TRANSITION PREDICTION IN LOW PRESSURE TURBINE (LPT) USING GAMMA THETA MODEL & PASSIVE CONTROL OF SEPARATION

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1 Proceedings of the ASME 2011 International Mechanical Engineering Congress & Exposition IMECE2011 November 11-17, 2011, Denver, Colorado, USA IMECE TRANSITION PREDICTION IN LOW PRESSURE TURBINE (LPT) USING GAMMA THETA MODEL & PASSIVE CONTROL OF SEPARATION Muhammad Aqib Chishty Khalid Parvez Sijal Ahmed Hossein Raza Hamdani Ammar Mushtaq Research Centre for Modeling and Simulation National University of Sciences and Technology (NUST) H-12, Islamabad, 44000, Pakistan ABSTRACT The boundary layer of low-pressure turbine blades has received a great deal of attention due to advent of high lift and ultra high lift LP turbines. At cruising condition, Reynolds number is very low in engine and LP turbine performance suffers mainly from losses due to the laminar separation bubble on suction surface. In this paper, T106A low pressure turbine profile has been used to study the behavior of boundary layer and subsequently, flow is controlled using the passive technique. Unsteady Reynolds Averaged Navier Stokes equations were solved using SST Gamma-Theta transition model for turbulence closure. Hybrid mesh topology has been used to discretize the computational domain, with highly resolved structured mesh in boundary layer (Y + < 1) and unstructured mesh in the rest of domain. Simulations were performed using commercial CFD code ANSYS FLUENT at Reynolds number (based on inlet velocity and chord length) and turbulence intensity of 0.4%. To study the effect of dimple on the flow separation, dimple has been positioned at different axial location on the suction side. It was found that shifting the dimple downstream results in controlled flow and reduced loss coefficient as compared to the case when no dimple is applied. INTRODUCTION In the last three decades, reduction of fuel cost and engine weight is the main concern of aero-engine manufacturers and aircraft industry. In order to reduce the engine weight and fuel consumption, current trend is to design LP turbine blades with high or ultra high lift. However, to maintain the aerodynamic performance of high lift LPT blade, key factor is to control laminar separation bubble on suction surface. The prescribed Reynolds number of LPT for flight at cruise conditions often results in formation of separation bubble on the suction side, subjected to the laminar separation that may or may not reattach as reported by Luo [1]. Aerodynamic performance of blade is dependent on the bubble size formulated by Mayle [2]. It has been noticed that in case of laminar flow there is more loss of fuel due to the formation of separation bubble rather than in case of turbulent flow because the turbulent flow has greater energy and doesn t give rise to separation, as it is hardly affected by pressure gradient. There are few parameters by which the transition process can be affected such as the free stream intensity, pressure gradient or roughness of blade [3]. Different types of transition mode in turbo machinery flows are Natural/bypass mode, Separation-induced mode and Wakeinduced mode. The current study deals with cascade T106A, which undergoes separation-induced mode and laminar separation bubble (LSB) is formed on suction side due to the adverse pressure gradient. Qiu [4] and Mayle [2] verified that the separated flow is fully turbulent and it increases the fluid energy which supports re-attachment of boundary layer to the blade surface. Generally, active and passive techniques are used for controlling flow separation in LP turbines. Passive techniques include geometry modification such as, grooves or riblets on blade, roughness, bumps and dimples. Lake [5] suggested that the dimple energizes the flow and forces the laminar boundary layer from transition to turbulent prior to flow separation thereby acting similar to vortex generator. Vincent [6] indentified that dimple acts as vortex generator and mixes the low energy boundary layer flow with high energy free stream flow. The effectiveness of dimples and v-grooves for 1 Copyright 2011 by ASME

