The simulation of hypersonic flows is computationally demanding due to the large gradients of the flow variables at hand, caused both by strong shock waves and thick boundary or shear layers. The resolution of those gradients imposes the use of extremely small cells in the respective regions. Taking turbulence into account intensifies the variation in scales even more. Furthermore, hypersonic flows have been shown to be extremely grid sensitive. For the simulation of fully three-dimensional configurations of engineering applications, this results in a huge amount of cells and, as a consequence, prohibitive computational time. Therefore, modern adaptive techniques can provide a gain with respect to both computational costs and accuracy, allowing the generation of locally highly resolved flow regions where they are needed and retaining an otherwise smooth distribution. In this paper, an h-adaptive technique based on wavelets is employed for the solution of hypersonic flows. The compressible Reynolds-averaged Navier-Stokes equations are solved using a differential Reynolds stress turbulence model, well suited to predict shock-wave/ boundary-layer interactions in high-enthalpy flows. Two test cases are considered: a compression corner at 15 deg and a scramjet intake. The compression corner is a classical test case in hypersonic flow investigations because it poses a shock-wave/turbulent-boundary-layer interaction problem. The adaptive procedure is applied to a twodimensional configuration as validation. The scramjet intake is first computed in two dimensions. Subsequently, a three-dimensional geometry is considered. Both test cases are validated with experimental data and compared to nonadaptive computations. The results show that the use of an adaptive technique for hypersonic turbulent flows at high-enthalpy conditions can strongly improve the performance in terms of memory and CPU time while at the same time maintaining the required accuracy of the results. Nomenclature b ij= anisotropy tensor c p = specific heat at constant pressure, pressure coefficient D ij = diffusion tensor for the Reynolds stresses, m 2 ∕s 3 δ ij = Kronecker delta d = spatial dimension E = specific total energy, m 2 ∕s 2 H = total specific enthalpy, m 2 ∕s 2 II = second invariant of the anisotropy tensor k = turbulent kinetic energy, m 2 ∕s 2 L = maximum refinement level l = local refinement level M = Mach number M ij = turbulent mass flux tensor for the Reynolds stresses, m 2 ∕s 3 μ = molecular viscosity, kg∕m · s P ij = production tensor for the Reynolds stresses, m 2 ∕s 3 p = pressure, Pa p t = total pressure, Pa q i = component of heat flux vector, W∕m 2 q t k = turbulent heat flux, W∕m 2 R ij = Reynolds stress tensor, m 2 ∕s 2 Re = Reynolds number, 1∕m Res drop = averaged density residual at which the adaptations are performed ρ = density, kg∕m 3 S ij = strain-rate tensor, 1∕s St = Stanton number T = temperature, K T w = wall temperature, K T 0 = total temperature, K t = time, s U = local velocity, m∕s u i = velocity component, m∕s W ij...
In contrast to external flow aerodynamics, where one-dimensional Riemann boundary conditions can be applied far up- and downstream, the handling of non-reflecting boundary conditions for turbomachinery applications poses a greater challenge due to small axial gaps normally encountered. For boundaries exposed to non-uniform flow in the vicinity of blade rows, the quality of the simulation is greatly influenced by the underlying non-reflecting boundary condition and its implementation. This paper deals with the adaptation of Giles’ well-known exact non-local boundary conditions for two-dimensional steady flows to a cell-centered solver specifically developed for turbomachinery applications. It is shown that directly applying the theory originally formulated for a cell-vertex scheme to a cell-centered solver may yield an ill-posed problem due to the necessity of having to reconstruct boundary face values before actually applying the exact non-reflecting theory. In order to ensure well-posedness, Giles’ original approach is adapted for cell-centered schemes with a physically motivated reconstruction of the boundary face values, while still maintaining the non-reflecting boundary conditions. The extension is formulated within the original framework of determining the circumferential distribution of one-dimensional characteristics on the boundary. It is shown that, due to approximations in the one-dimensional characteristic reconstruction of boundary face values, the new approach can only be exact in the limiting case of cells with a vanishing width in the direction normal to the boundary if a one-dimensional characteristic reconstruction of boundary face values is used. To overcome the dependency on the width of the last cell, the new boundary condition is expressed explicitly in terms of a two-dimensional modal decomposition of the flow field. In this formulation, vanishing modal amplitudes for all incoming two-dimensional modes can easily be accomplished for a converged solution. Hence we are able to ensure perfectly non-reflecting boundary conditions under the same conditions as the original approach. The improvements of the new method are demonstrated for both a subsonic turbine and a transonic compressor test case.
