Backward-Facing Step

The backward-facing step experiment of Driver and Seegmiller (Driver and Seegmiller, 1985) is a standard validation benchmark for RANS turbulence models. The predicted reattachment length downstream of the step is commonly used as a primary metric for assessing turbulence-model performance. The backward-facing step case verifies the $var element = document.getElementById("moose-equation-772fea94-2bc3-41fb-9819-1982ef65179d");katex.render("k", element, {displayMode:false,throwOnError:false});$ - $var element = document.getElementById("moose-equation-3e959057-24c6-4175-84a9-d29599013cf7");katex.render("\\tau", element, {displayMode:false,throwOnError:false});$ RANS model in NekRS by comparing the predicted skin-friction coefficient along the downstream wall with the experimental measurements of Driver and Seegmiller (Driver and Seegmiller, 1985).

Computational domain

The step is located at the origin, and the inlet and outlet boundaries are located at $var element = document.getElementById("moose-equation-125f4782-31db-4a56-aea5-103157b68187");katex.render("x/H=-4", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-91d3317d-ec9a-4ba8-b92f-a587ae816309");katex.render("x/H=40", element, {displayMode:false,throwOnError:false});$ , respectively, where $var element = document.getElementById("moose-equation-8b3ff1b5-4269-4cfd-9075-46c2b41499e5");katex.render("H", element, {displayMode:false,throwOnError:false});$ is the step height. The upstream and downstream channel heights are $var element = document.getElementById("moose-equation-754e804b-d908-4a78-8807-36a839b6732c");katex.render("8H", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-a62dcab1-0771-4f47-af63-7b95cc68bce8");katex.render("9H", element, {displayMode:false,throwOnError:false});$ , respectively. The Reynolds number based on the inlet velocity $var element = document.getElementById("moose-equation-6a610e18-7598-4289-affc-c1ac21743794");katex.render("U", element, {displayMode:false,throwOnError:false});$ and the step height is $var element = document.getElementById("moose-equation-5565e7d0-7d61-4cb6-bf6f-22387603f3e7");katex.render("Re=37{,}425", element, {displayMode:false,throwOnError:false});$ . The simulation is advanced to a quasi-steady state before the validation metrics are evaluated. Figure 1 shows the resulting streamwise velocity and turbulent kinetic energy fields.

Streamwise velocity and turbulent kinetic energy contours for the backward-facing step

Figure 1: Quasi-steady streamwise velocity and turbulent kinetic energy contours.

Verification criterion

The test is qualified by comparing the computed skin-friction coefficient along the downstream wall, $var element = document.getElementById("moose-equation-008c8a9c-c79b-4da1-9e13-d540390f8450");katex.render("x>0", element, {displayMode:false,throwOnError:false});$ , with the experimental measurements of Driver and Seegmiller (Driver and Seegmiller, 1985). The skin-friction coefficient is defined as

(1)var element = document.getElementById("moose-equation-ee24cfa0-64e6-47b6-b914-af8ee0fdd199");katex.render("C_f = \\frac{2\\tau_w}{\\rho_0 U^2},", element, {displayMode:true,throwOnError:false});

where $var element = document.getElementById("moose-equation-a4f8ce3e-bca7-45e8-9ac2-e3dba86108bb");katex.render("\\tau_w", element, {displayMode:false,throwOnError:false});$ is the wall shear stress, $var element = document.getElementById("moose-equation-fc8da381-ec47-444d-b602-2438464bf686");katex.render("\\rho_0", element, {displayMode:false,throwOnError:false});$ is the reference density, and $var element = document.getElementById("moose-equation-d903e25a-10ca-4c0f-aceb-a7f1b371ed0e");katex.render("U", element, {displayMode:false,throwOnError:false});$ is the reference inlet velocity. The test evaluates the $var element = document.getElementById("moose-equation-898016ca-8065-4c51-9328-f9adfc227d90");katex.render("L_2", element, {displayMode:false,throwOnError:false});$ norm of the difference between the computed and experimental skin-friction coefficients,

(2)var element = document.getElementById("moose-equation-b37bb05d-0997-4a9b-b922-62f1a3a694a2");katex.render("\\left\\lVert C_f-C_f^{\\mathrm{exp}}\\right\\rVert_{L_2}.", element, {displayMode:true,throwOnError:false});

Figure 2 compares the computed skin-friction coefficient profile with the experimental measurements. A polynomial fit to the experimental data is used to evaluate the error norm.

Computed and experimental skin-friction coefficient profiles downstream of the backward-facing step

Figure 2: Comparison of the computed skin-friction coefficient with the experimental measurements of Driver and Seegmiller (Driver and Seegmiller, 1985).

References

David M Driver and H Lee Seegmiller. Features of a reattaching turbulent shear layer in divergent channelflow. AIAA journal, 23(2):163–171, 1985.

BibTeX

@article{driver1985features,
    author = "Driver, David M and Seegmiller, H Lee",
    title = "Features of a reattaching turbulent shear layer in divergent channelflow",
    journal = "AIAA journal",
    volume = "23",
    number = "2",
    pages = "163--171",
    year = "1985"
}

RIS

TY  - JOUR
AU  - Driver, David M
AU  - Seegmiller, H Lee
TI  - Features of a reattaching turbulent shear layer in divergent channelflow
JO  - AIAA journal
PY  - 1985
VL  - 23
IS  - 2
SP  - 163
EP  - 171
ER  -

Plain Text

David M Driver and H Lee Seegmiller. Features of a reattaching turbulent shear layer in divergent channelflow. AIAA journal, 23(2):163–171, 1985.

Computational domain
Verification criterion
References