2 controlling the separated flow on LPT blades were tested by Lake [7]. Bearman [8] used shallow spherical dimples (h/d 0.1) where, h is the dimple depth (m) and D is the dimple surface diameter (m). They showed that the dimple caused early boundary layer transition without drag penalty and concluded that concave dimples are more efficient for drag reduction. Shallow dimples (h/d=0.088) more effectively reduce the drag as compared to smooth cylinder as reported by Bearman [9]. Experimental studies revealed that by using the dimple, separation point is moved towards trailing edge of blade. In this paper, single dimple is engraved on the suction side of T106A LPT blade at 55%, 60%, 65%, 70%, 75%, 80%, 85% and 90% of axial chord length to control the laminar separation at Re Shape of dimple used in this study is shown in Figure 1. Dimple depth and its height depend on parameters, such as, boundary layer thickness and Re. The literature review suggests a rule of thumb that a relation exists between the boundary layer thickness (δ), depth (h) and diameter (D) [9]. Gamma- Theta model [10] is used to captured the transitional effect and for thorough understanding of flow mechanism on the suction side of blade and inside the dimple. Pressure distribution graphs and normalized loss co-efficient are plotted for separation location as depicted in next sections. FIGURE 1: NOMENCLATURE OF DIMPLE NOMENCLATURE Re Reynolds number C Chord length C ax Axial chord length p Static pressure P t Total pressure P dyn Dynamic pressure Cp Pressure coefficient, (P t -p)/p dyn h Height of dimple/ bump D Diameter of dimple/ bump h s Height of the backward step l Length of the backward step γ Intermittency U Local velocity h D δ θ Momentum thickness ρ Density μ Molecular viscosity μ t Eddy viscosity δ Boundary layer thickness LSB Laminar separation bubble T.K.E Turbulent kinetic energy ω = (P in -P out )/P dyn in Loss coefficient P γ = f (F length, F onset ) Transitional sources E γ = f (F length, F onset ) Destruction sources P Θt = f (Re Θt ) Source term F length Influences the transition length F onset Controls the starting of the transition Re Θt Transition Reynolds number URANS Unsteady Reynolds Navier stroke s equation COMPUTATIONAL SETUP T106A is a well known low pressure turbine used to study laminar separation and its control. The details of T106A are specified in Table 1 [12]. ANSYS FLUENT finite volume based CFD commercial code along with its preprocessor Gambit is used in current study. Due to the presence of periodicity, the use of translational periodicity is made for computational efficiency which paves the way to model only a single blade. Figure 2 shows the Cascade T106A, which is designed according to parameters given in Table 1. TABLE 1: LP TURBINE CASCADE T106A SPECIFICATIONS Number of blades 5 Chord (mm) 198 Axial chord (mm) 170 Blade stagger ( o ) 30.7 Pitch (mm) 158 Span (mm) 375 Suction surface length (mm) Pressure surface length (mm) Inlet flow angle ( o ) 37.7 Design exit flow angle ( o ) 63.2 Outlet Reynolds number FIGURE 2: LP TURBINE CASCADE T106A [13] 2 Copyright 2011 by ASME

3 . Figure 3 shows the mesh topology used in this study in which the leading edge, trailing edge and the dimple surface are specified. Laminar boundary layer thickness (δ) formula [11] is used for the generation of boundary layer around the blade whereas unstructured meshing is used to discretize rest of the flow domain. The grid points are converged towards the blade surface which ensures that the computed y+ remains below 1. In each case, velocity inlet is used from where the flow enters at a certain angle and pressure outlet condition is used at the exit. Pitch-wise translational periodic boundary condition is applied. convergence criteria, net mass flow rate is computed up to The transport equations of SST transitional model are: (ργ) + (ρu i γ) = P t x γ E γ + i x i (ρre Θt ) + (ρu i Re Θt ) = P t x Θt + i x i μ + μ t σ f γ x i (1) σ Θt μ + μ t Re Θt x i (2) Here, first transport equation is for intermittency γ and second is for momentum thickness Reynolds number Re Θ. For inlet γ is set to 1 and for wall it is set to zero normal flux. For the conservation of the original model FST decay rate, γ is set to be equal to 1. These transport equations do not model the physics of transition process but form a frame work for implementation of transition correlations into general purpose CFD methods [10]. Numerical results change with the type and density of grid used for computations. Several mesh sizes were initially used in the present study to see the grid dependence of computed results. Grid independence study is done for 40000, and cells. Figure 4 shows the Cp plot comparison of different mesh sizes