Mary Ann Dembowski and Nicholas J. Georgiadis

Glenn Research Center, Cleveland, Ohio

An Evaluation of Parameters Influencing Jet

Mixing Using the WIND Navier-Stokes Code

NASA/TM—2002-211727

August 2002
The NASA STI Program Office . . . in Profile

Since its founding, NASA has been dedicated to

the advancement of aeronautics and space

science. The NASA Scientific and Technical

Information (STI) Program Office plays a key part

in helping NASA maintain this important role.

The NASA STI Program Office is operated by

Langley Research Center, the Lead Center for

NASA’s scientific and technical information. The

NASA STI Program Office provides access to the

NASA STI Database, the largest collection of

aeronautical and space science STI in the world.

The Program Office is also NASA’s institutional

mechanism for disseminating the results of its

research and development activities. These results

are published by NASA in the NASA STI Report

Series, which includes the following report types:

• TECHNICAL PUBLICATION. Reports of

completed research or a major significant

phase of research that present the results of

NASA programs and include extensive data

or theoretical analysis. Includes compilations

of significant scientific and technical data and

information deemed to be of continuing

reference value. NASA’s counterpart of peerreviewed formal professional papers but

has less stringent limitations on manuscript

length and extent of graphic presentations.

• TECHNICAL MEMORANDUM. Scientific

and technical findings that are preliminary or

of specialized interest, e.g., quick release

reports, working papers, and bibliographies

that contain minimal annotation. Does not

contain extensive analysis.

• CONTRACTOR REPORT. Scientific and

technical findings by NASA-sponsored

contractors and grantees.

• CONFERENCE PUBLICATION. Collected

papers from scientific and technical

conferences, symposia, seminars, or other

meetings sponsored or cosponsored by

NASA.

• SPECIAL PUBLICATION. Scientific,

technical, or historical information from

NASA programs, projects, and missions,

often concerned with subjects having

substantial public interest.

• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientific

and technical material pertinent to NASA’s

mission.

Specialized services that complement the STI

Program Office’s diverse offerings include

creating custom thesauri, building customized

data bases, organizing and publishing research

results . . . even providing videos.

For more information about the NASA STI

Program Office, see the following:

• Access the NASA STI Program Home Page

at http://www.sti.nasa.gov

• E-mail your question via the Internet to

help@sti.nasa.gov

• Fax your question to the NASA Access

Help Desk at 301–621–0134

• Telephone the NASA Access Help Desk at

301–621–0390

• Write to:

 NASA Access Help Desk

 NASA Center for AeroSpace Information

 7121 Standard Drive

 Hanover, MD 21076
Mary Ann Dembowski and Nicholas J. Georgiadis

Glenn Research Center, Cleveland, Ohio

An Evaluation of Parameters Influencing Jet

Mixing Using the WIND Navier-Stokes Code

NASA/TM—2002-211727

August 2002

National Aeronautics and

Space Administration

Glenn Research Center
Available from

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22100

The Aerospace Propulsion and Power Program at

NASA Glenn Research Center sponsored this work.

Available electronically at http://gltrs.grc.nasa.gov
NASA/TM2002-211727 1 

An Evaluation of Parameters Influencing Jet Mixing 

 Using the WIND Navier-Stokes Code 

Mary Ann Dembowski and Nicholas J. Georgiadis 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract

The WIND code, a Reynolds-averaged Navier-Stokes solver used for a variety of 

aerospace flow simulations, was investigated for a Mach 2 nozzle at a series of nozzle 

stagnation temperatures. Comparisons of WIND calculations are made to experimental 

measurements of axial velocity, Mach number, and stagnation temperature along the jet 

centerline. The primary objective was to investigate the capabilities of the two-equation 

turbulence models available in WINDversion 4.0, for the analysis of heated supersonic 

nozzle flows. The models examined were the Menter Shear Stress Transport (SST) 

model and the Chien k-ε model, with and without the compressibility correction due to 

Sarkar. It was observed that all of the turbulence models investigated produced solutions 

that did not agree well with the experimental measurements. The effects of freestream 

Mach number and turbulent Prandtl number specifications were also investigated. 

