In this paper, we establish a benchmark data set of a generic high-pressure (HP) turbine vane generated by direct numerical simulation (DNS) to resolve fully the flow. The test conditions for this case are a Reynolds number of 0.57 × 10 6 and an exit Mach number of 0.9, which is representative of a modern transonic HP turbine vane. In this study, we first compare the simulation results with previously published experimental data. We then investigate how turbulence affects the surface flow physics and heat transfer. An analysis of the development of loss through the vane passage is also performed. The results indicate that freestream turbulence tends to induce streaks within the near-wall flow, which augment the surface heat transfer. Turbulent breakdown is observed over the late suction surface, and this occurs via the growth of two-dimensional Kelvin–Helmholtz spanwise roll-ups, which then develop into lambda vortices creating large local peaks in the surface heat transfer. Turbulent dissipation is found to significantly increase losses within the trailing-edge region of the vane.

In the present paper, direct numerical simulation (DNS) studies of the compressible flow in the T106 linear cascade have been carried out. Various environmental variables, i.e., background turbulence level, frequency of incoming wakes, and Reynolds number, and a combination of these were considered for a total of 12 fully resolved simulations. The mechanisms dictating the observed flow phenomena, including the mixing and distortion of the incoming wakes, wake/boundary layer interaction, and boundary layer evolution impact on profile loss generation, are studied systematically. A detailed loss generation analysis allows the identification of each source of loss in boundary layers and flow core. Particular attention is devoted to the concerted impact of wakes distortion mechanics and the intermittent nature of the unsteady boundary layer. Further, the present study examines the validity of the Boussinesq eddy viscosity assumption, which invokes a linear stress–strain relationship in commonly used RANS models. The errors originating from this assumption are scrutinized with both time and phase-locked averaged flow fields to possibly identify shortcomings of traditional RANS models.

Modern low pressure turbines (LPT) feature high pressure ratios and moderate Mach and Reynolds numbers, increasing the possibility of laminar boundary-layer separation on the blades. Upstream disturbances including background turbulence and incoming wakes have a profound effect on the behavior of separation bubbles and the type/location of laminar-turbulent transition and therefore need to be considered in LPT design. Unsteady Reynolds-averaged Navier–Stokes (URANS) are often found inadequate to resolve the complex wake dynamics and impact of these environmental parameters on the boundary layers and may not drive the design to the best aerodynamic efficiency. LES can partly improve the accuracy, but has difficulties in predicting boundary layer transition and capturing the delay of laminar separation with varying inlet turbulence levels. Direct numerical simulation (DNS) is able to overcome these limitations but has to date been considered too computationally expensive. Here, a novel compressible DNS code is presented and validated, promising to make DNS practical for LPT studies. Also, the sensitivity of wake loss coefficient with respect to freestream turbulence levels below 1% is discussed.

A flow simulation Methodology (FSM) is presented for computing the time-dependent behavior of complex compressible turbulent flows. The development of FSM was initiated in close collaboration with C. Speziale (then at Boston University). The objective of FSM is to provide the proper amount of turbulence modeling for the unresolved scales while directly computing the largest scales. The strategy is implemented by using state-of-the-art turbulence models (as developed for Reynolds averaged Navier-Stokes (RANS)) and scaling of the model terms with a “contribution function.” The contribution function is dependent on the local and instantaneous “physical” resolution in the computation. This physical resolution is determined during the actual simulation by comparing the size of the smallest relevant scales to the local grid size used in the computation. The contribution function is designed such that it provides no modeling if the computation is locally well resolved so that it approaches direct numerical simulations (DNS) in the fine-grid limit and such that it provides modeling of all scales in the coarse-grid limit and thus approaches a RANS calculation. In between these resolution limits, the contribution function adjusts the necessary modeling for the unresolved scales while the larger (resolved) scales are computed as in large eddy simulation (LES). However, FSM is distinctly different from LES in that it allows for a consistent transition between RANS, LES, and DNS within the same simulation depending on the local flow behavior and “physical” resolution. As a consequence, FSM should require considerably fewer grid points for a given calculation than would be necessary for a LES. This conjecture is substantiated by employing FSM to calculate the flow over a backward-facing step and a plane wake behind a bluff body, both at low Mach number, and supersonic axisymmetric wakes. These examples were chosen such that they expose, on the one hand, the inherent difficulties of simulating (physically) complex flows, and, on the other hand, demonstrate the potential of the FSM approach for simulations of turbulent compressible flows for complex geometries.