Wall-bounded Turbulent Flows Research Articles

Spatial resolution issues in rough wall turbulence

The question whether spatial resolution effects should be accounted for when performing hot-wire (or particle image velocimetry) measurements in turbulent wall-bounded flows over rough surfaces in the fully rough regime is addressed and answered by exploiting an existing direct numerical simulation database of open-channel flows at Re_tau =500 over a rough surface consisting of randomly distributed roughness elements. The results show sizeable attenuation effects of the streamwise velocity fluctuation intensity, similar to smooth-wall flows with up to 70% for a wire width of around 100 viscous units. A suitable correction scheme is applied to successfully compensate for the spatial resolution effects. Both results indicate that spatial resolution effects are relevant also in fully rough flows and can be corrected a posteriori when the state-of-the-art criteria on sensor size cannot be achieved in experiments.Graphical

An eddy-viscosity model for turbulent flows of Herschel–Bulkley fluids

This article presents a new turbulence closure based on the k-ω SST model for predicting turbulent flows of Herschel–Bulkley fluids, including Bingham and power-law fluids. The model has been calibrated with direct numerical simulations (DNS) data for fully-developed pipe flow of shear-thinning and viscoplastic fluids. The new model shows good agreement in the mean velocity, average viscosity, mean shear stress budget and friction factor. The latter compares well also against correlations from the literature for a wide range of Reynolds numbers. With the new model, improvements are also observed in the iterative convergence, which is often difficult for calculations with yield-stress fluids. Additionally, three eddy-viscosity models for Newtonian fluids, namely the k-ω SST, k-kL and Spalart–Allmaras model, have been tested on turbulent Herschel–Bulkley flows. Results show that (i) the new model produces the best prediction; (ii) the standard SST model may be considered for simulations of weakly shear-thinning/viscoplastic fluids at high Reynolds numbers; (iii) the k-kL and the Spalart–Allmaras models appear to be unsuitable for turbulent Herschel–Bulkley flows. The new model is simple and appealing for engineering applications concerned with turbulent wall-bounded flows and is presented in a formulation that can be easily adapted to other generalised Newtonian fluids.

Linear instability and resonance effects in large-scale opposition flow control

Opposition flow control is a robust strategy that has been proved effective in turbulent wall-bounded flows. Its conventional set-up consists of measuring wall-normal velocity in the buffer layer and opposing it at the wall. This work explores the possibility of implementing this strategy with a detection plane in the logarithmic layer, where control could be feasible experimentally. We apply control on a channel flow at $Re_\tau = 932$ , only on the eddies with relatively large wavelengths ( $\lambda / h > 0.1$ ). Similarly to the buffer layer opposition control, our control strategy results in a virtual-wall effect for the wall-normal velocity, creating a minimum in its intensity. However, it also induces a large response in the streamwise velocity and Reynolds stresses near the wall, with a substantial drag increase. When the phase of the control lags with respect to the detection plane, spanwise-homogeneous rollers are observed near the channel wall. We show that they are a result of a linear instability. In contrast, when the control leads with respect to the detection plane, this instability is inactive and oblique waves are observed. Their wall-normal profiles can be predicted linearly as a response of the turbulent channel flow to a forcing with the advection velocity of the detection plane. The linearity, governing the flow, opens a possibility to affect large scales of the flow in a controlled manner, when enhanced turbulence intensity or mixing is desired.

Rescaling the near-wall predictive model for passive scalars in turbulent channel flow

The predictive model for near-wall velocity fluctuations [I. Marusic, R. Mathis, and N. Hutchins, “Predictive model for wall-bounded turbulent flow,” Science 329, 193–196 (2010)] is also valid for passive scalars transported in wall-bounded turbulent flows. However, the model parameters show strong Prandtl number (Pr) dependence under the viscous scaling. In the present study, we introduced the Prandtl-number-dependent length unit to scale the model parameters. Under the proposed scaling, the wall-normal positions of the outer peak of the scalar spectra coincide with 4.5ReτPr, where Reτ is the friction Reynolds number. With the large-scale signals extracted at this position as the model input, the Prandtl number dependence of the model parameters is greatly weakened, and the wall-normal position of zero modulation is independent of Prandtl numbers.

Neural-network based approach for modeling wall-impact breakage of agglomerates in particle-laden flows applied in Euler–Lagrange LES

The present study proposes a novel modeling approach for predicting the wall-impact breakage of agglomerates in wall-bounded particle-laden turbulent flows based on artificial neutral networks (ANN). The suggested model is especially useful for efficient Euler-Lagrange simulation methods relying on the hard-sphere approach and the equivalent-sphere model for the agglomerate structure, allowing LES predictions of high mass loadings. Based on the impact conditions, i.e., the impact velocity, the impact angle, the number of included primary particles and the diameter of the primary particles, the outcomes of the breakage events are forecasted using two pre-trained artificial neural networks. The first network is concerned with the prediction of the possibility of breakage and the resulting fragment size distribution, whereas the second network predicts the post-breakage velocities of the fragments. The supervised training of the employed networks relies on a database obtained by extensive DEM simulations of agglomerate wall-impacts covering wide ranges of impact conditions, which were partially reported in Khalifa and Breuer (2020, 2021) for developing a breakage model based on a dimensional analysis and regression techniques. In the present contribution, the database mainly comprising the normal or oblique impact case is extended by adding results for the practically relevant shear impact case of wall-bounded particle-laden flows at extremely small impact angles, i.e., 3° and practically flat (0.2°). In addition, the breakage behavior of agglomerates containing very small numbers of particles are investigated under different impact angles and primary particle sizes. The ANN model is employed in Euler-Lagrange LES predictions of duct flows taking three Reynolds numbers and agglomerates of two powders distinguished by the size of the primary particles into account. The results obtained are compared with those based on a previous regression model (Khalifa and Breuer, 2021). In general, a good agreement between the results is found. However, the new ANN model is more widely applicable since the shear impact case is taken into account, which leads to subtle differences enhancing the reliability of the predictions.

