Chunill Hah

Glenn Research Center, Cleveland, Ohio

Large Eddy Simulation of Transonic

Flow Field in NASA Rotor 37

NASA/TM—2009-215627

September 2009
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Chunill Hah

Glenn Research Center, Cleveland, Ohio

Large Eddy Simulation of Transonic

Flow Field in NASA Rotor 37

NASA/TM—2009-215627

September 2009

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

47th Aerospace Sciences Meeting

sponsored by the American Institute of Aeronautics and Astronautics

Orlando, Florida, January 5–8, 2009
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Available electronically at http://gltrs.grc.nasa.gov

This work was sponsored by the Fundamental Aeronautics Program 

at the NASA Glenn Research Center.

Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2009-215627 1

Large Eddy Simulation of Transonic Flow Field in NASA Rotor 37 

Chunill Hah 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

The current paper reports on numerical investigations on the flow characteristics in a transonic axial 

compressor, NASA Rotor 37. The flow field was used previously as a CFD blind test case conducted by 

American Society of Mechanical Engineers in 1994. Since the CFD blind-test exercise, many numerical 

studies on the flow field in the NASA Rotor 37 have been reported. Although steady improvements have 

been reported in both numerical procedure and turbulence closure, it is believed that all the important 

aspects of the flow field have not been fully explained with numerical studies based on the Reynolds 

Averaged Navier-Stokes (RANS) solution. Experimental data show large dip in total pressure distribution 

near the hub at downstream of the rotor at 100% rotor speed. Most original numerical solutions from the 

blind test exercise did not predict this total pressure deficit correctly. This total pressure deficit at the rotor 

exit was attributed to a hub corner flow separation by the author. Several subsequent numerical studies 

with different turbulence closure model also calculated this dip in total pressure rise. Also, several studies 

attributed this total pressure deficit to a small leakage flow coming from the hub in the test article. As the 

experimental study cannot be repeated, either explanation cannot be validated. The primary purpose of the 

current investigation is to investigate the transonic flow field with both RANS and a Large Eddy 

Simulation (LES). The RANS approach gives similar results presented at the original blind test exercise. 

Although the RANS calculates higher overall total pressure rise, the total pressure deficit near the hub is 

calculated correctly. The numerical solution shows that the total pressure deficit is due to a hub corner 

flow separation. The calculated pressure rise from the LES agrees better with the measured total pressure 

rise especially near the casing area where the passage shock interacts with the tip clearance vortex and 

flow becomes unsteady due to this interaction. The LES simulation also calculates the total pressure rise 

deficit near the hub and it agrees well with the measured data. 

Introduction 

One of the goals of the NASA Fundamental Aeronautics Program is the assessment of various 

computational fluid dynamic (CFD) codes now used by NASA and industry in the design and analysis of 

aircraft, spacecraft, propulsion systems, etc. The goal is to assess the current state of the art of these 

codes, then to periodically reassess the codes as advances are made in CFD. 

Several CFD codes for turbomachinery problems were assessed for the Subsonic Fixed Wing project. 

The codes were assessed for one or two transonic compressors designed and tested by Reid and Moore 

(Refs. 1 to 3) around 1978 at NASA Lewis Research Center (now Glenn). Reid and Moore designed four 

compressors to investigate the effects of blade camber and aspect ratio on compressor performance. The 

two compressors with low-aspect-ratio blades had the best performance and have since been retested and 

used for several CFD code assessment projects. 

The first compressor was an isolated rotor designated NASA Rotor 37. It was retested by Strazisar 

and Suder (Refs. 4 and 5) in the 1990s using both aerodynamic surveys and laser anemometry. Their data 

was used for a CFD blind test case conducted by International Gas Turbine Institute (IGTI) of the 

American Society of Mechanical Engineers (ASME) in 1994 (unpublished) and for a more detailed but 

nonblind test case conducted by AGARD (Refs. 6 and 7) in 1997-8. 

