Optimization of Turbo Machinery Validation Against Experimental Results

2009 – Current Trends in Design and Computation of Turbomachinery

Copyright © 2009 Concepts ETI, Inc. All rights reserved.

Optimization of Turbomachinery – Validation Against Experimental Results

Mark R. Anderson

Concepts NREC, White River Junction, Vermont, USA

Abstract: The long-term objective of engineering design software, or indeed any modeling

technique, is to improve the performance of the end product and to reduce the time and cost for

the project. This is particularly true in the case of testing, which can substantially increase time

and costs. Every analysis method, with the possible exception of Direct Numerical Simulation,

requires empirically based models to close the equations and render the problem tractable. For

this reason, and to confirm the soundness of the basic implementation, comprehensive validation

is required to ensure accurate results. Other issues such as grid quality and resolution also need

to be quantified so that users have a basic idea of how to achieve the best balance between

computational cost and accuracy. This publication outlines several examples of a comprehensive

CFD validation study and the key aspects such a program requires to be successful. Results are

shown for a wide variety of applications relevant to turbomachinery.

Keywords: Turbomachinery , CFD, validation, turbulence modeling, meanline modeling.

1. Introduction

The importance of validation in confirming any modeling approach is well recognized, and CFD is

no exception. Obviously, the more pertinent it is to the relevant problem, the better suited it is for

building confidence in the approach. Fortunately, a significant body of work is available through

the open literature for turbomachinery validation. The majority of these data are carefully

structured tests that emphasize a few particular aspects of the flow physics, such as two-

dimensional performance. Less common, but still important, are complex problems involving full

system performance.

To accomplish effective validation from a code development point of view, it is essential that the

process start simply and become progressively more complex. Otherwise, issues such as problems

in the implementation and modeling are lost in the complexity of the solution. For example, a

CFD validation that shows a 4% difference in efficiency from the test results for a full radial

compressor stage would rarely give the analyst the insight needed to identify the root cause of the

problem, such as a boundary condition implementation or equation of state error.

Obviously, consistency in setting up the model problem with the test is essential. This goes much

further than making sure the geometry and basic flow conditions are the same. It is important that

the data be reduced in a consistent fashion to that quoted in the test. Even a relatively basic

quantity such as efficiency can vary according to averaging technique, location of the

measurement, and thermodynamic assumptions used. More subtle parameters, such as the

measurement of turbulence intensity and length scale, can affect results as well. Many earlier test

ČKD Nové Energo & TechSoft Engineering


programs in turbomachinery dismissed this measurement as too esoteric to note, but flow behavior

can sometimes be significantly affected by it. Harder still to come by are test results with solid

data on the error bars of the measurements. It is important to note that differences in model and

test results are the products of both model and test error.

This paper presents some results of a systematic validation study conducted at Concepts NREC for

the purposes of validation and refinement of a Full Navier-Stokes CFD code. The solver, known

as the “MultiBlock” solver in the Pushbutton CFD®1

package, is an advanced, structured grid

solver developed specifically for turbomachinery. Some included features are: a 3rd

order AUSM

TVD scheme (Liou, 2006), full real equation of state, two-phase equilibrium capability, five state-

of-the-art turbulence models, and highly automated pre- and post-processing.

All results shown are for 3rd

order scheme settings with the Spalart-Allmaras (Spalart-Allmaras,

1992) turbulence model, unless otherwise noted. The general convention used in the graphs is that

the test results shown in symbols and CFD results are symbols connected with solid lines.

2. Flat Plate Boundary Layer

Perhaps the simplest turbulent flow solution that can be generated is the standard flat plate

solution. Despite its simplicity, a surprising number of issues come up when these cases are

scrutinized. The reason for this is the implementation of the wall functions or whether they are

even implemented at all. In fact, CFD solution results can show more sensitivity to the details of

the wall function than to the turbulence model itself. Strictly speaking, wall functions are not

necessary in a CFD code, but most practical problems require them. Without them, grid

resolutions must reach deep into the viscous sub-layer and require a huge number of grid cells.

