Proceedings of - tfd.chalmers.se

Proceedings of: ASME TURBO EXPO 2006

May 8-11, 2006, Barcelona, Spain

GT2006-90550

Performance and Off-Design Characteristics for Low Pressure Turbine Outlet Guide Vanes: Measurements and Calculations

Johan Hjärne Department of Applied Mechanics Chalmers University of Technology

412 96 Gothenburg, Sweden [email protected]

Jonas Larsson Department of Aero and Thermo Dynamics

Volvo Aero Corporation 461 81 Trollhättan, Sweden [email protected]

Lennart Löfdahl Department of Applied Mechanics Chalmers University of Technology

412 96 Gothenburg, Sweden [email protected]

ABSTRACT

This paper presents 2D and 3D-numerical simulations compared with experimental data from a linear Low Pressure Turbine/Outlet Guide Vane (LPT/OGV) cascade at Chalmers in Sweden. Various performance characteristics for both on and off design cases were investigated, including; pressure distributions, total pressure losses and turning. The numerical simulations were performed with the goal to validate simulation methods and create best-practice guidelines for how to accurately and reliably predict performance and off-design characteristics for an LPT/OGV. The numerical part of the paper presents results using different turbulence models and levels of mesh refinement in order to assess what is the most appropriate simulation approach. From these results it can be concluded that the k-ε Realizable model predicts both losses and turning most accurately for both on and off design conditions. 1 INTRODUCTION Cost and weight requirements on modern jet engines often lead to more highly loaded turbines with fewer stages. In un-geared two and three shaft engines this gives higher swirl angles into the LPT/OGV’s making the aerodynamic design of the OGV’s more difficult. Structural requirements frequently lead to non-cylindrical shrouds with complex three-dimensional polygonal shapes and sunken engine-mounts with bumps protruding into the gas-channel. This has sparked a renewed interest in design methods and validation cases for turbine OGV flows. A literature survey shows that very few, if any, measurements of realistic OGV flow-cases are publicly available. The aerodynamic function of the LPT/OGV is to turn the swirling

flow into an axial outlet flow angle with as low a pressure loss as possible at the design-point.

NOMENCLATURE C Axial chord for the OGV Cp Pressure distribution = (Ptot,in-Ps,OGV)/Pdyn,inPatm Atmospheric pressure Pdyn Dynamic pressure based on inlet velocity Ptot Total pressure above Patm Ptot,fs Total pressure in the downstream free stream ReC Reynolds number based on inlet conditions and chord x x-coordinate y y-coordinate z z-coordinate Greek Symbols α Inlet flow angle β Outlet pitch angle ε Turbulent dissipation ξ Total pressure losses = (Ptot-Ptot,fs)/Pdyn Acronyms Low-Re Calculation with resolved boundary layers LPT Low pressure turbine OGV Outlet Guide Vane wf Calculation using wall functions

1 Copyright © 2006 by ASME

2 EXPERIMENTAL SET UP The linear cascade used for the measurements is an open

circuit blower type. A 30kW fan is used to drive the flow through a diffuser and a flow conditioner (consisting of a honeycomb and three screens with different porosity). The flow is then accelerated in a 5:1 contraction before it enters the test section. The test section is built up of four parallel discs, two on each side, with the inner discs constituting the sidewalls of the 7 OGV’s, thus forming the cascade. The gap between the inner and outer discs is used for sucking out the boundary layers developed in the upstream sections. There is a suction system on either side, each being driven by a 7.5 kW fan. The two suction systems can thus be adjusted to ensure a straight and undisturbed flow field going into the cascade. A more detailed description of the test-facility has earlier been given by Hjärne et al. [1,2]

The grid used to generate free stream turbulence consisted of 5mm bars with a mesh size of 25mm, thus giving a solidity of 0.31. This was placed 450mm upstream of the cascade and parallel to the leading edge plane, see Fig. 1. Besides increasing the turbulence intensity from 0.5% to 5%, the parallel grid has two effects. The positive effect is that the inlet turbulence intensity is uniform in front of the cascade. The negative effect is that the grid deflects the inflow and as a result the outer side wall inclination had to be adapted so that the inlet incidence remained unchanged.

The periodicity has been checked and is illustrated in Fig. 2 and Fig. 3. The first figure shows the static pressure distribution around the three mid vanes. The variation from one vane to another is small for both the suction side and the pressure side. Figure 3 gives the total pressure distribution at the midpan position at 80% of the chord length downstream of the trailing edge.