used in this study from where it can be concluded that and 90000cells grid are giving much better results in comparison with the experimental data cells grid is much computationally intensive in contrast with cells grid, so 70000cells grid is used to decrease the computational power. The inlet velocity is calculated from outlet Re~ where the flow is coming at an angle of In order to study the effect of dimple on flow separation and energizing the boundary layer, a relation h= 0.52*δ and h/d= is used [9]. FIGURE 3: MESH TOPOLOGY AT LEADING EDGE, TRAILING EDGE AND DIMPLE The Pressure based solver is used because Re is low and due to highly un-steadiness in the flow transient case is run. In viscous model, the SST transition or Gamma-Theta [10] is used for the transient case. The main benefit of this model is concurrence with the CFD solver TRACE and it can be applied to every grid topology. This model is accurate for the prediction of transition. PISO algorithm is used in the pressure-velocity coupling scheme as it is recommended for transient flow calculations, especially for large time step-size. Least Squares Cell-Based Gradient Evaluation is used instead of Node-Based Gradient, as it is less computationally intensive and the accuracy of both is comparable in unstructured meshing. Second order upwind scheme is used for the calculation. For FIGURE 4: GRID INDEPENDENCE STUDY 3 Copyright 2011 by ASME

4 CFD VALIDATION The coefficient of pressure (Cp) plots of the numerical data and the available experimental data are compared for validation. While comparing similar geometries, the important thing is to maintain consistency between the meshes created for different conditions. The mesh size that produced adequate grid independent results is in computational setup section. Figure 5 shows the comparison of co-efficient of pressure of Steiger (experimental) and Gamma-Theta model (numerical) having an exit Re= with free stream turbulence intensity (FSTI) of 0.4%. The numerically computed plot is in good agreement with the Steiger s experimental plot. Suction and pressure side of blade are shown in the figure 5 for Steady state simulation. The peak value occur on suction side is x/c ax =0.60. LSB start building around x/c ax =0.78 and continues till x/c ax =0.90 and flow reattaches at x/c ax =0.96. baseline case around 78%C ax and the dimple is placed at 90%C ax, losses has been done before the dimple so it has no chance to trip the incoming laminar flow. FIGURE 4: CP PLOT OF DIMPLES AT DIFFERENT AXIAL LOCATION FIGURE 3: CP PLOT COMPARISON OF EXPERIMENTAL AND CFD RESULTS RESULT AND DISCUSSION Figure 6 shows the Cp plot comparison of baseline case with the dimple cases at different axial location, while the parameters used for dimple are h/ δ = 0.52 and h/d= (i.e. h=1.69mm and D=20mm). Dimple acts as a vortex generator (VG) and spikes in each case represent the location of dimple where this VG is formed. It can be perceived from the figure 6 that the separation is present on the suction side of smooth blade profile. The dimple at 55%C ax and 60%C ax do not control the separation as the peak of separation bubble is present. Onwards from the dimple at 60%C ax, separation is removed in each case. Figure 6 depicts that from 65%C ax to 85%C ax, there is no peak of separation bubble. The peak of separation is also removed in case of dimple at 90%C ax and the flow is captured inside the dimple but the normalized loss coefficient is high in that case. This happens because the flow separate in the Figure 7 shows the normalized pressure loss coefficient of baseline case and dimple case at different axial locations, which shows that maximum loss reduction is achieved in case of dimple at 85%C ax, the normalized loss coefficient is reduced by about 12% in comparison with the baseline case. It can also be seen that when the dimple is placed at 90%C ax, loss coefficient again starts to increase so the optimal location to put the dimple is 85%C ax. The results of dimple at 85%C ax are shown later. Normalized Loss Coefficient Dimple Axial Location (%cax) FIGURE 5: NORMALIZED LOSS COEFFICIENT FOR DIFFERENT DIMPLE AXIAL LOCATION Figure 8 shows Cp plot comparison of baseline case with dimple which is placed at 85%C ax. Dotted line shows the plot of without dimple case in which the separation bubble peak 4 Copyright 2011 by ASME