Below is an implementation of the Spalart-Allmaras turbulence model using a standard wall

function (straight line) that is modified in the sub-layer region (curved line). The results show a

fairly consistent replication of the dimensionless velocity distribution, and as such, free the user

from overly serious dependency on grid resolutions.

Fig. 1. Dimensionless velocity profiles of a turbulent boundary layer for several grid densities

Because the flat plate solution has little or no pressure gradient, one would not expect any

significant variation in results from one turbulence model to the next, as is seen below.

1 Pushbutton CFD is a registered trademark of Concepts ETI, Inc.



Fig. 2. Dimensionless velocity profiles of a turbulent boundary layer for the Spalart-Allmaras (left) and SST (right) (Mentor, 1993, and

Bardina, 1997) turbulence models

3. One-dimensionalized Flow

Several challenging examples of CFD solutions can be found in one-dimensionalized flow fields.

Although they are one-dimensional in nature, the solutions are typically two- or three-dimensional

CFD implementations that may or may not include boundary layer effects. One distinct advantage

of looking at problems such as these is that there are often closed form solutions to the flow field

or well-established empirical observations that can validate key models in the code.

3.1 Rough Duct Example

The first example shown below is the rough duct example (Schlichting, 1951). Here, the

dimensionless pressure drop through the long pipe-like duct is plotted as a function of Reynolds

number. It is interesting to note that the left-hand point is a duct section about the size of a typical

coffee stirrer. The point on the right is one kilometer in length and has the diameter of a large

pipeline. The result shows good agreement with the empirically derived model. The roughness

effect is accounted for in an adjustment of the wall function. Despite this simple implementation,

the results are quite acceptable.

Fig. 3. Loss in a duct from different wall roughness levels as a function of Reynolds number



3.2 Converging-Diverging Two-phase Flow Nozzle

Another example specifically tests a two-phase equation of state model used in the CFD code. The

case is a converging-diverging supersonic nozzle case using steam. As the flow passes through the

nozzle, the kinetic energy increases and the thermal energy decreases, passing into the two-phase

domain. Results are shown for previously published experimental and numerical results (Morre et

al., 1973, and Kermani et al., 2003). The CFD follows the test quite well up to about the x=0.1

point, where there is a slight blip in the experimental results. The reason for this is the finite rate

nature of the droplet formation in the test, whereas the CFD results are implemented in an

equilibrium formulation.

Fig. 4. Pressure distribution in a condensing nozzle flow

4. Two-dimensional and Quasi-three-dimensional Flow

Many, many cases relevant to turbomachinery can be solved using a fundamentally two-

dimensional approach. Blade-to-blade solvers and throughflow solvers are just two examples of

solution methods using a two-dimensional formulation that have been used industry wide for many

years. These solvers may account for three-dimensional effects (at least partially) through source

terms in the conservation equations. As mentioned previously, these cases can be invaluable for

model validation, since key flow phenomena can be present (such as turbulence, adverse pressure

gradients, and shock structures) that would be impossible to quantify in more complicated three-

dimensional solutions.

4.1 Two-dimensional Diffuser

A simple diverging nozzle series of experiments was performed in the mid-1960s (Reneau et al.,

1967) that provides an excellent basis for examining the performance of turbulence models using

controlled, adverse pressure gradients. Figure 5 shows one of the simple geometric shapes used in

the study and the pressure recovery as a function of divergence angle of the side walls. The results

plotted are for the Spalart-Allmaras turbulence model. Generally, good agreement was shown,

with the trailing off of pressure recovery due to separation captured reasonably well.



Fig. 5. Two-dimensional nozzle performance

4.2 Compressor Cascade by Stark

A shape more directly relevant to turbomachinery is shown below in Figure 6. The case is of a

moderate Mach number and moderately loaded compressor profile tested in a wind tunnel (Stark,

Hoheisel, 1981, AGARD 1990).

Fig. 6. Compressor cascade results

The grid used in the study is shown in Figure 7. The fine mesh and high quality of the grid,

particularly in the regions of high flow gradients, gives a solid basis for quantifying the solver

results without compromising issues of grid quality.

