Unsteady adjoint of pressure loss for a fundamental transonic turbine vane

High fidelity simulations, e.g., large eddy simulation are often needed for accurately predicting pressure losses due to wake mixing in turbomachinery applications. An unsteady adjoint of such high fidelity simulations is useful for design optimization in these aerodynamic applications. In this paper we present unsteady adjoint solutions using a large eddy simulation model for a vane from VKI using aerothermal objectives. The unsteady adjoint method is effective in capturing the gradient for a short time interval aerothermal objective, whereas the method provides diverging gradients for long time-averaged thermal objectives. As the boundary layer on the suction side near the trailing edge of the vane is turbulent, it poses a challenge for the adjoint solver. The chaotic dynamics cause the adjoint solution to diverge exponentially from the trailing edge region when solved backwards in time. This results in the corruption of the sensitivities obtained from the adjoint solutions. An energy analysis of the unsteady compressible Navier-Stokes adjoint equations indicates that adding artificial viscosity to the adjoint equations can potentially dissipate the adjoint energy while potentially maintain the accuracy of the adjoint sensitivities. Analyzing the growth term of the adjoint energy provides a metric for identifying the regions in the flow where the adjoint term is diverging. Results for the vane from simulations performed on the Titan supercomputer are demonstrated.Comment: ASME Turbo Expo 201

Investigation of finite-volume methods to capture shocks and turbulence spectra in compressible flows

The aim of the present paper is to provide a comparison between several finite-volume methods of different numerical accuracy: second-order Godunov method with PPM interpolation and high-order finite-volume WENO method. The results show that while on a smooth problem the high-order method perform better than the second-order one, when the solution contains a shock all the methods collapse to first-order accuracy. In the context of the decay of compressible homogeneous isotropic turbulence with shocklets, the actual overall order of accuracy of the methods reduces to second-order, despite the use of fifth-order reconstruction schemes at cell interfaces. Most important, results in terms of turbulent spectra are similar regardless of the numerical methods employed, except that the PPM method fails to provide an accurate representation in the high-frequency range of the spectra. It is found that this specific issue comes from the slope-limiting procedure and a novel hybrid PPM/WENO method is developed that has the ability to capture the turbulent spectra with the accuracy of a high-order method, but at the cost of the second-order Godunov method. Overall, it is shown that virtually the same physical solution can be obtained much faster by refining a simulation with the second-order method and carefully chosen numerical procedures, rather than running a coarse high-order simulation. Our results demonstrate the importance of evaluating the accuracy of a numerical method in terms of its actual spectral dissipation and dispersion properties on mixed smooth/shock cases, rather than by the theoretical formal order of convergence rate.Comment: This paper was previously composed of 2 parts, and this submission was part 1. It is now replaced by the combined pape

Large-Eddy Simulations of Flow and Heat Transfer in Complex Three-Dimensional Multilouvered Fins

The paper describes the computational procedure and results from large-eddy simulations in a complex three-dimensional louver geometry. The three-dimensionality in the louver geometry occurs along the height of the fin, where the angled louver transitions to the flat landing and joins with the tube surface. The transition region is characterized by a swept leading edge and decreasing flow area between louvers. Preliminary results show a high energy compact vortex jet forming in this region. The jet forms in the vicinity of the louver junction with the flat landing and is drawn under the louver in the transition region. Its interaction with the surface of the louver produces vorticity of the opposite sign, which aids in augmenting heat transfer on the louver surface. The top surface of the louver in the transition region experiences large velocities in the vicinity of the surface and exhibits higher heat transfer coefficients than the bottom surface.Air Conditioning and Refrigeration Project 9

Dynamic Smagorinsky Modeled Large-Eddy Simulations of Turbulence Using Tetrahedral Meshes

Eddy-resolving numerical computations of turbulent flows are emerging as viable alternatives to Reynolds Averaged Navier-Stokes (RANS) calculations for flows with an intrinsically steady mean state due to the advances in large-scale parallel computing. In these computations, medium to large turbulent eddies are resolved by the numerics while the smaller or subgrid scales are either modeled or taken care of by the inherent numerical dissipation. To advance the state of the art of unstructured-mesh turbulence simulation capabilities, large eddy simulations (LES) using the dynamic Smagorinsky model (DSM) on tetrahedral meshes are carried out with the space-time conservation element, solution element (CESE) method. In contrast to what has been reported in the literature, the present implementation of dynamic models allows for active backscattering without any ad-hoc limiting of the eddy viscosity calculated from the subgrid-scale model. For the benchmark problems involving compressible isotropic turbulence decay as well as the shock/turbulent boundary layer interaction benchmark problems, no numerical instability associated with kinetic energy growth is observed and the volume percentage of the backscattering portion accounts for about 38-40% of the simulation domain. A slip-wall model in conjunction with the implemented DSM is used to simulate a relatively high Reynolds number Mach 2.85 turbulent boundary layer over a 30 ramp with several tetrahedral meshes and a wall-normal spacing of either & = 10 or & = 20. The computed mean wall pressure distribution, separation region size, mean velocity profiles, and Reynolds stress agree reasonably well with experimental data