Turbulent time-events in channel with rough walls

This brief communication quantifies the time-events that contribute to the dynamics of wall-bounded flows with rough walls. Lumley’s Proper Orthogonal Decomposition (POD) methodology has been used to extract the energetic modes of the flow. We have used the concept of entropy, a representation of lack of organization in the flow, to represent the extent of spread of turbulent kinetic energy to higher modes. The rough-wall dynamics is dominated by fast activity (short time period) propagating modes and slow activity (long time period) roll modes. A single dominant timescale has been captured for all the propagating modes in flows over smooth walls; multiple dominant timescales representing various vortex shedding events are captured for rough walls. Variable-interval time averaging technique has been used to obtain the bursting frequency. The bursting frequency of rough-wall turbulence is higher compared to smooth-wall turbulence, suggesting that roughness enhances turbulence production activity. Another insightful observation for rough walls revealed by our study is that the vortex shedding frequency of roughness elements is much higher compared to the bursting frequency of rough-wall turbulence. POD provides a straightforward method to extract the natural frequency of shed vortices due to roughness, an important dynamical activity in rough-wall turbulent boundary layers.     

Plane-Couette flow between smooth and rough walls

A novel approach is utilized to acquire new experimental information on plane-Couette flow. To this end a rigid plate, functioning as the moving wall, is propelled through air by the carriage of a towing channel, and the fixed wall is a stationary bench. It is shown that, irrespective of the state of the walls, the critical Reynolds number, expressed in terms of relative wall velocity and wall spacing, is about 1,200. Findings support the notion of universality of turbulent flow structure in the wall region, but shed doubt on the conjecture of homogeneous shear-flow turbulence in the core.     

Anisotropy of the Reynolds stresses in a turbulent boundary layer on a rough wall

The measured anisotropy invariants of the Reynolds stress tensor in a self-preserving rough wall turbulent boundary layer indicate that the anisotropy is significantly smaller than in a smooth wall layer.RAA is grateful to Dr. P. Spalart for the DNS data. The support of the Australian Research Council is acknowledged.     

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.     

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.     

Smooth and rough turbulent boundary layers at high Reynolds number

A 2-D turbulent boundary layer experiment with zero pressure gradient (ZPG) has been carried out over a rough and a smooth surface using two cross hot-wire probes. Wind tunnel speeds of 10 m/s and 20 m/s were set up in order to investigate the effects of the upstream conditions and the Reynolds number on the downstream flow. For a given set of upstream conditions, such as the wind tunnel speed, trip wire size and location, the three components of the velocity field were measured from about 14 m from the inlet of the wind tunnel to 30 m downstream. This experiment is unique because it achieves Reynolds numbers as high as R120,000, for which measurements of the mean velocity are reported. It is shown that by fixing the upstream conditions, the mean deficit profiles collapse with the freestream velocity, , but to different curves depending on the upstream conditions and surface roughness. Moreover, the effects of the upstream conditions, the Reynolds number, and roughness are completely removed from the outer flow when the mean deficit profiles are normalized by the Zagarola/Smits scaling, . Consequently, the true asymptotic profile in the turbulent boundary layer is found in ZPG flow regardless of the range of Reynolds number, surface conditions and initial conditions.     

Turbulence statistics in rotating channel flows with rough walls

We performed direct simulations of channel flow subjected to rotation about a spanwise axis, comparing cases with smooth and rough walls. The destabilizing effect of roughness counteracts the stabilizing effect of rotation on the cyclonic (stable) side. When the surface is rough the Reynolds stresses remain significant at all rotation rates considered, even those that results in a quasi-laminar state when the wall is smooth. The wake fluctuations result in significant dispersive stresses, which give an important contribution to the generation of turbulence on the stable side, mainly through added production of shear stresses. The dispersive stresses are mostly associated with the channeling of the flow between roughness elements.     

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.     

On the Reynolds number scaling of vorticity production at no-slip walls during vortex-wall collisions

Recently, numerical studies revealed two different scaling regimes of the peak enstrophy Z and palinstrophy P during the collision of a dipole with a no-slip wall [Clercx and van Heijst, Phys. Rev. E 65, 066305, 2002]: Z μ Re^0.8{Z\propto{\rm Re}^{0.8}} and P μ Re^2.25{P\propto {\rm Re}^{2.25}} for 5 × 10² ≤ Re ≤ 2 × 10⁴ and Z μ Re^0.5{Z\propto{\rm Re}^{0.5}} and P μ Re^1.5{P\propto{\rm Re}^{1.5}} for Re ≥ 2 × 10⁴ (with Re based on the velocity and size of the dipole). A critical Reynolds number Re _c (here, Re_c ? 2×10⁴{{\rm Re}_c\approx 2\times 10^4}) is identified below which the interaction time of the dipole with the boundary layer depends on the kinematic viscosity ν. The oscillating plate as a boundary-layer problem can then be used to mimick the vortex-wall interaction and the following scaling relations are obtained: Z μ Re^3/4, P μ Re^9/4{Z\propto{\rm Re}^{3/4}, P\propto {\rm Re}^{9/4}} , and dP/dt μ Re^11/4{\propto {\rm Re}^{11/4}} in agreement with the numerically obtained scaling laws. For Re ≥ Re _c the interaction time of the dipole with the boundary layer becomes independent of the kinematic viscosity and, applying flat-plate boundary-layer theory, this yields: Z μ Re^1/2{Z\propto{\rm Re}^{1/2}} and P μ Re^3/2{P\propto {\rm Re}^{3/2}}.     