Fig. 7. CFD Grid used in a Pushbutton CFD study



Fig. 8. Solution results for Stark compressor cascade

Effects of solution results based on the turbulence model are shown in Figure 8 on the right-hand

side. The results show relatively little variation from one model to the next. The effect of grid

density can be more significant, as is shown below in Figure 9. The results are for loss and flow

turning as a function of grid density, quantified by average y+ on the blade surface. The results

show significant variation until a y+ of about 30. After that point, the solution becomes basically

grid independent. It is import to note that grid independence is sometimes never achieved in

practice, particularly for difficult flows with significant separation regions. The designer must

have some reasonable feel for the effect of grid density on the solution before performance can be

quoted with confidence.

Fig. 9. Grid resolution study for the Stark compressor cascade. The bold point indicates the grid where test results were drawn.



4.3 MAN Compressor Cascade

Another compressor cascade tested in the mid-1990s (Steinert et al., 1996, and Steinert, Starken,

1996) shows very good agreement with the pressure distribution for two different incidence

angles.

Fig. 10. Isentropic Mach number distributions for the MAN compressor cascade at two different incidence angles

In Figure 11, the results of loss for negative incidence angles on the left-hand side show excellent

agreement test data, with a slight over-prediction of loss at the lower Mach numbers in the CFD.

Results on the right-hand side show a radically different result, with the CFD diverging wildly

from the test data. This is the result of transitional behavior of the boundary layer. The Reynolds

number of the test series was such that the boundary layer on the suction side did not become

turbulent until a very significant distance downstream of the leading edge. At lower loading, the

effect was benign, even beneficial, resulting in lower loss. At high angles, the effect was to incite

a massive flow separation that would not otherwise occur due to the stabilizing effect of

turbulence. Designers must be aware of such instances where complicating factors can introduce

very non-linear behavior to the flow.

The final figure for this series shows the results of loss for two different grid topologies. Overall

grid numbers and clustering on the surface were essentially identical for this study, so the

dominant effect is due to topological differences in the grid. The O-grid topology in the solid line

shows a more accurate result due to the better quality of grid at the leading edge, resulting in less

numerical entropy. The H-grid (dashed line) shows a higher loss. This effect is perhaps somewhat

exaggerated due to the very low overall loss of the profile, but it is still significant.

Fig. 11. Results for the MAN compressor cascade



4.4 European Turbine Cascade Test Series

Next is an example of a turbine blade tested in four separate wind tunnels in Europe in the 1990s

(Kiock et al., 1986). The results are extremely valuable for validation purposes, since they clearly

show the error bar in the testing series. The variation in results is particularly evident in the

adverse pressure region of the suction side, as seen in Figure 12 below. The CFD results pass

nicely through the test data “cloud”. Loss and flow angle shown in Figure 13 compare nicely as

well.

Fig. 12. European turbine cascade test (dots) and CFD results (solid lines)

Fig. 13. European turbine cascade test (dots) and CFD results with various turbulence model solutions (solid lines)



4.5 Birmingham University Steam Turbine Cascade

A condensing steam profile was tested at the University of Birmingham that provided an excellent

test case for validating condensing flow cases (Bakhtar, 1994). The profile is that of a rotor or

stator tip that was tested in the subsonic to supersonic range. The results of pressure ratio around

the blade are shown in Figure 14. Note the blip in pressure similar to that seen on the converging-

diverging nozzle case that shows the effect of finite rate droplet kinetics in the test.

Fig. 14. University of Birmingham condensing steam turbine profile

5. Full Three-dimensional Flow

5.1 Hodson Turbine Test

A study conducted at Cambridge University provided some high level validation data for a fully

three-dimensional case specifically related to turbine secondary flow (Hodson, Dominy, 1987).

The experiment consisted of an untwisted profile with a well-defined velocity distribution at the

inlet. Figure 15 shows the general shape of the complex flow field resulting from the turning of

the rotational flow.

The results from CFD show good quantitative and qualitative agreement despite the fact that this

type of solution is quite sensitive to grid resolution, since a high degree of refinement is needed

throughout the whole flow volume, not just the boundary layer region.



