Tobias Knopp

A grid and flow adaptive wall-function method for RANS turbulence modelling

This paper presents a grid and flow adaptive wall-function method for RANS turbulence modelling with emphasis on aerodynamic flows. A near-wall grid adaptation technique ensures a locally appropriate resolution depending on both the near-wall flow physics to be captured and the range of validity of the wall-function model. The near-wall RANS solutions of the Spalart-Allmaras and SST k-@w turbulence model are investigated near stagnation points and subsequent not yet fully developed turbulent flow, and in regions of adverse pressure gradient before separation. These are compared with the corresponding turbulence model specific universal wall-functions and suggestions for the design of wall-function methods for non-equilibrium flows are given. Regions of non-equilibrium flow are detected by a flow based sensor and near-wall grid adaptation is then made possible due to the hybrid character of the wall-functions.

A Comparison of Detached-Eddy Simulation and Reynolds-Stress Modelling Applied to the Flow over a Backward-Facing Step and an Airfoil at Stall

Flow simulations with the DLR-TAU code of a backward-facing step and an airfoil at stall using two recent versions of detached-eddy simulation (DES), i.e. the delayed DES (DDES) and the improved delayed DES (IDDES), are compared to experiments and RANS computations with the h -Reynolds-stress model (RSM). For the massive separation behind the backward-facing step, both DES variants agree well with measured skin friction and velocity profiles, if a sufficiently fine mesh is applied. The near-wall h -RSM on the other hand overpredicts the separation length. For the stall of the HGR-01 airfoil, which is governed by gradually growing trailing-edge separations, the DES computations suffer from poor predictions of the developing boundary layer, issues with modelled-stress depletion and a delayed onset of resolved turbulence in the LES region. Overall, the application of DDES and IDDES to airfoil stall is considered unsuccessful in this study as even beyond maximum lift no turbulence is resolved in the separated region. For this flow, the h -RSM compares much better to PIV data and static pressure measurements.

Investigation of scaling laws in a turbulent boundary layer flow with adverse pressure gradient using PIV

We present an experimental investigation and data analysis of a turbulent boundary layer flow at a significant adverse pressure gradient at Reynolds number up to Reθ = 10, 000. We combine large-scale particle image velocimetry (PIV) with microscopic PIV for measuring the near wall region including the viscous sublayer. We investigate scaling laws for the mean velocity and for the total shear stress in the inner part of the boundary layer. In the inner part the mean velocity can be fitted by a log-law. In the outer part of the inner layer the log-law ceases to be valid. Instead, a modified log-law provides a good fit, which is given in terms of the pressure gradient parameter and a parameter for the mean inertial effects. Finally we describe and assess a simple quantitative model for the total shear stress distribution which is local in wall-normal direction without streamwise history effects.

Low-Dissipation Low-Dispersion Second-Order Scheme for Unstructured Finite Volume Flow Solvers

A new low-dissipation low-dispersion second-order scheme suitable for unstructured finite volume flow solvers is presented that is designed for vortical flows and for scale-resolving simulations of turbulence. The idea is that, by optimizing its dispersion properties, a standard second-order method can be improved significantly for such flows. The key is to include gradient information for computing face values of the fluxes and to use this additional degree of freedom to improve the dispersion properties of the scheme. The scheme is motivated by a theoretical consideration of the dispersion properties for a one-dimensional scalar transport equation problem. Then, the new scheme is applied using the DLR TAU-code for compressible flows and the DLR THETA-code for incompressible flows for simulations of the moving vortex problem and the Taylor–Green vortex flow. The improved accuracy for small-scale transportation and the easy implementation make this scheme a promising candidate for efficient scale-resolvin...

Detached-Eddy Simulation of Aerodynamic Flows Using a Reynolds-Stress Background Model and Algebraic RANS/LES Sensors

A new variant of delayed detached-eddy simulation (DDES) based on the Low-Re epsilon-h-RSM as RANS background model is presented which is optionally combined with novel algebraic sensors for the RANS/LES switch. The RSM is aimed to improve RANS-mode predictions of pressure-induced separations on smooth surfaces, while the new sensors eval- nuate boundary-layer properties to distinguish between attached and detached flow regions and place the RANS/LES interface at separation onset. After calibration and basic validation for decaying isotropic turbulence, the epsilon-h-based DDES is applied to a backward-facing nstep flow with massive separation and compared to experiments. The results are well in line with original DDES and can be further improved by applying stochastic forcing of the turbulent subgrid stresses. For the HGR-01 airfoil at stall, both the RSM-based approach and the algebraic sensors are found essential in capturing separation onset at the trailing nedge and ensuring LES mode in the separated flow. However, the actual DES computations still suffer from under-resolved turbulence in the separated LES region when compared to PIV measurements, which can neither be compensated by stochastic forcing, nor by a different RANS model or a local grid refinement. Thus, the need to extend the present nmethod by a more sophisticated forcing becomes evident.

