- 

NASA. Technical Paper 1385 

NASA 

' TP 

1385 

c. 1 ,', 

Onset of Condensation 

LOAN COPY: RZT 

AWL TECWNiCAL 

KJRTLAMD AFBV 

Effects 

With an NACA 0012-64 Airfoil 

Tested in the Langley 0.3-Meter 

Transonic Cryogenic Tunnel 

Robert M. Hall 

APRIL 1979 

NASA 

https://ntrs.nasa.gov/search.jsp?R=19790013872 2018-05-14T12:43:26+00:00Z
TECH LIBRARY KAFB, NM 

NASA Technical Paper 1385 

Onset of Condensation Effects 

With an NACA 0012-64 Airfoil 

Tested in the Langley 0.3-Meter 

Transonic Cryogenic Tunnel 

Robert M. Hall 

Larzgley Research Center 

Hampton, Virginia 

National Aeronautics 

and Space Administration 

Scientific and Technical 

Information Office 

1979 
SUMMARY 

A 0.137-meter NACA 0012-64 airfoil has been tested at a Oo angle of attack 

in the nitrogen-gas Langley 0.3-meter transonic cryogenic tunnel at free-stream 

Mach numbers of 0.75, 0.85, and 0.95 over a total pressure range from 1.2 to 

5.0 atmospheres. The onset of condensation effects as determined by varying 

stagnation temperature was found to correlate better with the amount of supercooling in the free stream than it did with the supercooling in the region of 

maximum local Mach number over the airfoil. Effects in the pressure distribution over the airfoil were generally seen to appear over its entire length at 

nearly the same total temperature. Both observations suggest that heterogeneous nucleation does occur in the free stream. The present results are compared 

to calculations made by Sivier and data gathered by Goglia. "he potential operational benefits realized from supercooling are presented in terms of increased 

Reynolds number capability at a given tunnel total pressure and reduced drivefan power and liquid nitrogen consumption if Reynolds number is held constant. 

Depending on total pressure and free-stream Mach number, these three benefits 

are found to vary respectively from 8 to 19 percent, 12 to 24 percent, and 9 to 

19 percent. An appendix is included which gives details of the data analysis 

and error estimates for the differences in pressure distributions. 

INTRODUCTION 

Cryogenic wind tunnels should normally be operated at the lowest possible 

total temperatures in order to maximize Reynolds number capability for a given 

total pressure and to minimize operating costs. The minimum operating temperatures are, however, limited by low-temperature behavior of the test gas. 

Either the test gas begins to condense or its equation of state changes so 

that the gas does not properly simulate the nearly ideal-gas behavior of air 

encountered in flight. By analyzing the equation of state for nitrogen gas 

over the operating ranges of existing and proposed transonic cryogenic wind 

tunnels, Adcock showed in reference 1 that low-temperature nitrogen approximates an ideal gas during flow simulations for total pressures under 10 atmospheres and for Mach numbers up to 2. Consequently, for operating conditions 

within these limits, the lower temperature boundary appears to be determined 

by the onset of condensation of the nitrogen test gas. "he low-temperature 

boundary is important from an operational viewpoint because it determines, on 

the one hand, the maximum Reynolds number capability for a fixed tunnel total 

pressure and, on the other hand, the most economical total temperature and 

pressure at which to operate the tunnel for a fixed test Reynolds number. 

The present condensation investigation employs a pressure-instrumented 

0.137-meter NACA 001 2-64 airfoil mounted at Oo angle of attack in the Langley 

8.3-meter transonic cryogenic tunnel. Changes in the pressure distribution over 

the airfoil were used to detect the onset of condensation effects at transonic 

speeds just as changes in pressure distributions in divergent nozzles were used 

in references 2 to 6 to detect the onset of condensation effects at supersonic 
and hypersonic speeds. The airfoil was tested at free-stream Mach numbers of 

0.75, 0.85, and 0.95 over a total pressure range of 1.2 to 5.0 atmospheres in 

order to determine for a range of Mach numbers and pressures the total temperature at which condensation influences the flaw about the airfoil. 

A goal of the Langley condensation program is predicting the onset of condensation effects not only in the 0.3-meter tunnel but in larger tunnels such 

as the National Transonic Facility (2.5-meter square test section) under construction at the Langley Research Center. At the present time, however, how 

to extend the results presented herein to a larger facility is not clear. The 

larger tunnel circuit should allow more time for the evaporation of the injected 

liquid nitrogen used for absorbing the heat of the drive fan. As discussed later 

in this paper, this added time could decrease the severity of heterogeneous 

nucleation. But, with longer test sections and wing chord lengths, the larger 

tunnels will be much more susceptible to increased droplet growth both in the 

test section and over the model. The question of the effects of length needs 

to be addressed before the present results can be confidently extended to other 

facilities. 

SYMBOLS 

a 

cP 

AcP 

C 

i 

M 

m 

n 

P 

9 

R 

RC 

r 

T 

2 

speed of sound, 

static pressure 

m/sec 

P - P, 

coefficient, 

9, 

difference in Cp defined by equation (A6) 

airfoil chord, 0.137 m 

summation index 

Mach number 

slope of linear regression fit defined by equation (Al) 

number of condensation-free pressure distributions along a path 

of nominally constant Mach and Reynolds numbers 

pressure, atm (1 atm = 101 kPa) 

dynamic pressure, atm 

Reynolds number per meter 

chord Reynolds number per meter 

correlation coefficient as defined in equation (A41 

temperature, K 
AT supercooling defined by equation (1) , K 

X linear dimension along airfoil chord line, m 

1-1 viscosity, N-s/m2 

P density, kg/m3 

0 standard deviation 

Subscripts: 

e conditions along the isentrope at onset ofcondensation effects 

2 local cod itions 

0 values corrected for Mach number effect 

S conditions atintersection of isentrope and vapor pressure curve 

t total conditions 

W f ree-stream conditions 

Abbreviations: 

IN2 liquid nitrogen 

min. minimum 

1 sat. saturation 

A bar over a symbol indicates a mean value. 

MINIMUM OPERATING TEMPERATURES 

The minimum operating temperature, as determined by the onset of condensation, has an impact on both the maximum Reynolds number capability and the 

operating cost of nitrogen-gas cryogenic wind tunnel cooled by injection of 

liquid nitrogen. The reasons for these effects can be understood by reviewing the effects of changing tunnel temperature upon the test gas. As shown in 

figure 1 (a), the density p increases while the viscosity u and the speed 

of sound a decrease as the total temperature Tt decreases for a fixed value 

of tunnel total pressure pt. As shown in figure 1 (b) , this behavior of the 

gas properties as Tt decreases leads to a dramatic increase in unit Reynolds 

number R, a decrease in drive power required, and no change in dynamic pressure q. Since the rate of increase in R is itself increasing at the lower 

temperatures, it is important to operate the tunnel at as law a temperature as 

possible. The law-temperature limit obviously fixes the maximum R capability 

of a cryogenic tunnel running at its highest possible pressure. However, if 

this maximum R capability is not necessary, the minimum temperature boundary 

3 

I 
impacts on the operating costs of the tunnel. The greater the gain in R due 

to low-temperature operation, the less pt is required to obtain the operating R of interest. Since drive-fan power is proportional to pt and 

decreases with decreasing Tt, minimizing Tt reduces drive-fan power and, 

consequently, reduces the amount of injected liquid nitrogen required to absorb 

the heat of the drive fan. Both reductions decrease direct operating costs, 

which are split with about 90 percent going to the injected liquid nitrogen and 

only 10 percent going to power the drive fan. (Specific details about drive 

power required and operating costs are given in refs. 7 and 8.) 

To estimate the minimum operating temperature for a given value of tunnel 

total pressure, one might choose the value of tunnel total temperature which 

would just allow saturation to occur at the maximum local Mach number MxImax 

over the test model. However, references 2 to 6 as well as investigators working in the Langley 0.3-meter transonic cryogenic tunnel point out that the 

onset of condensation effects tends to occur below saturation temperatures. 

The amount of this temperature difference is normally measured by the supercooling at the onset of condensation effects AT which is defined as 

AT = Ts - Te 

where Ts is the static temperature at the point where the isentrope crosses 

the vapor pressure curve and Te is the static temperature on the isentrope 

where effects are first seen. The magnitude of the supercooling for various 

tunnel pressures and Mach numbers determines the minimum operating temperatures 

and, consequently, the maximum benefits to be gained from cryogenic operation. 

