nelson, "Investigation of the quasi-steady approach 

used in transient two-phase flow analysis", United States, 1988, pp. Pages: 24. 

[19] Andreani, M., and G. Yadigaroglu," Prediction methods for dispersed flow film boiling", 

International Journal of Multiphase Flow Vol. 20, No. Sup, 1994, pp. 1. 

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Film Boiling -II. Assesment Using Quasi-Steady-State Data and Comparison with Results of 1-D 

Analyses", Int. J. Heat Mass Transfer Vol. 40, No. 8, 1997, pp. 1773-1793. 
5-2 

[21] Andreani, M., and G. Yadigaroglu," A 3-D Eulerian-Lagrangian model of dispersed flow 

film boiling including a mechanistic description of the droplet spectrum evolution - I. The 

thermal-hydraulic model", International Journal of Heat and Mass Transfer Vol. 40, No. 8, 1997, 

pp. 1753-1772. 

[22] Kawaji, M., and S. Banerjee," Application of a multifield model to reflooding of a hot 

vertical tube: Part 1 - Model structure and interfacial phenomena", Journal of Heat Transfer 

(Transcations of the ASME (American Society of Mechanical Engineers), Series C) ; Vol/Issue: 

109:1, 1987, pp. Pages: 204-211. 

[23] Kawaji, M., and S. Banerjee," Application of a multifield model to reflooding of a hot 

vertical tube: Part 2 - Analysis of experimental results", Journal of Heat Transfer (Transcations 

of the ASME (American Society of Mechanical Engineers), Series C) ; Vol/Issue: 110:3, 1988, 

pp. Pages: 710-720. 

[24] Sun, X., M. Ishii, and J.M. Kelly," Modified two-fluid model for the two-group interfacial 

area transport equation", Annals of Nuclear Energy Vol. 30, No. 16, 2003, pp. 1601-1622. 

[25] Delhaye, J.-M.," Some issues related to the modeling of interfacial areas in gas-liquid 

flows, II. Modeling the source terms for dispersed flows", Comptes Rendus de l'Academie des 

Sciences - Series IIB - Mechanics Vol. 329, No. 6, 2001, pp. 473-486. 

[26] Delhaye, J.-M.," Some issues related to the modeling of interfacial areas in gas-liquid 

flows I. The conceptual issues", Comptes Rendus de l'Academie des Sciences - Series IIB - 

Mechanics Vol. 329, No. 5, 2001, pp. 397-410. 

[27] Serre, G., and D. Bestion, "Progress in improving two-fluid model in system code using 

turbulence and interfacial area equations", NURETH-11, 2005. 

[28] Renksizbulut, M., and M.C. Yuen," Experimental study of droplet evaporation in a hightemperature air stream", J. Heat Transfer ; Vol/Issue: 105, 1983, pp. pp. 384–388. 

[29] Todd, D.R., and H. Tang," Application of the Biasi CHF Correlation: Purposeful 

Interpretation or Historical Accident?" ASME, 2007. 

[30] Ingebo, R.D.," Drag coeficients for droplets and solid spheres in clouds accelerating in 

air streams", NACO - Technical Note 3762, 1956. 

[31] Beard, K.V., and H.R. Pruppacher," A wind tunnel investigation of collection kernels for 

small water drops in air", Q. J. R. Meteorol. Soc. Vol. Volume 97, 1971, pp. pp. 242–248.