20 th Annual CFD Symposium, August 09-10, 2018, Bangalore LARGE EDDY SIMULATION OF FLOW OVER NOZZLE GUIDE VANE OF A TRANSONIC HIGH PRESSURE TURBINE Bharathan R D, Manigandan P, Vishal Tandon, Sharad Kapil, Dr Ramana Murty S V and Kishore Prasad D Turbine Group, Gas Turbine Research Establishment, C.V. Raman Nagar, Bangalore-560093, INDIA. E-mail: bharathan@gtre.drdo.in Abstract: Fifth generation fighter aircraft engines demand thrust to weight ratios in excess of 8 and moderate Specific Fuel Consumption. This calls for lower weight and higher component efficiencies. To improve turbine efficiency, it is necessary to understand the aerodynamic loss generation mechanism in the flow field. Since most such mechanisms are unsteady in nature, it is often necessary to carry out unsteady analysis of the turbine stage. It is desirable to study the loss generation mechanisms in the stationary Nozzle Guide Vanes (NGVs) and the rotor blades through unsteady analysis. In this paper, NGV of a transonic high pressure turbine has been analysed using Large Eddy Simulation (LES) and the results have been compared with Reynolds Averaged Navier Stokes (RANS) simulations and Unsteady RANS (URANS) simulations. The investigation is focused on the mechanisms of loss generation in the NGV at low Reynolds number condition of 1.5x10 6 (high altitude low Mach number condition) where shock boundary layer interactions are predominant. Keywords: Eddy, profile loss, secondary loss, NGV, rotor, efficiency, suction side. Nomenclature: P0 Ps T0 β S C O Tmax h M Rh Rt YN Total Pressure Static Pressure Total Temperature Blade exit angle Pitch Chord Throat Maximum Thickness Blade height Mach number Radius at hub Radius at tip NGV Pressure loss coefficient Introduction: The actual flow field in turbo-machinery environment is highly three dimensional and unsteady. Flow unsteadiness can be related to different concurrent physical mechanisms such as potential, wake and shock interactions of the turbine stage. Potential flow interaction is associated with non-uniform pitch-wise pressure which develops inside each stator and rotor. Viscous phenomena are responsible for the growth of the boundary layer and wakes. In transonic turbine stage shock system can cause shock interactions with adjacent blades and related pressure fluctuations. Turbine unsteady flows have been studied numerically and experimentally by various researchers [1-4]. In CFD, turbulence is modelled in Unsteady Reynolds Averaged Navier Stokes (U-RANS) simulations using models such as
k-ω, k-ε and k-ω with Shear Stress Transport (SST) which, although are very effective in the design of these turbines, are not precise in the resolution of small and large eddies. Direct Numerical Simulation (DNS), in which the turbulence of the flows is not modelled, but evaluated by using length and time scales small enough to capture turbulence of all frequencies and length scales, is computationally intensive. Large eddy simulations (LES) strike a balance between the full turbulence modelling and DNS by modelling turbulence due to small eddies and directly resolving large eddies. Description of the Turbine Stage: The High Pressure (HP) Turbine stage under consideration is a single stage, cooled, transonic, low aspect ratio turbine with a parabolic work distribution which is designed to drive a compressor. The aerodynamic design of the HP Turbine is carried out on the basis of the design approach consisting of 1D Mean-line design, 2D Hub to tip design, Aerofoil profile generation, 2D Blade to blade flow analysis, stacking and 3D Navier Stokes solution. The salient features of the base-line NGV considered in the study are shown in Table 1. Sl. No. Table 1 Turbine Salient Features Parameters Value 1. Stagger angle (deg) 51.5 2. O/S 0.3256 3. Blade inlet angle (deg) 0.0 4. Blade outlet angle (deg) -70.64 5. Tmax / C (%) 20.32 6. S/C 0.727 7. h/c 1.2 8. Inlet mach number 0.152 The turbine rotor inlet velocity triangle and flow path of the NGV are shown in Fig.1 and Fig. 2 respectively. Fig. 1 Rotor Inlet Velocity Triangle Fig. 2 Flow Path of NGV Grid Generation and Numerical Method: The computational grid for the NGV is generated using CFX-Turbo grid [5] software. The grids are multi block, structural hexahedra with Automatic Topology and Meshing (ATM) optimized topology. Choi et al [6] provide the appropriate grid size to be chosen based on the flow Reynolds number. Accordingly, the NGV has been modeled with a grid size of 300 million to match with NGV flow Reynolds number. Y+ of less than 1 has been maintained at all walls and sufficient grid points have been placed on the boundary layer. The grid skew angle is between 25 and 155 degree, aspect ratio is less than 100
and expansion ratio is less than 1.2. The view of the computational and grid domain is shown in Fig. 3 and 4. Fig. 3 Computational Domain of NGV Fig. 4 NGV Grid Domain The three dimensional, multi block, parallel flow solver CFX-14.5 [7] developed by ANSYS is used for this analysis. Time dependent equations are solved for turbulent flow. The governing equations are discretized using finite element based finite volume method. The solution algorithm follows a second order backward Euler transient scheme and central difference advection scheme (which is recommended for LES because of its dissipative nature). Runge Kutta integration scheme coupled with multi grid, implicit residual smoothing and local time stepping convergence acceleration technique are used in the inner iteration of 5 for each time step. The effects of turbulence are modeled with LES Scale turbulence model, in order to predict the unsteady effects resulting from viscous interaction and kinetic momentum transfer from large eddies to small eddies. The rationale behind the large-eddy simulation technique is a separation between large and small scales. The governing equations for LES are obtained by filtering the time-dependent Navier- Stokes equations in the physical space. The filtering process effectively filters out the eddies whose scales are smaller than the filter width or grid spacing used in the computations. The resulting equations thus govern the dynamics of the large eddies. A filtered variable is denoted by an over bar and is defined by φ(x) = φ(x )G(x; x )dx D Where, D is the fluid domain, and G is the filter function that determines the scale of the resolved eddies. The unresolved part of a quantity φ as defined by φ = φ φ The filtered momentum equation can be written in the following way t (ρu i) + (ρu x i U j ) = p + [μ ( U i + U )] + τ ij j x i x j x j x i x j Where, τ ij denotes the sub grid-scale stress. It includes the effect of the small scales and is defined by τ ij = ρu i U j + ρ U i U j