Profile losses of the turbine blade and secondary flow losses are the main source of aerodynamic loss in a low pressure turbine. However, not much attention has been paid in the interaction between these two loss sources. This paper investigates the interaction mechanisms between a separated boundary layer on the suction side and the secondary flow in blade passages. The high speed cascade wind tunnel of the University of the Federal Armed Forces Germany has been used to achieve the required operation conditions, generating a flow separation on the suction side. The profile of this cascade has been chosen due to the flow separation behavior on the suction side of the blade at low Reynolds numbers. Different measurements techniques are conducted to further investigate the effects seen in CFD. The aim of this paper is to investigate the interaction phenomena between the secondary flow and a separation bubble at different Reynolds numbers. The development and change of the boundary layer in the axial and radial directions on the suction side of the turbine blade are presented and discussed. The results show discrepancies between the numerical prediction and the experimental data on the suction side of the blade rise as the effects of the secondary flow increase. Furthermore, the increasing influence of the radial pressure gradient of the secondary flow leads to a noticeable reduction in the length of the separation bubble close to the endwall region.
Labyrinth seals on shrouded blades are an effective way for reducing efficiency penalties, as compared to free ended blades. Due to the difficulties of gaining optical access to cavity regions, mostly pressure measurements are available in the literature, from which the details of the flow must be inferred. The use of numerical tools can provide insight in the flow topology and therefore help obtaining a better understanding of the factors (geometric, thermodynamic and aerodynamic) which can affect the performance of the machine. Whilst in the main passage relatively high Mach numbers are to be found (0.3–1.3), the flow field in the cavities is dominated by extremely low flow speeds with strong recirculation patterns. The treatments of such flows, where large disparities between the acoustic and convective speed exist, are known to be highly problematic if density-based solution methods are employed. As the flow conditions approach the incompressibility limit a degradation of the convergence behaviour can be observed, leading, potentially to incorrect solutions. In order to overcome these problems preconditioning methods can be conveniently applied to the Navier-Stokes equations. In the current work the formulation of a fully implicit local preconditioning method with domain control of the Mach number dependency is presented. Numerical simulations of turbomachine components are generally performed on truncated domains. In order to prevent unphysical reflections at open boundaries and interfaces non-reflecting boundary conditions have been developed, e.g. [6, 8]. As reported in the available literature, low Mach preconditioning can cause stability problems and strongly impair the quality of the results especially in proximity of the domain’s boundaries. As shown in [14, 21] an appropriate scaling treatment of the boundary conditions is also required to alleviate such issues. In the current work non-reflecting boundary conditions, based on the formulation of Giles [6, 8], have been suitably modified to work reliably also in the limit of incompressible flows. To prove the robustness and accuracy of the algorithm implemented in the DLR’s CFD code TRACE, a canonical testcase representing an abstraction of the flow topology found in a labyrinth seal, such as a lid-driven cavity, is shown. Finally, the simulation of the steady flow in a multistage, shrouded low-pressure turbine is presented. For this, a classic RANS approach has been adopted using the k-ω model to illustrate the effectiveness of the developed method in a typical industrial application. Of particular significance and interest is the analysis of the mass conservation properties of the numerical scheme attained at mixing planes between rotor and stator and at non-matching grid interfaces, denoted as “zonal” and “zonal-mixed” interfaces.
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