Introduction

Computational fluid dynamics (CFD) codes have become an attractive option for the 

analysis of aerospace systems due to advances in flow solver and computer hardware 

technologies. For the investigation of one particular class of flows, that of aircraft engine 

exhaust nozzles, Reynolds-averaged Navier-Stokes (RANS) solvers have been used 

extensively. In the RANS approach, all effects of turbulence are replaced with a 

turbulence model. However, with realistic nozzle flows typically dominated by turbulent 

mixing, the accuracy of a flow simulation is usually determined by the capabilities of the 

turbulence model employed. Previous studies, such as those of Barber et al.1 and 

Georgiadis et al.2

 have indicated that turbulence models available for exhaust nozzle flow 

simulations have difficulty in accurately predicting the effects of compressibility, high 

temperatures, and three dimensional flow features. 

Due to these deficiencies in RANS methods, interest has arisen in more sophisticated 

techniques such as Large Eddy Simulation (LES). However, the routine use of LES 

methods to calculate nozzle and jet flows to a high degree of accuracy is not yet possible. 

This is due to the requirement of prohibitively large computational grids and very long 

computer run times using LES for even simple configuration nozzles at low Reynolds 

numbers.3,4 As a result, RANS methods will still be the practical technique for 

calculating nozzle and jet flows in the foreseeable future, and it is necessary to identify 

the capabilities of currently available RANS methods. 
NASA/TM2002-211727 2 

In the current study, an assessment of the WIND code-version 4.0, a production-use 

RANS solver,5

 is made for a supersonic round nozzle that was tested for a series of nozzle 

stagnation temperatures. The primary objective of this study is to investigate the 

turbulence models most frequently used in WIND for nozzle and jet flow analyses. In 

addition, the effects of other computational settings are also investigated including 

variation of the turbulent Prandtl number, the Mach number set for the ambient air 

surrounding the jet, and incorporation of a correction for compressibility. 

Experimental Nozzle Configuration

The present study uses the benchmark experiments performed at the NASA Langley 

Research Center (LaRC) Jet Noise Laboratory.6 These experiments investigated an 

axisymmetric water-cooled Mach 2 nozzle with an exit diameter, D = 3.60 in. (91.44 

mm). Five sets of data were collected from the cases, with the nozzle plenum stagnation 

temperature varied as indicated in Table 1. The nozzle operated at fully expanded 

conditions for this series of cases. The Reynolds number, based on D, varied from 1.3 ×

106

 to 8.3 × 106. 

Table 1: Experimental nozzle flow conditions 

Run 

no. 

Ttj, °F Ttj, °R 

 6 104 563.67 

21 455 914.67 

41 900 1359.67 

51 1550 2009.67 

61 2000 2459.67 

Computational Model

The computational grid used for these nozzle calculations was a slightly modified version 

of that used for calculations discussed in reference 1. This axisymmetric grid, shown in 

figure 1, consisted of three zones as follows. The first zone represented the internal 

nozzle region, with 121 axial points and 81 vertical points. The grid was slightly 

clustered to the exit of the nozzle, where an interface to the downstream mixing zone was 

placed. The grid was clustered to the wall such that two points were placed within the 

laminar sublayer of the developing boundary layer along the nozzle wall. The second 

zone is positioned above the nozzle and represents the inflow of the ambient air. The 

original grid used in reference 1 had 9 axial points and 34 vertical points. Because initial 

calculations with the WIND code indicated stability problems in this region, this zone 

was modified by increasing the number of axial points from 9 to 41, and moving the 

physical position of the inflow slightly further upstream. This modification improved the 

stability characteristics of the calculations discussed later in this report. The third zone 
NASA/TM2002-211727 3 

was the nozzle exhaust region downstream of zones one and two. This zone had 121 

axial and 121 vertical points. The interface of zone three with zones one and two formed 

a contiguous, point to point match. In addition, 8 vertical points were placed at the 

location of the nozzle lip, which is represented by the vertical line between blocks one 

and two at the interface with block three. These additional points were carried through 

zone three to help resolve the flow development just downstream of the nozzle lip. 

Grid sensitivity studies discussed in reference 1 indicated that the original grid was 

sufficient using five Navier-Stokes solvers utilized in that work. Since the WIND code 

used in the current study was derived from NASTD, one of the solvers in the former 

investigation, further grid sensitivity analyses were not conducted here. 

