TY - JOUR

T1 - Turbulence model form errors in separated flows

AU - Klemmer, Kerry S.

AU - Wu, Wen

AU - Mueller, Michael E.

N1 - Funding Information:
K.S.K. gratefully acknowledges the Charlotte Elizabeth Procter Fellowship from Princeton University. The planar jet simulations presented in this article were performed on computational resources supported by the Princeton Institute for Computational Science and Engineering (PICSciE) and the Office of Information Technology's High Performance Computing Center and Visualization Laboratory at Princeton University.
Publisher Copyright:
© 2023 American Physical Society.

PY - 2023/2

Y1 - 2023/2

N2 - In turbulence modeling, model form errors are introduced in the prediction of the Reynolds stresses through the Boussinesq hypothesis and other modeling choices, such as the specific form of the eddy viscosity. These linear eddy viscosity models have known points of failure in flows that feature significant complexity, such as separated flows. In this work, an implied models approach is used to better understand the sources and dynamics of model form error in separated flows through a priori analysis, focusing on the Boussinesq hypothesis using exact inputs for determining the eddy viscosity. In the implied models approach, a transport equation is derived for the model error through the transport equation implied by the model for the quantity of interest; that is, the Reynolds stresses in this work. A boundary layer over a flat plate with a statistically stationary separation bubble is analyzed and shown to have two error modes corresponding to the qualitative behavior of turbulent wall-bounded and turbulent free-shear model form errors. The wall-bounded mode is observed sufficiently upstream of the separation bubble, and the free-shear mode is observed near and within the separation bubble, with a superposition of these two modes observed in the intermediate regions. These results indicate on the one hand a complex picture of model error that changes through the flow but on the other hand a simple picture of model error that comprises elements of canonical flows. Therefore, calibration of turbulence models against simpler canonical flows can capture the main modes of model failure in more complex flows.

AB - In turbulence modeling, model form errors are introduced in the prediction of the Reynolds stresses through the Boussinesq hypothesis and other modeling choices, such as the specific form of the eddy viscosity. These linear eddy viscosity models have known points of failure in flows that feature significant complexity, such as separated flows. In this work, an implied models approach is used to better understand the sources and dynamics of model form error in separated flows through a priori analysis, focusing on the Boussinesq hypothesis using exact inputs for determining the eddy viscosity. In the implied models approach, a transport equation is derived for the model error through the transport equation implied by the model for the quantity of interest; that is, the Reynolds stresses in this work. A boundary layer over a flat plate with a statistically stationary separation bubble is analyzed and shown to have two error modes corresponding to the qualitative behavior of turbulent wall-bounded and turbulent free-shear model form errors. The wall-bounded mode is observed sufficiently upstream of the separation bubble, and the free-shear mode is observed near and within the separation bubble, with a superposition of these two modes observed in the intermediate regions. These results indicate on the one hand a complex picture of model error that changes through the flow but on the other hand a simple picture of model error that comprises elements of canonical flows. Therefore, calibration of turbulence models against simpler canonical flows can capture the main modes of model failure in more complex flows.

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U2 - 10.1103/PhysRevFluids.8.024606

DO - 10.1103/PhysRevFluids.8.024606

M3 - Article

AN - SCOPUS:85149643574

SN - 2469-990X

VL - 8

JO - Physical Review Fluids

JF - Physical Review Fluids

IS - 2

M1 - 024606

ER -