Figure 1 The experimental set up.

3 INSTRUMENTATION Two traversing systems controlled by stepper motors have

been used to measure the flow field both upstream and downstream. The five hole pressure probes used for the different traverses have been manufactured at Chalmers and were calibrated between –20 to 20 degrees for both pitch and yaw angles.

Figure 2 Cp distribution for the three mid OGVs in the cascade for the on design-point.

Figure 3 The downstream wakes of the total pressure normalized with inlet dynamic head.

The inlet measurements were conducted 285mm upstream of the cascade with a discretization of 20mm in both y and z direction. The typical total pressure variation was below 2% of the dynamic head. The upstream traversing system was also used to measure the incoming boundary layer height along the sidewalls. In order to obtain a boundary layer height similar to what is present in a real engine, the boundary layer was tripped with a 1.5 mm wire placed 300 mm upstream of the blade leading edge. The height of the turbulent boundary layer was 9.6mm at 200mm upstream of the leading edge plane.

The downstream traversing system was used to measure the pressure distribution over the three mid wakes at mid span, 176mm downstream of the trailing edge. A discretization of 1mm in the y-direction was used. 4 OGV DESIGN

The OGV geometry used for these investigations has been developed at Chalmers as a demonstrator for OGV validation cases. The OGV is a 2D geometry profile which is extended in the span direction (z-direction), The on-design requirement for this vane is to turn an incoming flow field with an inlet flow angle of 30 degrees to an axial outflow and the off-design requirements are ± 10 degrees incidence without total mid-span separation. The periodicity around the OGV’s is measured with


static pressure taps placed at 25%, 50% and 75% of the span see Fig. 4. In total there are 77 pressure taps on each blade. The characteristics of the OGV and the flow conditions are presented in table 1.

Figure 4 Location of the pressure taps on the OGV

Table 1 Cascade geometry data

Number of vanes 7 Chord length (mm) 220 Pitch to chord ratio 0.91 Aspect ratio (Span to Chord ratio) 0.91 Inlet Reynolds number 280000 Inlet flow angles (°) 20,30,40 Turbulence intensity (%) 5 Incoming boundary layer height (mm) 9.6 5 NUMERICAL CALCULATIONS

In this paper both 2D and 3D CFD calculations are preformed with the numerical software FLUENT [4] (v. 6.1.22 and v 6.2.16). Three different types of turbulence models, k-ε Realizable, k-ω SST and Spalart-Allmaras have been used and compared with experimental results. Since the kω-SST model is badly implemented in FLUENT v. 6.1.22 a newer version of FLUENT 6.2.16 was used for this model only. The other models were also tested with the newer FLUENT version, however no major changes were seen.

The 2D calculations are valuable from an initial design point of view where it is interesting to know how accurate a 2D simulation for the midspan profile predicts losses, pressure distributions and outlet pitch angles compared to a 3D model where the secondary flow field comes into account. The mesh generators used were Gambit (pre-processor to FLUENT) for the 2D meshes and ICEM-HEXA for the 3D meshes. Side views of the computational domains for the 2D and 3D calculations are depicted in Fig. 5 and 6. The inlet boundary condition was placed 0.9*C upstream of the blade leading edge and the outlet boundary condition was placed 0.9*C downstream of the trailing edge.

A mesh dependence study was performed using two different mesh sizes for both the 2D and 3D domain. For the 2D mesh a baseline mesh with 1.4*104 mesh cells and a refined mesh with 5*104 cells were tested. In the 3D case the baseline mesh had 6.9*105 mesh cells and the refined mesh had

1.35x106 cells. The turbulence model used for this study was the k-ε Realizable with resolved boundary layers.

Figure 5 Baseline 2D mesh consisting of 1.4*104 cells

Figure 6 Baseline 3D mesh consisting of 6.9*105 cells

To check the grid sensitivity the mass averaged total pressure outlet losses, ξ, were calculated at 3 downstream positions between 0.25*C and 0.8*C of the OGV trailing edge. Figure 7 compares the total pressure loss coefficients for both the 2D and 3D mesh sizes. The difference in pressure loss between the two different mesh sizes for the 2D models is only 0.6% whilst the corresponding value for the 3D mesh is 0.015%. Therefore the two baseline meshes were considered to be sufficiently refined in order to obtain results which were independent of the grid?