Boundary condition types and zone interfacing were set for calculations with WIND 

using the GMAN pre-processor. An arbitrary inflow was specified for both the nozzle 

plenum (zone one) and the freestream inflow (zone two). The inner wall of the nozzle 

was set as a no-slip, adiabatic surface. The axis of symmetry is set as an inviscid wall, but 

was further specified as axisymmetric within the WIND run data file. The top and bottom 

faces of zones two and three were also set as inviscid walls. The right face of zone three 

was specified an outflow. In the WIND run data file, the actual flow conditions were 

specified corresponding to the boundary condition types set with GMAN, and are 

described next. 

In the experiment, the surrounding air was at rest with the pressure and temperature 

corresponding to 14.7 psi and 530° R, respectively. The majority of cases were run 

assuming a small forward freestream velocity corresponding to Mach 0.01. To determine 

the effect of the ambient air settings, two other freestream conditions, corresponding to 

Mach 0.1 and Mach 0.2 were investigated for selected cases, as will be discussed in the 

results section. The nozzle plenum stagnation pressure was set to 115.02 psi for all cases, 

and the stagnation temperatures were set to the values indicated in table 1. 

The turbulence models used within WIND version 4.0 for this study were the Menter 

two-equation model,7,8 also known as the Shear-Stress Transport model (SST) and the 

Chien two-equation k-ε model.9

 The SST model applies the k-ω form of its equations in 

near wall-bounded regions and the k-ε form in free shear layer regions. In addition, the 

Chien model was used with and without the Sarkar compressibility correction.10,11 The 

Sarkar compressibility correction effectively increases the rate of the turbulent kinetic 

energy dissipation and then lowers the resultant turbulent viscosity. Finally, the turbulent 

Prandtl number, which is frequently set to a default value of 0.9 in production flow 

solvers such as WIND, was varied from 0.5 to 0.9 while using the SST turbulence model. 

Results

The first comparisons to be discussed investigated effects of the freestream Mach

number. This value is ideally set to the conditions of the air surrounding the jet, but 

compressible flow solvers such as WIND have trouble converging the extreme 

differential between the slow freestream air and the supersonic jet. Beginning with the 
NASA/TM2002-211727 4 

unheated nozzle case (104 °F) WIND calculations were obtained using the SST 

turbulence model for each of the three freestream Mach numbers, 0.01, 0.10, and 0.20. 

While Mach 0.01 models the ambient air stream most closely, figure 2 indicates that the 

jet spread rate is substantially overpredicted as was also reported in reference 1. As in 

the previous work, the overpredictions are due to deficiencies in the turbulence models 

for highly compressible flow. In figure 2 and all following figures, x/D = 0 represents 

the nozzle exit. As the freestream Mach number is increased to 0.1 and 0.2, the jet mixing 

rate is reduced. The conclusion that the Mach 0.2 case compares best with the 

experimental data should not be drawn, however, because the “closer” agreement is a 

result of turbulence model inadequacy being compensated for by the modified freestream 

conditions. Similar results were obtained for calculations obtained with the nozzle 

stagnation temperature set to 1550 °F, as shown in figure 3. The centerline stagnation 

temperature profiles do not show much sensitivity, which is to be expected since the 

freestream stagnation temperature does not vary much between Mach 0.01 and Mach 

0.20 while holding the static temperature fixed. 

The next set of results examine the effects of varying the turbulent Prandtl number. As 

mentioned previously, a value of 0.9 is the default value when using WIND and other 

similar production flow solvers. However, in free shear layers, a value for the turbulent 

Prandtl number closer to 0.5 has been suggested.12 The 1550 °F nozzle stagnation 

temperature case was investigated using WIND again with the SST turbulence model and 

turbulent Prandtl number settings of 0.5, 0.7, and 0.9. Centerline profiles of axial 

velocity and Mach number shown in figures 4(a) and 4(b), respectively, indicate little 

effect of varying the turbulent Prandtl number. The centerline stagnation temperature, 

figure 4(c), does decay faster as the turbulent Prandtl number is reduced. These results 

cannot justify a particular setting for the turbulent Prandtl number but indicate that the 

turbulent thermal transport is significantly affected by the value used. Some efforts such 

as those of Kenzakowski et al.13 have begun to investigate a variable turbulent Prandtl 

number model for more accurate treatment of complex exhaust nozzle flows with thermal 

transport as a dominant flow feature. 