EXPERIMENTAL APPARATUS 

Tunnel 

The Langley 0.3-meter transonic cryogenic tunnel is a continuous flow, 

fan-driven tunnel, which uses nitrogen as a test gas and is cooled by injecting liquid nitrogen directly into the stream. Variation of the rate of liquid 

nitrogen injection provides an approximate total temperature range from 80 to 

350 K, while the total pressure can be varied from 1.2 to 5.0 atm. The combined low temperature and high pressure can produce a Reynolds number of over 

330 x lo6 per meter. Some of the design features and operational characteristics of the 0.3-meter tunnel have been reported by Kilgore in reference 9. A 

sketch of the 0.3-meter tunnel is shown in figure 2. 

The liquid nitrogen used to cool the tunnel and absorb the heat of the 

drive fan is injected into the tunnel through a series of 11 nozzles arranged 

on three different struts, or spray bars, at the three injection stations shown 

in figure 2. Full details of this arrangement are included in reference 9. 

However, for one of the tests during the present investigation (details to be 

mentioned in the section entitled "Results and Discussion") , the spray-bar system was removed and injection was carried out by injection through just four 

4 
nozzles at injection station 1. This change, of course, necessitated larger 

liquid-flow rates per nozzle. 

Airfoil and Installation 

A 0.1 37-m NACA 0012-64 airfoil was used for these tests. The airfoil 

had 20 pressure orifices spaced at 5 percent chord intervals on both the top 

and bottom surfaces with the first orifice at the leading edge. For the tests 

at M, values of 0.75 and 0.95, a rearward-facing orifice was added to the 

trailing edge of the airfoil. The airfoil was installed between flats in the 

octagonal test section, with the leading edge 0.62 m from the beginning of 

the test section. The angle of attack of the airfoil was zero for all tests. 

A sketch of the airfoil is given in figure 3. 

The pressure distributions over the airfoil may be influenced by wall 

interference effects because of the relatively large chord of the airfoil compared to the size of the test section. However, wall interference should not 

affect the occurrence of condensation, and no attempt has been made to correct 

the data for wall interference effects. 

Data Acquisition and Error Estimate 

The tunnel parameters were first recorded; then a differential pressure 

transducer was used in a scanning-valve system to step through and record the 

pressures around the airfoil. The time to acquire all of the data for a complete pressure distribution was 50 sec. During the 50-sec acquisition period, 

the tunnel conditions were observed to fluctuate by the following amounts: 

M, fO.003; Tt, f0.5 K; and pt, f0.002 to k0.012 aim, depending on pt 

itself. 

The manufacturer specified the accuracy of the pressure transducer to be 

0.5 percent of full scale. However, the precision of the transducer proved to 

be an order of magnitude better than the specified accuracy based upon scatter 

in the values of pressure from data point to data point and from day to day. 

For the transducer used in the tests at M, = 0.75 and 0.95, the precision was 

f0 .0004 atm. For the smaller transducer used in the test at M, = 0.85, the 

precision was f0.0002 atm. There was no significant error introduced by either 

the signal-conditioning or data-acquisition systems. An estimate of the uncertainty in Cp due to the imprecision of the pressure transducers and the fluctuating tunnel conditions is given in the appendix. 

TESTS 

Data Sampled 

To determine the total temperature at which condensation effects do occur 

and to investigate the influence of free-stream Mach number and total pressure 

on the onset of condensation effects, the airfoil was tested at free-stream 

Mach numbers of 0.75, 0.85, and 0.95 over a total pressure range of 1.2 to 

5 
5.0 atm. The test envelopes were bounded in pt by the 1 .2- to 5.0-atm pressure limits of the tunnel and were bounded,in Tt by total temperatures corresponding to saturated flow at Ml,max and those corresponding to saturation 

in the reservoir section. Total conditions which fall lower in Tt than the 

reservoir saturation line are unobtainable since the injected liquid nitrogen 

used for cooling cannot provide cooling when Tt is below the vapor-pressure 

curve. Total temperatures above those along the line of local saturation offer 

no possibility of condensation in a pure nitrogen test gas so they are used in 

this study only as a way of obtaining data unaffect.ed by condensation effects 

for comparison purposes. 

To explore each of the regions of interest in the pt and Tt plane, 

paths of constant chord Reynolds number Rc and M, were used to traverse the 

region of interest. Since along each of the paths both M, and R, were held 

constant, systematic deviation in pressure coefficients at any x/c position 

over the airfoil was taken to be the result of condensation effects. Five 

paths of constant Rc and M, are shown for the M, = 0.85 test in figure 4. 

The R, along each path varied from 16 x 1 O6 at the low-pressure traverse to 

42 x 1 O6 at the high-pressure traverse. Along these five paths, a total of 

201 pressure distributions were recorded and analyzed. Similar envelopes were 

drawn and investigated for M, = 0.75 and M, = 0.95, except that only three 

paths of constant & and Y, were used in these cases. These envelopes are 

shown in figures 5 and 6. During the investigation of the high-pressure path 

for the M, = 0.95 test, a fan drive-power limit was encountered so M, was 

reduced from 0.95 to 0.93 for that path alone. 

Data Analysis 

In order to determine the pt and Tt at which the onset of condensation 

effects occurs along a constant M, and R, path, a data analysis procedure 

was developed. The main objective of the data analysis procedure was to be able 

to correct values of Cp on an orifice-by-orifice basis in cases where the pressure distribution over the airfoil was taken at a slightly different M, than 

desired. With such a correction, data along the path that normally would have 

had to be disregarded due to small differences in M, could be used. Having 

a more complete data base available for analysis made it easier to detect the 

total temperature at which differences in ACpl occurred because of the 

effects of condensation. By examining all t e orlfices over the airfoil, an 

appropriate onset total temperature could be chosen for the airfoil as a whole. 

Further details of the data analysis procedure are presented in the appendix. 

CR' 

The Beattie-Bridgeman equation of state for gaseous nitrogen (see ref. 10) 

has been used to provide accurate values for the isentropic flow properties of 

the nitrogen gas. In unpublished studies, Adcock has shown that for isentropic 

flow the Beattie-Bridgeman equation gives nearly the same results as the 

Jacobsen equation used in reference 1 . 

6 
RESULTS AND DISCUSSION 

Data Presentation and Comments 

The data .are summarized by a series of figures for each value of M, 

covered in this study: 0.75, 0.85, and 0.95. Each series includes averaged, 

condensation-free pressure distributions for each path of constant Rc, graphs 

showing the onset Tt for condensation effects at each orifice as a function 

of x/c for each path, and a summary plot for each M, showing the onset conditions for each path in a plane where Tt is plotted against pt. (All values 

of Tt plotted in the orif ice onset graphs are rounded to the nearest 0.5 K 

because of the possible 0.5-K drift in tunnel total temperature during data 

acquisition.) The results for each value of M, are then grouped together to 

determine whether or M, correlates with the onset of condensation 

effects. 

The orifice onset graphs showing the Tt at which condensation is first 

detected use four different symbols for four different situations. When normal 

onset is detected, a circle is plotted at the appropriate x/c,Tt location. 

When no orifice onset is detected, a square is plotted at the minimum Tt at 

which data were taken. When excessive scatter obscures any trends, a triangle 

is plotted at the minimum Tt. When an orifice pressure tube develops a leak, 

a diamond is plotted at the minimum Tt. Also, the airfoil onset Tt shown 

is not taken to be an average of orifice onset Tt's but is conservatively 

taken to be the warmest orifice onset Tt that appears systematic. The uncertainty band about the onset Tt is drawn to include the highest value of orifice onset Tt, whether or not the deviation is systematic. 

The fir st test described is the M, = 0.75 test. The averaged, 

condensation-free pressure distributions in figures 7, 8, and 9 give the 

average values of Cp at each orifice with no effects of condensation present. 

The graphs containing orifice onset Tt plotted against x/c are shown in 

figures 10, 11 , and 12. It is interesting to note that in figures 11 and 12 

the effects of condensation are only apparent over the first half of the airfoil, which seems to downplay the importance of any condensate growth over the 

airfoil itself. The summary plot of onset conditions is shown in figure 13. 

The pressure distributions for the five lines of constant R, for the 

M,= 0.85 test exhibit a recompression shack at x/c = 0.65 and are shown 

in figures 14, 15, 16, 17, and 18. The graphs showing orifice onset Tt as a 

function of x/c are shown in figures 19, 20, 21 , 22, and 23. With the possible 

exception of figure 23, effects appear to occur at about the same Tt over the 

length of the airfoil. There is no obvious sensitivity to condensation effects 

behind the shock or, for that matter, before the shock in the region of high 

local Mach number. Along the Rc = 42 x 1 O6 path as shown in figure 23, there 

does appear to be possible sensitivity behind the shock location. At x/c 

values of 0.75 and 0.85 the onset value of Tt appeared to be 100.5 K, which 

is above the trend of effects occurring at about 96.0 or 96.5 K for the majority 

of orifices. While the onset Tt of 100.5 K may be correct, there is scatter 

in the plots of ACp against Tt for each of the orifices that were combined 

to form figure 23. Because of the uncertainties involved and because of the 

lack of agreement between orifice onset Tt'S behind the shock location at 

7 
x/c = 0.65 in figure 23, the airfoil onset Tt was chosen to be 98.5 K with 

a possible error bar extending from 96.5 to 100.5 K. The summary plot of onset 

conditions for the M, = 0.85 test is given in figure 24. 

