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We conducted a direct numerical simulation (DNS) study to investigate the impact of surface undulation steepness on rough wall turbulent heat transfer. The flow geometry was turbulent open-channel flow over three-dimensional sinusoidal rough surfaces. To examine the effects of steepness, we systematically varied the streamwise and spanwise wavelengths of the sinusoidal roughness while keeping the roughness height constant. The friction Reynolds number ranged from 180 to 600, and we considered a passive scalar with the fluid Prandtl number was 0.7, assuming air flow conditions. In the fully rough regime, the velocity roughness function is expressed as a function of the inner-scaled equivalent sand grain roughness k s + independent of steepness, whereas the steeper surfaces with shorter wavelengths result in larger temperature roughness functions at the same k s + value. Analysis of the physical mechanisms that increases the roughness function shows that the pressure drag primarily contributes to the increase in the velocity roughness function, while the temperature roughness function is mainly augmented by the roughness-induced wall heat transfer term, correlating with the steepness of the surface undulations. It is also suggested that the effective slope, which quantifies the steepness of rough surfaces, could improve the predictive accuracy of existing correlations for the temperature roughness function. • DNS of turbulent heat transfer over sinusoidal roughness is performed. • Effects of steepness of rough surfaces on turbulent heat transfer are studied. • Spatial and Reynolds averaged equations are analyzed. • Predictive model of temperature roughness function is proposed. [ABSTRACT FROM AUTHOR]

We discuss wall-modeling of turbulent heat transfer of water channel flows with temperature-dependent viscosity via direct numerical simulations. We considered a top-cooled wall (293[K]) and a bottom-heated wall (353[K]) and varied the friction Reynolds numbers from 300 to 1000. The fluid viscosity varied depending on the local fluid temperature, whereas the other physical properties were assumed to be constant. The results show that semi-local scaling based on the local viscosity and wall friction velocity reasonably accounts for the effects of variable viscosity on turbulent flows, except in the vicinity of the wall, where wall cooling intensifies the turbulent vortical motion, leading to increased semi-locally scaled eddy diffusivities compared with those near the heated wall. In the vicinity of the cooled wall, turbulent transport is enhanced by increased viscous transport, which transfers more turbulent kinetic energy toward the cooled wall. The effectiveness of semi-local scaling for wall-modeling was validated by performing a wall-modeled large-eddy simulation at R e τ = 1000 , where we incorporated the semi-local viscous length scale into the classical mixing-length model. The modified mixing-length model reasonably reproduced the effects of variable viscosity on turbulent flows. • DNS of turbulent water channel flow with temperature-dependent viscosity is performed. • Effects of temperature-dependent viscosity on turbulence is studied. • Effectiveness of semi-local scaling based on local viscosity and friction velocity is investigated. • Wall-model for variable viscosity turbulent flows is proposed and assessed. [ABSTRACT FROM AUTHOR]

• A novel second moment closure model for rough wall turbulence is developed. • Double averaging theory is applied to derive the roughness effects on turbulence. • The drag force effects of roughness on the Reynolds stress are faithfully treated. • Promising results are obtained in turbulence over rough walls. An advanced second moment closure for rough wall turbulence is proposed. In contrast to previously proposed models relying on an empirical correlation based on equivalent sand grain roughness, the proposed model mathematically derives roughness effects by applying spatial and Reynolds averaging to the governing equations. The additional terms in the momentum equations are the drag force and inhomogeneous roughness density terms. The drag force term is modeled with respect to the plane porosity and plane hydraulic diameter. The two-component limit pressure-strain model is applied to the additional pressure-strain term, which is related to the external force terms. An evaluation of turbulence over surfaces with randomly distributed semi-spheres confirms that the developed model reasonably reproduces the effects of roughness on mean velocity, Reynolds stress, and energy dissipation. Turbulence over rough surfaces of marine paint is also simulated to assess the predictive performance for higher Reynolds number turbulent flows over real rough surfaces. The developed model successfully reproduces the dependence of the Reynolds number on roughness effects. Moreover, qualitative agreement of the skin friction increase with the experimental data is confirmed. [ABSTRACT FROM AUTHOR]