While the freestream Mach number and turbulent Prandtl number variations were 

investigated only for selected cases, the turbulence model investigations were conducted 

for all of the nozzle operating conditions listed in Table 1 using the SST and Chien k-ε

turbulence models. The SST model is currently one of the most popular turbulence 

models used in WIND and similar production-use RANS solvers because it uses a k-ω

formulation in wall-bounded regions and a k-ε formulation in free shear layers. The k-ε

formulation used within SST differs slightly from the free shear layer form of standard kε models, with the most significant difference occurring in the ε equation diffusion 

coefficient, σε. Models such as the Chien and Jones-Launder14 formulations use σε = 

1.30, while the k-ε formulation used within SST uses σε = 1.17. Reference 15 mentions 

that this is done in the SST approach to more accurately calculate the logarithmic portion 

of the boundary layer. 

The Chien model as implemented in WIND provides the option to include the 

compressibility correction due to Sarkar.10,11 As a result, three WIND solutions were 

obtained for each of the five operating conditions listed in Table 1, the first using the SST 
NASA/TM2002-211727 5 

model, the second using the standard Chien model, and the third using the Chien model 

incorporating the Sarkar compressibility correction. All of these cases were run using a 

freestream Mach number of 0.01 and the default setting in WIND for the turbulent 

Prandtl number, 0.9. 

Figures 5 through 9 compare centerline profiles of axial velocity, Mach number, and 

stagnation temperature for the three WIND solutions to the experimental data of Seiner. 

The stagnation temperature is not shown for the unheated case with nozzle plenum 

temperature set to 104 °F. For each operating point, the Chien k-ε solution obtained with 

no compressibility correction predicts the fastest mixing, and much faster than indicated 

by the experimental data. The SST solutions also consistently predict a faster mixing rate 

than the data. Compared with the baseline Chien model solutions, the SST results predict 

a longer potential core, but then a steeper slope in jet decay further downstream. These 

results are most likely due to the differences in σε used by the Chien and SST k-ε

formulations. 

The Chien model results obtained with the Sarkar compressibility correction indicate the 

longest potential cores and slowest mixing of any of the solutions obtained for all of the 

temperatures investigated. In all cases, these solutions obtained with the compressibility 

correction overpredict the potential core length. Further downstream, the rate of decay is 

still slightly overpredicted for the unheated nozzle case, but this trend reverses for the 

higher temperatures. 

Figure 10 provides the centerline velocity profile variations with temperature for the 

experimental data and computational approaches. While figures 5 to 9 indicated that 

none of the WIND solutions were able to match the experimental data at any particular 

operating point, figure 10 further indicates that not even the trends of jet decay variation 

with nozzle stagnation temperature that were observed in the experiments were able to be 

simulated adequately with the computational approaches employed here. 

Conclusions

The results of this study indicate the current status of the WIND flow solver to simulate 

heated supersonic round nozzle exhaust flows. Two-equation turbulence models, such as 

the SST and the Chien k-ε formulations in WIND used in this study, are the most 

frequently used option within production flow RANS solvers for nozzle exhaust 

simulations. The results presented in this report indicate that models such as these do not 

predict supersonic nozzle flows accurately. These results are consistent with those in 

previous studies such as those of references 1 and 2. Simple corrections for 

compressibility, such as that due to Sarkar, reduce the overpredictions in jet mixing rate, 

but also result in jet potential core lengths that are longer than those observed in the 

experiments across the temperature range. 

The results of the freestream Mach number dependence investigation indicate that for 

exhaust nozzle flows exiting into ambient air, it is necessary to set the freestream Mach 

number as low as possible. While doing so slows the convergence characteristics of 

RANS solvers such as WIND, failure to do this will likely result in artificially slower jet 
NASA/TM2002-211727 6 

mixing rates. At Mach 0.2, the highest freestream Mach number investigated here, the jet 

mixing was the lowest of any investigated, and in general was closest to the experimental 

data. However, the conclusion that simulating jet flows with artificially elevated 

freestream Mach number should not be drawn from these results, because the “closer” 

agreement observed was the result of the compensation of the modified freestream 

conditions for the turbulence model inadequacy. 

The turbulent Prandtl number investigation indicates that the setting of this parameter can 

significantly affect thermal transport in the jet plume. Because the turbulent Prandtl 

number is believed to vary significantly in high temperature jet flows, simple tuning of 

the turbulent Prandtl number for a particular case will not likely enable more accurate 

predictions. While some work has been initiated to formulate a variable turbulent Prandtl 

number model, it will likely be some time before a rigorous capability is demonstrated. 