The last test condition is that of M, = 0.95. As mentioned in the section entitled "Data Sampled," the high-pressure path at + = 40 x lo6 is 

tested at M, = 0.93 instead of at 0.95, so there is a difference in M, 

between the first two paths and the path for + = 40 x lo6. The unaffected 

pressure distributions are shown in figures 25, 26, and 27, and the orifice 

onset graphs are presented in figures 28, 29, and 30. Among the onset Tt's 

for the Rc = 17 x lo6 path, no one area seems to be more sensitive than any 

other. (See fig. 28.) However, onset Tt's for the Rc = 27 x lo6 path in 

figure 29 may show signs of an increased sensitivity at about x/c = 0.40 in 

the region of increasing local Mach number although the trend is not conclusive. 

The third path at Rc = 40 x 1 O6 , shown in figure 30, shows an apparently uniform onset Tt over the airfoil. There were no data taken along this path 

between Tt = 100.5 and 103.5 K; consequently, there is no resolution of effects 

between these two temperatures, and this lack of resolution may contribute to 

the fairly uniform distribution of onset Tt. The lack of resolution is indeed 

unfortunate as can be seen in figure 31 which shows no effects at Tt = 103.5 K 

but well-developed effects at 100.5 K for ACp plotted against Tt for the 

orifice at x/c = 0.95. For this path, onset Tt for the airfoil is chosen 

to be 102.0 K with the error bar spanning 1 00.5 to 1 03.5 K. The summary plot 

for onset conditions for the M, = 0.95 test is given in figure 32. 

The results for all of the M, tests are now grouped together to determine whether M1,max or M, correlates with the onset of condensation effects. 

The question of which Mach number is important arises because of the uncertainty 

in the mode of nucleation taking place. This uncertainty is discussed in the 

next section. 

The first pair of figures comparing all of the onset results is constructed 

for the supercooling as defined in equation (1). In equation (l), the value of 

Ts is the static temperature at which the isentrope, starting at the onset 

values of pt and Tt, crosses the vapor-pressure curve. The value of Te is 

the static temperature along the same isentrope at M = MIImax in figure 33(a) 

and at M = M, in figure 33 (b) . In both cases the value of AT is plotted 

as a function of the onset pt for each path of contant Rc. In figure 33(a), 

the supercooling was nearly constant at 7 K over the pressure range for 

M, = 0.75, was roughly equal to 11 K over the pressure range for M, = 0.85, and 

was 12 and 14 K for the two lower pressure paths at M, = 0.95 and then dropped 

to 11 K for the upper pressure path. In figure 33(b), the supercooling based 

on M, remained between 2 and 3 K over the pressure range for both M, = 0.75 

and 0.85. However, the supercooling for the M, = 0.95 test was 1 and 2 K for 

the lower pressure paths, but dropped to -1 K for the upper pressure path. Even 

with the behavior of the upper pressure path for the M, = 0.95 test, there 

seems to be much better correlation of the values for supercooling when assuming 

M, is the pertinent Mach number rather than M1,max. 

A second pair of figures again compares all of the onset results, but the 

comparison is now made in a plane where loglo p is plotted against T. Static 

values of PIT are calculated from the pt and Tt at onset and are calcu8 
lated assuming an isentropic expansion to either Mi,max or M,. Figure 34(a) 

shows the p,T as calculated assuming M1,max is the Mach number of interest 

while figure 34(b) shows the p,T as calculated assuming M, is the important 

Mach number. Figure 34 suggests, as does figure 33, that the onset data correlate much better with M, than with M1,max. 

The seemingly early onset of effects in the upper pressure path of the 

M, = 0.95 test may be the result of a tunnel configuration change that was made 

before the data for this path were taken. The spray-bar system used for injection of the liquid nitrogen, as described in the section "Experimental Apparatus," was removed for another investigation in the 0.3-meter tunnel. The 

spray-bar system remained out for the tunnel entry during which the data were 

obtained for the upper pressure path of the M, = 0.95 test. With the spray 

bars removed, the liquid was injected from 4 nozzles flush with the interior 

tunnel wall at injection station 1 instead of from the 11 nozzles at the three 

different injection stations. Consequently, the liquid injected may not have 

broken up and evaporated as effectively as it did with the 11 nozzles. The 

additional unevaporated drops may have formed the increased number of nucleation sites necessary to decrease the amount of supercooling realized. Because 

of the tunnel configuration change, the data from the upper pressure path of 

the M, = 0.95 test are not presented in any additional comparison graphs. 

Furthermore, the possible difference in effects due to differences in injection 

procedure would suggest that the number and location of the injection nozzle 

may be important factors in predicting the onset of condensation effects for 

different facilities. 

Implications of the Data 

Condensation effects can be caused by three different modes of nucleation, 

where nucleation is taken to mean the formation of a stable liquid droplet. 

The three different modes are homogeneous, heterogeneous, and binary nucleation. 

These three processes differ according to the manner in which they overcome an 

energy barrier to droplet formation and hence to droplet growth. In-depth discussion of the three types can be found in references 2 to 4 and 11 to 14. The 

different modes can briefly be summarized as in the following discussion. 

Homogeneous nucleation can occur when the gas undergoes supercooling, a 

condition which will decrease the energy barrier to liquid droplet formation. 

When enough supercooling occurs, the gas molecules will be able to overcome the 

energy barrier to droplet formation, and massive nucleation rates are likely. 

Heterogeneous nucleation may occur when there are liquid or solid impurities 

suspended in the vapor at the time the flow first expands past the vapor-pressure 

curve and begins to supercool. The energy barrier to formation, which is so 

important for homogeneous condensation, is not so significant here because the 

impurities in the vapor can act as a catalyst for the condensation process. 

Consequently, little or no supercooling is needed before stable droplet growth 

occurs. What prevents heterogeneous nucleation from always dominating the homogeneous process is that it requires extremely large concentrations of impurity 

sites to influence the flow, pointed out by Oswatitsch in reference 15. The 

third type of nucleation possible is binary. This process occurs when a mixture 

of two different gases condenses into droplets which are composed of both types 

9 
of molecules. The binary process is discussed specifically in references 11 

to 14. The combination of the two species can effectively change the energy 

barrier to nucleation so that condensation will occur earlier than analysis 

would predict for either of the species acting singly. 

The data from the present experiment do seem to suggest which nucleation 

process might be taking place. First, no condensation seems to occur until at 

least 7 K of supercooling has taken place at the T,max location. If binary 

nucleation takes place with some sort of impurity vapor in the nitrogen used 

for cooling the tunnel, then its effects are either undetectable or occur at 

temperatures low enough to be confused with homogeneous or heterogeneous nucleation of the nitrogen test gas. The purity of the liquid nitrogen injected for 

cooling is approximately 99.95 percent in the present experiments, so binary 

nucleation is unlikely. Second, none of the orifice onset Tt plots show any 

systematic trend toward condensation first appearing in the region of maximum 

supercooling, which is the region of high local Mach number. Since the amount 

of supercooling is so important for homogeneous nucleation, these results are 

not consistent with what one would expect if homogeneous nucleation were occurring. The effects may actually be the result of heterogeneous nucleation 

occurring upstream of the model in the test section. Under these circumstances 

the airfoil would experience the influence of these droplets over its length 

at about the same Tt although local sensitivity to the condensate in the 

free stream may vary over the airfoil because of differences in local Mach 

number or pressure gradient. 

If condensate in the free stream causes the effects, the possible source 

for the impurity sites could be the injected liquid nitrogen used for cooling 

the tunnel. At the very low temperatures of these tests, the injected liquid 

may not completely evaporate in the time it takes to travel from the injection 

stations to the test section. (See fig. 2.) The partially evaporated droplets 

may provide the high concentration of nucleation sites needed for heterogeneous 

condensation. Some evidence for heterogeneous nucleation from unevaporated 

droplets in the free stream comes from figures 33 and 34. These figures show 

stronger correlation between the onset of effects and M than the onset of 

effects and MI ,ma?. Further evidence comes from the smgller amount of supercooling realized wlth the upper pressure path of the Ma = 0.95 test. Because 

the configuration without spray bars is less efficient at breaking up the 

injected liquid nitrogen, the smaller amount of supercooling seems to result 

from an increased number of liquid drops on which condensation growth could 

occur. Finally, the author's unpublished results from independent experiments 

using total pressure probes in the 0.3-meter tunnel support the present findings 

that heterogeneous nucleation occurs down the length of the test section. 