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Figure 7 Mesh sensitivity study for both the 2D and 3D mesh cases, showing the mass averaged total pressure loss at different downstream positions of the cascade.


Turbulence Modeling As already mentioned the aerodynamic function of the

LPT/OGVs is to turn the swirling flow from the last low-pressure turbine rotor into an axial direction. This de-swirling gives a diffusive flow with growing boundary layers, strong secondary flows, and increases the risk of separation on the vane surfaces as well as the end-walls. In terms of turbulence modeling this is a very challenging case to predict. For this reason three different turbulence models were tested. The three models chosen are: Shih’s realizable k-ε model [5]

This is the most commonly used turbulence model in FLUENT. It is similar to the classical k-ε model but has a variable Cµ and a modified ε equation. The main advantage with the Realizable version for the present application is that it works much better than a classical k-ε model in regions with strong deceleration and acceleration, for example in the leading edge region and the region around the suction side pressure minimum. Note that this is a high-Re model which needs to be complemented with a low-Re model close to the walls if a grid with resolved boundary layers is used. Menter’s SST k-ω model [6, 7]

This model has become increasingly popular in the last few years and it is now regarded a standard model in the turbomachinery field. It is a low-Re model which works well with resolved boundary layers. The SST k-ω model has been known to work especially well for cases with adverse pressure gradients and separations. It is also commonly used in heat-transfer applications. Spalart-Allmaras model [8]

This is a one-equation model which solves a transport equation for the eddy-viscosity. It has been used extensively in aerospace applications and lately it has also become more and more common in the turbomachinery field. Its main merit is that it is very robust, it seldom leads to numerical problems and it rarely produces very unphysical results. The version used in this work includes the strain/vorticity based production term modification proposed by Dacles-Mariani [9]. The Spalart-Allmaras model is a low-Re model which works well with resolved boundary layers.

In addition to these models two different types of near-wall treatment were tested with the realizable k-ε model: Non-equilibrium wall-functions [10]

This model is based on the classical wall-function approach [11] but in addition it includes a law-of-the-wall which is sensitized to pressure gradients and employs a turbulent kinetic energy budget which takes historical effects into account. The main merit of the non-equilibrium wall-functions over the standard wall-functions is that it works much better in cases with strong streamwise pressure gradients. From the author’s experience this model is very suitable for quick design-iterations and works very well as long as no massive separations occur. For these calculations the mesh consisted of 2.8*105 mesh cells.

Enhanced wall-treatment/two-layer model [12, 13, 14] When used on fine grids with resolved boundary layers

(y+ < 1) this model employs a Wolfstein [12] one-equation model in the inner parts of the boundary layers. This model is matched to the k-ε model in the outer region following the work by Jongen [13]. The length-scale is computed according to Chen & Patel [14]. This two-layer approach is very attractive. It avoids the ad-hoc damping functions used in many other low-Re models and it seldom leads to any numerical problems. For cases with large separations and 3-dimensional boundary layers, the low-Re two-layer model is normally superior to a wall-function approach.

The CFD simulations were computed for incompressible,

viscous, low-speed conditions with the inlet velocity profiles used in the calculations having been taken from the measurements. The calculations with the resolved boundary layers (low Re k-ε Realizable, kω-SST and Spalart-Allmaras) were run with a segregated double precision solver and a second order upwind scheme, while the calculation for the k-ε Realizable with wall functions used a single precision solver together with a second order upwind scheme. The y+ mean value on the OGV for the 2D cases with the low Reynolds models was 0.5 and when wall functions was used it was 50. The same figures for the 3D cases were 0.2 and 40 respectively. 4 RESULTS

The numerical investigation is two parted; both a 2D and a 3D analysis have been conducted and compared with the experimental results. The evaluated properties are the pressure distribution around the OGV (Cp), the downstream wake distribution, the mass averaged total pressure losses, (ξ) and the outlet pitch angle (β).The Cp values are calculated according to Eq. 1 and the results are presented below.

indyn

OGVsintot

PPP

Cp,

,, −= (1)

Cp distribution Figure 8 and 11 present comparisons between the

numerical results and the experiments for the on-design case (30 degrees inlet angle). The results for the two equation models k-ε Realizable and kω-SST, show similar results for both the 2D and the 3D solution but the one equation model from Spalart-Allmaras shows a big deviation for the 3D case. The difference is due to separation on the suction side starting after the suction peak in the corner between the vane and the endwall. Further downstream the separation almost reaches mid-span.