This paper describes calculations of isolated Rotor 37 flow field made using the H3D code. H3D is a 

multiblock Navier-Stokes analysis code for turbomachinery developed by Hah (Refs. 8 and 9). Hah is one 
NASA/TM—2009-215627 2

of 10 participants of the 1994 CFD blind test workshop that was sponsored by the International Gas 

Turbine Institute of the American Society of Mechanical Engineers. Numerical results with a modified 

two-equation turbulence model were presented during the workshop. Some improvements on the 

numerical procedures have been implemented on the original code. The flow fields at different operating 

conditions are calculated again and the calculated flow fields are very similar to the original solutions 

presented during the original ASME workshop. 

The numerical results were further analyzed and published in a separate paper by Hah and Loellbach 

(Ref. 10). The code has been widely applied to study various transonic compressors since then (Refs. 11 

to 13). The numerical results have been compared with available test data from many different transonic 

compressors. The code has been predicting the characteristics of all the tested compressors fairly well if 

various uncertainties of measurement are considered. Although absolute values of one-dimensional 

performance numbers, like total pressure/temperature rise, were not matched exactly, expected 

differences among different designs were predicted fairly well for design guidance. The code was used to 

develop swept rotor concept in transonic fan/compressor (Ref. 14). Several attempts have been made to 

improve the turbulence model in the code. So far, we have not found any turbulence model that performs 

universally better for the variety of flow fields in different transonic compressors. 

A Large Eddy Simulation (LES) capability has been added to the code (Ref. 15). The LES procedure 

is applied primarily to capture transient characteristics of the compressor flow more realistically. Accurate 

understanding of unsteady interactions among passage shock, tip leakage vortex, and vortex shedding in a 

transonic compressor at near stall operation remains one of the challenges for compressor designers. 

Test Rotor and Test Facility 

Rotor 37 is a low aspect ratio inlet rotor for a core compressor. It has 36 multiple circular-arc (MCA) 

blades and a design pressure ratio of 2.106 at a mass flow of 20.19 kg/sec. It was originally designed and 

tested at NASA Lewis Research Center (now Glenn) in the late 1970s by Reid and Moore (Refs. 1 and 3). 

The rotor was retested in a single-stage compressor facility at NASA Glenn by Suder, et al. (Refs. 4 and 

5). Radial distributions of static and total pressure, total temperature, and flow angle were measured at 

two axial stations located 4.19 cm upstream and 10.67 cm downstream of the blade hub leading edge, 

labeled stations 1 and 4 in Figure 1. Detailed laser anemometry measurements were made of the velocity 

field within the rotor and wake at several axial stations and on five spanwise planes also shown in 

Figure 1. 

The IGTI of ASME sponsored a blind test exercise for turbomachinery CFD codes with this flow 

field at the 39th International Gas Turbine Conference held in The Hague, Netherlands (unpublished) in 

1994. The same test case was later used by the AGARD Propulsion and Energetics Panel Working Group 

26 as a CFD test case for examining the effects of grid and turbulence modeling on solution accuracy. 

Flow field at design speed and 98% of maximum flow rate was examined in detail. Three details of 

the measurements proved to be especially difficult to predict: 

(1) Most codes over predicted the overall pressure and temperature ratios and under predicted the 

efficiency. Predicted pressure ratios varied by nearly 10% and predicted efficiencies varied by about 

6 points. 

(2) Most codes failed to predict the total pressure distribution downstream of the rotor below 

40% span. The data shows a region of low total pressure that has been called a “pressure deficit.” This 

terminology implies that there is something wrong with the flow in that region and has prompted much 

discussion in the literature. Hah, et al. (Ref. 10) suggested that the deficit is due to a corner stall on the 

rotor suction surface, while Shabbir, et al. (Ref. 16) showed some evidence that it is due to air leaking 

into the flow path from the gap between the stationary and rotating parts of the hub at the rotor leading 

edge. Chima, et al. (Ref. 17) suggested that the low total pressure is an intrinsic feature of the rotor that 

tends to be smeared out by the central-difference schemes used by many CFD codes. 
NASA/TM—2009-215627 3

(3) All codes over predicted the total temperature downstream of the rotor above 90% span by as 

much as 17 °C. The discrepancy was generally worse with algebraic turbulence models than with 

turbulent transport models. It was only mentioned briefly in the AGARD report, but it is either a 

fundamental problem with CFD methods for turbomachinery or an unrecognized error in the experimental 

results. In unpublished results provided after the ASME blind test case Strazisar and Suder calculated the 

total temperature close to the rotor trailing edge using laser measurements of tangential velocity and the 

Euler turbine equation. These temperatures were similar to the probe measurements further downstream, 

suggesting that the probe measurements may be correct. 