Comparison to Other Works 

While it appears that heterogeneous nucleation is the cause of condensation 

in the present experiments, most of the previous condensation investigations 

have concentrated on homogeneous nucleation. Some of these investigations were 

concerned with nitroger, gas, and two references, 16 and 17, are used here for 

comparison with the present data. A traditional means of presenting onset of 

condensation effects data is in the plane where loglo p is plotted against T. 

10 
As mentioned in the previous section, there is some question as to the process 

of nucleation and hence in the relevant condition to plot in the plane where 

loglo p is plotted against T. For the present comparisons, the static values 

of p and T as calculated for the Mllmax condition were used because, 

regardless of the source of the effects, this amount of supercooling was realized in the region of maximum local Mach number before effects were detected. 

Using the log1 0 p plotted against T format allows the present results 

to be compared with the analytical nitrogen-gas work done by Sivier in reference 16. His computer calculations assumed homogeneous nucleation and used 

classical liquid-droplet theory. A curve fit (unpublished) by Adcock to 

Sivier's calculated onset points for conditions of higher pressure and lower 

onset Mach number has been plotted together with the present onset conditions 

in figure 35, where Adcock's curve fit is represented by 

1 

- = 0.01461 - 0.004962 log1 0 p + 0.0001959 (loglo p)2 

Te 

There is good agreement in trends between the curve fit to Sivier's prediction 

and the present results although the present onset points occur closer to the 

vapor-pressure curve than predicted for homogeneous nucleation. Again, heterogeneous nucleation would be consistent with the data because it would explain 

onset occurring before the prediction for homogeneous nucleation. However, 

many of the I& = 0.85 and 0.95 onset points do approach Sivier's onset line 

for homogeneous nucleation. If Sivier's predictions are accurate and if heterogeneous nucleation indeed occurs in the present data, then significantly more 

supercooling may not be possible for the M, = 0.85 and 0.95 tests even if the 

impurity sites were eliminated, since the onset line is already close to 

Sivier's homogeneous nucleation line. 

The present results can also be compared with previous experimental 

results. Goglia (ref. 17) has taken data that show condensation onset in the 

same static pressure and temperature range as considered in the present study. 

When Goglia's data and the present experimental data are plotted together, as 

in figure 36, the agreement is especially good considering that the present 

results consist of subsonic and supersonic data from a 0.137-111 airfoil and 

that Goglia's data are based on rapid expansions in a nozzle 0.114 m long at 

Mach numbers from 2.00 to 3.25. Although one would normally expect more supercooling with the larger velocity gradients in the nozzle, this supercooling 

does not appear in the data comparison. In fact, the trend of Goglia's data 

falls close to the present I& = 0.75 data but seems to have somewhat less 

supercooling than was experienced during the present M, = 0.85 or 0.95 tests. 

Goglia concludes that the condensation he detected appeared to be the result 

of homogeneous nucleation of the nitrogen test gas. However, the gas he used 

was only 95-percent-pure nitrogen and contained a 5-percent impurity of oxygen. 

Even though this fact was well recognized and investigated by Goglia, there 

may be some effects of heterogeneous nucleation on his onset points. (Arthur 

and Nagamatsu in ref. 6 detected a mild decrease in supercooling of about 1 

to 2 K for a 5-percent oxygen impurity.) 

11 
Whether or not the condensation in the present investigation was the 

result of heterogeneous or homogeneous nucleation, the magnitude of the supercooling seems comparable to what others have seen or predicted in the same 

pressure range. 

Benefits Realized 

One of the primary motivations for the present experiments was to determine the increase in Reynolds number capability that might be possible when 

testing an airfoil with supercooled flow. This increase was determined for the 

NACA 0012-64 airfoil, and figure 37 shows the percent increase realized at the 

temperature at which condensation effects were first detected. The percent 

increase was calculated by dividing the + corresponding to pt and Tt at 

onset by the Rc corresponding to pt at onset but with a Tt which allows 

local saturation only. As can be seen in figure 37, the M, = 0.75 test realized the smallest percent gain in capability at 8 percent, while the M, = 0.95 

test realized the largest at 19 percent. The M, = 0.75 and 0.85 tests appear 

to show a decrease in gain with increasing pt, while a trend for the M, = 0.95 

test cannot be predicted because of the lack of a high-pressure-path data point. 

Error bars shown are calculated from the uncertainty in the value of Tt for 

the onset of condensation effects over the airfoil. 

The second motivation for the present experiment was to determine percent 

decreases in drive-fan power required and in the amount of liquid nitrogen (LN2) 

injected when unit Reynolds number is held constant and the supercooling is used 

to decrease both pt and Tt. Since the energy required for producing the 

amount of LN2 injected is much greater than the energy used by the drive fan, 

reductions in direct operating costs while at test conditions will be much 

closer to the percent decrease in LN2 required than to the decrease in drivefan power required. 

The decrease in drive-fan power realized is shown in figure 38. The trends 

are, of course, similar to the increase in Reynolds number capability shown in 

figure 37. For the M, = 0.75 test, the decrease in drive power required 

remained relatively constant at 12 percent over the pressure range while for 

the M, = 0.85 test, the decrease in drive power varied from 20 to 19 percent. 

Decreases of 23 and 24 percent were found for the two low-pressure paths in the 

M, = 0.95 test. The decrease in LN2 required to absorb drive-fan heat is 

shown in figure 39. (For an insulated tunnel such as the Langley 0.3-meter 

transonic cryogenic tunnel, the injected LN2 required to absorb the heat flow 

into the tunnel through the tunnel shell insulation is relatively constant over 

the temperature range of the present tests and is only on the order of 1 percent 

of the amount required to absorb the heat of the drive fan. Consequently, heat 

leakage through the shell has no effect on the data described in fig. 39 and 

has not been included.) For the M, = 0.75 test, the reduction in required 

LN2 varied from 10 to 9 percent at the higher pressures. For M, = 0.85, the 

reduction varied from 16 percent at the lower pressures to 15 percent at the 

higher pressures. The M, = 0.95 test had a reduction high of 19 percent and 

a low of 18 percent. 

12 
CONCLUDING REMARKS 

An experimental program was undertaken to determine the onset of condensation effects in the pressure distribution about a 0.137-meter NACA 0012-64 

airfoil tested in the Langley 0.3-meter transonic cryogenic tunnel at freestream Mach numbers of 0.75, 0.85, and 0.95 over a total pressure range from 

1.2 to 5.0 atmospheres. Orifice pressure measurements were recorded at 5 percent chord intervals and were analyzed to determine the total temperature at 

which deviations first occurred in the orifice pressure coefficient. 

The onset of condensation effects was found to correlate more with the 

amount of supercooling in the free stream than with the supercooling in the 

region of maximum local Mach number over the airfoil. Effects in the pressure 

distribution over the airfoil were generally seen to appear over its entire 

length at nearly the same total temperture. Both observations suggest the 

possibility of heterogeneous nucleation occurring in the free stream. Comparisons of the present onset results are made with calculations made by Sivier and 

data gathered by Goglia. 

The potential operational benefits of the supercooling realized were analyzed in terms of increased Reynolds number capability at a given tunnel total 

pressure and reduced drive-fan power and liquid nitrogen consumption if Reynolds 

number is held constant. Depending on total pressure and free-stream Mach number, these three benefits are found to vary respectively from 8 to 19 percent, 

12 to 24 percent, and 9 to 19 percent. Since operating costs at typical test 

conditions are approximately 10 percent due to drive-fan power and 90 percent 

due to liquid nitrogen injection, reduction in operating costs will be very 

close to the percentage reduction in liquid nitrogen consumption. 

Although the present experimental data form a preliminary basis for predicting minimum operating temperatures for nitrogen-gas wind tunnels, it is 

just one of several steps that are needed for a more complete understanding of 

the problem. More work is needed in the following areas: tests of other airfoil pressure distributions, including angle-of-attack effects, to determine 

the sensitivity of the onset of condensation effects to different local velocities and gradients; experiments utilizing light scattering to follow the 

injected liquid nitrogen droplets around the tunnel circuit to determine whether 

they may be causing heterogeneous nucleation in the test section; and studies 

to determine scaling effects so that the present results may be extended to 

tunnels of other' sizes. 

