Meng Huang Lu

Rough-wall layer modeling using the Brinkman equation

A flow model to facilitate the Reynolds-averaged Navier-Stokes (RANS) type of calculations of the turbulent flow over rough walls is proposed. Given that the roughness region is thin compared to the thickness of the boundary layer, the turbulent flow is viewed as consisting of two regions: (1) where the medium is entirely fluid and the RANS equations can be applied, and (2) a region of two phases where the fluid meanders around the solid roughness elements. The method of volume-averaging often used in the study of porous medium flows is applied in the rough-wall layer region. The resulting parameters such as porosity allow a direct inclusion of the geometric characteristics of the roughness element and their pattern in the model equations. In this formulation, the Brinkman equation, a reduced form of the volume-averaged Navier-Stokes (VANS) equations has been used. We have experimented with adapting an existing low Reynolds number eddy-viscosity, two-equation turbulence model developed for smooth walls, to provide closure to the RANS equations. The results shown are for a NACA 0012 airfoil with three different surface coverage using the same roughness.

New Two-Equation Closure for Rough-Wall Turbulent Flows Using the Brinkman Equation

A new flow-physics-based modeling of surface-roughness effects is developed for the Reynolds-averaged Navier-Stokes equations numerical calculations of high-Reynolds-number turbulent flows over rough walls. In the proposed approach, we model the fluid dynamics of the volume-averaged flow in the near-wall rough layer by using the Brinkman equation. The porosity can be calculated based on the volumetric characteristics of the roughness, and the permeability is modeled. The Reynolds-averaged Navier-Stokes equations are solved numerically above the near-wall rough layer, and a low-Reynolds-number k-e model is employed in all regions. In this paper, we present the computational results, including the skin-friction coefficient, the log-law mean velocity, the roughness function, the turbulent kinetic energy, and the Reynolds shear stress. The results show that the new rough-wall-layer modeling approach well predicts the skin-friction coefficient, the log-law mean velocity, the roughness function, and the Reynolds shear stress.

Application of a two-layer model for implicit large-eddy simulations using a high-order compact scheme

The two-layer approximate boundary conditions are implemented for implicit large-eddy simulations (ILES) using a parallel high-order flow solver, which employs a sixth-order spatial formulations and tenth-order low-pass filter providing dissipation only at the high wave numbers represented by the mesh, and no subgrid-scale model is needed. The computational results of the mean streamwise velocity, the rms velocity fluctuations, and the Reynolds shear stress for turbulent channel flows are in good agreement with the direct numerical simulations data. The calculated results of the turbulent channel flows indicate that the two-layer model is a feasible method to model the solid boundaries for ILES. The 3D instantaneous flow structure shows that the flow physics is properly captured and described. The calculated results also show that the total computation time can be significantly reduced.

A new rough wall layer modeling using the Brinkman equation in turbulent boundary layers

A new flow physics-based surface roughness model is developed for RANS (Reynolds averaged Navier-Stokes) numerical calculations of high Reynolds number turbulent flows over rough walls. In the proposed approach, the fluid dynamics of the volume-averaged flow in the near-wall rough layer is modeled by using the Brinkman equation. The porosity can be calculated based on the volumetric characteristics of the roughness and the permeability is modeled. The RANS equations are solved numerically above the near-wall rough layer, while a low-Reynolds-number k-e model is employed through out the whole domain. The computational results, including the skin friction coefficient, the log-law mean velocity profile, the roughness function, the turbulent kinetic energy, and the Reynolds shear stress are presented. The results show that the new rough wall layer modeling approach predicts well the skin friction coefficient, the log-law mean velocity, the roughness function, and the Reynolds shear stress.

Numerical Study of Roughness Effects on a NACA0012 Airfoil Using a New Two-Equation Closure of the Rough Wall Layer Modeling

The effect of surface roughness on the aerodynamic characteristics of the NACA0012 airfoil is investigated numerically. The turbulent incompressible flows over a rough NACA0012 airfoil with two-dimensional wire roughness covered entire and partial surfaces at different angles of attack are simulated. The fluid dynamics of the volume-averaged flow in the near-wall rough layer is modeled by using the Brinkman equation. The porosity can be calculated based on the volumetric characteristics of the roughness and the permeability is modeled. A new two-equation closure is employed to solve the turbulent quantities. The computational results, including the lift, drag, and surface pressure coefficients, and mean velocity profiles, are presented. The results show that the rough wall layer modeling approach predicts well the surface roughness effects on the aerodynamic characteristics of the NACA0012 airfoil in the surface pressure and lift coefficients.

