Jan G. Wissink

DNS of separating, low Reynolds number flow in a turbine cascade with incoming wakes

Abstract Three-dimensional direct numerical simulations (DNS) of flow in a low-pressure turbine cascade at high angle of attack have been performed. The large angle of attack is found to cause separation at the leading edge and somewhat upstream of the trailing edge along the suction side of the blade. The separation bubble at the leading edge is small and any disturbances generated are damped downstream by the accelerating flow due to the favourable pressure gradient. The boundary layer at the downstream half of the suction side separates as soon as the impingement of free-stream disturbances, stemming from a passing wake, ends. The separated boundary layer is very unstable. After some transient time, small disturbances cause it to roll up. Shortly after free-stream disturbances impinge again, it completely vanishes. Near the trailing edge the flow remains turbulent at all times. As in the simulations performed by Wu and Durbin [J. Fluid Mech. 446 (2001) 199–228] longitudinal vortical structures along the downstream half of the pressure side of the blade are obtained by straining of passing wakes. Along the upstream half of the suction side similar longitudinal vortices are found to be formed by severe stretching of the wake by the strong main flow. Because of this stretching, these vortices are almost aligned with the surface of the blade as they impinge on the boundary layer. In contrast to the vortical structures found at the pressure side, the suction side vortical structures only exist for a short time.

Large-eddy simulation of flow around low-pressure turbine blade with incoming wakes

The flow around a low-pressure turbine rotor blade with periodically incoming wakes at a realistic Reynolds number is computed by means of large-eddy simulation (LES). The computed results are discussed in terms of phase-averaged and mean quantities. A comparison is made with an existing direct numerical simulation (DNS) for the same geometry and operating conditions. Particular attention is devoted to flow structures associated with the incoming wakes and their effect on the boundary layers. The analysis of the flowfield reveals patterns similar to those encountered in DNS and in LES of flow in the same geometry at a lower Reynolds number. Noticeable differences occur in the suction-side boundary layer, which exhibits a complete transition to turbulence for the present case

Direct numerical simulations of transition in a compressor cascade: the influence of free-stream turbulence

The flow through a compressor passage without and with incoming free-stream grid turbulence is simulated. At moderate Reynolds number, laminar-to-turbulence transition can take place on both sides of the aerofoil, but proceeds in distinctly different manners. The direct numerical simulations (DNS) of this flow reveal the mechanics of breakdown to turbulence on both surfaces of the blade. The pressure surface boundary layer undergoes laminar separation in the absence of free-stream disturbances. When exposed to free-stream forcing, the boundary layer remains attached due to transition to turbulence upstream of the laminar separation point. Three types of breakdowns are observed; they combine characteristics of natural and bypass transition. In particular, instability waves, which trace back to discrete modes of the base flow, can be observed, but their development is not independent of the Klebanoff distortions that are caused by free-stream turbulent forcing. At a higher turbulence intensity, the transition mechanism shifts to a purely bypass scenario. Unlike the pressure side, the suction surface boundary layer separates independent of the free-stream condition, be it laminar or a moderate free-stream turbulence of intensity T u ~ 3%. Upstream of the separation, the amplification of the Klebanoff distortions is suppressed in the favourable pressure gradient (FPG) region. This suppression is in agreement with simulations of constant pressure gradient boundary layers. FPG is normally stabilizing with respect to bypass transition to turbulence, but is, thereby, unfavourable with respect to separation. Downstream of the FPG section, a strong adverse pressure gradient (APG) on the suction surface of the blade causes the laminar boundary layer to separate. The separation surface is modulated in the instantaneous fields of the Klebanoff distortion inside the shear layer, which consists of forward and backward jet-like perturbations. Separation is followed by breakdown to turbulence and reattachment. As the free-stream turbulence intensity is increased, T u ~ 6.5 %, transitional turbulent patches are initiated, and interact with the downstream separated flow, causing local attachment. The calming effect, or delayed re-establishment of the boundary layer separation, is observed in the wake of the turbulent events.