The limitations of the WIND code demonstrated here for supersonic nozzle flowfields, 

using standard two-equation turbulence models, are representative of nearly all currently 

available production-use RANS solvers. As a result, the calculations discussed in this 

report can be used to benchmark current capabilities against future developments. Efforts 

to improve the capability to predict nozzle flowfields by incorporating more sophisticated 

turbulence model approaches into WIND such as an explicit algebraic Reynolds stress 

model are underway. Improved thermal transport models, such as a variable turbulent 

Prandtl number formulation, should also be investigated. 

 

References

(1) Barber, T.J., Chiappetta, L.M., DeBonis, J.R., Georgiadis, N.J., and Yoder, D.A., 

“Assessment of Parameters Influencing the Prediction of Shear Layer Mixing,”

Journal of Propulsion and Power, Vol. 15, No. 1, 1998, pp. 45–53. 

(2) Georgiadis, N.J., Yoder, D.A., and DeBonis, J.R., “A Comparison of Three NavierStokes Solvers for Exhaust Nozzle Flowfields,” AIAA Paper 99–0748, Jan. 1999. 

(3) DeBonis, J.R. and Scott, J.N., “A Large-Eddy Simulation of a Turbulent 

Compressible Round Jet,” AIAA Paper 2001–2254, May 2001. 

(4) Georgiadis, N.J., Alexander, J.I.D., and Reshotko, E., “Development of a Hybrid 

RANS/LES Method for Compressible Mixing Layer Simulations,” AIAA Paper 

2001–0289, Jan. 2001. 

(5) Nelson, C.C. and Power, G.D., “CHSSI Project CFD-7: The NPARC Alliance Flow 

Simulation System,” AIAA Paper 2001–0594, Jan. 2001. 

(6) Seiner, J.M., Ponton, M.K., Jansen, B. J., and Lagen, N. T., “The Effects of 

Temperature on Supersonic Jet Noise Emission,” DGLR/AIAA 14th Aeroacoustics 

Conference, Aachen, Germany, AIAA Paper No. 92–02–046, May 1992. 

(7) Menter, F. R., “Two-Equation Eddy-Viscosity Turbulence Models for Engineering 

Applications,” AIAA Journal, Vol. 32, No. 8, 1994, pp. 1598–1605. 

(8) Menter, F. R., “Zonal Two Equation k-ω Turbulence Models for Aerodynamic 

Flows,” AIAA Paper 93–2906, July 1993. 

(9) Chien, K.-Y., “Predictions of Channel and Boundary Layer Flows with a LowReynolds-Number Turbulence Model,” AIAA Journal, Vol. 20, No. 1, 1982, 

pp. 33–38. 
NASA/TM2002-211727 7 

(10) Sarkar, S., Erlebacher, G., Hussaini, M.Y., and Kreiss, H.O., “The Analysis and 

Modeling of Dilatational Terms in Compressible Turbulence,” Journal of Fluid 

Mechanics, Vol. 227, 1991, pp. 473–493. 

(11) Sarkar, S., and Lakshmanan, B., “Application of a Reynolds Stress Turbulence 

Model to the Compressible Shear Layer,” AIAA Journal, Vol. 29, No. 5, 1991, 

pp. 743–749. 

(12) Wilcox, D.C., Turbulence Modeling for CFD, DCW Industries, Second Ed., 1998. 

(13) Kenzakowski, D.C., Papp, J., and Dash, S.M., “Evaluation of Advanced Turbulence 

Models and Variable Prandtl/Schmidt Number Methods for Propulsive Flows,” 

AIAA Paper 2000–0885, Jan. 2000. 

(14) Jones, W.P., and Launder, B.E., “The Prediction of Laminarization with a TwoEquation Model of Turbulence,” International Journal of Heat and Mass Transfer, 

Vol. 15, Feb. 1972, pp. 301–314. 