Fig. 15. Hodson turbine test and comparison to CFD

5.2 Eckardt Compressor O

The Eckardt O compressor was a famous test done in Germany with very detailed measurements

for performance and internal flow distribution measured via a laser (Eckardt, 1975, 1976, 1980).

The series is one of the best documented compressor tests available in the open literature.



Fig. 16. Eckardt O Compressor

5.3 Ricardo Radial Turbine

A radial turbine case solution, extensively tested and documented starting in the 1950s, is shown

below (Hiett, 1956, 1958, 1962, 1963).

The plot on the right-hand side shows the flow angles calculated at the inlet nozzles. The second

figure is the efficiency versus U/Ct ratio for several rotational speeds and pressure ratios. This is

interesting in terms of accuracy of the solution, as well as the extraordinary tendency for radial

turbine performance to collapse on this term. The right-hand plot shows the non-dimensional

mass flow versus pressure ratio.

Fig. 17. Ricardo radial turbine with CFD results (points) at various rotational speeds



6. Conclusion

The cases reviewed in this publication represent a small, but still significant, set of interesting

examples for CFD validation of turbomachinary problems. Extra care was taken to eliminate

superfluous errors that can result from inadequate grid resolution, poor grid quaility, or improper

boundary condition setup.

For validation to be truly useful, it must present the user with three things:

1) It must represent a statistically significant number of cases. Only then can the user be

sure that dumb luck did not merely give canceling errors.

2) It must reflect what a skilled user can reasonably expect to achieve without knowing the

answer beforehand. If a number of factors are tweaked to match the results, then the

exercise is really one of curve fitting and not validation.

3) It must consist of examples that are pertinent to the user’s problem.

These results generated through Concepts NREC’s Pushbutton CFD product represent some of the

best examples available for general turbomachinery validation. The results show very good

agreement overall, with specific cases highlighted to demonstrate interesting challenges that still

remain in CFD modeling.

7. Reference

1. Bakhtar, F., M., Ebrahimi, M., and Webb, R.A., 1994, On the Performance of a Cascade

of Turbine Rotor Tip Section Blading in Nucleating Steam Part 1: Surface Pressure

Distributions, Proc Instn Mech Engrs, Vol. 209, pp. 115-124.

2. Bardina, J.E., Huang, P.G., Coakley, T.J., 1997, Turbulence Modeling Validation, AIAA

97-2121.

3. Hodson, H.P., Dominy, R.G., 1987, Three Dimensional Flow in a Low-Pressure Turbine

Cascade at Its Design Condition, Journal of Turbomachinery, Vol. 109, April 1987.

4. Hodson, H.P., Dominy, R.G., 1987, Off Design Performance of a Low-Pressure Turbine

Cascade, Journal of Turbomachinery, Vol. 109, April 1987.

5. Eckardt, D., 1976, Detailed Flow Investigations Within a High-Speed Centrifugal

Compressor Impeller, Journal of Fluids Engineering, Sept 1976.

6. Eckardt, D., 1976, Detailed Flow Investigations Within a High-Speed Centrifugal

Compressor Impeller, ASME 76-FE-13.

7. Eckardt, D., 1975, Instantaneous Measurements in the Jet-Wake Discharge Flow of a

Centrifugal Compressor Impeller, Journal of Engineering for Power, July 1975.

8. Eckardt, D., 1980, Flow Field Analysis of Radial and Backswept Centrifugal Compressor

Impellers, Part 1: Flow Measurements Using a Laser Velocimeter, “Performance

Prediction of Centrifugal Pumps and Compressors”, ASME 1980.

9. Eckardt, D., private communication.

10. Hiett , 1962, First Report on Aerodynamic Performance Tests on Cold Rig, M.I.R.A.

Radial Inflow Turbine, Engineering Report DP.6845, Ricardo & Co Engineers.

11. Hiett, 1956, D.I.G.T. Radial Inflow Turbine, Scroll and Nozzle Performance, Part I,

Engineering Report 1365A, Ricardo & Co Engineers.