Numerical Procedure 

The H3D code is a multiblock Navier-Stokes analysis code for turbomachinery blade rows. The code 

solves the full steady and unsteady Navier-Stokes equation in body-fitted grids. A modified two-equation 

turbulence model is used for turbulence closure. The governing equations are solved with a pressurebased implicit method using a fully conservative control volume approach. A third-order accurate 

interpolation scheme is used for the discretization of convection terms and central differencing is used for 

the diffusion terms. The method is of second-order accuracy with smoothly varying grids. For the timedependent terms, an implicit second-order scheme is used and a number of sub-iterations are performed at 

each time step. Details of the numerical method and applications to transonic flows are given by Hah and 

Wennerstrom (Ref. 18). 

A Large Eddy Simulation (LES) method was applied in the present study. The LES procedure was 

applied primarily to capture unsteady flow interactions among passage shock, tip leakage vortex, and 

vortex shedding more realistically. With spatially filtered Navier-Stokes equations, the subgrid-scale 

stress tensor term must be modeled properly for the closure of the governing equations. A Smagorinskytype eddy-viscosity model was used for the subgrid stress tensor, and the standard dynamic model by 

Germano et al. (Ref. 19) was applied. 

The computational grid for a single blade passage consists of 198 nodes in the blade-to-blade 

direction, 124 nodes in the spanwise direction, and 560 nodes in the streamwise direction. The inflow 

boundary was located 6 average blade heights upstream of the rotor leading edge and the outflow 

boundary was located one blade height from the trailing edge. The rotor tip clearance geometry is 

accurately represented by 20 nodes in the blade-to-blade direction, 20 nodes in the spanwise direction, 

and 360 nodes in the streamwise direction. The I-grid topology is used to reduce grid skewness and a 

single-block grid is used. The computational grid near the rotor is shown in Figure 2. All the 

computations were performed with NASA’s Columbia super computer system, which allows parallel 

computation with up to 512 processors. 

Standard boundary conditions for an isolated rotor were applied at the boundaries of the 

computational domain. Circumferentially averaged static pressure at the casing was specified to control 

the mass flow rate. Nonreflecting boundary conditions were applied at the inlet and the exit boundaries. 

Overall Flow Structure 

Steady Reynolds averaged Navier-Stokes (RANS) calculations were performed first to obtain 

compressor characteristics at the design rotor speed. Calculated flow fields at the peak efficiency and the 

near stall condition are first compared with the measured data. Spanwise distribution of the total pressure 

rise at the rotor exit was investigated in detail with the calculated flow field. LES simulations were 

performed at 3 operating conditions to examine whether LES produces improved results along with any 

additional flow physics. Measured pressure, temperature rise and adiabatic efficiency characteristics of 

the rotor at the design rotor speed are shown in Figures 3, 4, and 5. The time-averaged LES solutions that 

are shown in Figures 3 and 4 were obtained by averaging instantaneous solutions over 1000 time steps. 
NASA/TM—2009-215627 4

