TY - JOUR

T1 - Higher-order realizable algebraic Reynolds stress modeling based on the square root tensor

AU - Inagaki, Kazuhiro

AU - Ariki, Taketo

AU - Hamba, Fujihiro

N1 - Publisher Copyright:
© 2019 American Physical Society.

PY - 2019/11/5

Y1 - 2019/11/5

N2 - In this study, realizable algebraic Reynolds stress modeling based on the square root tensor [Phys. Rev. E 92, 053010 (2015)10.1103/PhysRevE.92.053010] is further developed for extending its applicability to more complex flows. In conventional methods, it was difficult to construct an algebraic Reynolds stress model satisfying the realizability conditions when the model involves higher-order nonlinear terms on the mean velocity gradient. Such higher-order nonlinear terms are required to predict turbulent flows with three-dimensional mean velocity. The present modeling based on the square root tensor enables us to make the model always satisfy the realizability conditions, even when it involves higher-order nonlinearity. To construct a realizable algebraic Reynolds stress model applicable to turbulent flows with three-dimensional mean velocity, a quartic-nonlinear eddy-viscosity model is proposed. The performance of the model is numerically verified in a turbulent channel flow, a homogeneous turbulent shear flow, and an axially rotating turbulent pipe flow. The present model gives a good result in each turbulent flow. Note that the mean swirl flow in an axially rotating turbulent pipe flow is reproduced because the present model involves cubic nonlinearity. Such a higher-order realizable algebraic Reynolds stress model, involving quartic nonlinearity on the mean velocity, is expected to be useful in numerically stable predictions of turbulent flows with three-dimensional mean velocity.

AB - In this study, realizable algebraic Reynolds stress modeling based on the square root tensor [Phys. Rev. E 92, 053010 (2015)10.1103/PhysRevE.92.053010] is further developed for extending its applicability to more complex flows. In conventional methods, it was difficult to construct an algebraic Reynolds stress model satisfying the realizability conditions when the model involves higher-order nonlinear terms on the mean velocity gradient. Such higher-order nonlinear terms are required to predict turbulent flows with three-dimensional mean velocity. The present modeling based on the square root tensor enables us to make the model always satisfy the realizability conditions, even when it involves higher-order nonlinearity. To construct a realizable algebraic Reynolds stress model applicable to turbulent flows with three-dimensional mean velocity, a quartic-nonlinear eddy-viscosity model is proposed. The performance of the model is numerically verified in a turbulent channel flow, a homogeneous turbulent shear flow, and an axially rotating turbulent pipe flow. The present model gives a good result in each turbulent flow. Note that the mean swirl flow in an axially rotating turbulent pipe flow is reproduced because the present model involves cubic nonlinearity. Such a higher-order realizable algebraic Reynolds stress model, involving quartic nonlinearity on the mean velocity, is expected to be useful in numerically stable predictions of turbulent flows with three-dimensional mean velocity.

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U2 - 10.1103/PhysRevFluids.4.114601

DO - 10.1103/PhysRevFluids.4.114601

M3 - Article

AN - SCOPUS:85075267653

SN - 2469-990X

VL - 4

JO - Physical Review Fluids

JF - Physical Review Fluids

IS - 11

M1 - 114601

ER -