UFR 336 Test Case
HiFiTURBDLR rounded step
Semiconfined flows
Underlying Flow Regime 336
Test Case Study
Brief Description of the Study Test Case
In the framework of the HiFiTURB project, four different geometries with different boundarylayer properties were designed. Each configuration was computed for two different Reynolds numbers. The configuration concerns a turbuluent boundary layer incipient to separation where the flow is on the brink of separation but does not separate at the Reynolds number based on the step height . The geometry of this UFR is shown in Fig. 2. The geometry comprises three main sections: An upstream section with , the curvedstep section with length and the downstream section with . The length of the step is fixed for all geometries, while the height is adapted to generate the desired APG. For the incipient separation testcase the step height equals .
Figure 2: Flow Domain 

The parametric geometry definition for the curvedstep sections is given in [6] and is depicted in Fig. 2. The origin is set at the beginning of the curvedstep section.
with , , and .
CFD Methods
SSG/LRR model
For the entire computational domain, a structured 2D mesh was created using Pointwise V18.2. Sensitivity studies were carried out on various meshes and the final mesh used in this UFR contains a total of points. Along the bottom contour points are used in streamwise direction with a smaller spacing in the curvedstep region. In the wallnormal direction points are used, of which are concentrated near the wall. The wallnormal growth ratio is approximatively and the dimensionless distance from the wall is along the bottom wall for all meshes and simulation scenarios. The computational mesh close to the step is shown in Figure Fig. 3.
Figure 3: Computational Mesh for RANS SSG/LRR simulation 

For the inflow boundary located at a reservoirpressure inflow boundary condition is used. This boundary condition prescribes total pressure and total density. The inflow direction is by default perpendicular to the boundary face and a constant velocity is prescribed defined by the Mach number . The turbulent kinetic energy entering the flow domain is computed according to the defined value of the turbulent intensity, which is set to and the turbulent viscosity is defined using the ratio of eddy to molecular dynamic viscosity set to . Both values of the turbulent kinetic energy and the turbulent viscosity are required for defining reference values for the turbulent quantities (Reynolds stresses and specific turbulent dissipation rate) used for the inflow boundary condition and are selected based on bestpractise. For the outflow boundary at an exitpressure outflow boundary condition is used. The exit pressure is adapted during the simulation to match the reference pressure at the coordinate point in agreement with the original Disotell case. The upper boundary is a permeable farfield Riemann boundary condition located from the bottom wall and computed via the approximate Riemann method of Roe. The SSG/LRR computations were conducted with a 3D solver. Hence, a symmetry boundary condition is used on both side planes of the 2D domain and the solver is operated in a 2D manner (only one cell in spanwise direction). Reference parameters for are presented in Table 2.
Parameter  
Value 
with the Mach number , the exit pressure , total inflow pressure , total inflow density , total inflow temperature , static pressure at the reference position , static density at the reference position , static temperature at the reference position and the static pressure at the reference position
Simulations were performed using the DLR inhouse software TAU [8] where the sevenequation omegabased Differential Reynolds stress turbulence model SSG/LRR [16] including the length scale correction [17] is already implemented. TAU is a FiniteVolumebased unstructured cellcentered on dualgrids code of secondorder accuracy. For the computations performed here, the meanflow and turbulence convective terms are discretized using secondorder central schemes together with Matrix Dissipation. LowMach number preconditioning was applied and steady computations using a LUSGS scheme were performed. All results presented in this report are based on fully converged simulations.
This UFR was designed based on the SSG/LRR model results, hence, at a predefined checkpoint at boundarylayer quantities were extracted to be matched by the DNS.
k model
The RANS k computations have been performed by the University of Bergamo using the CFD code MIGALE. The solver uses the Discontinuous Galerkin (DG) method for the spatial discretization of the governing equations, here the compressible Reynoldsaveraged NavierStokes equations coupled with the k closure model of Wilcox [32][28]. The DG method implemented in code MIGALE is able to guarantee highaccuracy (here up to sixthorder) on meshes made of elements of arbitrary shape [29][30]. The steadystate numerical solutions are sought by means of a Newton’s globalization strategy named pseudotransient continuation, e.g, [31]. Simulations have been performed on a 2D grid made of quadrilateral elements with quadratic edges (see Fig. 4 and Fig. 5) with a DG polynomial degree equal to (sixth order). Wall resolution in streamwise () and wallnormal () directions at different streamwise locations is reported in the following table
The wall resolution takes into account of the degree of the DG polynomial approximation. In particular, it is defined as
,
being the viscous length scale and the number of Degrees of Freedom per equation within the mesh element, here .
The flow problem is statistically twodimensional since the turbulent flow is homogeneous in the span direction. As the k computations were perfomed with a 3D solver, a symmetry boundary condition is used on the side planes of the twodimensional domain and only one cell in the spanwise direction is considered.
The computational domain of the RANS k simulations is designed to match the value of the boundary layer thickness, , predicted by the uDNS at the checkpoint, cf. DNS_15. To this purpose, a precursor computation on a zeropressuregradient flat plate of length was carried out. To mimic a freestream approaching the plate, the domain was extended upstream of the solid wall and a symmetry condition was set on the lower part of this extension. For the HiFiTURBDLR rounded step, the length of the noslip wall upstream of the checkpoint was set equal to the distance from the leading edge of the precursor flat plate to the streamwise coordinate where , i.e., . Accordingly, the leading edge of the noslip solid wall is located at . To mitigate spurious perturbations possibly originating at the outlet boundary, a “sacrificial buffer” is created downstream of the rounded step, i.e., at . In this region, a symmetry condition is set on the horizontal boundary and mesh coarsening is applied to reduce the solution gradients. A nearwall detail of the domain together with the imposed boundary conditions is shown in Fig. 6.
At the inlet boundary, located at , the total pressure and temperature are set to the values and , respectively. The turbulent intensity at the domain entrance is and the ratio of eddy to molecular dynamic viscosity is equal to . At the outlet boundary, placed at , the static pressure is imposed. The upper boundary is a permeable farfield Riemann boundary condition and is located from the solid wall upstream of the step and computed via the exact Riemann solver.
Figure 4: Detail of the near wall mesh for the RANS k model simulation 

Figure 5: Detail of the computational grid region around the rounded step for the RANS k model simulation 

Figure 6: Detail of the wall region flow domain together with the imposed boundary conditions for the RANS k model simulation 

Data provided
Data provided here are the wall quantities and profiles with results from both, SSG/LRR as well as k, simulations and Reynolds Stress profiles from SSG/LRR simulations. All quantities are nondimensionalised using the step height and the freestream velocity :
 WallQuantities.dat contains the following wall quantities extracted at the curved step viscous wall:
where and are local values, and are reference values at the reference position and is the magnitude of walltangential velocity at the boundary edge.
 profiles.dat contains the velocity and ReynoldsStress profiles in the vertical direction:
Contributed by: Erij Alaya and Cornelia Grabe — Deutsches Luftund Raumfahrt Zentrum (DLR)
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