Wall-resolved large-eddy simulation of turbulent channel flows with rough walls

Turbulent flows over rough surfaces widely exist in nature and industry. Investigating its mechanism is of theoretical and practical significance. In this work we simulate the turbulent channel flow with rough walls using large-eddy simulation with rough elements resolved using the curvilinear immersed boundary method and compare the results obtained in this work with those in the paper by Yuan and Piomelli( J. Fluid Mech., vol. 760, pp. R1, 2014), where the volume of fluid method was employed for modeling rough elements. The mean streamwise velocity profiles predicted by the two methods agree well with each other. Differences in Reynolds stresses and dispersive stresses are observed, which are attributed to the different approaches in dealing with the complex geometry of the rough surface.     

Parallel spectral-element—Fourier simulation of turbulent flow over riblet-mounted surfaces

The flow in a channel with its lower wall mounted with streamwise V-shaped riblets is simulated using a highly efficient spectral-element—Fourier method. The range of Reynolds numbers investigated is 500 to 4000, which corresponds to laminar, transitional, and turbulent flow states. Our results suggest that in the laminar regime there is no drag reduction, while in the transitional and turbulent regimes drag reduction up to 10% exists for the riblet-mounted wall in comparison with the smooth wall of the channel. For the first time, we present detailed turbulent statistics in a complex geometry. These results are in good agreement with available experimental data and provide a quantitative picture of the drag-reduction mechanism of the riblets.This work was supported by National Science Foundation Grants CTS-8906432, CTS-8906911, and CTS-8914422, AFOSR Grant No. AFOSR-90-0124, and DARPA Grant No. N00014-86-K-0759. The computations were performed on the Cray Y/MP's of NAS at NASA Ames and the Pittsburgh Supercomputing Center, and on the Intel 32-node iPSC/860 hypercube at Princeton University.     

Implicit large-eddy simulation applied to turbulent channel flow with periodic constrictions

The subgrid-scale (SGS) model in a large-eddy simulation (LES) operates on a range of scales which is marginally resolved by discretization schemes. Accordingly, the discretization scheme and the subgrid-scale model are linked. One can exploit this link by developing discretization methods from subgrid-scale models, or the converse. Approaches where SGS models and numerical discretizations are fully merged are called implicit LES (ILES). Recently, we have proposed a systematic framework for the design, analysis, and optimization of nonlinear discretization schemes for implicit LES. In this framework parameters inherent to the discretization scheme are determined in such a way that the numerical truncation error acts as a physically motivated SGS model. The resulting so-called adaptive local deconvolution method (ALDM) for implicit LES allows for reliable predictions of isotropic forced and decaying turbulence and of unbounded transitional flows for a wide range of Reynolds numbers. In the present paper, ALDM is evaluated for the separated flow through a channel with streamwise-periodic constrictions at two Reynolds numbers Re = 2,808 and Re = 10,595. We demonstrate that, although model parameters of ALDM have been determined for isotropic turbulence at infinite Reynolds number, it successfully predicts mean flow and turbulence statistics in the considered physically complex, anisotropic, and inhomogeneous flow regime. It is shown that the implicit model performs at least as well as an established explicit model.      

Direct numerical simulation of turbulent heat transfer on the Reynolds analogy over irregular rough surfaces

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.     

Two-layer turbulent flow over a rough rotating surface

A model of turbulent incompressible fluid flow over a rough surface under the action of the Coriolis force with a turbulent transfer coefficient corresponding to the Prandtl mixing length is proposed. A solution of the problem, asymptotic in the small Coriolis parameter, is presented for horizontally uniform steady-state flow. It is shown that for a small Coriolis parameter the velocity profile and the turbulent transfer coefficient can differ substantially from the limiting expressions known from Prandtl theory. The smaller the roughness coefficient, the greater the difference.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 61–67, July–August, 1995.     

Error of large-eddy simulation in the wall pressure fluctuation of a turbulent channel flow

We analyze the error of large-eddy simulation(LES) in wall pressure fluctuation of a turbulent channel flow. To separate different sources of the error, we conduct both direct numerical simulations(DNS)and LES, and apply an explicit filter on DNS data to obtain filtered DNS(FDNS) data. The error of LES is consequently decomposed into two parts: The first part is the error of FDNS with respect to DNS,which quantifies the influence of the filter operation. The second part is the difference between LES and FDNS induced by the error of LES in velocity field. By comparing the root-mean-square value and the wavenumber-frequency spectrum of the wall pressure fluctuation, it is found that the inaccuracy of the velocity fluctuations is the dominant source that induces the error of LES in the wall pressure fluctuation.The present study provides a basis on future LES studies of the wall pressure fluctuation.     