• Rough wall is macroscopically modelled by the spatial averaging theory. • Spatially averaged drag force is modelled with porosity and hydraulic diameter. • Turbulence over modelled and resolved rough walls are performed by the LBM. • Randomly distributed semi-sphere cluster is considered for the rough wall. • Momentum/turbulent transports near resolved/modelled rough walls are discussed. To simulate turbulent flow over a rough wall without resolving complicated rough geometries, a macroscopic rough wall model is developed based on spatial (plane) averaging theory. The plane-averaged drag force term, which arises through averaging the Navier–Stokes equations in a plane parallel to a rough wall, can be modeled using a plane porosity and a plane hydraulic diameter. To evaluate the developed model, direct and macroscopic model simulations for turbulence over irregularly distributed semi-spheres at Reynolds number of 300 are carried out using the D3Q27 multiple-relaxation time lattice Boltzmann method. The results show that the developed model can be used to predict rough wall skin friction. The results agree quantitatively with standard turbulence statistics such as mean velocity and Reynolds stress profiles with the fully resolved DNS data. Since velocity dispersion occurs inside the rough wall and is found to contribute to turbulence energy dissipation, which the developed model cannot account for, the developed model fails to reproduce dispersion-related turbulence energy dissipation. However, it is found that the plane-averaged drag force term can successfully recover the deficiency of dispersion-related turbulence energy dissipation. [ABSTRACT FROM AUTHOR]

To clarify the effects of surface topology on the scaling of roughness effects, we conduct experiments on turbulent rough-walled channel flows from transitionally to fully rough regimes. We considered three-dimensional irregular rough surfaces with different effective slope E S , skewness factor S k , and fixed roughness height scales. The E S values are varied from 0.09 to 0.72 for positively and negatively skewed surfaces with S k = ± 0. 4. It is revealed that the transitional behavior to the fully rough regime is not influenced by S k , but rather by E S. The transition to the fully rough regime for surfaces with E S ≥ 0. 18 is insensitive to the E S values, whereas wavy surfaces with E S = 0. 09 lead to a moderate transition. The equivalent sand-grain roughness k s steeply increases with increasing E S values from 0.09 to 0.36, whereas a further increase in the E S value does not significantly influence k s. It is also found that positively skewed surfaces with S k = + 0. 4 yield larger k s values compared to surfaces with S k = − 0. 4 ; this S k effect is more pronounced for wavy surfaces with small E S values. • Turbulent flows over three-dimensional irregular rough surfaces are studied. • Particle image velocimetry and pressure measurements are performed. • Effects of the skewness and effective slope of rough surfaces on hydrodynamics are discussed. • Scaling of the roughness function and equivalent sand-grain roughness is explored. [ABSTRACT FROM AUTHOR]

To discuss the turbulent flow physics over porous walls, direct numerical simulation (DNS) of a porous-walled channel flow at the bulk Reynolds number of 3000 is performed by the D3Q27 multiple-relaxation time lattice Boltzmann method. The presently considered porous layer, whose porosity is 0.71, consists of interconnected staggered cube arrays. For understanding the influence of the wall permeability on turbulence, DNS of an impermeable rough walled channel flow is also conducted. By two-point autocorrelation, one-dimensional energy spectrum and proper orthogonal decomposition (POD) analyses, the existence and characteristics of the transverse pressure waves induced by the Kelvin–Helmholtz (K–H) instability over the porous and rough walls are elucidated. The structure, wave lengths and power spectra of the transverse waves are discussed in detail. The influence of the K–H instability on turbulence is also clarified. [ABSTRACT FROM AUTHOR]

To discuss turbulent transport processes inside porous media, high resolution large eddy simulations by the D3Q27 multiple relaxation time lattice Boltzmann method and their data analysis are performed. The focused porous medium structures are square rod arrays, staggered cube arrays, fractal cube arrays and open cell foam. Although the second moments appearing in the double averaged momentum equation in porous media are the macro-scale Reynolds stress, the micro-scale Reynolds stress and the dispersive covariance, it is found that the micro-scale Reynolds stress and the dispersive covariance become dominant in the present porous medium flows. It is also found that the turbulent anisotropy and the magnitudes of those second moments are totally different among the cases due to the porous structures. Their transport mechanisms are discussed through the budget terms of the transport equations. [ABSTRACT FROM AUTHOR]

A three-dimensional twenty-seven (D3Q27) discrete velocity multiple-relaxation-time lattice Boltzmann method is developed. The proposed scheme is validated in fully developed turbulent channel, pipe and porous medium flows through direct and large eddy simulations. The direct numerical simulation of the turbulent channel flow confirms that the present scheme is as reliable as the spectrum method for simulating turbulence. Through the large eddy simulations of the pipe and porous medium flows, the present scheme shows its satisfactory accuracy for simulating turbulent flows bounded by circular walls that is failed by the three-dimensional nineteen (D3Q19) model. [ABSTRACT FROM AUTHOR]

