Proposed Wall Function Models for Heat Transfer around a Cylinder with Rough Surface in Cross Flow

Abstract

This paper proposes wall function models to simulate the heat transfer around a cylinder in cross flow with an isothermal and rough surface. The selected case has similitudes with aircraft wing icing: the ice roughness shape, height and distribution. Moreover, the flow is somewhat similar to that found on iced airfoil; and the surface is isothermal like when icing. The Reynolds-Averaged Navier-Stokes, turbulence, energy and mass conservation 7-equation system is solved by two Computational Fluid Dynamics (CFD) codes. To represent accurately the effects of roughness on the heat transfer, the present authors had to modify both codes and to propose new thermal wall functions for them. In addition, it was implemented a momentum wall function that is not so common in CFD codes but it is a standard in aircraft icing simulation. Basically, the present paper is focused on presenting the simulation results improvement obtained by the implementation of thermal wall functions that also considered the effect thermal resistance of viscous sub-layer on convective heat transfer. The numerical results were compared to experimental data of heat transfer around cylinders with an isothermally heated surface and equivalent sand grain roughness height of K s /D = 900 • 10 −5. For the selected case, the flow regime was trans-critical at Reynolds numbers Re = u e • D/ν = 2.2 • 10 5. Due to significant blockage effects present in the experimental data, the tunnel walls were also meshed and simulated. In sum, the implementation into CFD codes was considered adequate because the results were close to experimental data around the whole cylinder surface, not only along the leading edge or the separated region. The results accuracy were improved when compared with CFD factory original models. However, the results indicate that further works on wall functions and their validation are required before using CFD in wing aircraft icing.

Modeling of Ice Accretion over Aircraft Wings Using a Compressible OpenFOAM Solver

“…International Journal of Aerospace Engineering rough. Therefore, the thermal wall function derived by Lima da Silva et al [15] has been implemented to study the roughness effect, in which the roughness effect is considered by using the momentum and heat transfer analogy factor. Here, α t is the turbulent thermal diffusivity.…”

Experimental and Numerical Determination of the Head Loss of a Pressure Driven Flow through an Unlined Rock-Blasted Tunnel

“…The turbulent eddy viscosity is then computed from these two parameters. The OpenFOAM kqRWallFunction [35] was used as boundary condition at the wall for the k equation and the epsilonWallFunction [35] was used for ε.…”

“…The main difference between the standard model and what was used in the current project was the treatment of the tunnel walls. The wall friction for rough walls was based on the nutkRoughWallFunction in OpenFOAM [35] where a reduced eddy viscosity ν Tw close to the wall was used:…”

Numerical Simulation of Roughness Effects of Ice Accretion on Wind Turbine Airfoils

“…Thus RWFs should provide additional models that account for roughness. Recently, Da Silva et al [13] applied a new ν t wall function base on the work of Suga et al [14]. In addition, Knopp et al [15] and Chedevergne and Aupoix [16] provided k and ω wall functions that are capable to adapt for the presence of roughness on the surface.…”

“…The studied ice profiles were collected from the site and tested in a wind tunnel after being molded and attached to the airfoil. In this work, three different RWFs were implemented in OpenFOAM ® v6 [17] and compared: Knopp et al [15] RWF, which will be referred to in this work as DLR-RWF, Da Silva et al [13] RWF, which will be referred to as Momentum-RWF, and Chedevergne and Aupoix [16] RWF fitted to Colebrook's experimental results, which will be referred as Colebrook-RWF.…”