5 is present. Solid line in the figure 8 represents the dimple case in which separation is removed from the original position and the peak in that case represents the VG that is formed due to dimple and this is the position where the dimple is actually placed. From graph we conclude that the coefficient of pressure is increased in dimple case. Its means that the static pressure is decreased in the direction of flow and in dimple case flow is much accelerated than the baseline case, when no dimple is applied. Hence, dimple energizes the incoming flow, which removes separation. to which point the flow is laminar. The interval of laminar shear layer is [0, 0.78]. The close view of laminar shear layer is also shown in Figure 11. After that interval, separation occurred and incoming laminar flow is converted to turbulent due to the dimple. According to the Kelvin-Helmholtz instability, there is a velocity shear between two layers of fluids, disturbances occur in that interval which will grow exponentially. Just before the dimple laminar shear layer ends. FIGURE 6: CP PLOT COMPARISON OF BASELINE CASE WITH DIMPLE AT 85%C ax Figure 9 shows the velocity contours of baseline case with the streamlines superimposed at trailing side of the blade. The flow separation point, LSB and the flow reattachment point are marked in the figure 9. As the flow is laminar (low energy flow) so the chance of separation is high and when flow separates from the blade surface it produce, losses which in return decreases the efficiency. From the figure 9, it is clear that inside the laminar boundary layer, viscosity effects are present due to which high pressure gradient region is created. With the help of this pressure gradient, flow leaves the surface and reverses its direction. Figure 10 indicates that the single dimple is effective to control the separation. Dimple acts as a VG, a recirculation zone is produced inside the dimple, which trip the laminar flow into turbulent (energized flow). This recirculation zone inside the dimple is also shown in the Figure 10. The VG inside the dimple forced the flow to attach with the surface and LSB is completely removed. The transition from laminar to turbulent occurs just after the dimple. Due to this transition of flow loss coefficient is reduced in dimple case. Figure 11 shows the vorticity plot on the blade with the dimple on 85%C ax, where the laminar shear layer is visible just before the separation point. Vorticity actually depicts, up FIGURE 7: VELOCITY CONTOURS FOR BASELINE CASE WITH SUPERIMPOSED STREAMLINES FIGURE 8: VELOCITY CONTOURS OF DIMPLE AT 85%C ax WITH SUPERIMPOSED STREAMLINES 5 Copyright 2011 by ASME

6 The Gamma-Theta model is capable to capture the basics of unsteady transition phenomenon of the flow. γ or Intermittency factor is the fraction of time that motion is turbulent. Figure 12 and figure 13 shows the contours of γ of baseline case and dimple at 85%C ax case respectively. It is clear that near the wall γ ~ 0, and when it attains some positive value, transition started, as we are moving away from the wall γ ~ 1. It means that near the wall, damped eddies are present due to velocity fluctuations as we are moving away from the wall, γ approaches to unity. FIGURE 11: INTERMITTENCY PLOT OF DIMPLE AT 85%C ax FIGURE 9: VORTICITY PLOT OF DIMPLE AT 85%C ax Figure 14 and figure 15 shows the formation of turbulent boundary layer which is captured by plotting the contours of Turbulence Kinetic Energy (T.K.E) for baseline and with dimple case. In figure 14, the flow is turbulent at the trailing edge of suction side. The interval for turbulent region in that case is [0.90, 1] and before this interval laminar separation bubble is formed. It has been noticed that this turbulent region is increased by the use of passive devices. In figure 15, the flow becomes turbulent earlier than the baseline case. Flow is fully attached after the dimple because dimple creates the turbulence and pressure gradients are overcome by this early turbulence FIGURE 10: INTERMITTENCY PLOT OF WITHOUT DIMPLE FIGURE 12: T.K.E CONTOURS OF BASELINE CASE WITHOUT DIMPLE 6 Copyright 2011 by ASME