(15) Menter, F.R. and Rumsey, C.L., “Assessment of Two-Equation Turbulence Models 

for Transonic Flows,” AIAA Paper 94–2343, June 1994. 
NASA/TM2002-211727 8 

(a) entire grid 

(b) detail near nozzle exit plane 

Fig. 1. Computational grid 
NASA/TM2002-211727 9 

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20

Seiner Data

SST, Mach 0.01

SST, Mach 0.10

SST, Mach 0.20

U / Ujet

x / D

(a) centerline axial velocity 

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

0 5 10 15 20

Seiner Data

SST, Mach 0.01

SST, Mach 0.10

SST, Mach 0.20

Mach No.

x / D

(b) centerline Mach number 

Fig. 2. Comparison of SST solutions at Tt

 = 104 F with varying freestream Mach 

number. 
NASA/TM2002-211727 10 

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20

Seiner Data

SST, Mach 0.01

SST, Mach 0.10

SST, Mach 0.20

U / Ujet

x / D

(a) centerline axial velocity 

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

0 5 10 15 20

Seiner Data

SST, Mach 0.01

SST, Mach 0.10

SST, Mach 0.20

Mach No.

x / D

(b) centerline Mach number 

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 5 10 15 20

Seiner Data

SST, Mach 0.01

SST, Mach 0.10

SST, Mach 0.20

Tt / Tt-jet

x / D

(c) centerline stagnation temperature 

Fig. 3. Comparison of SST solutions at Tt

 = 1550 F with varying freestream Mach 

number. 
NASA/TM2002-211727 11 

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20

Seiner Data 

Prt = 0.5

Prt = 0.7

Prt = 0.9

U / Ujet

x / D

(a) centerline axial velocity 

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

0 5 10 15 20

Seiner Data

Prt = 0.5

Prt = 0.7

Prt = 0.9

Mach No.

x / D

(b) centerline Mach number 

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 5 10 15 20

Seiner Data

Prandtl No. = 0.5

Prandtl No. = 0.7

Prandtl No. = 0.9

Tt / Tt-jet

x / D

(c) centerline stagnation temperature 

Fig. 4. Comparison of SST solutions at Tt

 = 1550 F with varying turbulent Prandtl 

number. 
NASA/TM2002-211727 12 

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20

Seiner Data

SST

Chien

Chien with Sarkar

U / Ujet

x / D

(a) centerline axial velocity 

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

0 5 10 15 20

Seiner Data

SST

Chien

Chien with Sarkar

Mach No.

x / D

(b) centerline Mach number 

Fig. 5. Comparison of solutions at Tt

 = 104 F using different turbulence models. 
NASA/TM2002-211727 13 

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20

Seiner Data

SST

Chien

Chien with Sarkar

U / Ujet

x / D

(a) centerline axial velocity 

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

0 5 10 15 20

Seiner Data

SST

Chien

Chien with Sarkar

Mach No.

x / D

(b) centerline Mach number 

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 5 10 15 20

Seiner Data

SST

Chien

Chien with Sarkar

Tt / Tt-jet

x / D

(c) centerline stagnation temperature 

Fig. 6. Comparison of solutions at Tt

 = 455 F using different turbulence models. 
NASA/TM2002-211727 14 

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20

Seiner Data

SST

Chien

Chien with Sarkar

U / Ujet

x / D

(a) centerline axial velocity 

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

0 5 10 15 20

Seiner Data

SST

Chien

Chien with Sarkar

Mach No.

x / D

(b) centerline Mach number 

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 5 10 15 20

Seiner Data

SST

Chien

Chien with Sarkar

Tt / Tt-jet

x / D

(c) centerline stagnation temperature 

Fig. 7. Comparison of solutions at Tt

 = 900 F using different turbulence models. 
NASA/TM2002-211727 15 

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20

Seiner Data

SST

Chien

Chien with Sarkar

U / Ujet

x / D

(a) centerline axial velocity 

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

0 5 10 15 20

Seiner Data

SST

Chien

Chien with Sarkar

Mach No.

x / D

(b) centerline Mach number 

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 5 10 15 20

Seiner Data

SST

Chien

Chien with Sarkar

Tt / Tt-jet

x / D

(c) centerline stagnation temperature 

Fig. 8. Comparison of solutions at Tt

 = 1550 F using different turbulence models. 
NASA/TM2002-211727 16 

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20

Seiner Data

SST

Chien

Chien with Sarkar

U / Ujet

x / D

(a) centerline axial velocity 

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

0 5 10 15 20

Seiner Data

SST

Chien

Chien with Sarkar

Mach No.