Langley Research Center 

National Aeronautics and Space Administration 

Hampton, VA 23665 

March 9, 1979 

13 

I 
APPENDIX 

DATA ANALYSIS AND ERROR ESTIMATES 

Data Analysis Procedure 

Because of the importance of the data reduction technique upon the detection of the onset of condensation effects, this section of the appendix is 

included in order to describe in detail the M, correction procedure and to 

explain the procedure for determining airfoil onset Tt. Examples of the 

various steps are included for the M, = 0.85 and Rc = 16 x 1 O6 path. 

The M, correction procedure is employed in order to eliminate as much 

as possible the effect of Mach number when Cp's are compared along a path 

of constant El, and %. While M, is nominally constant along a path, many 

pressure distributions are recorded at values of M, that vary from the nominal value by ?0.010. To determine whether an M, dependence exists at a 

given x/c location, a linear regression technique is applied to condensationfree values of Cp plotted as a function of M,. In this manner, if there is 

a correlation between Cp and M, all of the data can be corrected to a 

single value of M,. If there is little or no correlation between C+ and 

M, then a weak dependence is assumed to exist, and no correction is assumed 

to be necessary. Thus, all of the data along a given path of constant M, 

and Rc can be used. 

The first step of the M, correction procedure is to apply a linear 

regression technique to condensation-free values of Cp at a given x/c as 

a function of M,. Using standard definitions, as found for example in reference 18, the slope of the linear regression fit would be given by 

n 

m= 

i=l 

where 

14 
I "" 

APPEND I X 

and 

n 

The correlation coefficient r, which is an indication of goodness of fit, is 

given by 

where if r = 0, there is no correlation, and if I rI = 1, there is perfect correlation. For the present analysis, if Irl > 0.5, then the correlation is considered strong enough for m to be used in correcting a given M, to another 

value. If - I r I < 0.5, the dependence between C and M, is considered weak, 

and m is assumed to be zero. Three xamples OF various values of r are 

shown in figure 40 for the M, = 0.85 and Rc = 16 x lo6 path. Figure 40(a) 

shows the linear regression fit to Cp for x/c = 0.00 (the orifice at the 

leading edge of the airfoil) as a function of M,. In this case r = 0.15 and, 

indeed, there seems to be little correlation between M, and 5. Consequently, 

no attempt is made to manipulate or correct these data for small differences in 

M,. Figure 40(b) shows the values of Cp for x/c = 0.40 as a function of 

M,. In this case r = 0.49; therefore, this linear curve fit barely fails to 

meet the correlation test. Figure 40(c) illustrates the values of 5 for 

x/c = 0.80 that lead to r = 0.92. As seen in figure 40(c), good correlation 

exists between Cp and M , and differences in Cp due to differences in M, 

can be removed by correctigg values of Cp to a glven Mm,O by setting 

where Cp,o is the corrected value of Cp and m is the slope of the linear 

fit. Again, m is assumed to be equal to zero in equation (A5) if Irl < 0.5. 

Once the linear regression technique has been applied to the values of Cp 

for each orifice along the path, a set of intermediate graphs is drawn before 

the airfoil onset Tt is determined. For each orifice a value of ACp is 

plotted as a function of Tt where 

15 
APPENDIX 

In equation (A6), CpI0 is corrected with respect o Mar and CpIav is an 

average of condensatlon-free values of CpI0 for that orlf ice. (Condensationfree values were determined by establishing crude onset values of Tt without 

the benefit of correction procedures; then a temperature buffer of at least a 

2 K temperature was added. Final onset values of Tt were then checked to 

insure that Cp,av was indeed free from condensation effects.) An example of 

ACp plotted agamst Tt with and without correction is shown in figure 41 for 

x/c = 0.80 and r = 0.92. Figure 41(a) shows the uncorrected data and figure 41 (b) shows the values of Cp after correction. As can be seen, considerable "order" is added to the data by the correction process, and this order 

permits easier identification of the Tt at which Cp for this x/c location 

begins to depart from its unaffected average value. Not always, however, was 

Irl > 0.5, and so this simplification was not always possible. Whether or not 

1'1 > 0.5, graphs similar to figure 41 (a) or 41 (b) are then drawn for each 

orifice location over the airfoil. These graphs are used to determine at what 

Tt each of the orifices first experiences systematic departure from its 

unaffected average value of CpI0. 

These orifice onset temperatures are then plotted as a function of x/c 

as was shown in figure 19. The orifice onset plots are the key analysis graphs 

because they provide an overview of the effects on the airfoil as a whole. 

There is experimental uncertainty in the onset point for each orifice; consequently, it is helpful to see all of the orifice onset Tt'S together so that 

a particularly low or high value can be checked for possible error. The airfoil 

onset Tt is not aken to be an average of orifice onset Tt's; rather it is 

taken to be the warmest orifice onset Tt that appears systematic. Uncertainty 

bars are drawn to encompass the highest orifice onset Tt, whether the deviation 

appears systematic or not. 

The data analysis procedure described herein was more sensitive to condensation onset than previous analyses described in references 19, 20, and 21. 

In references 19 and 20, pressure distributions were superimposed to detect 

differences, but no correction was made to Cp for differences in M, and, 

consequently, much of the data could not be used. Reference 21 used the ACp 

plotted against Tt format at 0-, 25-, 50-, and 75-percent-chord locations but 

still did not include the correction technique for Mach number. 

Error Estimate for Graphs With A$ Plotted Against Tt 

During the present experiment, fluctuations in wind-tunnel conditions were 

the principal source of error during the 50-sec period required to record the 

data. Tunnel conditions were observed to fluctuate with standard deviations of 

the following magnitudes : apt of k0.005 atm (varied with M, and Rc) ; 

of kO.003; and of kO.5 K. The manufacturer's stated accuracy in the 

static-pressure measurements was 0.5 percent of full scale. A representative 

standard deviation due to these fluctuations is calculated herein for ACp, as 

16 
APPENDIX 

where n would be the number of samples used in the average. The variance of 

cpl0 can be written from equation (AS) as 

where f is defined as 

U 2 

f 

If there is much more relative error in .(Ma - Malo) than in m, the variance 

in f results primarily from the variance in the difference in Mach numbers. 

Since is an arbitrarily defined constant, U2 may be written f 

Consequently, equations (AS) to (A10) lead to 

It now remains to discuss (5 , the variance associated with error in the 2 

cP 

values of Cp before the Q correction procedure. Cp is defined as 

17 
APPENDIX 

P - P, 

q, 

cp = 

Although Cp is strictly a function of Rc and M, as Schlichting explains 

in reference 23, the value of Cp calculated from an experiment may be sensitive to errors or fluctuations in p, pt, Tt, and M,. In other words, one 

must distinguish between actual Cp,Cp,act, and calculated Cp,Cp,calc. During the present experiment, the prlmary difference between Cp,act and Cp,calc 

was lack of simultaneity; tunnel conditions were recorded at some time and the 

static value of p at an orifice may have been recorded at a time up to 50 sec 

later. Calculation of the impact of all the fluctuations upon the possible 

error in Cp,calc are presented in the following discussion except for the 

dependence of Cp,calc on Tt. Since Tt only enters the dependence of 

Cp,calc through Rc and since the Rc dependence was weak, no error in Cp 

due to Tt was calculated. An equation for the variance of Cp can be written 

as 

The next three paragraphs describe the calculation of the partial derivatives. 

aCp,calc 

apt 

The calculation of the first partial derivative begins with 

rewriting equation (A1 2) : 

Pt 

Since this derivative is calculated assuming M, and R are constant, 

sequently, equation (A1 4) gives 

P 

- = Constant 

Pt 

18 
APPENDIX 

or 

ap I -P - " 

apt IM,R,x/c Pt 

Since the tunnel conditions pt, p, and %, are recorded at some time 1 and 

p is recorded at some time 2, any fluctuation in Cp,calc due to changes in 

pt beween time 1 and time 2 are reflected in the value of p. With variables 

taken at time 1 (subscripted as a 1) and p taken at time 2 (subscripted as 2) , equation (A14) can be written as 

so that 

acp, calc 1 ap2 - "- 

apt M,,R,x/c M,,R,x/c %t1 apt 

or combining with equation (A16) and dropping the subscripts 1 and 2 gives 

acp, calc 

If the isentropic relation for a perfect gas with its ratio of specific heats 

equal to 1.4 is assumed, equation (A19) can be written as 

aCp,calc 

19 
APPENDIX 

acp, calc 

a " 

The partial derivative is found when the linear regression step 

in the Mach correction technique is performed as described in the data analysis I 

a Cp, calc 

aMa 

procedure. The value of is equal to the value of the slope m as 

shown in the equation 

aCp,calc 

=m 

aMm 

because m is just the linear regression fit to calculated values of Cp as 

a function of M-. As before, when the correlation coefficient r does not w 

acp, calc 

reflect good correlation, then , like m, is assumed to be equal to 

zero. aMoo 

acp , calc 

The calculation of the third partial derivative is simply where 

ap 

Cp,calc is in error because of instrument error in p. Consequently, 

OK, in terms of M and pt for the isentropic flow of a perfect gas with a 

ratio of specific Eeats equal to 1.4, 

2 

7PtMm 

At this point, all of the partial derivatives in equation (A13) are known 

and can be combined with the observed or known values Of Opt, OM^, and ap. 