An advanced second-moment closure for the double-averaged turbulence equations of porous medium and vegetation flows is proposed. It treats three kinds of second moments which appear in the double-averaged momentum equation. They are the dispersive covariance, the volume averaged (total) Reynolds stress and the micro-scale Reynolds stress. The two-component-limit pressure–strain correlation model is applied to model the total Reynolds stress equation whilst a novel scale-similarity non-linear k – ε two-equation eddy viscosity model is employed for the micro-scale turbulence. For the dispersive covariance, an algebraic relation is applied. Model validation in several fully developed homogeneous porous medium flows, porous channel flows and aquatic vegetation canopy flows is performed with satisfactory agreement with the data. [ABSTRACT FROM AUTHOR]

• Interface turbulence of a porous layer flow is accurately simulated by the LBM. • Rough wall turbulence is also simulated to elucidate the permeability effects. • The porous layer is modelled by interconnected cubes. • The sizes and energy of the Kelvin–Helmholtz instability induced waves are analyzed. • Relation between turbulence quantities/structures and the K-H waves is discussed. The effect of rough surface topography on heat and momentum transfer is studied by direct numerical simulations of turbulent heat transfer over uniformly heated three-dimensional irregular rough surfaces, where the effective slope and skewness values are systematically varied while maintaining a fixed root-mean-square roughness. The friction Reynolds number is fixed at 450, and the temperature is treated as a passive scalar with a Prandtl number of unity. Both the skin friction coefficient and Stanton number are enhanced by the wall roughness. However, the Reynolds analogy factor for the rough surface is lower than that for the smooth surface. The semi-analytical expression for the Reynolds analogy factor suggests that the Reynolds analogy factor is related to the skin friction coefficient and the difference between the temperature and velocity roughness functions, and the Reynolds analogy factor for the present rough surfaces is found to be predicted solely based on the equivalent sand-grain roughness. This suggests that the relationship between the Reynolds analogy factor and the equivalent sand-grain roughness is not affected by the effective slope and skewness values. Analysis of the heat and momentum transfer mechanisms based on the spatial- and time-averaged equations suggests that two factors decrease the Reynolds analogy factor. One is the increased effective Prandtl number within the rough surface in which the momentum diffusivity due to the combined effects of turbulence and dispersion is larger than the corresponding thermal diffusivity. The other is the significant increase in the pressure drag force term above the mean roughness height. [ABSTRACT FROM AUTHOR]

• Turbulence over a porous medium is simulated by the lattice Boltzmann method. • Porous medium is modelled by piled up perforated plates. • Influence of wall permeability on turbulence statistics is extensively investigated. • The characteristics wavelength of turbulent vortex structure is discussed. A series of direct numerical simulations of turbulent porous-walled channel flows is performed to extensively investigate the influence of wall permeability on turbulence modification. The bulk mean Reynolds number is fixed at 3000, and porous media consisting of perforated plates are considered in the lower side of the channel. The mean-permeability Reynolds number is varied from 14 − 118 by varying the hole size of the perforated plates. A spectral analysis reveals the presence of two characteristic perturbation modes, namely, the streamwise perturbation mode originating from the Kelvin–Helmholtz (K–H) type of instability and the spanwise perturbation mode. When the mean permeability Reynolds number is relatively low, the streamwise perturbation model by the K–H instability is dominant, and this increases the coherence of the wall-ward turbulence motion, thus resulting in considerable turbulence enhancement. However, as the mean permeability Reynolds number increases further, the streamwise perturbations tend to decrease in strength, and the streamwise elongated high- and low-speed streaky structure, the mean spacing of which is much longer than that over a smooth wall, is developed owing to the spanwise perturbation mode. In this regime, the turbulence enhancement effect is weakened because of an increased slippage velocity at the porous interface. [ABSTRACT FROM AUTHOR]

Abstract: The performance of the analytical wall-function (AWF) of Craft et al. [Craft, T.J., Gerasimov, A.V., Iacovides, H., Launder, B.E., 2002, Progress in the generalisation of wall-function treatments. Int. J. Heat Fluid Flow 23, 148–160.] is improved for predicting turbulent heat transfer in recirculating and impinging flows. Since constant parameters of the eddy viscosity formula were used to derive the AWF, the prediction accuracy of the original AWF tends to deteriorate in complex flows where those parameters need changing according to the local turbulence. To overcome such shortcomings, the present study introduces a functional behaviour on the strain parameter into the coefficient of the eddy viscosity of the AWF. The presently modified version of the AWF is validated in turbulent heat transfer of pipe flows, channel flows, back-step flows, pipe flows with abrupt expansion and plane impinging slot jets. The results confirm that the present modification successfully improves the performance of the original AWF for all the flows and heat transfer tested. [Copyright &y& Elsevier]