For the 20 degrees inlet flow angle (off design -10 degrees) Fig. 9 and 12 show a lot of similarity between all the models for both 2D and 3D simulations

For the 40 degrees inlet flow angle (off design +10 degrees), shown in Fig. 10 and 13, some differences can be seen. To begin with, it can be seen from the figures that the Cp distributions for all the measured vanes, OGV low. OGV mid and OGV up, see Fig. 1, are included since the cascade is very close to separation. As can be seen in the figures “OGV up” shows a kink on the decelerating part of the suction side which implies a local separation. However, the two lower vanes show similar


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Figure 8 Cp distribution at design-point (30˚ inlet angle) for the 2D simulation

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Figure 9 Cp distribution at -10˚ off-design (20˚ inlet angle) for the 2D simulations

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Figure 10 Cp distribution at +10˚ off-design (40˚ inlet angle) for the 2D simulations

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Figure 11 Cp distribution at design-point (30˚ inlet angle) for the 3D simulation

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Figure 12 Cp distribution at -10˚ off-design (20˚ inlet angle) for the 3D simulations

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Figure 13 Cp distribution at +10˚ off-design (40˚ inlet angle) for the 3D simulations


results in which no kink is visible, thus showing that separation does not occur on these two vanes. It is important to note that this local separation on the upper OGV Results in the periodicity being quite poor for this experiment.

For the 2D simulations shown in Fig. 10 the only model that showed separation was the kω-SST model. The separation begins (negative x-wall shear stress) just downstream of the suction peak and does not reattach itself to the OGV again. As a result of the separation, the kω-SST model fails to show the suction peak, it does however predict the later part of the pressure side of the OGV very well. The calculations from the two k-ε Realizable models as well as the SA model provided results which were fairly close to the measurements on the suction side of two lower vanes, with the pressure side showing more difference.

Looking at the 3D calculations shown in Fig. 13, some interesting observations can be made. The calculations revealed that none of the models showed full mid span separation, but all of the models show negative x-wall shear stress values in the end wall suction side corner, with this region gradually extending towards midspan as it approaches the TE. This corner separation extends differently from the wall towards mid span between the different models and this explains the differences in the Cp values. In table 2 the spanwise extension of the corner separation is presented. Again the two k-ε Realizable calculations predict the suction peak the best. Moving away from the suction peak towards the trailing edge the k-ε Realizable with wall functions predicts both the pressure side and the suction side fairly well for the two lower OGV’s, with experimental results showing no separation.

The near wall models are clearly more affected by the corner separation, as shown in table 2, with the upper OGV comparing more closely in the region where the kink is visible in the Cp distribution. Even though the calculations are slightly different from the experimental results, they ho however predict the same trend on the suction side. The k-ε Realizable predicts both the pressure side and the suction side better than the other two models.

Table 2 %-span at trailing edge covered by the corner separation at 40 degrees inlet flow angle

Model % span k-ε Realizable 68.5 k-ε Realizable wf 46 kω-SST 70 Spalart-Allmaras 80

Downstream wake profiles

Figure 14 shows the wake profiles computed in 2D with the different turbulence models at the design-point for the OGV’s. For comparison the measured wake profile at mid-span is also included. The kω-SST model predicts both the width and the depth of the wake very well. The Spalart-Allmaras model and the two variants of the Realizable k-ε model predict the wake-depth fairly well but show some differences with regards to the width. It is worth noting that both the k-ε Realizable and the Spalart-Allmaras model seem to over-predict the width of the suction-side boundary layer whereas all models have a slight tendency to under-predict the width of the pressure-side

boundary layer. This is due to limitations in the models’ ability to account for the strong streamwise pressure gradients on the suction side. It can also partly be explained by the fact that there might be a laminar region on the suction-side of the OGV’s upstream of the suction-peak. The later explanation is supported by the fact that the width of suction-side boundary-layer seems to agree better for the off-design case with 40 degrees inlet angle as shown in Fig. 16. For the 40 degrees case the pressure peak is very close to the leading edge (see Fig. 10) with any laminar regions being likely to be small in this case.

The wake profiles obtained in 3D at mid-span for the design-point with 30˚ inlet angle are shown in figure 17. The results are very similar to the 2D results described above. The main difference is that the Spalart-Allmaras model in this case predicts a 3D separation in the suction-side/end-wall corner as described above. This leads to an under-prediction of the turning at mid-span and a slight error in the location of the wake downstream. Otherwise the predicted wake-depth and width are very similar to the 2D results for all turbulence models.