The value of ap was first taken to be the manufacturer's value for accuracy 

20 
APPEND I X 

of 0.5 percent of full scale, but this value gave a contribution to the error 

bar in Cp on the order of 10 times the actual fluctuations in Cp. What was 

needed for the purpose of differentiating between condensation-induced and 

random deviations in Cp was ap based on transducer precision. Consequently, 

instead of basing up on the stated accuracies of 0.0170 and 0.0085 atm for 

the two transducers used, the values of Op were based on the observed two precisions of 0.0004 and 0.0002 ah. These low magnitudes in ap made the contribution of the instrument error to the total error negligible. 

If isentropic relations for a perfect gas with the ratio of specific heats 

equal to 1.4 are assumed and if ap is negligible, equations (A1 1 ) , (A1 3) , (A20) , and (A21) can be combined to give 

The error bars used in the graphs in the data analysis procedure where ACp 

is plotted against Tt were calculated with the value of a~c just given. P 

21 
REFERENCES 

1. Adcock, Jerry B.:, Real-Gas Effects Associated With One-Dimensional Transonic 

Flow of Cryogenic Nitrogen. NASA TN D-8274, 1976. 

2. Wegener, P. P.; and Mach, L. M.: Condensation in Supersonic and Hypersonic 

Wind Tunnels. Advances in Applied Mechanics, Volume V, H. L. Dryden and 

Th. von K&&, eds., Academic Press, 1958, pp. 307-447. 

3. Wegener, P. P.: Nonequilibrium Flow With Condensation. Acta Mech. vol. XXI, 

no. 1-2, 1975, pp. 65-91. 

4. Daum, Fred L.; and Gyarmathy, George: Condensation of Air and Nitrogen in 

Hypersonic Wind Tunnels. AIAA J., vol. 6, no. 3, Mar. 1968, pp. 458-465. 

5. Goglia, Gennaro L.; and Van Wylen, Gordon J.: Experimental Determination 

of Limit of Supersaturation of Nitrogen Vapor Expanding in a Nozzle. 

Trans. ASME, Ser. C: J. Heat Transfer, vol. 83, no. 1, Feb. 1961, 

pp. 27-32. 

6. Arthur, P. D.; and Nagamatsu, H. T.: Effects of Impurities on the Supersaturation of Nitrogen in a Hypersonic Nozzle. Memo. No. 7 (Contract 

No. DA-O4-495-0rd-19), GALCIT, Mar. 1 , 1952. 

7. Adcock, Jerry B.; and Ogburn, Marilyn E.: Power Calculations for Isentropic 

Compressions of Cryogenic Nitrogen. NASA TN D-8389, 1977. 

9. Kilgore, Robert A.: Design Features and Operational Characteristics of the 

Langley Pilot Transonic Cryogenic Tunnel. NASA TM X-72012, 1974. 

10. Beattie, James A.; and Bridgeman, Oscar C.: A New Equation of State for 

Fluids. 11. Application to Helium, Neon, Argon, Hydrogen, Nitrogen, 

Oxygen, Air and Methane. J. American Chem. Soc., vol. 50, no. 12, 

Dec. 1928, pp. 31 33-31 38. 

11. Stauffer, D.: Kinetic Theory of Two-Component ("Heteromolecular") 

Nucleation and Condensation. J. Aerosol SCi., VOl. 7, no. 4, July 1976, 

pp. 31 9-333. 

12. Wegener, Peter P.; and Wu, Benjamin J. C.: Homogeneous and Binary 

Nucleation: New Experimental Results and Comparisons With Theory. 

Faraday Discuss. Chem.S~c.~ No. 61, 1976, pp. 77-82. 

13. Wilemski, Gerald: Binary Nucleation. I. Theory Applied to Water-Ethanol 

Vapors. J. Chem. Phys., vol. 62, no. 9, May 1, 1975, pp. 3763-3771. 

22 
14. Wilemski, Gerald: Binary Nucleation. 11. Time Lags. J. Chem. Phys., 

vol. 62, no. 9, May 1, 1975, pp. 3772-3776. 

15. Oswatitsch, K1. (M. Flint, transl.): Condensation Phenomena in Supersonic 

Nozzles. R.T.P. Transl. No. 1905, British Min. Aircraft Prod. (From 

2. Angew. Math. & Mech., vol. 22, no. 1 , Feb. 1942, pp. 1-1 4.) 

16. Sivier, Kenneth D.: Digital Computer Studies of Condensation in Expanding 

One-Component Flows. ARL 65-234, U.S. Air Force, Nov. 1965. (Available 

from DX as AD 628 543.) 

17. Goglia, Gennaro Louis: Limit of Supersaturation of Nitrogen Vapor Expanding in a Nozzle. Ph. D. Diss., Univ. of Michigan, 1959. 

18. Freund, John E.: Mathematical Statistics. Second ed. Prentice-Hall, Inc., 

c.1971. 

19. Hall, Robert M.: Preliminary Study of the Minimum Temperatures for Valid 

Testing in a Cryogenic Wind Tunnel. NASA TM X-72700, 1975. 

20. Hall, Robert M.; and Ray, Edward J.: Investigation of Minimum Operating 

Temperatures for Cryogenic Wind Tunnels. J. Aircr., vol. 14, no. 6, 

June 1977, pp. 560-564. 

21. Hall, Robert M.: An Analysis of Data Related to the Minimum Temperatures 

for Valid Testing in Cryogenic Wind Tunnels Using Nitrogen as the Test 

Gas. NASA TM X-73924, 1976. 

22. Crandall, Keith C.; and Seabloom, Robert W.: Engineering Fundamentals 

in Measurements, Probability, Statistics, and Dimensions. McGraw-Hill 

Book Co., c.1970. 

23. Schlichting, Hermann (J. Kestin, transl.): Boundary-Layer Theory. Sixth ed. 

McGraw-Hill Book Co., Inc., c.1968. 

23 
4 

3 

Values 

relative 2 

to 322 K 

1 

P 8 

a 

P 

-\ 

I 1 I 

6 

Values 

relative 4 

to 322 K 

2 

0 100 200 300 

I 

400 

Total temperature, Tt, K 

(a) Gas properties. 

0 

I I I I 

100 200 300 400 

Total temperature, Tt, K 

(b) Test conditions and drive power. 

Figure 1 .- Effect of temperature reduction for M,= 1 .O, pt = 1 atm, and 

constant reference length. 
-ANacelle section 

Tunnel anchor 

m 

Figure 2.- Schematic of Langley 0.3-meter transonic cryogenic tunnel. 
c= 0.137 m -4; 

Figure 3.- Two-dimensional NACA 0012-64 airfoil with orifices spaced at 5-percent-chord 

locations. Trailing-edge orifice was added €or tests with M, = 0.75 and 0.95. 
5- 

4- 

Local saturation, 

3- 

2- 

1, I I . . ""1- 

75 85 95 ~ 105 115 125 I 

Tt' K 

Figure 4.- Five paths of constant R, for M, = 0.85 test. 

lo6 

27 
5- 

Free-stream 

Local saturation, 

= 0.93 

I I 

75 85 95 105 115 125 

Tt’ K 

Figure 5.- Three paths of constant Q for M, = 0.75 test. 

28 
5- 

Free-stream 

saturation, Rc 

M, = 0.93 y 40 X lo6 

Local saturation, 

Ml,max = 1.35 

Local saturation, 

75 85 95 105 115 125 

Tt’ K 

Figure 6.- Three paths of constant for I$,, = 0.95 test. 

(Rc = 40 x 1 O6 path taken with M, = 0.93.) 

W 

h, 
-.8 

-. 6 

-. 4 

-. 2 

cP O 

.2 

.4 

0 

0 

0 

Figure 7.- Average unaffected pressure distribution for 

Rc = 15 x 1 O6 path of I&, = 0.75 test. 

30 
0 

00 

OO 

OO 

0 0 ~ 

0 

0 

0 

I 1 1 I 1 1- .I I I 1 

.2 .4 .6 .8 1.0 

x/c 

31 
0 

0 

1 

.8 

0 

0 

0 

Figure 9.- Average unaffected pressure distribution for 

Rc = 41 x lo6 path of M, = 0.75 test. 