Flow Field From RANS Simulation 

The choke mass flow was calculated as 20.92 kg/s with RANS and 20.91 kg/s with LES. The 

measured choke flow rate is 20.93 kg/s. Both the RANS and LES calculate the choke mass flow rate 

within the measurement error range. The corrected mass flow rates in Figures 3, 4, and 5 are 

nondimensional values with the calculated choke mass. Suder and Celestina (Ref. 4) reported uncertainty 

range of the measurements in Figures 3, 4, and 5. The uncertainty range was as high as 10% of the 

measured value at certain operating point. Results shown in Figures 3, 4, and 5 show that the code 

calculates more optimistic performance of the compressor than the measurement. Higher pressure rise and 

higher temperature rise are calculated than the measurements. However, the overall trend is fairly well 

calculated. The code calculates changes in adiabatic efficiency at different operating conditions fairly well 

even though the calculated values are higher than the measured values. The measurements show some 

unusual compressor performance near the choke condition, which can be contributed to some 

measurement uncertainty. According to various studies, it seems that calculations with some recent 

turbulence closure models give better agreement with the measurements for this transonic rotor. However, 

we have not found any specific model which performs universally well for different transonic compressor 

flow fields. Detailed flow field was surveyed at the flow rate of 0.98, which was used as blind test case in 

1994. Further flow measurements were also conducted at lower mass flow rate at 0.93. Detailed flow 

structures at the near peak (flow rate of 0.98) and near stall (flow rate of 0.93) are examined with the 

numerical solution. 

Calculated distributions of total pressure rise at four different mass flow rates are compared with 

measured values at the mass flow rate of 0.98 in Figure 6. Results in Figure 6 show two clear trends. 

(1) The total pressure deficit near the hub is clearly calculated at all mass flow rates. 

(2) The pressure rise profile changes significantly with a very small change in mass flow rate. 

To study the origin of this pressure deficit near the hub, calculated flow field at 98% mass flow rate is 

further examined. Mach number distributions at four spanwise locations are shown in Figure 7. 

Calculated Mach number distributions at 70 and 95% span agrees fairly well with the laser measurement 

reported by Suder and Celestina (Ref. 4). Mach number distribution at 12% span indicates flow separation 

near the training edge at this span. Mach number distribution near the suction surface of the blade is 

shown in Figure 8. Corresponding velocity vectors are given in Figure 9. Results in Figures 8 and 9 

indicate that there is a three-dimensional corner flow separation near the hub. The total pressure deficit 

near the hub shown in Figure 6 is the results of this corner flow separation. Rotor 37 is a highly loaded 

transonic compressor rotor. Due to very high aerodynamic loading, the passage shock extends all the way 

to the hub as shown in Figure 8. The three-dimensional corner separation is due the interaction of the 

passage shock with the hub boundary layer. 

Distributions of total temperature rise at four different mass flow rates are compared with the 

measurement in Figure 10. The shapes of the temperature profile are very similar at different mass flow 

rate. However, the absolute values are very sensitive to a small change in mass flow rate. Overall, 

numerical results agree better near the hub section. Like most previously reported CFD results, the code 

predicts higher temperature rise toward the casing. Compared to published results from different codes, 

the calculated temperature rise agrees better with the measurement. As shown in this section, the flow 

field in this highly loaded compressor is very sensitive to a small change in mass flow rate. Further 

measurements at 60% rotor design speed by Suder and Celestina (Ref. 4) show that the dip in the total 

pressure distribution in Figure 6 disappears. The code calculates no large corner stall at 60% rotor design 

speed and calculated total pressure rise profile matches very well with the measurements as reported by 

Hah and Loellbach (Ref. 10). 

Calculated total pressure and total temperature distributions at the measurement station 4 at near stall 

condition are compared with the measurement in Figure 11. Again calculation shows hub corners tall at 

this operating condition and the profile agrees with the measurement. Also the calculation predicts higher 
NASA/TM—2009-215627 5

pressure rise near the tip section compared to the measurement. As shown in Figures 7 and 11, the current 

RANS simulation calculates higher pressure rise near the tip than the measurement. This might be due to 

the fact that the current RANS does not model the interaction between the passage shock and the tip 

clearance vortex accurately. On the other hand, the RANS calculates pressure rise near the hub section 

fairly well. 