Figure 15 and 18 shows results in 2D and 3D at off-design conditions with an inlet angle of 20 degrees. The results for this case are very similar to the results obtained at the design-point. In this case the Spalart-Allmaras model does not predict any separation and hence the turning and the wake-location is better predicted than at the design-point.

The results for 40 degrees inlet angle show more difference. Results from the 2D simulations are shown in figure 16. The realizable k-ε model under-predicts the wake-depth slightly, especially when used as a low-Re model with resolved boundary layers. The most correct wake depth is obtained with the Spalart-Allmaras model. The SST k-ω model predicts a wake which is both too deep and too wide and is due to separation

In this case the results obtained in 3D show some discrepancies compared to the 2D results. The reason for this is that at this high-incidence angle all models with wall-functions predict a varying degree of separation in the suction-side/end-wall corner, see table 2, and this of course affects both the turning and the pressure-distribution at mid-span. The best results for the wake-width and depth are in this case obtained with the two variants of the realizable k-ε model. Both the Spalart-Allmaras and the SST k-ω models show almost complete separation at midspan.


Figure 14 Downstream wake profiles at design-point (30˚ inlet angle) for the 2D simulation

Figure 15 Downstream wake profiles at -10˚ off-design (20˚ inlet angle) for the 2D simulations

Figure 16 Downstream wake profiles at +10˚ off-design (40˚ inlet angle) for the 2D simulations

Figure 17 Downstream wake profiles at design-point (30˚ inlet angle) at mid-span for the 3D simulation

Figure 18 Downstream wake profiles at -10˚ off-design (20˚ inlet angle) at mid-span for the 3D simulations

Figure 19 Downstream wake profiles at +10˚ off-design (40˚ inlet angle) at mid-span for the 3D simulations


Losses 2D The total pressure losses are calculated according to Eq. 2.

Ptot is the mass averaged total pressure 0.8*C downstream of the trailing edge and Ptot,fs is the total pressure outside the wakes at the same position downstream. Pdyn is the inlet dynamic pressure. Both the numerical and the experimental losses are evaluated at mid span as opposed to a mass average over the whole outlet.

dyn

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=ξ (2)

Figure 20 presents the 2D numerical losses compared to the experimental results when varying the inlet flow angle. For the lowest inlet flow angle and the on-design case the best prediction comes from the kω-SST model. This is in accordance with the good wake prediction this model showed as described above. All the other models show an over prediction of the losses.

When the inlet flow angle is 40º the two k-ε Realizable models are closest to the experimental value, especially the solution with resolved boundary layers. The kω-SST model shows a large over-prediction and the reason for the high losses is that this model separates when the inlet flow angle is 40º. The Spalart-Allmaras model has the same trend as the k-ε Realizable with wall functions but it predicts higher losses.

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Figure 20 Losses for the 2D numerical simulations compared with experimental results. Losses 3D

Figure 21 presents the losses for the 3D cases. Again the two k-ε Realizable calculations and the kω-SST model show the best results and now the results for the two lower inlet flow angles show very similar results compared to the experiment. For the highest inlet flow angle the kω-SST model separates as for the 2D case and it is the k-ε Realizable with wall functions which is closest to the experimental prediction. This is due to the low Re variant having an endwall suction side separation which increases the losses. For the 3D case, the SA model over predicts the losses as well.

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Figure 21 Losses for the 3D numerical simulations compared with the experimental results.

Outlet pitch angle distribution 2D Since the swirling flow out from the LPT/OGV is in direct

connection with total pressure loss, the outlet pitch angle is an important parameter to study. The mass averaged variation of outlet pitch angles, β, are presented in Fig. 22 and 23.

For the 2D results depicted in Fig. 22, the models follow the same trend as the experiments. It is Interesting to see that the two k-ε Realizable calculations show quite different results. For the on design case the low Re variant over predicts the turning while the wall function variant under predicts the turning. For the highest inlet angle the prediction from the wall function case is very good while the low Re variant under-predicts by more than 1 degree. This might however be explained by the fact that the comparisons are made for the mid vane where no separation occurs. The kω-SST model is very similar to the low Reynolds k-ε Realizable for the two lower inlet angles but under predicts at the higher angle because of the separation. The Spalart-Allmaras is comparable to the low Re variant of the k-ε Realizable. All the models under-predict the turning at 20 degree inlet flow.