A second-order closure for the new rough wall layer modeling using the Brinkman equation in turbulent boundary layers

A second-order turbulence closure for the new rough wall layer modeling using the Brinkman equation is developed to improve the predictive capability of a previously developed k-e turbulence closure for the new flow physics-based surface roughness model in rough wall turbulent boundary layers. In the proposed approach, the fluid dynamics of the volume-averaged flow in the near-wall rough layer is modeled by using the Brinkman equation. The porosity can be calculated based on the volumetric characteristics of the roughness and the permeability is modeled. A new interface stress jump condition including the Reynolds stress components are also developed for a second-order turbulence closure. The Reynolds-averaged Navier-Stokes equations are solved numerically above the near-wall rough layer, while a second-order turbulence closure is employed in all regions. The computational results, including the skin friction coefficient, the log-law mean velocity, the roughness function, the Reynolds stresses, and the turbulent kinetic energy, are presented. The results show that the new rough wall layer modeling approach with a second-order closure predicts well the skin friction coefficient, the log-law mean velocity, the roughness function, and the Reynolds shear stress.

Calculations of Turbulent Flow around Airfoils with Attached Flexible Fin using an Immersed Boundary Method

The aim of the present paper is to develop a numerical method to simulate flow over rigid/moving boundaries using immersed boundary technique. The Navier-stokes equations are discretized in space on a non-staggered grid using second order accurate finite difference formulae. An interpolation scheme is used for grid points adjacent to the immersed boundary to determine the velocity and pressure at these points. This immersed technique using bilinear interpolation approach is used to simulate flow around moving boundaries in both cartesian and body fitted co-ordinates. The discrete momentum equations are integrated in time by using a four-stage explicit Runge-Kutta scheme. The ability of this method to simulate flows around rigid stationary bodies is verified by validating flows past a circular cylinder and a NACA0012 airfoil on fixed Cartesian grids. Then the turbulent flow around a NACA0012 airfoil is simulated by using two different kinematic models to actively control the motion of the flap. For these flows the grid around the airfoil is a body conforming C-Grid where as the unsteady motion of the flap is modeled by introducing appropriate forcing on the momentum equation. The results from these two models are discussed. The results show a reduction in the average drag coefficient for the all the models compared to the baseline NACA0012 airfoil. The average lift coefficients calculated using models I exhibited a reduction in the lift coefficient compared to the baseline NACA0012 airfoil where as model II showed lift enhancement.

Implicit Large-Eddy Simulations of Rough-Wall Turbulent Channel Flows

A rough wall layer modeling approach is developed for implicit large-eddy simulations (ILES) of high Reynolds number turbulent flows over rough walls. The fluid dynamics of the averaged flow in the near-wall rough layer is modeled using the Brinkman equation, while the outer free flow region is resolved using ILES. Fully developed turbulent channel flows with rod and mesh roughness on both walls are calculated. The computational results of the mean streamwise velocity, fluctuating velocity, one-dimensional streamwise energy spectra, and the three-dimensional instantaneous flow structures are presented. The results show that the present rough wall layer modeling approach for ILES predicts well the log-law mean velocity, and fluctuating velocity profiles in the outer layer region. The flow structures indicate that complex three-dimensional incoherent spanwise vortical structures are formed. The quasi-streamwise structures formed above the roughness elements are locally interrupted by modeled roughness effects or other incoherent structures, and as a result, a high-energy layer is developed above the roughness elements.

Numerical Study of Roughness Effects on a NACA 0012 Airfoil Using a New Second-Order Closure of the Rough Wall Layer Modeling

The aerodynamic characteristics of a rough NACA 0012 airfoil with different surface roughness conditions at various angles of attack are investigated numerically. A new flow physics-based surface roughness modeling approach with a second-order turbulence closure developed for high Reynolds number Reynolds-averaged Navier-Stokes equations type of calculations is used. The fluid dynamics of the volume-averaged flow in the near-wall rough layer is modeled by using the Brinkman equation. The resulting parameters, such as porosity, allow a direct inclusion of the geometric characteristics of the roughness element and their pattern in the model equations. The computational results, including the surface pressure, lift, and drag coefficients, and mean velocity profiles, are presented. The results show that this new second-order closure of the rough wall layer modeling approach predicts well the effects of surface roughness on the aerodynamic characteristics of a rough NACA 0012 airfoil before the separation occurs.