Large eddy simulation of droplet dispersion for inhomogeneous turbulent wall flow

A large eddy simulation (LES) coupled with a Lagrangian stochastic model has been applied to the study of droplet dispersion in a turbulent boundary layer. Droplets are tracked in a Lagrangian way. The velocity of the fluid particle along the droplet trajectory is considered to have a large-scale part and a small-scale part given by a modified three-dimensional Langevin model using the filtered subgrid scale (SGS) statistics. An appropriate Lagrangian correlation timescale is considered in order to include the influences of gravity and inertia. Two-way coupling is also taken into account. The inter-droplet collision has been introduced as the main mechanism of secondary breakup. A stochastic model for breakup has been generalized for coalescence simulation, thereby two phenomena, coalescence and breakup are simulated in the framework of a single stochastic model. The parameters of this model, selectively for coalescence and for breakup, are computed dynamically by relating them to the local resolved properties of the dispersed phase compared to the main fluid. The model is validated by comparison with an agglomeration model and with experimental results on secondary breakup. The LES coupled with Lagrangian particle tracking and the model for droplet coalescence and breakup is applied to the study of the atmospheric dispersion of wet cooling tower plumes. The simulations are done for different droplet size distributions and volume fractions. We focused on the influence of these parameters on mean concentration, concentration variance and mass flux profiles.     

Two-point statistics of coherent structures in turbulent flow over riblet-mounted surfaces

Direct numerical simulations (DNS) of turbulent flow over a drag-reducing and a drag-increasing riblet configuration are performed. Three-dimensional two-point statistics are presented for the first time to quantify the interaction of the riblet surfaces with the coherent, energy-bearing eddy structures in the near-wall region. Results provide statistical evidence that the averaged organization of the streamwise vortices in the drag-reducing case is lifted above the riblet tip, while in the drag-increasing case the streamwise vortices are embedded further into the riblet cove. In the spanwise direction, the cores of the streamwise vortices over the riblet surfaces are shown to be closer to each other than those for flow over the smooth wall, and wider riblet spacing leads to more reduction on their spanwise distances. In the cases with riblets the streamwise vortices have longer streamwise lengths, but their inclination angles do not change much.     

Temporal large-eddy simulation of unstratified and stably stratified turbulent channel flows

Recently, Pruett et al. [Pruett, C.D., Gatski, T.B., Grosch, C.E., Thacker, W.D., 2003. The temporally filtered Navier–Stokes equations: properties of the residual stress. Phys. Fluids 15, 2127–2140] proposed an approach to large-eddy simulation (LES) based on time-domain filtering; their approach was termed temporal large-eddy simulation or TLES. In a continuation of their work, Pruett and collaborators tested their methodology by successfully performing TLES of unstratified turbulent channel flow up to Reynolds number of 590 (based on channel half-height and friction velocity) [Pruett, C.D., Thomas, B.C., Grosch, C.E., Gatski, T.B., 2006. A temporal approximate deconvolution model for LES. Phys. Fluids 18, 028104, 4p]. Here, we carefully analyze the TLES methodology in order to understand the role of its key components and in the process compare TLES to more traditional approaches of spatial LES. Furthermore, we extend the methodology to stably stratified turbulent channel flow.     

The magnetic field in inhomogeneous turbulent flow

We consider a particular model of magnetohydrodynamic turbulents. The most fundamental assumption we make is that the velocity correlation time is negligible. By using a selective summation of the perturbation theory series an exact equation for the magnetic field is obtained when the mean square value of the velocity depends on coordinates, i.e., when the turbulence isinhomogeneous. The result makes it possible to obtain the macroscopic Maxwell's equations, i.e., the equations for the large-scale components of the electromagnetic field.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 12–18, January–February, 1971.In conclusion, the author thanks R. Z. Sagdeev and V. E. Zakharov for a discussion of the results.     