1 - -.J 

1.0 

32 
't 

88 

Local sat. Tt 88.8 Onset 0 

M, sat. Tt 85.5 No onset detected 0 

Reservoir sat. Tt 78.9 

Data min. ---- Tt 80.4 

Orifice 

onset 86 

Tt' K 

- 

r Airfoil onset Tt 

p,

/ 

0 0 

0 00 0 """""" CI"" "- 

I 78 6 I 1 I I I I I I I 1 

.20 .40 .60 .80 1.00 

x/c 

Figure 10.- Orifice onset Tt's and resulting airfoil onset Tt 

for R, = 15 x 106 path of & = 0.75 test. 

33 
96 

94 

92 

Orifice 

onset 90 

Tt' K 

88 

84 

82 

Local sat. Tt 95.1 Onset 

Moo sat. Tt 91.6 No onset detected 0 

Reservoir sat. Tt 84.7 

Data min.---- Tt 86.3 

0 

- 

- 

- 

r Airfoil onset Tt 

I 

- 

0 n n U V """- - - --O-U~"c1[3-Cl 

0 .20 .40 .60 .80 1.00 

x/c 

Figure 11.- Orifice onset Tt's and resulting airfoil onset Tt for 

R, = 24 x lo6 path of M, = 0.75 test. 

34 
Local sat. Tt 103.0 Onset 0 

Moo sat. Tt 99.4 No onset dected 0 

Reservoir sat. Tt 92.1 Excessive scatter 

Data min. ---- Tt 94.7 

loo t r- Airfoil onset Tt 

981,\, \ \ 1- \/\ \ \ \ \ \ \ 

/- Or ifice \\\\ 

onset 

90 g2t I I I I I I I I I 1 

0 .20 .40 .60 .80 1.00 

x/c 

I 

Figure 12.- Orifice onset Tt's and resulting airfoil onset Tt for 

Rc = 41 x 1 O6 path of M, = 0.75 test. 

35 
5- Onset of 

effects curve 

Local saturation, 

= 0.93 

Free-stream 

"1."' 

75 85 95 105 115 

Tt' K 

_J 

125 

Figure 13.- Onset of condensation effects for M, = 0.75 test. 

Error bars shown indicate possible experimental error. 

36 
-.8 

-. 6 

-. 4 

-. 2 

O 

.2 

.4 

- 

- Ooo 

- O0 

0 

0 - 0 

0 0 

0- 

u 

0 

- 0 

- 

0 Bad or if ice 

0 .2 .4 .6 .8 1.0 

x/c 

Figure 14 .- Average unaffected pressure distribution for 

Rc = 16 x lo6 path of M, = 0.85 test. 

37 . 
-.8 

-. 6 

-.4 

-. 2 

0 

.2 

.4 

1 1 1 1 1 1 "~-1 1 1 1 

0 .2 .4 .6 .8 1.0 

x/c 

Figure 15 .- Average unaffected pressure distribution for 

R, = 26 x 1 O6 path of M, = 0.85 test. 

38 
0 

0 

OO 

0 

0 

I. -1 1 "I. -1- I 1- I I 1 

.2 .4 .6 .8 1.0 

x/c 

Figure 16.- Average unaffected pressure distribution for 

R, = 34 x IO6 path of Ma = 0.85 test. 

39 
0 0 0 

I 

.6 

0 

" 

J 

0 

- 0 " 

0 

0 

Figure 17.- Average unaffected pressure distribution for 

R, = 38 x lo6 path of M, = 0.85 test. 

0 

1 

1.0 

40 
-.tj t- O00 

i 

0 -.2 - 0 

0 0 

.2 

O 5 

- 

.4 - 

1.2 " I I I I I 1 1 I I I 

.2 .4 .6 .8 1.0 

x/c 

0 

0 

0 Bad orif ice 

Figure 18.- Average unaffected pressure distribution for 

R, = 42 x 1 O6 path of M, = 0.85 test. 

41 
Local sat. Tt 95.3 Onset 0 94r M~ sat. Tt 87.3 

92 t Reservoir sat. Ti 79.1 Excessive scatter A 

Data min.---- Tt 81.3 

Or Lfice 

onset 

Airfoil onset Tt 

80 - 

78 I I I I I I I I I I 

0 .20 .40 .60 .80 1.00 

x/c 

Figure 19.- Orifice onset Tt'S and resulting airfoil onset Tt for 

R, = 16 x lo6 path of M, = 0.85 test. 

42 
Local sat. Tt 101.8 Onset 0 

Moo sat. Tt 93.5 No onset detected 0 

Reservoir sat. Tt 84.9 Excessive scatter A 

Data min.---- Tt 86.2 

96 

94 

Orifice 

Tt' K 

90 0 0 0 

O0 00 0 

84 .. I 1. - I I -1 1 -1 1 I 

0 .20 .40 .60 .80 1.00 

x/c 

43 
i 

Local sat. Tt 105.9 Onset 

Mm sat. Tt 97.2 No onset detected 

Reservoir sat. Tt 88.3 Excessive Scatter 102 

lo4 F 0 

0 

n 1 Data min. ---- Tt 90.3 

98 

Orifice 96 

onset 

94 Tt, K 

92 

90 """" O-AA-"" 

88 860 t .20 1"- -1 .40 1. " 1 - .60 1"- I .80 ~l- .". 1.2 1.00 

x/c 

Figure 21.- Orifice onset Tt's and resulting airfoil onset Tt for 

Rc = 34 x lo6 path of M, = 0.85 test. 

44 
102 

lo4 F 

Local sat. 

Moo sat. 

Reservoir sat. Tt 

Data min.---- 

Tt 

Tt 

Tt 

107.5 Onset 0 

98.7 No onset detected 0 

89.7 Excessive scatter 

90.8 

/- Airfoil onset Tt 

45 
Local sat. Tt 109.2 Onset 0 

M, sat. Tt 100.3 

lo6 r Reservoir sat. Tt 91.1 Excessive scatter 

104 t Data min.---- Tt 93.1 Bad orifice 0 

Or ifice 

onset 

Tt' K 

0 0 

-""-"Lo" -" 

9Q I I 

0 .20 .60 .80 1.00 040 x/c 

Figure 23.- Orifice onset Ttls and resulting airfoil onset Tt for 

Rc = 42 x lo6 path of M = 0.85 test. a0 

46 
& 

Onset of 

effects curve 

- Local s 

Mt ,max 

Free-stream 

saturation 

M, = 0.8g 

1 . .. .. 1 ~ . ~~.~ 1 

'ahration, 

= 1.2 

75 85 95 105 115 125 

I 

Tt, K 

Figure 24.- Onset of condensation effects for M = 0.85 test. 

Error bars shown indicate possible experimegtal error. 

47 
-.8 

-.6 - O0 

- 

-.4 - 0O0 0 

-.2 - 0 0000 

0 

cP ocso . .. ~~ ~- .. . ". ~ " 

.2 - 

.4 - 

(3 Bad orifice 

I I 1 .~ I I -1.- -1.. ~ I - I ~- J 

0 .2 .4 .6 .8 1.0 

48 
-.8 - 

-.6 - 

-.4 - 

-.2 - 

0 C". 

.2 - 

.4 - 

0 

0 

0 Bad orifice 

0 

OOO 0 

.2 .4 .6 

x/c 

1.0 

Figure 26.- Average unaffected pressure distribution for 

R, = 27 x lo6 path of M, = 0.95 test. 

49 
-.8 

-. 6 

-. 4 

-. 2 

cp O[ 

.2 

.4 

0 

0 OO 

0 

0 .2 

0 Bad orifice 

J .l 1 1 I. 1 

.4 .6 x/c .8 

Figure 27.- Average unaffected pressure distribution for 

R, = 40 x 1 O6 path of M, = 0.95 test. (M, = 0.93 

for this path.) 

50 
Local sat. Tt 100.7 Onset 0 

MW sat. Tt 89.6 No onset dected 0 

Reservoir sat. Tt 79.1 Excessive scatter A 

Data min.---- Tt 80.0 

94 

92 F Airfoil onset Tt 

90 I 

88 

Orifice 86 

onset 

Tt' K 84 

82 

80 no"-"" A- - - 

78 

0 .20 .60 .80 1.00 .40 x/c 

I 

Figure 28.- Orifice onset Tt's and resulting airfoil onset Tt for 

R, = 17 x 106 path of M, = 0.95 test. 