7 which forced the separated flow to attach with the surface. Flow is transition to turbulent just after that interval [0.85, 1]. FIGURE 13: T.K.E CONTOURS OF DIMPLE AT 85%C ax Figure 16 shows the view inside the dimple where the separated shear layer with its reattachment point is shown. A strong force is acting from the wall on the shear layer but due to the separated shear layer it will keep it away from the wall, so shear layer reattached just after the dimple. Due to this phenomenon, losses has been reduced (lower loss of kinetic energy, pressure loss coefficient etc) and thin boundary layer is achieved behind the dimple. As the separation is removed by applying the dimple, pressure losses will be reduced which in returns increased the efficiency of the engine. But, there is a recirculation zone inside the dimple which will affect the incoming flow but this affect is ignorable. FIGURE 14: VORTEX GENERATOR INSIDE THE DIMPLE The elimination of LSB, thinning of boundary layer and reattachment of separated shear layer caused the reduction in pressure loss coefficient and efficiency of the gas turbine engine is improved. CONCLUSION In this study, a single dimple is used in a very effective manner to energize the incoming laminar flow and also the best location of dimple is specified. The same h/d ratio of dimple is engraved on different axial location to find the best location. It is noticed that as the dimple is shifted towards the trailing side, loss coefficient is reduced because at the trailing side flow is more energized and separation chances are low. Losses again start too increased if we cross the 90%C ax axial location because 80%C ax is the location where the separation started. One more interesting thing is noticed here, that the loss reduction at 80%C ax and 85%C ax are approximately same; just have a difference of The conclusion to this study is that, the best location to put the dimple is the separation point where the flow actually separate. It has been noticed that before the separation point (55%C ax, 60%C ax, 65%C ax, 70C ax, 75%C ax ) and after the separation point (i.e., 90%C ax ) dimple is not much effective. At 55%C ax and 60%C ax separation is not controlled (shown in the previous section) and it is controlled after 65%C ax. So for finding the dimple location in any study, we just need to find out the separation point. The best location to put the dimple is where the separation starts. In this way, the flow is efficiently controlled by the dimple and losses can be reduced. This study opens the new doors of research in controlling flow on LPT. Some of the worth mentioning ones are: shape optimization of dimple and variation in turbulence intensity. ACKNOWLEDGMENTS Authors would like to thank Principal RCMS Sikandar Hayat Mirza for providing excellent research atmosphere in the centre. We are also grateful to Aamer Shahzad for his valuable inputs and discussions during this research work. REFERENCES [1] Luo, H., Qiao, W., Xu, K., Passive Control of Laminar Separation Bubble with Spanwise Groove on a Low-speed Highly Loaded Low-Pressure Turbine Blade, J. Therm Sci Vol. 18, No. 3, pp , 2009 [2] Mayle, R. E., The Role of Laminar-Turbulent Transition in Gas Turbine Engines, ASME Journal of Turbo machinery, Vol. 113, Issue 4, pp ,.1991 [3] Schlichting, H., Boundary Layer Theory, 7 th Ed, McGraw-Hill, New York, USA, 1979 [4] Qui, S., Simon, T.W, An Experimental Investigation of Transition as Applied to Low Pressure Turbine Suction Surface Flows. International Gas Turbine Institute and Aeroengine Congress and Exposition, Orlando, FL, 1997 [5] Lake, J.P., Flow Separation Prevention on a Turbine Blade in Cascade at Low Reynolds Number. PhD Thesis, Air 7 Copyright 2011 by ASME

8 Force Institute of Technology, Wright-Patterson AFB, Ohio, 1999 [6] Vincent, Maple, R.C., CFD investigation of Laminar Flow Over a Dimpled Surface Indentation, AIAA Paper , 2006 [7] Lake, J.P., P. I., Rivir, R. B., Reduction of Separation Losses on Turbine Blade with Low Reynolds Number, AIAA Paper , 1999 [8] Bearman, P.W., Harvey, J.K., Golf ball aerodynamics, Aeronautical Quarterly, 27. pp , 1976 [9] Bearman, P. W., Harvey, J.K. Control of Circular Cylinder Flow by the use of Dimples, AIAA Journal, Vol. 31, No 10, pp , 1993 [10] Langtry, R.B., Menter, F. R., Transition Modeling for General CFD Applications in Aeronautics, AIAA Paper , 2006 [11] Anderson J. D., Emeritus, Fundamental of Aerodynamics, McGraw-Hill, New York, USA, pp 809, Chap 18, [12] Stieger R., Hollis D., Hodson H., Unsteady Surface Pressures Due To Wake Induced transition In A Laminar Separation Bubble On A LP Turbine Cascade, Proceedings of ASME Turbo Expo 2003, GT , 2003 [13] Stieger R, The Effects of Wakes on Separating Boundary Layers in Low Pressure Turbines, PhD Thesis, Cambridge University Engineering Department, Copyright 2011 by ASME