12. Hiett and Palmer, 1956, D.I.G.T. Radial Inflow Turbine, Cold Tests on Turbine B, Scroll

and Nozzle Performance, Part II, 1956, Engineering Report 1368, Ricardo & Co

Engineers.

13. Hiett and Palmer, 1956, D.I.G.T. Radial Inflow Turbine, Cold Tests on Turbine B,

Turbine A and Turbine D, Engineering Report 1381, Ricardo & Co Engineers.

14. Hiett, 1956, D.I.G.T. Radial Inflow Turbine, Mechanical Design and Operating

Experience of Cold Test Rig, Engineering Report 1382, Ricardo & Co Engineers, Sept.

1956.

15. Hiett, 1958, D.I.G.T. Radial Inflow Turbine , Cold Tests on Turbine B, and Turbine A

and Turbine D, Engineering Report 1412, Ricardo & Co Engineers, Dec. 1958.

16. Hiett, D.I.G.T. Radial Inflow Turbine, Cold Tests on Turbine C and Turbine A, Hot Tests

on Turbine A, Engineering Report 1436, Ricardo & Co Engineers.

17. Hiett, 1963, D.I.G.T. Radial Inflow Turbine, Cold Tests on Turbine BA, and Turbine C,

and Turbine A., Engineering Report 1467, Ricardo & Co Engineers.

18. Kermani, M.J. , Gerber, A.J., and Stockie, J.M., 2003, Thermodynamically based

moisture prediction using Roe’s scheme, Univ. of New Brunswick, Fredericton, Canada.

19. Kiock, R., Lehthaus, F., Baines, N., Sieverding, C., 1986, The Transonic Flow Through a

Plane Turbine Cascade as Measured in Four European Wind Tunnels, Journal of

Engineering for Gas Turbines and Power, April 1986, Vol. 108.

20. Liou, Meng-Sing, 2006, A sequel to AUSM, Part II: AUSM+-Up for All Speeds, Journal

of Computational Physics, 214, 137-170.

21. Mentor, F.R., 1993, Zonal Two Equation k-w Turbulence Models for Aerodynamic

Flows, AIAA Paper 93-2906.

22. Moore, M.J., Walters, P.T., Crane, R.I., and Davidson, B.J., 1973, Predicting the Fog

Drop Size in Wet Steam Turbines, Inst. of Mechanical Engineers (UK), Wet Steam Conf.

4, Univ. of Warwick, Paper C37/73.

23. Reneau, L.R., Johnston, J.P., and Kline, S.J., 1967, Performance and Design of Straight,

Two-Dimensional Diffusers, Journal of Basic Engineering, March, pp. 141-150.

24. Schuster, P., Schmidt-Eisenlohr, 1980, U., Flow Field Analysis of Radial and Backswept

Centrifugal Compressor Impellers, Part 2: Comparison of Potential Flow Calculation and

Measurements, Performance Prediction of Centrifugal Pumps and Compressors”, ASME

1980.

25. Schlichting, H., 1951, Boundary-Layer Theory, Springer Berlin / Heidelberg.

26. Stark, U., Hoheisel, H., 1981, The Combined Effects of Axial Velocity Density Ratio on

Compressor Cascade Performance, Transactions of the ASME, Journal of Engineering

for Power, Vol. 107, January 1981, pp. 247-255.

27. Spalart, P.R., Allmaras, S.R., 1992, A One-Equation Turbulence Model for Aerodynamic

Flows, AIAA 92-0439.

28. Steinert, Eisenburg, Starken, 1991, Design and Testing of a Controlled Diffusion Airfoil

Cascade for Industrial Axial Flow Compressor Application”, Journal of Turbomachinery,

Vol. 113.

29. Steinert, Starken, 1996, Off Design Transition and Separation Behavior of a CDA

Cascade, Journal of Turbomachinery, Vol. 118.

30. Test Cases for Computation of Internal Flows in Aero Engine Components, 1990,

AGARD Advisory Report No. 275.

Optimization of Turbo Machinery Validation Against Experimental Results

Documents

Transcript of Optimization of Turbo Machinery Validation Against Experimental Results