Just ahead of rotor leading edge, there is a small gap between the stationary part of the hub and the 

rotating part of the hub, and there might be a small amount of leakage flow coming from this gap. As is 

widely known, the flow field in a transonic compressor is extremely sensitive to a small change in the 

geometry and flow condition. Shabbir et al. (Ref. 16) did numerical study on the effects of this leakage 

flow on the exit profile of total pressure rise. They assumed variety of flow profiles coming out of the gap 

as no measured data are available. Their study indicated that the total pressure rise can be altered quite bit 

even with about 0.25% of total mass flow. As mentioned before, the total pressure rise at the rotor exit 

does not show any deficit near the hub at 60% rotor speed according to measurements as well as the 

calculation. If the pressure rise deficit near the hub at 100% rotor design speed is due to the hub leakage 

flow, further explanation is required why the hub deficit disappears at 60% rotor design speed. 

Flow Field From LES Simulation 

Large Eddy Simulation was applied to see whether LES can simulate flow field better compared to 

RANS. As observed from the RANS simulation with the currently applied turbulence model, flow field 

near the casing is not well represented with the RANS. Flow interactions among tip leakage vortex, 

passage shock, and vortex shedding in a transonic compressor are inherently unsteady. Although steady 

RANS calculates certain aspect of average flow field, detailed unsteady flow mechanisms are difficult to 

calculate realistically. LES was applied to calculate flow fields at the choke condition, near the peak 

efficiency condition and near stall condition. The choke flow rate from the LES is 20.91 kg/s. Figure 12 

shows an instantaneous distribution of Mach number at mid span at near peak efficiency. Instantaneous 

velocity vectors are given in Figure 13. Shock induced boundary layer separation and resulting vortex 

shedding are well calculated. Mach number distributions from the averaged LES simulation at 95% span 

are shown in Figure 14 along with the measured values. The Mach number distributions from the 

averaged LES solution matches much better with the measurement than RANS results shown in Figure 7. 

RANS calculation with conventional turbulence closure scheme do not simulate interaction between the 

passage shock and the tip leakage vortex accurately. On the other hand, LES simulates this interaction 

much more realistically and the results agree very well with the measurement. Changes in Mach number 

distribution at the blade tip at near stall are shown in Figures 15 and 16 shows changes in velocity vectors 

at the blade tip for the near stall condition. As shown in Figures 15 and 16, the flow field becomes 

unsteady due to interactions among the passage shock, tip leakage vortex, and vortex shedding. Due to 

this self-induced unsteadiness, flow incidence at the leading edge changes as much as 5° and the tip core 

vortex oscillates significantly. 

Calculated distributions of total pressure and total temperature at the rotor exit with LES are shown in 

Figures 17 and 18. Compared to the results with the RANS simulation, it looks like the LES removed 

some over prediction of pressure and temperature rise near the casing by RANS. As the results in 

Figure 17 indicate, the dip in total pressure rise near the hub is calculated also with the LES. 

Instantaneous velocity vectors near the suction side from LES simulation are shown in Figure 19. Hub 

corner stall is clearly shown in Figure 19 as was the case with RANS simulation. 
NASA/TM—2009-215627 6

Concluding Remarks 

The H3D turbomachinery analysis code was used to predict the performance of Rotor 37 transonic 

compressor rotor. Both RANS and LES modes were used to investigate detailed flow features. RANS 

calculations were performed to examine how the H3D code with the applied turbulence closure calculates 

the measured compressor performance. Although the code predicts more optimistic aerodynamic 

performance than measurement, many aspects of this highly loaded compressor flow field are fairly well 

calculated if difficulty and uncertainty of measurements are considered. The RANS calculates total 

pressure deficit near the hub very well even with the currently applied turbulence closure. Also, total 

temperature rise near the casing is calculated fairly well compared to previously published CFD results. 

LES simulation shows better agreement with the measurements especially near the casing. This might be 

due to the fact that the LES can simulate flow interactions among passage shock, tip leakage vortex, and 

vortex shedding correctly. The LES seems to represent unsteady flow interactions much more 

realistically. Practical application of LES to calculate unsteady flow fields in transonic compressors 

requires further developments and validations. However, some early results presented in the current study 

show very promising aspects of the LES. 