x / D

(b) centerline Mach number 

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 5 10 15 20

Seiner Data

SST

Chien

Chien with Sarkar

Tt / Tt-jet

x / D

(c) centerline stagnation temperature 

Fig. 9. Comparison of solutions at Tt

 = 2000 F using different turbulence models. 
NASA/TM2002-211727 17 

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20

Seiner Data, Tt-jet = 104 F

Seiner Data, Tt-jet = 455 F

Seiner Data, Tt-jet = 900 F

Seiner Data, Tt-jet = 1550 F

Seiner Data, Tt-jet = 2000 F

U / Ujet

x / D

(a) Seiner data 

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20

SST, Tt-jet = 104 F

SST, Tt-jet = 455 F

SST, Tt-jet = 900 F

SST, Tt-jet = 1550 F

SST, Tt-jet = 2000 F

U / Ujet

x / D

(b) SST calculations 

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20

Chien, Tt-jet = 104 F

Chien, Tt-jet = 455 F

Chien, Tt-jet = 900 F

Chien, Tt-jet = 1550 F

Chien, Tt-jet = 2000 F

U / Ujet

x / D

(c) Chien calculations 

Fig. 10. Centerline axial velocity with varying nozzle stagnation temperature. 
NASA/TM2002-211727 18 

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20

Chien, Sarkar, Tt-jet = 104 F

Chien, Sarkar, Tt-jet = 455 F

Chien, Sarkar, Tt-jet = 900 F

Chien, Sarkar, Tt-jet = 1550 F

Chien, Sarkar, Tt-jet = 2000 F

U / Ujet

x / D

(d) Chien (with Sarkar) calculations 

Fig. 10. Centerline axial velocity with varying nozzle stagnation temperature 

(concluded). 
This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.

REPORT DOCUMENTATION PAGE

2. REPORT DATE

19. SECURITY CLASSIFICATION

 OF ABSTRACT

18. SECURITY CLASSIFICATION

 OF THIS PAGE

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources,

gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this

collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson

Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503.

NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. Z39-18

298-102

Form Approved

OMB No. 0704-0188

12b. DISTRIBUTION CODE

8. PERFORMING ORGANIZATION

 REPORT NUMBER

5. FUNDING NUMBERS

3. REPORT TYPE AND DATES COVERED

4. TITLE AND SUBTITLE

6. AUTHOR(S)

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

11. SUPPLEMENTARY NOTES

12a. DISTRIBUTION/AVAILABILITY STATEMENT

13. ABSTRACT (Maximum 200 words)

14. SUBJECT TERMS

17. SECURITY CLASSIFICATION

 OF REPORT

16. PRICE CODE

15. NUMBER OF PAGES

20. LIMITATION OF ABSTRACT

Unclassified Unclassified

Technical Memorandum

Unclassified

National Aeronautics and Space Administration

John H. Glenn Research Center at Lewis Field

Cleveland, Ohio 44135–3191

1. AGENCY USE ONLY (Leave blank)

10. SPONSORING/MONITORING

 AGENCY REPORT NUMBER

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546–0001

Available electronically at http://gltrs.grc.nasa.gov

August 2002

NASA TM—2002-211727

E–13478

WU–708–90–43–00

24

An Evaluation of Parameters Influencing Jet Mixing Using the WIND

Navier-Stokes Code

Mary Ann Dembowski and Nicholas J. Georgiadis

Turbulent mixing; Supersonic jet; Reynolds-averaged Navier Stokes; Turbulence models

Unclassified -Unlimited

Subject Categories: 02 and 07 Distribution: Nonstandard

The WIND code, a Reynolds-averaged Navier-Stokes solver used for a variety of aerospace flow simulations, was

investigated for a Mach 2 nozzle at a series of nozzle stagnation temperatures. Comparisons of WIND calculations are

made to experimental measurements of axial velocity, Mach number, and stagnation temperature along the jet centerline.

The primary objective was to investigate the capabilities of the two-equation turbulence models available in WIND,

version 4.0, for the analysis of heated supersonic nozzle flows. The models examined were the Menter Shear Stress

Transport (SST) model and the Chien k-ε model, with and without the compressibility correction due to Sarkar. It was

observed that all of the turbulence models investigated produced solutions that did not agree well with the experimental

measurements. The effects of freestream Mach number and turbulent Prandtl number specifications were also investigated.

Responsible person, Nicholas J. Georgiadis, organization code 5860, 216–433–3958.