HiFi-TURB-DLR rounded step

Semi-confined flows

Underlying Flow Regime 3-36

Description

Introduction

The present UFR is one of multiple industrially-relevant flow phenomena that are being investigated as part of the European project “HiFi-TURB”, that has received funding from the European Union’s Horizon 2020 research and innovation programs under grant agreement n° 814837. The aim of the project is to use Artificial Intelligence (AI) to modify available turbulence models in order to obtain a more accurate prediction of the key flow features for a range of selected reference test cases. The geometry of this UFR was designed by the Center of Computer Applications in AeroSpace Science and Engineering (C²A²S²E) at the DLR Institute of Aerodynamics and Flow Technology. The key flow feature investigated is a turbulent boundary layer (TBL) subjected to an adverse pressure gradient (APG) over a smooth surface with and without flow separation and reattachment, in which state-of-the-art Reynolds-Averaged Navier-Stokes (RANS) models are known to fail in accurately predicting the flow and which is of importance, e.g. in external aerodynamics. The designed curved step geometry is a generic curved surface. The 2D geometry allows for a well-defined and computationally affordable Direct Numerical Simulations (DNS). Geometric variations of the test case were designed to achieve attached flow, incipient, moderate and strong separation. For the incipient configuration, computational results were obtained by several project partners using well-known RANS turbulence models as well as DNS computations performed by project partners from the University of Bergamo. The latter are presented in this UFR.

Figure 1: HiFi-TURB-DLR rounded step incipient configuration

Review of UFR studies and choice of test case

The design of the test case to study the UFR is a modified version of the Disotell body [‌6][‌7], which is an axisymmetric test body consisting of four parts: an Elliptical Nose section, a Constant-Radius Forebody section, a contoured Boat-tail section and a constant Aftbody section. The main focus region is the Contoured Boat-tail section with APG and possible separation and reattachment. The Aftbody is exchangeable to allow geometry variation. The strength of APG and hence the tendency of the flow to separate can be increased by reducing the radius of the Constant-Radius Aftbody section.

The idea of an axisymmetric set-up is very attractive for a wind tunnel experiment to provide a test case which is suitable for comparison with DNS: In wind-tunnel experiments using a planar model with APG, the boundary layer in the intersection between the test model and the wind tunnel side wall has a different behavior than the boundary layer in the centerline section of the test model. As a consequence, the DNS of the flow in the centerline section is not comparable with that of the wind tunnel due to the side wall effects. E.g., corner-flow separation at the side walls can lead to a displacement effect on the flow in the centerline. Furthermore, the computational costs for a DNS/LES of the full wind tunnel experiment including all wind tunnel walls is prohibitively large. To accurately consider the separated flow region in the DNS, a span of at least 90 or even 120 degrees would be needed for axisymmetric flow, which would lead to a large number of mesh nodes in circumferential direction. However, three additional aspects were found to be more severe. First, the resolution cost for the region of transition from laminar to turbulent flow was estimated to be excessively large in case of a cone-type nose in an axisymmetric set-up compared to a 2D planar domain. Second, the additional question arose, whether the fluid dynamical mechanisms and turbulence in the region of separated flow and reattachment for an axisymmetric case are comparable to the 2D planar case, which was considered the relevant situation for airfoil wings and turbine blades. The third concern was that the spanwise resolution in this case could be much larger than for a 2D planar case due to the contraction of the surface in streamwise direction.

An additional issue was the treatment of the boundary opposite to the test body. For the NASA experiment, there is a clear blockage of the test model in the wind tunnel. This means, to reproduce experimental data for the test model, the wind tunnel walls need to be considered in the numerical set-up. As the inlet section before the test body is long enough, the boundary layer on the wind tunnel walls becomes substantially thick and cannot be neglected by using inviscid walls. The Reynolds number of the wind tunnel wall boundary layers was seen to be much larger than in the region of interest on the test body. The additional computational cost for the treatment of these boundary layers by DNS were found to be much higher than for the DNS on the test body. Therefore, the revised proposal of the test case is designed as a generic 2D planar test case without any tunnel walls but with a far-field boundary opposite to the test body instead.

The modified set-up as a 2D planar case with a far-field boundary led to some modifications of the original contour geometry. The removal of the opposite wind tunnel wall caused a significant change of the expansion ratio of the flow upstream and downstream of the contoured ramp, leading to a reduction of the pressure gradient and the tendency of the flow to separate. As a remedy, the polynomial form of the contour was maintained and the parameter which controls the step height was varied.

Contributed by: Erij Alaya and Cornelia Grabe — Deutsches Luft-und Raumfahrt Zentrum (DLR)