51 
Local sat. Tt 107.4 Onset 0 

M, sat. Tt 95.7 No onset dected 0 

Reservoir sat. Tt 84.9 Excessive scatter 

Data min.---- Tt 86.6 

96 

94 

92 

Orifice 

onset 

Tt' K 0 00 0 

88 - 

-n o-- 86 - """ -A- A" - - 

84 I 1- 1 ." I 1 1 1 I "" 1 I 

0 .20 .40 .60 .80 1.00 

x/c 

52 
A 

Local sat. Tt 112.6 Onset 0 

Moo sat. Tt 100.9 

Reservoir sat. Tt 90.2 Excessive scatter A 

Data min.---- 90.2 Bad orifice 0 

104 Airfoil onset Tt 

102 

100 - 

0 

Orifice 98 

onset 0 

- 0 

Tt' K 96 -0 

94 - 

92 - 

90 F"oo--- ""A" " 

88 - 1. .- 1 I -1 1 1 1 1 I 1 

0 .20 .40 x/c .60 .80 1.00 

Figure 30.- Orifice onset Tt's and resulting airfoil onset Tt for 

Rc = 40 x IO6 path with M, = 0.93. 

53 
*03praiy Tt 0 

M=O " 

-02 t 0 

Om 

M2,rnax 

X/C = 0.95 

Error 

bar 

0 0 

0 

0 

IIIIlIIlIIIIIIIIIIIIlll.lllltll.ll1.lII.IIIIlIllIII~~LII111l~1J 

Tt' K 

70 80 90 I00 110 120 130 

Figure 31 .- AC+ plotted against Tt for M, = 0.93 and Rc = 40 x 106. 

Unaffected average value of Cp = -0.035. 

54 
J Free-stream 

saturation, 

M, = 0.93 

75 85 95 105 115 125 

37 K 

Figure 32.- Onset of condensation effects for M, = 0.95 test. 

Error bars shown indicate possible experimental error. 

55 
16 

14 

12 

10 

AT, K 8 

6 

4 

2 

0 

Mm 

0 0.75 

0 0.85 

0.95 

I I 1 ". . 1 _I 

1 2 3 4 5 

(a) Supercooling based on MI ,max. 

Figure 33.- Supercooling for all M, tests. Error bars shown 

indicate possible experimental error. 

56 
6 

4 

2 

AT, K 

0 

-2 

-4 

4 

Mm 

0 0.75 

0 0.85 

A 0.95 

t 

1 2 3 

Pt 9 atm 

(b) Supercooling based on M,. 

4 5 

Figure 33.- Concluded. 

57 
1 

-1 

/ MKI 

0 0.75 

0 0.85 

0.95 

Vapor-pressure curve 

60 65 70 75 80 85 90 

(a) Static values based on M = Ml,max. 

Figure 34.- Static values of p, T at onset. Error bars 

shown indicate possible experimental error. 

58 
1- 

0- 

-1 L 

60 

Vapor-pressure curve 

M, 

0 0.75 

0 0.85 

a 0.95 

65 70 

I I 

Y5 

1 -I 

80 

u 

85 90 

T? K 

(b) Static values based on M = c. 

Figure 34.- Concluded. 

59 
Curve fit to 

Sivier ' s 

conditions 

t 

MCa 

0 0.75 

0 0.85 

a 0.95 

-1 ~ I 1 1 .I = 1 .J 

60 65 70 75 80 85 90 

Figure 35.- Data compared with Adcock's curve fit to Sivier's analytically 

determined onset conditions. Error bars indicate possible experimental 

error. 

60 
1 

-1 

Sivler' s onset 

Test 

Curve fit to 

Vapor-pressure curve 

0 0.75 

0 0.85 

a 0.95 

0 &glia's 

60 65 70 75 80 85 90 

T, K 

Figure 36.- Present data compared with Goglia's data from reference 17. 

61 
16 

12 

Percent 

increase in Rc 

8 

4 

0 

9 I 

E 

Mm 

0 0.75 

0 0.85 

A 0.95 

f 

Q 

Figure 37.- Percent increase in Reynolds number capability at onset. 

Error bars shown indicate possible experimental error. 

62 
28 

J 

24 

20 

16 

Percent 

decrease in power 

12 

8 

4 

0 

i P 

Ma 

0 0.75 

0 0.85 

A 0.95 

Figure 38.- Percent decrease in drive-fan power at onset. Error 

bars shown indicate possible experimental error. 

63 
20 

16 

12 

Percent 

decrease in LN2 

8 

4 

0 

i 

P h 

Mco 

0 0.75 

0 0.85 

A 0.95 

f 

d 

[ _- 

1 2 3 4 5 

Figure 39.- Percent decrease in LN2 required to absorb drive-fan heat. 

Error bars shown indicate possible experimental error. 

64 
1.22 

1.21 

cp 1.20 

1.19 

1.18 

x/c = 0 

0 

0 

1 

.85 

Moo 

(a) r = 0.15. 

IO 1 

.86 .87 

Figure 40.- Examples of curve fits and resulting correlation coefficient r. 

65 
-. 49 

-. 50 

-. 51 

-. 52 

X/C = 0.40 

0 

2’ 

0 

0 

~ lo 0 1 

.84 .8 5 .86 .8 7 

Moo 

(b) r = 0.49. 

Figure 40.- Continued. 

66 
-.02 - 

-.03 - 

-.04 - 

cP 

-.05 - 

-. 07 

.84 .8 

1 

5 .86 

1 ” 

.8 7 

X/C = 0.80 

Mco 

(c) 1: = 0.92. 

Figure 40.- Concluded. 

67 
. Ot 

.02 

.01 

ACP 0 

-.01 

-. 02 

-.03 

- Saturation Tt for - 

- = O " Ml,rnax 

0 

00 

- 0 

X/C = 0.80 

r = 0.92 

0 

0 

0 

0 0 

0 

0 

0 

0 

70 80 90 100 110 120 130 

Tt' K 

(a) Before M, correction procedure. 

Figure 41.- Improvement in graphs of ACp plotted against Tt with Mach 

correction for M, = 0.85 and Rc = 16 x lo6. Unaffected average 

value of Cp = -0.042. 

6% 

L . . - . ... . . . . . . . . . 
Saturation Tt for - 

M = 0 Mal Ml,max 

.01 *O2I 

"01 

/ Onset of effects 

0°8 

0 

0 

0 

8 

X/C = 0.80 

r = 0.92 

Error 

bar 

(b) After M, correction procedure. 

Figure 41.- Concluded. 

69 
1. Report No. 2. Government Accession No. 1 3. Recipient's Catalog No. 

NASA TP-1385 I 

4. Tltle and Subtitle I 5. Report Date 

ONSET OF CONDENSATION EFFECTS WITH AN NACA 0012-64 April 1973 

AIRFOIL TESTED IN THE LANGLEY 0.3-METER TRANSONIC 6. Performmg Organization Cde 

CRYOGENIC TUNNEL 

7. Author(s) 8. Performmg Organization Report No, 

Robert M. Hall L-12581 

10. Work Unit No, 

9, Performing Organization Name and Address 505-06-43-08 

NASA Langley Research Center 

Hampton, VA 23665 11. Contract or Grant No, 

~~ ~~~~~~ 

13. Type of Report and Perlod Covered 

12. Sponsorrng Agency Name Technical Paper 

National Aeronautics and Space Administration 

Washington, DC 20546 14. Sponsoring Agency Code 

1 

15. Supplementary Notes 

16. Abstract 

A 0.1 37-meter NACA 0012-64 airfoil has been tested at a Oo angle of attack in 

the nitrogen-gas Langley 0.3-meter transonic cryogenic tunnel at free-stream Mach 

numbers of 0.75, 0.85, and 0.95 over a total pressure range from 1.2 to 5.0 atmspheres. The onset of condensation effects as determined by varying the stagnation temperature was found to correlate better with the amount of supercooling in 

the free stream than it did with the supercooling in the region of maximum local 

Mach number over the airfoil. Effects in the pressure distribution over the airfoil were generally seen to appear over its entire length at nearly the same total 

temperature. Both observations suggest that heterogeneous nucleation does occur 

in the free stream. The benefits realized from supercooling are presented in 

terms of increased Reynolds number capability at a given tunnel total pressure and 

reduced drive-fan power and liquid nitrogen consumption if Reynolds number is held 

constant. Depending on total pressure and free-stream Mach number, these three 

benefits are found to vary respectively from 8 to 19 percent, 12 to 24 percent, 

and 9 to 19 percent. The appendix gives details of the data analysis and error 

estimates. 

17. Key Words (Suggested by Author(r)) 18. Distribution Statement 

Cryogenic wind tunnels 

Condensation 

Minimum temperatures 

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Unclassified Unclassified 69 $5.25 

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