UFR 3-36 Test Case

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Test Case Study

Brief Description of the Study Test Case

The geometry of this UFR alongside the mesh is shown in Fig. 1. The geometry comprises three main sections: Constant-Width Forebody section ${L_{F}}$ with the largest width ${Y_{F}}$, Contoured Boat-tail section ${L_{B}}$ with the contoured width ${Y_{B}}$ and Constant-Width-Aftbody section ${L_{A}}$ with the smallest width ${Y_{A}}$. The width of the last section is modified to generate the desired APG. This modification is achieved through the variation of ${\sigma }$, which is the ratio of ${Y_{A}}$ to ${Y_{F}}$.

Figure 1: Flow Domain and grid of RANS simulations

The parametric geometry definition for the three relevant sections is given in [‌6] and is depicted in Fig. 1. The axial origin ${x=0}$ is set at the beginning of the Boattail section.

${\begin{aligned}y_{wall}&=y_{F}=H/(1-\sigma )\qquad \mathrm {for} \qquad -L_{F}<x/H\leq 0\\y_{wall}&=y_{B}=a_{1}+a_{2}x^{3}+a_{3}x^{4}+a_{4}x^{5}\qquad \mathrm {for} \qquad 0<x/H\leq L_{B}\qquad \qquad (1)\\y_{wall}&=Y_{A}=\sigma H/(1-\sigma )\qquad \mathrm {for} \qquad L_{B}<x/H\leq L_{B}+L_{A}\\\\\end{aligned}}$

with ${a_{1}=H/(1-\sigma )}$, ${a_{2}=-10H/L_{B}^{3}}$, ${a_{3}=15H/L_{B}^{4}}$ and ${a_{4}=-6H/L_{B}^{5}}$.

CFD Methods

Reynolds-Averaged Navier-Stokes computations

For the entire computational domain, a structured 2D mesh was created using Pointwise V18.2. Sensitivity studies were carried out. The final mesh contains a total of 266.112 points. Along the body contour 448 points are used in streamwise direction with a smaller spacing in the focus region. In the normal direction to the body wall 298 points are used, 98 of which are concentrated near the body wall region. The body wall-normal growth ratio is approximatively 1.077 and the dimensionless distance from the wall is ${y^{+}<1}$ along the body wall for all meshes and simulation scenarios. For the inflow boundary situated at ${x=-4.5R_{max}}$ a reservoir-pressure 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. For the outflow boundary at ${x=7.6{max}}$ an exit-pressure outflow boundary condition is used. The exit pressure is adapted during the simulation to match the reference pressure at the coordinate point ${Z_{ref}=(-0.15m,0m,0.18m)}$. The upper boundary is a far-field boundary condition situated ${68R_{max}}$ from the viscous body wall. Symmetry boundary condition is used on both side planes of the 2D domain. Different Reynolds numbers were simulated, two of them are presented in Table 2 with the corresponding reference parameters. Here we use a definition of the Reynolds number based on ${R_{max}}$ as Reynolds length.

DNS Computations

The test case is designed as a numerical experiment with the aim of comparing RANS results to DNS data. For the set-up of the DNS, the inflow boundary conditions are different, e.g. a recycling method can be used to generate the turbulent input or synthetic turbulence can be injected. It is also possible to numerically trip the boundary layer from laminar to turbulent to generate the desired turbulent boundary layer. Hence, to ensure a comparison to the results achieved with RANS turbulence models, a reference position upstream of the APG-area is defined where boundary-layer properties need to match between RANS and DNS computations to permit the comparison downstream in the region of interest. The reference position is located at ${x/H=-3.51}$. Depending on the generation of turbulence at the inlet, the computational domain needs to be adapted to ensure the correct boundary-layer properties at the reference position. If numerical tripping is performed, the laminar and turbulent distances need to be determined upstream of the reference position by precursor simulation as displayed in Figure 3.

At the reference position, the properties of the turbulent boundary layer are determined by the Reynolds number based on the momentum thickness Reθ and the Reynolds number based on the friction velocity Reτ. For the incipient and the moderate separation case, for the SA-neg model with RC and QCR, with and without LowRe-Modification, the numbers are given in Table 3.

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

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