Static Pressure (Pa) Boundary and Initial Conditions: The boundary conditions are inlet total pressure (P0), inlet total temperature (T0) profile, inlet flow angle, and exit static pressure. The analysis was carried out for high altitude low Mach number condition where the Reynolds number is relatively lower (1.5 x 10 6 ). The walls are assumed to be adiabatic. LES scale is used as turbulent model. The run has been performed for a total time of 2 s with an initial time step taken as 1e-7 s. Upper courant number is 0.5 and the maximum coefficient of convergence control is 5. As this is not a transient analysis involving time variant boundary conditions, the LES results converge to a more or less similar solution irrespective of the initial condition. Steady state analysis results are used as initial guess to LES analysis to expedite convergence. This LES analysis is carried out on Aeries parallel computer using 100 parallel processors (4GB RAM per processor). Solution backup files were saved for every 25 th time step. Time taken for obtaining a converged solution was thirty days. Results and Discussions: Fig 4 shows the blade loading over the NGV for three different time steps. It is observed that the unsteady effects are by and large absent on the pressure side and upstream of the throat on the suction side. Even so, the variation in peak Mach number is minimal. There is some variation at the NGV exit because of vortex shedding that happens as a result of a trailing edge of finite radius without cusp. 1.3E+06 Time Step 1 Time Step 2 1.1E+06 Time Step 3 9.0E+05 7.0E+05 5.0E+05 0 0.25 0.5 0.75 1 Streamwise (0-1) Fig. 4 NGV Mean Section Blade Loading Fig 5 shows the blade to blade Mach number distribution of the mean section of the NGV. A very minimal boundary layer thickening is observed on the aerofoil suction side where there is shock boundary layer interaction near the throat. The phenomenon of vortex shedding is also clearly captured
in Fig 5 downstream of the trailing edge. The frequency at which it is shed is also measurable, and will be a useful input for studying stator-rotor interactions. Fig. 5 Blade to Blade Mach Number Distribution Figures 6, 7 and 8 show the mean section static entropy contour plots obtained from LES, URANS and RANS analyses respectively. It can be seen that LES (Fig 6) captures the phenomenon of vortex shedding with its characteristics such as the alternate shedding of vortices from the pressure and suction sides similar to a von Karman vortex sheet. In Fig 7, although the trailing edge vortex is captured, the alternate shedding phenomenon is not captured. This is largely because the URANS does not have the ability to resolve large and small eddies which result from such vortex shedding to the extent that LES is capable of doing. Fig 8 shows that RANS analysis captures trailing edge eddies to an even lesser extent and gives an averaged picture of flow over the aerofoil. Fig. 6 Mean Section Static Entropy Contour Plot (LES)
Fig. 7 Mean Section Static Entropy Contour Plot (URANS) Fig. 8 Mean Section Static Entropy Contour Plot (RANS) The profile loss coefficient for the NGV is defined as the ratio of the total pressure drop across the NGV to the exit dynamic head and it is given by formula Y N = (P 01 P 02 ) (P 02 P s )
0.2 0.16 LES URANS RANS Y N 0.12 0.08 0.04 0 0 0.2 0.4 0.6 0.8 1 Span Normalised Fig. 9 Comparison of Spanwise pressure loss Fig 9 shows the comparison of variation of pressure loss coefficient in the spanwise direction as obtained from LES (time-averaged), URANS (time-averaged) and RANS analyses. It is observed that the losses follow a bath-tub distribution in all cases with relatively high losses near the hub and tip due to end wall boundary layers. It is also seen that the losses as predicted by LES are less than RANS but more than URANS. This can be explained in terms of the qualitative and quantitative resolution of vortices being shed at the trailing edge. In Fig 8, it is observed that the trailing edge wake entropy generation is thick and consistent over a large portion of the post trailing edge flow. The loss generated at the free sheer flow interface at the junction of the flows from the pressure and suction sides is on the higher side compared to others. In URANS, the opposite is true (Fig 7), with the entropy generation due at trailing edge being under-predicted. LES on the other hand give a picture of alternate vortex shedding from the pressure and suction side with both spatial and temporal variation in losses due to vortices. The losses peak at the time of vortex shedding and ebb during the short duration before the next vortex is shed. Time averaged plot (Fig 6) reveals an intermediate loss which is neither as high as RANS nor as low as URANS. Conclusion: A transonic HP turbine NGV has been analyzed using LES for high altitude low Mach number condition and the same has been compared with URANS and RANS analyses. It is found that LES captures the boundary layer thickening because of shock-boundary layer interaction, as well as the shedding of vortices at the trailing edge of the aerofoil. This trailing edge vortex data can be used as input to perform similar large eddy simulations of the rotor blade. It is also observed that URANS and RANS do not resolve the trailing edge eddies in sufficient detail. It is also shown that LES predicts lesser losses than RANS, but more losses than URANS.
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