References 

1. Reid, L. and Moore, R.D., “Design and Overall Performance of Four Highly-Loaded, High Speed 

Inlet Stages for an Advanced, High Pressure Ratio Core Compressor,” NASA TP–1337, 1978. 

2. Reid, L. and Moore, R.D., “Performance of a Single-Stage Axial-Flow Transonic Compressor With 

Rotor and Stator Aspect Ratios of 1.19 and 1.26, Respectively, and With Design Pressure Ratio of 

1.82, NASA TP–1338, 1978. 

3. Reid, L. and Moore, R.D., “Experimental Study of Low Aspect Ratio Compressor Blading,” ASME 

Paper 80-GT-6, Mar. 1980. 

4. Suder, K.L., and Celestina, M.L., “Experimental and Computational Investigation of the Tip 

Clearance Flow in a Transonic Axial Compressor Rotor,” NASA TM–106711, 1994. 

5. Suder, K.L., Chima, R.V., Strazisar, A.J., and Roberts, W.B., “The Effect of Adding Roughness and 

Thickness to a Transonic Axial Compressor Rotor,” ASME J. Turbomachinery, vol. 117, Oct. 1995, 

pp. 491–505. 

6. Dunham, J. ed. “CFD Validation for Propulsion System Components,” AGARD Advisory Report 

355, AGARD, Neuilly-Sur-Seine, France, May, 1998. 

7. Dunham, J. and Meauzé, “An AGARD Working Group Study of 3-D Navier-Stokes Codes Applied 

to Single Turbomachinery Blade Rows,” ASME Paper 98-GT-50, June, 1998. 

8. Hah, C., 1984, “A Navier-Stokes Analysis of Three-Dimensional Flows Inside Turbine Blade Rows 

at Design and Off-Design Conditions,” ASME Journal of Engineering for Gas Turbines and Power, 

vol. 106, pp. 421–429. 

9. Hah, C., 1986, “A Numerical modeling of Endwall and Tip-Clearance Flow of an Isolated 

Compressor Rotor,” ASME Journal of Engineering for Gas Turbines and Power, vol. 108, pp. 15–21. 

10. Hah, C. and Loellbach, J., “Development of Hub Corner Stall and its Influence on the Performance of 

Axial Compressor Blade Rows,” ASME Paper 97-GT-42, June, 1977. 

11. Hah, C. and Reid, L., 1992, “A Viscous Flow Study of Shock-Boundary Layer Interaction, Radial 

Transport, and Wake Development in a Transonic Compressor,” ASME Journal of Turbomachinery, 

vol. 114, no. 2, pp. 538–547. 

12. Hah, C., Copenhaver, W.W., and Puterbaugh, S.L., 1993, “Three-Dimensional Flow Phenomena in a 

Transonic High-Throughflow, Axial-Flow Compressor Stage,” ASME Journal of Turbomachinery, 

vol. 115, no. 2, pp. 240–248. 

13. Hah, C., Rabe, D.C., Sullivan, T.J., and Wadia, A.R., 1996, “Effects of Inlet Distortion on the Flow 

Field in a Transonic Compressor Rotor,” ASME Journal of Turbomachinery, vol. 120, no. 2, pp. 233–

246. 
NASA/TM—2009-215627 7

14. Puterbaugh, S.L., Copenhaver, W.W, Hah, C., and Wennerstrom, A.J., 1997, “A Three-Dimensional 

Shock Loss Model applied to an AFT-Swept, Transonic Compressor Rotor,” ASME Journal of 

Turbomachinery, vol. 119, no. 3, pp. 452–459. 

15. Hah, C. and Y. Lee, 2007, “Unsteady Pressure Field Due to Interactions Among Tip Leakage Vortex, 

Trailing Edge Vortex, and Vortex Shedding in a Ducted Propeller,” ASME Paper, GT2007–27407. 

16. Shabbir, A., Celestina, M.L., Adamczyk, J.J., and Strazisar, A.J., “The Effect of Hub Leakage Flow 

on Two High Speed Axial Compressor Rotors,” ASME Paper 97-GT-346, June, 1997. 

