Session G21: Boundary Layer Flows over Rough Surfaces I

Direct numerical simulation of turbulent forced convection with roughness

We present direct numerical simulations of turbulent forced convection over explicitly gridded three-dimensional sinusoidal roughness. The minimal channel is used to circumvent the high cost of simulating high Reynolds number flows, in which only the near-wall flow is captured. As the roughness Reynolds number, k⁺, is increased, the Hama roughness function, ΔU⁺, tends towards the fully rough asymptote which scales with the logarithm of k⁺. In this fully rough regime, the skin-friction coefficient is constant with bulk Reynolds number, Re_b. Meanwhile, the temperature difference between smooth- and rough-wall flows, ΔΘ⁺, appears to tend towards a constant value. This corresponds to the Stanton number (the temperature analogue of the skin-friction coefficient) monotonically decreasing with Re_b in the fully rough regime. While Reynolds analogy, or similarity between momentum and heat transfer, breaks down for the bulk skin-friction and heat-transfer coefficients, similar distribution patterns between the heat flux and viscous component of the wall shear stress is observed. Instantaneous visualizations of the temperature field show a thin thermal diffusive sublayer following the roughness geometry in the fully rough regime, resembling the viscous sublayer of a contorted smooth wall.   

Wall-Roughness Eddy Viscosity for Reynolds-Averaged Closures

An approach to modeling the effect of rough surfaces on turbulent boundary-layer flow is presented.  It is based on the concept of a rough-wall eddy viscosity, in which the pressure and viscous drag forces which arise on account of flow past roughness elements are recast as an equivalent viscous shear force
within the roughness sublayer at the surface.  This shear force can be modeled as an apparent body force or as a wall-roughness eddy viscosity and carries information on both the flow Reynolds number and the roughness height.  The modeling approach is developed and evaluated as part of k--ε and k--ε--v^' closures.   When the wall-roughness eddy viscosity is modeled in proportion to k⁺_s^3/4 where k⁺_s is the sand-grain roughness in wall units, it yields predictions of drag coefficients which are in excellent agreement with those from reference data for flow in rough-walled pipes, over a wide range of surface-roughness heights and Reynolds numbers.  Its predictions are also in good agreement with experimental data for zero and favorable pressure gradient boundary layers over fully-rough surfaces.   

Direct Numerical Simulation of Turbulent Flow over Random Roughness

Direct numerical simulations (DNS) are performed to study the effects of a random rough wall on turbulent channel flow at $Re_{\tau}=400$ and $Re_{\tau}=600$. The surface geometry matches the experiments of Flack and Schultz (private communication). The skin friction coefficient of the DNS shows good agreement with the experimental results. The mean velocity profiles and velocity fluctuations are compared to smooth channel flow. Pressure fluctuations are more intense in the roughness layer. The mean momentum budget is examined. It is seen that roughness causes the transition from viscous to inertial dominance to occur closer to the wall compared to a smooth wall.   

Direct numerical simulations of Taylor-Couette turbulence: dynamics of the fully rough regime

Due to its abundance in nature and industry, the study of turbulent flows over rough surfaces is of paramount importance. The key question is how any rough geometry maps to its fluid dynamic behavior. However, the study of open systems is hampered by accurate measurements of the skin-friction drag and the presence of very long spatial structures.  In this research, we employ Direct Numerical Simulations (DNSs) of a closed system, Taylor-Couette flow. Whereas before we have focused on transitionally rough surfaces, here we focus on the local and global fluid flow response over fully rough surfaces. In particular we study the azimuthal (streamwise) velocity and angular velocity profiles for varying friction Reynolds number and constant viscous roughness heights.
  

Investigation of secondary flows in turbulent pipe flows with three-dimensional sinusoidal walls

The occurrence of secondary flows is systematically investigated via Direct Numerical Simulations (DNSs) of turbulent flow in a rough wall pipe at friction Reynolds numbers of 540. In this study, the peak-to-trough height of the roughness elements, which consist of three-dimensional sinusoidal roughness, is fixed at 120 viscous units while the wavelength of the roughness elements is varied. The solidity or effective slope (ES) of the roughness ranges from the sparse regime (ES = 0.18 with a viscous roughness wavelength, λ⁺ of 848) to the closely packed roughness/dense regime (ES = 0.72, λ⁺ = 212). The time-independent dispersive stresses, which arise due to the stationary features of the flow, are analysed and are found to increase with increasing roughness wavelength. These dispersive stresses are related to the occurrence of secondary flows and are maximum within the roughness canopy. Above the crest of the roughness elements, the dispersive stresses reduce to zero at wall-normal heights greater than half of the roughness wavelength. This study has found that the size and wall-normal extent of the secondary flows scales with the roughness wavelength and can reach wall-normal heights of almost half of the pipe radius.