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Figure 22 Outlet pitch angle variation when varying inlet flow angle for the 2D calculations


Outlet pitch angle distribution 3D The 3D results presented in Fig. 23 show that all models

under predict the turning for the three different inlet flows. The low Re k-ε Realizable model gives the best results for the on design angle and the lower inlet angle. Again, because of suction side corner separation the difference is bigger for the highest inlet flow. The wall function variant of the k-ε Realizable and the kω-SST has the same behavior for the two lower inlet angles but because the latter separates for the highest angle, the results were less accurate. With the S-A model showing separation at the design angle, it can be concluded that this model provides poor results after the 20 degree inlet flow angle.

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Figure 24 Outlet pitch angle variation when varying inlet flow angle for the 3D calculations 5 CONCLUSIONS AND BEST PRACTICE GUIDE LINE

This paper presents results for three different turbulence models compared to experimental results from a linear LPT/OGV cascade. The numerical results are compared to the experimental results in terms of mid-span pressure distribution, downstream wake distribution, losses and the outlet pitch angles. Both on and off design conditions have been investigated and the results are summarized below.

• When no separation occur, on-design point and -10º incidence, all turbulence models except the Spalart-Allmaras model, predicts the correct pressure distribution in both 2D and 3D for on and off design conditions. The Spalart-Allmaras model predicts a big corner separation by the design point. For the +10 degree inlet case, the kω-SST showed separation and therefore showed poor agreements with experimental results. The best Cp prediction for +10º incidence comes from the k-ε Realizable with wall functions.

• For the wake region downstream, the model which best predicted the distribution at the two lower inlet flow angles was the kω-SST model, with the calculations comparing very well with those obtained experimentally. The two k-ε Realizable solutions give good results considering the depth of the wake, while the width is over predicted. However for the highest inlet flow angle these two models are far better than the kω-SST model since the latter shows a bigger suction side endwall corner separation.

• Considering the downstream losses the best predictions comes from the two k-ε Realizable and the kω-SST model for the two lower inlet flow angles in the 3D simulations. For the highest inlet flow angle the kω-SST model separates and therefore the level of the predicted losses is too high. An interesting fact for the losses is that the best prediction came from the k-ε Realizable using wall functions. This might however be explained by the fact that the comparisons are made for the mid vane where no separation seems to occur.

• The prediction of outlet pitch angles showed good results at the design-point for all models except for the Spalart-Allmaras model in the 3D case. For the off design cases the resemblance is however worse. The two k-ε Realizable models and the kω-SST model are very similar for the two lower inlet flow angles but for the highest angle the k-ε Realizable models are clearly better.

As a best practice guideline to design a non separating

OGV the authors recommend using the k-ε Realizable model with wall functions at the initial design stage. The advantage being that the smaller mesh size results in a shorter computational time. In addition it also shows satisfactory predictions of the pressure distributions, losses and the outlet pitch angles. For more detailed analysis it is suggested to use either the k-ε Realizable or the kω-SST model with resolved boundary layers. Both these models show conservative predictions of losses and separations which is good from a design point of view.

ACKNOWLEDGEMENTS The present work is a part of the project COOL supported

by the Swedish Gas Turbine Center (GTC), and funded by Siemens, Volvo Aero Corporation and Energimyndigheten. The permission for publication is gratefully acknowledged.

REFERENCES [1] Hjärne, J., Larsson, J. and Löfdahl, L., 2003, “Design of a Modern Test-Facility for LPT/OGV flows,” ASME paper GT2003-38083 [2] Hjärne, J., Larsson, J. and Löfdahl, L., 2005, “Experimental Evaluation of the Flow Field in a State of the Art Linear Cascade with Boundary-Layer Suction,” ASME paper GT2005-68399 [3] Hjärne, J., 2001, “Aerodynamic Analysis of Outlet Guide Vane Flows,” Diploma thesis, Chalmers University of Technology, Göteborg [4] FLUENT 6, 2001, Users manual, Fluent Incorporated, Lebanon, NH, USA [5] Shih, T.-H., Liou, W. W., Shabbir, A. Z., Yang, and Zhu, J., 1995, “A New Eddy-Viscosity Model for High Reynolds Number Turbulent Flows - Model Development and Validation”, Computers Fluids, 24(3), pp 227-238


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