Turbulent boundary layer at the initial portion of a pipe with rough walls

The development of a turbulent boundary layer at the initial portion of a pipe with rough walls is considered in the framework of the boundary-layer theory. It is shown that the consideration of roughness can be carried out by introducing into the standard law of friction a function which takes into account this factor. An experimental investigation is carried out on a test portion of a pipe with natural roughness whose relative value equals 10^–3. The range of Reynolds numbers is 5.1 · 10⁴-3.4 · 10⁵. The method of calculation proposed here leads to results which satisfactorily agree with the data of the experimental investigation.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 109–116, September–October, 1971.     

Fully explicit and self-consistent algebraic Reynolds stress model

A fully explicit, self-consistent algebraic expression (for Reynolds stress) which is the exact solution to the Reynolds stress transport equation in the weak-equilibrium limit for two-dimensional mean flows for all linear and some quasi-linear pressure-strain models, is derived. Current explicit algebraic Reynolds stress models derived by employing the weak-equilibrium assumption treat the production-to-dissipation (P/) ratio as a constant, resulting in an effective viscosity that can be singular away from the equilibrium limit. In this paper the set of simultaneous algebraic Reynolds stress equations in the weak-equilibrium limit are solved in the full nonlinear form and the eddy viscosity is found to be nonsingular. Preliminary tests indicate that the model performs adequately, even for three-dimensional mean-flow cases. Due to the explicit and nonsingular nature of the effective viscosity, this model should mitigate many of the difficulties encountered in computing complex turbulent flows with the algebraic Reynolds stress models.This research was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-19480.     

An explicit algebraic Reynolds stress model in turbulence

A new algebraic Reynold stress model is constructed with recourse to the realizability constraints. Model coefficients are made a function of strain and vorticity invariants through calibration by reference to homogeneous shear flow data. The anisotropic production in near‐wall regions is accounted for substantially by modifying the model constants C_{ε(1, 2)} and adding a secondary source term in the ε equation. Hence, it reduces the kinetic energy and length scale magnitudes to improve prediction of adverse pressure gradient flows, involving flow separation and reattachment. To facilitate the evaluation of the turbulence model, some extensively used benchmark cases in the turbulence modelling are convoked. The comparisons demonstrate that the new model maintains qualitatively good agreement with the direct numerical simulation (DNS) and experimental data. Copyright © 2006 John Wiley & Sons, Ltd.     

Reynolds stress and vorticity in turbulent wall flows

Experimental measurements in a boundary layer and a large-eddy simulation of plane channel flow have been used to study the dynamics of vorticity and mass transport in the nearwall region. It was found that Reynolds stress generation occurs in the vicinity of quasi-streamwise vortices, and that smoke particles tend to be ejected from the wall near these vortical structures.     

Computation of recirculating swirling flow with the GLM Reynolds stress closure

A Reynolds stress closure based on the generalized Langevin model (GLM), developed by Haworth and Pope^[3,4], is applied to the flow calculation with swirl-induced recirculation. The purpose of the work is to assess the performance of this model under the complex flow conditions caused by the presence of strong swirl which gives rise to both unconventional recirculation in the vicinity of the symmetry axis and strong anisotropy in the turbulence field. Comparison of the computational results are made both with the experimental data of Roback and Johnson^[11] and the computational results obtained with the typical isotropization of production model (IPM) and thek-ε type Boussinesq viscosity model.     

Explicit algebraic Reynolds stress model for shock-dominated flows

Shock waves drastically alter the nature of Reynolds stresses in a turbulent flow, and conventional turbulence models cannot reproduce this effect. In the present study, we employ explicit algebraic Reynolds stress model (EARSM) to predict the Reynolds stress anisotropy generated by a shockwave. The model by Wallin and Johansson (2000) is used as the baseline model. It is found to over-predict the post-shock Reynolds stresses in canonical shock turbulence interaction. The budget of the transport equation of Reynolds stresses computed using linear interaction analysis shows that the unsteady shock distortion mechanism and the pressure–velocity correlations are important. We propose improvement to the baseline model using linear interaction analysis results and redistribute the turbulent kinetic energy between the principle Reynolds stresses. The new model matches DNS data for the amplification of Reynolds stresses across the shock and their post-shock evolution, for a range of Mach numbers. It is applied to oblique shock/boundary-layer interaction at Mach 5. Significant improvements are observed in predicting surface pressure and skin friction coefficient, with respect to experimental measurements.     

An iterative data-driven turbulence modeling framework based on Reynolds stress representation

Data-driven turbulence modeling studies have reached such a stage that the basic framework is settled, but several essential issues remain that strongly affect the performance. Two problems are studied in the current research: (1) the processing of the Reynolds stress tensor and (2) the coupling method between the machine learning model and flow solver. For the Reynolds stress processing issue, we perform the theoretical derivation to extend the relevant tensor arguments of Reynolds stress. Then, the tensor representation theorem is employed to give the complete irreducible invariants and integrity basis. An adaptive regularization term is employed to enhance the representation performance. For the coupling issue, an iterative coupling framework with consistent convergence is proposed and then applied to a canonical separated flow. The results have high consistency with the direct numerical simulation true values, which proves the validity of the current approach.     

An extension of the second moment closure model for turbulent flows over macro 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.