Coupling the algebraic model of bypass transition with EARSM model of turbulence

The article deals with numerical solution of the laminar-turbulent transition. A mathematical model consists of the Reynolds-averaged Navier-Stokes equations, which are completed by the explicit algebraic Reynolds stress model (EARSM) of turbulence. The algebraic model of laminar-turbulent transition, which is integrated to the EARSM, is based on the work of Kubacki and Dick (Int. J. Heat Fluid Flow 58, 68–83, 2016) where the turbulent kinetic energy is split in to the small-scale and large-scale parts. The algebraic model is simple and does not require geometry data such as wall-normal distance and all formulas are calculated using local variables. A numerical solution is obtained by the finite volume method based on the HLLC scheme and explicit Runge-Kutta method.

[1]  Jiří Holman,et al.  Unsteady Flow past a Circular Cylinder Using Advanced Turbulence Models , 2016 .

[2]  T. Arts,et al.  Aero-thermal investigation of a highly loaded transonic linear turbine guide vane cascade: A test case for inviscid and viscous flow computations , 1990 .

[3]  M. Drela.  XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils , 1989 .

[4]  E. Dick,et al.  An algebraic model for bypass transition in turbomachinery boundary layer flows , 2016 .

[5]  Michael A. Leschziner,et al.  Average-State Jacobians and Implicit Methods for Compressible Viscous and Turbulent Flows , 1997 .

[6]  Jiří Fürst,et al.  Development of a coupled matrix-free LU-SGS solver for turbulent compressible flows , 2018, Computers & Fluids.

[7]  Antti Hellsten,et al.  New two-equation turbulence model for aerodynamics applications , 2004 .

[8]  R. LeVeque.  Finite Volume Methods for Hyperbolic Problems: Characteristics and Riemann Problems for Linear Hyperbolic Equations , 2002 .

[9]  Klaus Gersten,et al.  Boundary-Layer Theory - 8th Revised and Enlarged Edition , 2000 .

[10]  Johan C. Kok,et al.  Resolving the Dependence on Freestream Values for the k- Turbulence Model , 2000 .

[11]  Tony Arts,et al.  Aero-Thermal Performance of a Two Dimensional Highly Loaded Transonic Turbine Nozzle Guide Vane: A Test Case for Inviscid and Viscous Flow Computations , 1990 .

[12]  F. Menter,et al.  A One-Equation Local Correlation-Based Transition Model , 2015 .

[13]  Jirí Fürst,et al.  Numerical Simulation of Compressible Turbulent Flows Using Modified EARSM Model , 2013, ENUMATH.

[14]  D. K. Walters,et al.  A Recommended Correction to the kT−kL−ω Transition-Sensitive Eddy-Viscosity Model , 2017 .