17. Chima, R.V. and Liou, M.-S., “Comparison of the AUSM+

 and H-CUSP Schemes for 

Turbomachinery Applications,” AIAA Paper AIAA–2003–4120. Also NASA/TM—2003-212457. 

18. Hah, C. and Wennerstrom, A.J., 1991, “Three-Dimensional Flow Fields Inside a Transonic 

Compressor With Swept Blades,” ASME Journal of Turbomachinery, vol. 113, no. 1, pp. 241–251. 

19. Germano, M., Piomelli, U., Moin, P., and Cabot, W.H., 1991, “A Dynamic Subgrid-Scale EddyViscosity Model,” Journal of Fluid Mechanics, vol. A3, pp. 170–176. 

Figure 1.—Rotor 37 cross section and measurement stations. 

Figure 2.—Computational grid near the Rotor 37. 
NASA/TM—2009-215627 8

 

 

0.92 0.94 0.96 0.98 1

mass flow rate

1.7

1.8

1.9

2

2.1

2.2

Pt

measurement

RANS

LES

0.92 0.94 0.96 0.98 1

mass flow rate

1.2

1.25

1.3

1.35

Tt

measurement

RANS

LES

0.92 0.94 0.96 0.98 1

mass flow rate

0.8

0.82

0.84

0.86

0.88

0.9

efficiency

measurement

RANS

LES

1 1.5 2 2.5 3

Pt

0

20

40

60

80

100

% span

measurement

99.5% choke flow

99.3% choke flow

98.45% choke flow

98% choke flow

Figure 3.—Pressure rise characteristics of the rotor 

at design rotor speed. 

Figure 4.—Temperature rise characteristics of the rotor 

at design rotor speed. 

Figure 5.—Adiabatic efficiency of the rotor at design 

rotor speed. 

Figure 6.—Comparison of total pressure distribution 

downstream of Rotor 37. 
NASA/TM—2009-215627 9

Figure 7(a).—Mach number distribution at 5% span, near peak efficiency, rotor design speed. 

Figure 7(b).—Mach number distribution at 12% span, near peak efficiency, rotor design speed. 

Flow separation 
NASA/TM—2009-215627 10

Figure 7(c).—Mach number distribution at 70% span, near peak efficiency, rotor design speed. 

 

Figure 7(d).—Mach number distribution at 95% span, near peak efficiency, rotor design speed. 
NASA/TM—2009-215627 11

Figure 8.—Mach number distribution near the suction surface, near peak efficiency, rotor design speed. 

Figure 9.—Velocity vectors near the suction surface, near peak efficiency, rotor design speed. 

Hub corner stall 

Hub corner stall 
NASA/TM—2009-215627 12

 

 

Figure 11(b).—Comparison of total temperature distribution 

downstream of Rotor 37, near stall, rotor design speed. 

1 1.1 1.2 1.3 1.4

Tt

0

20

40

60

80

100

% span

measurement

99.5% choke flow

99.3% choke flow

98.45% choke flow

98% choke flow

1 1.5 2 2.5 3

Pt

0

20

40

60

80

100

% span

measurement

93% choke flow

1 1.1 1.2 1.3 1.4

Tt

0

20

40

60

80

100

% span

measurement

93% choke flow

Figure 10.—Comparison of total temperature 

distribution downstream of Rotor 37. 

Figure 11(a).—Comparison of total pressure rise 

downstream of Rotor 37, near stall, rotor design 

speed. 
NASA/TM—2009-215627 13

Shock induced 

flow separation 

Figure 12.—Instantaneous Mach number 

distribution at mid-span, near peak 

efficiency from LES. 

Figure 13.—Instantaneous velocity vectors at 

mid-span, near peak efficiency from LES. 
NASA/TM—2009-215627 14

Figure 14(a).—Calculated time-averaged 

Mach number distribution at 95% span, 

near peak efficiency from LES. 