An Algebraic Sensor for the RANS-LES Switch in Delayed Detached-Eddy Simulation

A new hybrid RANS-LES method of DDES-type for flows over airfoil sections with small/incipient separation is presented. It alters the RANS-LES switch based on the function f d in the DDES formulation. Regions of attached boundary layer flow, the separation point and the subsequent region of separation are detected by sensors. They are based on a combination of algebraic properties of the mean velocity profiles in wall-normal direction and of integral boundary layer quantities, namely the shape factor H 12. While the RANS length scale l RANS is used in attached boundary layers, the LES length scale C DESΔ is used in regions of separated flow. In particular, thin regions of (incipiently) separated flow are treated in LES mode except for a near-wall region where l RANS is used. Moreover, in the vicinity of the separation point or in the entire separation region, a stochastic SGS model can be used as a simple method to force the generation of turbulent content.

Hybrid RANS/LES simulations of a three-element airfoil

In this paper the Spalart-Allmaras based Delayed Detached Eddy Simulation (DDES [1]) and Improved Delayed Detached Eddy Simulation (IDDES [2]) are used to simulate the flow about an industrially relevant airfoil-configuration with deployed high-lift devices. Here, the potential advantage of the computationally very challenging hybrid approaches over pure RANS simulations in the case of incipient separation is investigated.

Scale-Resolving Simulations with a Low-Dissipation Low-Dispersion Second-Order Scheme for Unstructured Flow Solvers

A new low-dissipation low-dispersion second-order scheme is applied to scale-resolving flow simulations using compressible and incompressible unstructured finite volume solvers. In wall-resolved and wall-modeled large-eddy simulations of the plane channel flow, the new scheme yields substantial improvements compared to the more dissipative/dispersive standard central scheme over a considerable range of Reynolds numbers. For general hybrid Reynolds-averaged Navier–Stokes/large-eddy simulations, a numerical blending approach is derived that uses a local sensor function to switch between the new scheme in the large-eddy simulation branch and the standard scheme in inviscid flow regions. After determining a suitable sensor formulation, the hybrid numerical scheme is applied to simulate a backward-facing step flow, for which satisfactory results and a reduced grid sensitivity are obtained. To demonstrate its potential in relevant aeronautical flows, the new scheme is successfully applied to hybrid Reynolds-ave...

Simulation of Wing and Nacelle Stall

Numerical stall simulations are challenging in terms of physical models involved, overall computation effort, and the needed efforts for validation. The present paper describes coordinated, fundamental research into new simulation methodologies and their validation for wing and nacelle stall that also include the effects of atmospheric gusts. The research is ncarried out by the DFG funded Research Unit FOR 1066, which is composed of German Universities and the German Aerospace Center, DLR. The Research Unit investigates advanced models of turbulence, advanced physics-based gust models, and new numerical approaches for gust simulation. These modeling and computational activities are nsupplemented by new validation experiments, that aim at providing stall data on wings and engine nacelles with well defined, generic distortions of the onset flow.

Scale-Resolving Simulations with a Low-Dissipation Low-Dispersion Second-Order Scheme for Unstructured Finite-Volume Flow Solvers

A new low-dissipation low-dispersion 2nd-order scheme is applied to scale-resolving flow simulations using compressible and incompressible unstructured finite-volume solvers. In wall-resolved and wall-modeled nLES computations of the channel flow the new scheme yields substantial improvements compared to the more dissipative/dispersive basic central scheme over a considerable range of Reynolds numbers. For general hy- nbrid RANS/LES simulations a numerical blending approach is applied which uses a local sensor function to switch between the new scheme in LES regions and the basic central scheme in the outer flow field. After nan a-priori determination of a consistent sensor function, the hybrid numerical scheme is used to simulate a backward-facing step flow, where satisfactory results and reduced grid sensitivity are obtained. To demon- nstrate its potential in relevant aeronautical flows, the new scheme is successfully applied to hybrid RANS/LES computations of a 3-element airfoil near stall and a rudimentary landing gear with massive flow separation. Note that this paper is jointly published with a companion paper by Lowe et al., in which the low-dissipation low-dispersion 2nd-order scheme is derived and theoretically analyzed, followed by a basic assessment for fundamental numerical test cases.