A dynamic global-coefficient mixed subgrid-scale model for large-eddy simulation of turbulent flows

A dynamic global-coefficient mixed subgrid-scale eddy-viscosity model for large-eddy simulation of turbulent flows in complex geometries is developed. In the present model, the subgrid-scale stress is decomposed into the modified Leonard stress, cross stress, and subgrid-scale Reynolds stress. The modified Leonard stress is explicitly computed assuming a scale similarity, while the cross stress and the subgrid-scale Reynolds stress are modeled using the global-coefficient eddy-viscosity model. The model coefficient is determined by a dynamic procedure based on the global-equilibrium between the subgrid-scale dissipation and the viscous dissipation. The new model relieves some of the difficulties associated with an eddy-viscosity closure, such as the nonalignment of the principal axes of the subgrid-scale stress tensor and the strain rate tensor and the anisotropy of turbulent flow fields, while, like other dynamic global-coefficient models, it does not require averaging or clipping of the model coefficient for numerical stabilization. The combination of the global-coefficient eddy-viscosity model and a scale-similarity model is demonstrated to produce improved predictions in a number of turbulent flow simulations.     

Adverse pressure gradient turbulent flows over rough walls

An experimental study of a fully developed turbulent channel flow and an adverse pressure gradient (APG) turbulent channel flow over smooth and rough walls has been performed using a particle image velocimetry (PIV) technique. The rough walls comprised two-dimensional square ribs of nominal height, k = 3 mm and pitch, p = 2k, 4k and 8k. It was observed that rib roughness enhanced the drag characteristics, and the degree of enhancement increased with increasing pitch. Similarly, rib roughness significantly increased the level of turbulence production, Reynolds stresses and wall-normal transport of turbulence kinetic energy and Reynolds shear stress well beyond the roughness sublayer. On the contrary, the distributions of the eddy viscosity, mixing length and streamwise transport of turbulence kinetic energy and Reynolds shear stress were reduced by wall roughness, especially in the outer layer. Adverse pressure gradient produced a further reduction in the mean velocity (in comparison to the results obtained in the parallel section) but increased the wall-normal extent across which the mean flow above the ribs is spatially inhomogeneous in the streamwise direction. APG also reinforced wall roughness in augmenting the equivalent sand grain roughness height. The combination of wall roughness and APG significantly increased turbulence production and Reynolds stresses except in the immediate vicinity of the rough walls. The transport velocities of the turbulence kinetic energy and Reynolds shear stress were also augmented by APG across most part of the rough-wall boundary layer. Further, APG enhanced the distributions of the eddy viscosity across most of the boundary layer but reduced the mixing length outside the roughness sublayer.     

Eigensensitivity analysis of subgrid-scale stresses in large-eddy simulation of a turbulent axisymmetric jet

The study of complex turbulent flows by means of large-eddy simulation approaches has become increasingly popular in many scientific and engineering applications. The underlying filtering operation of the approach enables to significantly reduce the spatial and temporal resolution requirements by means of representing only large-scale motions. However, the small-scale stresses and their effects on the resolved flow field are not negligible, and therefore require additional modeling. As a consequence, the assumptions made in the closure formulations become potential sources of model-form uncertainty that can impact the quantities of interest. The objective of this work, thus, is to perform a model-form sensitivity analysis in large-eddy simulations of an axisymmetric turbulent jet following an eigenspace-based strategy recently proposed. The approach relies on introducing perturbations to the decomposed subgrid-scale stress tensor within a range of physically plausible values. These correspond to discrepancy in magnitude (trace), anisotropy (eigenvalues) and orientation (eigenvectors) of the normalized, small-scale stresses with respect to a given tensor state, such that propagation of their effects can be assessed. The generality of the framework with respect to the six degrees of freedom of the small-scale stress tensor makes it also suitable for its application within data-driven techniques for improved subgrid-scale modeling.     

A turbulent boundary layer over a two-dimensional rough wall

Particle image velocimetry (PIV) measurements and planar laser induced fluorescence (PLIF) visualizations have been made in a turbulent boundary layer over a rough wall. The wall roughness consisted of square bars placed transversely to the flow at a pitch to height ratio of λ/k = 11 for the PLIF experiments and λ/k = 8 and 16 for the PIV measurements. The ratio between the boundary layer thickness and the roughness height k/δ was about 20 for the PLIF and 38 for the PIV. Both the PLIF and PIV data showed that the near-wall region of the flow was populated by unstable quasi-coherent structures which could be associated to shear layers originating at the trailing edge of the roughness elements. The streamwise mean velocity profile presented a downward shift which varied marginally between the two cases of λ/k, in agreement with previous measurements and DNS results. The data indicated that the Reynolds stresses normalized by the wall units are higher for the case λ/k = 16 than those for λ/k = 8 in the outer region of the flow, suggesting that the roughness density effects could be felt well beyond the near-wall region of the flow. As expected the roughness disturbed dramatically the sublayer which in turn altered the turbulence production mechanism. The turbulence production is maximum at a distance of about 0.5k above the roughness elements. When normalized by the wall units, the turbulence production is found to be smaller than that of a smooth wall. It is argued that the production of turbulence is correlated with the form drag.     