Figure 14(b).—Measured Mach number 

distribution at 95% span, near peak 

efficiency. 
NASA/TM—2009-215627 15

Figure 15(a).—Instantaneous Mach number distribution 

at time 1, blade tip and near stall condition. 

Figure 15(b).—Instantaneous Mach number distribution 

at time 2, blade tip and near stall condition. 

Figure 15(c).—Instantaneous Mach number distribution 

at time 3, blade tip and near stall condition. 
NASA/TM—2009-215627 16

Figure 16(a).—Instantaneous velocity 

vectors at time step 1, blade tip and 

near stall condition. 

Figure 16(b).—Instantaneous velocity 

vectors at time step 2, blade tip and 

near stall condition. 

Figure 16(c).—Instantaneous velocity 

vectors at time step 3, blade tip and 

near stall condition. 
NASA/TM—2009-215627 17

Figure 17(a).—Comparison of total pressure profile downstream 

of Rotor 37 near peak efficiency. 

Figure 17(b).—Comparison of total pressure profile downstream of 

Rotor 37 near stall condition. 

1 1.5 2 2.5 3

Pt

0

20

40

60

80

100

% span

measurement

LES

1 1.5 2 2.5 3

Pt

0

20

40

60

80

100

% span

measurement

LES
NASA/TM—2009-215627 18

 

Figure 19.—Instantaneous velocity vectors near 

suction surface, near peak efficiency from LES.

1 1.1 1.2 1.3 1.4

Tt

0

20

40

60

80

100

% span

measurement

LES

1 1.1 1.2 1.3 1.4

Tt

0

20

40

60

80

100

% span

measurement

LES

Hub corner stall

Figure 18(a).—Comparison of total temperature 

profile downstream of Rotor 37 near peak 

efficiency. 

Figure 18(b).—Comparison of total temperature 

profile downstream of Rotor 37 near stall condition. 
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4. TITLE AND SUBTITLE

Large Eddy Simulation of Transonic Flow Field in NASA Rotor 37 

5a. CONTRACT NUMBER

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5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Hah, Chunill 

5d. PROJECT NUMBER

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5f. WORK UNIT NUMBER

WBS 561581.02.08.03.21.02 

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

National Aeronautics and Space Administration 

John H. Glenn Research Center at Lewis Field 

Cleveland, Ohio 44135-3191 

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

The current paper reports on numerical investigations on the flow characteristics in a transonic axial compressor, NASA Rotor 37. The flow 

field was used previously as a CFD blind test case conducted by American Society of Mechanical Engineers in 1994. Since the CFD blindtest exercise, many numerical studies on the flow field in the NASA Rotor 37 have been reported. Although steady improvements have been 

reported in both numerical procedure and turbulence closure, it is believed that all the important aspects of the flow field have not been fully 

explained with numerical studies based on the Reynolds Averaged Navier-Stokes (RANS) solution. Experimental data show large dip in 

total pressure distribution near the hub at downstream of the rotor at 100% rotor speed. Most original numerical solutions from the blind test 

exercise did not predict this total pressure deficit correctly. This total pressure deficit at the rotor exit was attributed to a hub corner flow 

separation by the author. Several subsequent numerical studies with different turbulence closure model also calculated this dip in total 

pressure rise. Also, several studies attributed this total pressure deficit to a small leakage flow coming from the hub in the test article. As the 

experimental study cannot be repeated, either explanation cannot be validated. The primary purpose of the current investigation is to 

investigate the transonic flow field with both RANS and a Large Eddy Simulation (LES). The RANS approach gives similar results 

presented at the original blind test exercise. Although the RANS calculates higher overall total pressure rise, the total pressure deficit near 

the hub is calculated correctly. The numerical solution shows that the total pressure deficit is due to a hub corner flow separation. The 

calculated pressure rise from the LES agrees better with the measured total pressure rise especially near the casing area where the passage 

shock interacts with the tip clearance vortex and flow becomes unsteady due to this interaction. The LES simulation also calculates the total 

pressure rise deficit near the hub and it agrees well with the measured data.

15. SUBJECT TERMS

Transonic; Shock; Compressor 

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