Analysis of DNS and LES of Flow in a Low Pressure Turbine Cascade with Incoming Wakes and Comparison with Experiments

The flow around a low-pressure turbine rotor blade with incoming periodic wakes is computed by means of DNS and LES. The latter adopts a dynamic sub-grid-scale model. The computed results are compared with time-averaged and instantaneous measured quantities. The simulation sreveal the presence of elongated flow structures, stemming from the incoming wake vorticity, which interact with the pressure side boundary layer. As the wake approaches the upstream half of the suction side, its vortical structures are stretched and align with the main flow, resulting in an impingement at virtually zero angle of attack. Periodically, in the absence of impinging wakes, the laminar suction side boundary layer separates in the adverse pressure gradient region. Flow in the laminar separation bubble is found to undergo transition via a Kelvin–Helmholtz instability. Subsequent impingement of the wake inhibits separation and thus promotes boundary layer reattachment. LES provides a fair reproduction of the DNS results both in terms of instantaneous, phase-averaged, and time-averaged flow fields with a considerable reduction in computational effort.

Direct numerical simulation of flow and heat transfer in a turbine cascade with incoming wakes

Direct numerical simulations (DNS) of flow in a turbine cascade with heat transfer have been performed. The set-up of the simulations was chosen in close accordance with previous experiments. Three of the experimental situations were simulated: one without free-stream turbulence and two with periodically incoming wakes of different frequency and with different levels of background fluctuation. Hence, the calculations allow us to study the influence of impinging wakes and background fluctuations on the development of the boundary layers and the local Nusselt number along the surfaces of the heated blade. Along the suction side, the pressure gradient is first favourable and then turns adverse near the trailing edge and the boundary layer remains laminar for the case without free-stream turbulence with the Nusselt number showing the typical decay from the leading to the trailing edge. With periodic wakes and background turbulence, transition occurs when the pressure gradient turns adverse, but intermittency persists so that the boundary layer is not fully turbulent when the trailing edge is reached. In this region, the heat transfer is increased significantly by an amount comparable to that found in the experiments. In the pre-transitional region with favourable pressure gradient, the flow acceleration stretches the free-stream vortices, aligning their axis with the flow direction, thereby forming streamwise vortical structures. These increase the laminar heat transfer in this region by 20-30 %, which is, however, much less than observed in the experiments. On the pressure side, the pressure gradient is favourable along the entire blade so that the boundary layer remains laminar. Here, the wakes, through their impingement, also generate streamwise vortical structures which, because of the low convection speed on this side, have a very long lifetime compared to the structures along the suction side. Also these structures increase the laminar heat transfer by about 30 %, which for the case with the highest wake frequency is again much less than in the experiments. The simulated average level of fluctuations in the laminar parts of the boundary layers is comparable or even higher than that in the experiments so that it seems likely that a difference in the spectral contents causes the discrepancies. The wake turbulence entering the calculation domain corresponds to that in far wakes with relatively small-scale structures, whereas in the experiments the wakes most probably still carried some large-scale fluctuations of the size of the wake width, which have been found to be more effective in increasing laminar heat transfer.

Direct Numerical Simulations of Transitional Flow in Turbomachinery

An overview is provided of various direct numerical simulations (DNS) of transitional flows in turbine-related geometries. Two flow cases are considered: the first case concerns separating flow over a flat plate and the second case flows in turbine cascades. In the first case, in which Re=60,000, either an oscillating oncoming flow (1) or a uniform flow with and without oncoming turbulent free-stream fluctuations (2) is prescribed at the inlet. In both subcases (1) and (2), separation is induced by a contoured upper wall. In (1), the separated boundary layer is found to roll up due to a Kelvin-Helmholtz (KH) instability. This rolled-up shear layer is subject to spanwise instability and disintegrates rapidly into turbulent fluctuations. In (2), a massive separation bubble is obtained in the simulation without oncoming free-stream fluctuations. A KH instability is eventually triggered by numerical round-off error and is followed again by a rapid transition. With oncoming turbulent fluctuations, this KH instability is triggered much earlier and transition is enhanced, which leads to a drastic reduction in size of the separation bubble. The second case, concerning flow in turbine cascades, includes (I) flow in the T106 turbine cascade with periodically oncoming wakes at Re=51,800 and (2) flow and heat transfer in a MTU cascade with oncoming wakes and background turbulence at Re =72,000. In the simulation of flow in the T106 cascade with oncoming wakes, the boundary layer along the downstream half of the suction side is found to separate intermittently and subsequently rolls up due to a KH instability leading to separation-induced transition. At times when the wakes impinge separation is suppressed. In the simulations of flow around a MTU turbine blade, evidence of by-pass transition in the suction-side boundary-layer flow is observed while the pressure-side boundary layer remains laminar in spite of significant fluctuations present. In agreement with the experiments, the impinging wakes cause the heat transfer coefficient to increase significantly in the transitional suction-side region close to the trailing edge and by about 30% on the pressure side. The large increase in heat transfer in the pre-transitional suction-side region observed in the experiments could not be reproduced. The discrepancy is explained by differences in spectral contents of the turbulence in the oncoming wakes.