Unsteady flow over a rough bottom

The unsteady motion of an ideal incompressible fluid with a free surface, developing from a state of rest, is considered. The flow is assumed to be irrotational, continuous and two-dimensional; it may be the result either of an initial disturbance of the free boundary or of a given boundary pressure distribution. The rigid boundaries of the flow region are fixed, and the free surface does not cross them at any time during the motion. The fluid is located in a uniform gravity force field and there is no surface tension. A method which in the case of localized roughness of the bottom makes it possible to find the shape of the free surface at any moment of time with predetermined accuracy is proposed. The method involves reducing the initial linear problem to a Volterra integral equation of the second kind, the kernel of this equation being a nonlocal operator. This operator has a smoothing effect, which makes it possible to reduce the solution of the initial problem to the solution of an infinite, perfect lyregular system of Volterra integral equations for a denumerable set of auxiliary functions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 111–119, November–December, 1989.The author is grateful to I. V. Sturova and B. E. Protopopov for useful discussions and criticism.     

Squeeze flow of soft solids between rough surfaces

Newtonian liquids and non-Newtonian soft solids were squeezed between parallel glass plates by a constant force F applied at time t=0. The plate separation h(t) and the squeeze-rate were measured for different amplitudes of plate roughness in the range 0.3–31 m. Newtonian liquids obeyed the relation Vh ³ of Stephan (1874) for large plate separations. Departures from this relation that occurred when h approached the roughness amplitude were attributed to radial liquid permeation through the rough region. Most non-Newtonian materials showed boundary-slip that varied with roughness amplitude. Some showed slip that varied strongly during the squeezing process. Perfect slip (zero boundary shear stress) was not approached by any material, even when squeezed by optically-polished plates. If the plates had sufficient roughness amplitude (e.g. about 30 m), boundary slip was practically absent, and the dependence of V on h was close to that predicted by no-slip theory of a Herschel-Bulkley fluid in squeeze flow (Covey and Stanmore 1981, Adams et al. 1994).     

A spatiotemporal decomposition of a fully inhomogeneous turbulent flow field

The three-dimensional orthogonal spatial modes and their temporal counterparts have been extracted from a large-eddy simulation of turbulent flow over a surface-mounted cube, using a space-time symmetric version of proper orthogonal decomposition (POD), proposed by Aubry et al. (1991). A relatively small domain of interest, located immediately above the top face of the flow obstacle, has been selected for the application of POD. Within that volume of interest, time records of the velocity field have been sampled at 6000 locations simultaneously. The space-time duality of POD can be demonstrated by deriving two alternative eigenvalue problems for either the orthogonal spatial modes or the orthogonal temporal modes. For a particular case, the choice between the two alternatives can be done on the basis of computational convenience and of data-storage requirements. The results show that the first spatiotemporal mode can be identified with the mean flow. The second spatiotemporal mode is dominated by the alternating vortex shedding from the side edges of the flow obstacle. A Fourier analysis of the second temporal mode leads to a Strouhal number of S=0.125 which corresponds to the measured Strouhal number for the vortex shedding (Martinuzzi, 1992). The third and the fourth spatiotemporal modes are connected with the rolls created at the horizontal leading edge of the cube. For the flow field investigated, the dual space-time point of view of POD is rather realistic in the sense that the first four spatiotemporal modes can actually be observed in the flow.This work is currently supported by the German Research Society (DFG), Priority Research Program, Project No. We 705/3 (Wengle /Römer). We also gratefully acknowledge the support by the Universität der Bundeswehr München (UniBwM) and by the Leibniz Computing Center of the Bavarian Academy of Sciences (LRZ).     

Experimental simulation of capillary effect on rough flat surfaces

The movement of the liquid column inside the slit was utilized to experimentally simulate the characteristics of the capillary force per unit length for different rough flat surfaces. The movement of the liquid column was achieved by continuously changing the slit interval. The maximum climb height and contact angle of the liquid column were observed during this process to study the relationship between capillary force and contact surface roughness. Based on the assumption that the microstructures on the rough surfaces are of the same form and continuously and uniformly distributed, it is shown that the capillary force per unit length under homogeneous wetting is independent of the roughness. For heterogeneous wetting, the capillary force per unit length is positively correlated with the roughness. The results also indicate that the appearance of “contact line pinning” is caused by insufficient capillary force along the direction of liquid column movement.