Richard Pichler

Compressible Direct Numerical Simulation of Low-Pressure Turbines—Part I: Methodology

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.

Direct Numerical Simulations of a High-Pressure Turbine Vane

In this paper we establish a benchmark data set of a generic high-pressure 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 million and an exit Mach number of 0.9, which is representative of a modern transonic high-pressure 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 free-stream 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.

Direct Numerical Simulations of a High Pressure Turbine Vane

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Machine Learning for Turbulence Model Development Using a High-Fidelity HPT Cascade Simulation

The validity of the Boussinesq approximation in the wake behind a high-pressure turbine blade is explored. We probe the mathematical assumptions of such a relationship by employing a least-squares technique. Next, we use an evolutionary algorithm to modify the anisotropy tensor a priori using highly resolved LES data. In the latter case we build a non-linear stress-strain relationship. Results show that the standard eddy-viscosity assumption underpredicts turbulent diffusion and is theoretically invalid . By increasing the coefficient of the linear term, the farwake prediction shows minor improvement. By using additional non-linear terms in the stress-strain coupling relationship, created by the evolutionary algorithm, the near-wake can also be improved upon. Terms created by the algorithm are scrutinized and the discussion is closed by suggesting a tentative non-linear expression for the Reynolds stress, suitable for the wake behind a high-pressure turbine blade. NOMENCLATURE ai j Anisotropy tensor. k Turbulent kinetic energy. k′ Normalized turbulent kinetic energy: k/kmax ∗Address all correspondence to this author. N Population size; number of training data points (context specific) M Number of GEP solutions Pk Turbulent kinetic energy production: τi j∂x jUi Si j Strain rate: 1 2 (∂x jUi +∂xiU j) S′ i j Deviatoric component of strain rate: Si j − 3 δi jSkk. tI Turbulent time scale: 1/ω . Ui Time-averaged velocity vector s Intrinsic coordinate along the wake center line, normalized by axial chord. x, y Cartesian coordinates, normalized by axial chord. β Optimization parameter in least-squares regression. ∂φ Shorthand for ∂ ∂φ . As a differential operator, it acts on everything to the right within a term. ε Least squares model error. μt Eddy-viscosity. ρ Time-averaged density. τi j Reynolds stress: ρuiuj. ω Specific dissipation rate. Ωi j Rotation rate tensor: 2 (∂x jUi −∂xiU j)

Compressible DNS of a Low Pressure Turbine Subjected to Inlet Disturbances

In modern low pressure turbines (LPT), reducing the number of airfoils in a turbine leads to an increase in the blade loading, which inevitably increases the possibility of laminar separation.

Compressible Direct Numerical Simulation of Low-Pressure Turbines: Part I — Methodology

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. 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.

Compressible Direct Numerical Simulation of Low-Pressure Turbines: Part II — Effect of Inflow Disturbances

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.Copyright

Modeling of Discrete Tip Injection in a Two-Dimensional Streamline Curvature Method

Fluid injection at the tip of highly loaded compressor rotors is known to be effective in suppressing the onset of rotating stall and eventually compressor instability. However, using such stability enhancement methods in a multistage compressor might not only stabilize certain stages but has also an impact on radial and axial matching. In order to account for tip injection during the early stages of compressor design, this paper focuses on the development of a method to model the physical effects underlying tip injection within a streamline curvature method. With the help of system identification it could be shown that a rotor subject to the discrete jets of tip injection adapts to the varying flow conditions according to a first order model. This information was used to generate a time-dependent input for the steady equations used with a streamline curvature method and eventually to model the unsteady response of the rotor to tip injection. Comparing the results obtained with the enhanced streamline curvature model to measurement results, good agreement could be shown which raised confidence that the influence of tip injection on axial and radial matching was sufficiently captured.Copyright

High-Fidelity Simulations of a Linear HPT Vane Cascade Subject to Varying Inlet Turbulence

The effect of inflow turbulence intensity and turbulence length scales have been studied for a linear high-pressure turbine vane cascade at Reis = 590,000 and Mis = 0.93, using highly resolved compressible large-eddy simulations employing the WALE turbulence model. The turbulence intensity was varied between 6% and 20% while values of the turbulence length scales were prescribed between 5% and 20% of axial chord. The analysis focused on characterizing the inlet turbulence and quantifying the effect of the inlet turbulence variations on the vane boundary layers, in particular on the heat flux to the blade. The transition location on the suction side of the vane was found to be highly sensitive to both turbulence intensity and length scale, with the case with turbulence intensity 20% and 20% length scale showing by far the earliest onset of transition and much higher levels of heat flux over the entire vane. It was also found that the transition process was highly intermittent and local, with spanwise parts of the suction side surface of the vane remaining laminar all the way to the trailing edge even for high turbulence intensity cases.