DNS of a Laminar Separation Bubble Affected by Free-Stream Disturbances

A series of direct numerical simulations of laminar, separating flow affected by various levels of free-stream disturbances has been performed. The free-stream disturbances were found to trigger a Kelvin-Helmholtz instability. The size of the separation bubble was found to be significantly reduced and the location of re-attachment was found to move upstream when the level of free-stream disturbances was increased. Downstream, the near-wall turbulent flow only very slowly assumes “normal” turbulent boundary layer statistics.

Low-diffusivity scalar transport using a WENO scheme and dual meshing

Interfacial mass transfer of low-diffusive substances in an unsteady flow environment is marked by a very thin boundary layer at the interface and other regions with steep concentration gradients. A numerical scheme capable of resolving accurately most details of this process is presented. In this scheme, the fifth-order accurate WENO method developed by [13] was implemented on a non-uniform staggered mesh to discretize the scalar convection while for the scalar diffusion a fourth-order accurate central discretization was employed. The discretization of the scalar convection-diffusion equation was combined with a fourth-order Navier-Stokes solver which solves the incompressible flow. A dual meshing strategy was employed, in which the scalar was solved on a finer mesh than the incompressible flow. The order of accuracy of the solver for one-dimensional scalar transport was tested on both stretched and uniform grids. Compared to the fifth-order WENO implementation of [10], the [13] method was found to be superior on very coarse meshes. The solver was further tested by performing a number of two-dimensional simulations. At first a grid refinement test was performed at zero viscosity with shear acting on an initially axisymmetric scalar distribution. A second refinement test was conducted for an unstably stratified flow with low diffusivity scalar transport. The unstable stratification led to buoyant convection which was modelled using a Boussinesq approximation with a linear relationship between flow temperature and density. The results show that for the method presented a relatively coarse mesh is sufficient to accurately describe the fluid flow, while the use of a refined dual mesh for the low-diffusive scalars is found to be beneficial in order to obtain a highly accurate resolution with negligible numerical diffusion.

Direct Numerical Simulation of By-Pass and Separation-Induced Transition in a Linear Compressor Cascade

Direct Numerical Simulation (DNS) of flow through a linear compressor cascade with incoming free-stream turbulence was performed. On the pressure side, the boundary layer flow is found to undergo by-pass transition: The incident vortical disturbances trigger the formation of elongated boundary layer perturbation jets (or streaks) with amplitudes on the order of 10% of the mean flow. The inception of turbulent spots, which leads to breakdown, is triggered on the backward perturbation jets (negative u-fluctuations). The turbulent patches spread and finally merge into the downstream, fully turbulent region. The suction surface boundary layer is initially subject to a Favorable Pressure Gradient (FPG), followed by a strong Adverse Pressure Gradient (APG). The FPG suppresses the formation of boundary layer streaks. The result is a stabilized boundary layer that does not undergo transition. Farther downstream, the strong APG causes the laminar boundary layer to separate, which is followed by turbulent reattachment.Copyright

Large-Scale Computations of Flow Around a Circular Cylinder

A series of Direct Numerical Simulations of three-dimensional, incompressible flow around a circular cylinder in the lower subcritical range has been performed on the NEC SX-8 of HLRS in Stuttgart. The Navier-Stokes solver, that is employed in the simulations, is vectorizable and parallellized using the standard Message Passing Interface (MPI) protocol. Compared to the total number of operations, the percentage of vectorizable operations exceeds 99.5% in all simulations. In the spanwise direction Fourier transforms are used to reduce the originally three-dimensional pressure solver into two-dimensional pressure solvers for the parallel (x, y) planes. Because of this reduction in size of the problem, also the vectors lengths are reduced which was found to lead to a reduction in performance on the NEC. Apart from the performance of the code as a function of the average vectorlenght, also the performance of the code as a function of the number of processors is assessed. An increase in the number of processors by a factor of 5 is found to lead to a decrease in performance by approximately 22%.