Reynolds-Averaged Navier-Stokes System Research Articles

Numerical simulation of a low Prandtl number flow over a backward facing step with an anisotropic four-equation turbulence model

In recent years the use of liquid metals has become more and more popular for heat transfer applications in many fields ranging from IV generation fast nuclear reactors to solar power plants. Due to their low Prandtl number values, the similarity between dynamical and thermal fields cannot be assumed and sophisticated heat turbulence models are required to take into account the anisotropy of the turbulent heat transfer involving liquid metals. In the present work, we solve an anisotropic four-equation turbulence model coupled with the Reynolds Averaged Navier Stokes system of equations to simulate a turbulent flow of liquid sodium over a vertical backward-facing step. We implement an explicit algebraic model for Reynolds stress tensor and turbulent heat flux that takes into account flow anisotropic behavior. We study forced and mixed convection regimes when a uniform heat flux is applied on the wall behind the step. Linear isotropic approximations for eddy viscosity and eddy thermal diffusivity underestimate the turbulent heat flux components while this anisotropic model shows a better agreement with DNS results.

Numerical simulation of forced and mixed convection turbulent liquid sodium flow over a vertical backward facing step with a four parameter turbulence model

Liquid metals are promising fluids for engineering applications since they have interesting physical properties such as high thermal conductivity and low kinematic viscosity with respect to the values of common operating fluids, i.e. air and water. This implies low Prandtl number values and therefore the similarity assumption between velocity and temperature fields does not hold. In the present work we solve a four parameter turbulence model coupled with the Reynolds Averaged Navier Stokes system of equations to simulate a turbulent flow of liquid sodium over a vertical backward facing step. On the wall behind the step a uniform heat flux is applied in order to study both forced and mixed convection flow regimes. This model for turbulent heat transfer, taking into account different boundary conditions, is analyzed and compared with the Kays correlation and Direct Numerical Simulation data. Profiles of velocity, turbulent kinetic energy, turbulent heat flux, temperature and its squared fluctuations are provided for two simulated Richardson number values, namely 0 and 0.338. Obtained results show a reasonable agreement with reference Direct Numerical Simulation values.

Space-time discontinuous Galerkin method for the numerical simulation of the compressible turbulent gas flow through the porous media

The article is concerned with the numerical simulation of the compressible turbulent gas flow through the porous media using space-time discontinuous Galerkin method.The mathematical model of flow is represented by the system of non-stationary Reynolds-Averaged Navier-Stokes (RANS) equations. The flow through the porous media is characterized by the loss of momentum. This RANS system is equipped with two-equation k-omega turbulence model. The discretization of these two systems is carried out separately by the space-time discontinuous Galerkin method. This method is based on the piecewise polynomial discontinuous approximation of the sought solution in space and in time. We present some numerical experiments to demonstrate the applicability of the method using own-developed code.

Space-time discontinuous Galerkin method for the numerical simulation of viscous compressible gas flow with the k-omega turbulence model

In this article we deal with the numerical simulation of the non-stationary compressible turbulent flow described by the Reynolds-Averaged Navier-Stokes (RANS) equations. This RANS system is equipped with two-equation k-omega turbulence model. The discretization of these two systems is carried out separately by the space-time discontinuous Galerkin method. This method is based on the piecewise polynomial discontinuous approximation of the sought solution in space and in time. We use the numerical experiments to demonstrate the applicability of the shown approach. All presented results were computed with the own-developed code.

Finite volume - space-time discontinuous Galerkin method for the numerical simulation of compressible turbulent flow in time dependent domains

The article is concerned with the numerical simulation of the compressible turbulent flow in time dependent domains. The mathematical model of flow is represented by the system of non-stationary Reynolds- Averaged Navier-Stokes (RANS) equations. The motion of the domain occupied by the fluid is taken into account with the aid of the ALE (Arbitrary Lagrangian-Eulerian) formulation of the RANS equations. This RANS system is equipped with two-equation k − ω turbulence model. These two systems of equations are solved separately. Discretization of the RANS system is carried out by the space-time discontinuous Galerkin method which is based on piecewise polynomial discontinuous approximation of the sought solution in space and in time. Discretization of the two-equation k − ω turbulence model is carried out by the implicit finite volume method, which is based on piecewise constant approximation of the sought solution. We present some numerical experiments to demonstrate the applicability of the method using own-developed code.

Adjoint optimal control problems for the RANS system

Adjoint optimal control in computational fluid dynamics has become increasingly popular recently because of its use in several engineering and research studies. However the optimal control of turbulent flows without the use of Direct Numerical Simulation is still an open problem and various methods have been proposed based on different approaches. In this work we study optimal control problems for a turbulent flow modeled with a Reynolds-Averaged Navier-Stokes system. The adjoint system is obtained through the use of a Lagrangian multiplier method by setting as objective of the control a velocity matching profile or an increase or decrease in the turbulent kinetic energy. The optimality system is solved with an in-house finite element code and numerical results are reported in order to show the validity of this approach.

3D Unsteady Simulation of a Modern High Pressure Turbine Stage Using Phase Lag Periodicity: Analysis of Flow and Heat Transfer

Unsteady 3D Reynolds-averaged Navier–Stokes (RANS) simulations have been performed on a highly loaded transonic turbine stage, and results are compared with steady calculations and experiments. A low Reynolds number k-ε turbulence model is employed to provide closure for the RANS system. A phase lag boundary condition is used in the tangential direction. This allows the unsteady simulation to be performed by using only one blade from each of the two rows. The objective of this paper is to study the effect of unsteadiness on rotor heat transfer and to glean any insight into unsteady flow physics. The role of the stator wake passing on the pressure distribution at the leading edge is also studied. The simulated heat transfer and pressure results agree favorably with the experiment. The time-averaged heat transfer predicted by the unsteady simulation is higher than the heat transfer predicted by the steady simulation everywhere, except at the leading edge. The shock structure formed, due to stator-rotor interaction, is analyzed. Heat transfer and pressure at the hub and casing are also studied. Thermal segregation is observed that leads to the heat transfer patterns predicted by steady and unsteady simulations to be different.