Properties of the compressibility and transport motion in wall-bounded turbulent flows at Mach 8

The compressibility effect and transport motion in highspeed turbulent boundary layer (TBL) is a fundamental problem because they dominate the average and statistical characteristics. Using the statistical methods and flow visualization technology, flat-plate TBLs at [Formula: see text] with high- and low-wall temperatures, [Formula: see text] and 1.9, are investigated based on the direct numerical simulation (DNS) datasets. Compared with previous studies, this study considers relative higher Mach number and strong cold wall temperature condition at the same time. First, the turbulent Mach number and turbulent intensity show that the compressibility effects are enhanced by the cooling process. Second, the high-order statistical moments and structure parameters confirm cold wall that causes stronger compressibility and the corresponding increased intensities of local streamwise and wall-normal transport motions. Finally, for uncovering the relationship between the compressibility effect and turbulent transport, more in-depth visualization analyses of velocity streaks are performed. It is found that ‘knot-like’ structures are generated when cooling the wall, and they lead to stronger intermittent, which results in the rapid increase of local compressibility effect and the wall-normal transport motion. Our research sheds light on providing a theoretical basis for further understanding the compressibility effects of TBL at high Mach number.

On locally embedded two-scale solution for wall-bounded turbulent flows

Recent findings on wall-bounded turbulence have prompted a new impetus for modelling development to capture and resolve the Reynolds-number-dependent influence of outer flow on near-wall turbulence in terms of the ‘foot-printing’ of the large-scale coherent structures and the scale-interaction associated ‘modulation’. We develop a two-scale method to couple a locally embedded near-wall fine-mesh direct numerical simulation (DNS) block with a global coarser mesh domain. The influence of the large-scale structures on the local fine-mesh block is captured by a scale-dependent coarse–fine domain interface treatment. The coarse-mesh resolved disturbances are directly exchanged across the interface, while only the fine-mesh resolved fluctuations around the coarse-mesh resolved variables are subject to periodic conditions in the streamwise and spanwise directions. The global near-wall coarse-mesh region outside the local fine-mesh block is governed by the augmented flow governing equations with forcing source terms generated by upscaling the space–time-averaged fine-mesh solution. The validity and effectiveness of the method are examined for canonical incompressible channel flows at several Reynolds numbers. The mean statistics and energy spectra are in good agreement with the corresponding full DNS data. The results clearly illustrate the ‘foot-printing’ and ‘modulation’ in the local fine-mesh block. Noteworthy also is that neither spectral-gap nor scale-separation is assumed, and a smooth overlap between the global-domain and the local-domain energy spectra is observed. It is shown that the mesh-count scaling with Reynolds number is potentially reduced from $O(R{e^2})$ for the conventional fully wall-resolved large-eddy simulation (LES) to $O(Re)$ for the present locally embedded two-scale LES.

Entropy and Turbulence Structure.

Some new perspectives are offered on the spectral and spatial structure of turbulent flows, in the context of conservation principles and entropy. In recent works, we have shown that the turbulence energy spectra are derivable from the maximum entropy principle, with good agreement with experimental data across the entire wavenumber range. Dissipation can also be attributed to the Reynolds number effect in wall-bounded turbulent flows. Within the global energy and dissipation constraints, the gradients (d/dy+ or d2/dy+2) of the Reynolds stress components neatly fold onto respective curves, so that function prescriptions (dissipation structure functions) can serve as a template to expand to other Reynolds numbers. The Reynolds stresses are fairly well prescribed by the current scaling and dynamical formalism so that the origins of the turbulence structure can be understood and quantified from the entropy perspective.

Wall-function-based weak imposition of Dirichlet boundary condition for stratified turbulent flows

Wall-function-based weak imposition of Dirichlet boundary condition (WFWD) has seen success in maintaining numerical accuracy with reduced near-wall resolution for modeling wall-bounded turbulent flows. In this work, we extend the formulation of WFWD to stably stratified flows. The performance of the extended formulation is validated with two canonical numerical experiments, namely stratified turbulent channel flow and stable atmospheric boundary layer, demonstrating its effectiveness and potential in modeling wall-bounded stratified turbulent flows. Comparisons are made against results of the original formulation of weak imposition of Dirichlet boundary condition (WD), as well as direct numerical or large-eddy simulations whenever available. Our results show that WFWD with a smooth wall function offers improved accuracy over its WD counterpart in predicting one-point statistics of the turbulent channel flow at various degrees of stratification. Furthermore, on account of adopting a rough wall function WFWD successfully predicts the occurrence of super-geostrophic jet as well as statistics that are in good agreement with highly-resolved large-eddy simulations. Our findings suggest that formulating the weak imposition of Dirichlet boundary condition based on wall functions could mitigate shortcomings of WD when factors like roughness play a non-negligible role.

Enhancing heat transport in multiphase Rayleigh–Bénard turbulence by changing the plate–liquid contact angles

This numerical study presents a simple but extremely effective way to considerably enhance heat transport in turbulent wall-bounded multiphase flows, namely by using oleophilic walls. As a model system, we pick the Rayleigh–Bénard set-up, filled with an oil–water mixture. For oleophilic walls, using only $10\,\%$ volume fraction of oil in water, we observe a remarkable heat transport enhancement of more than $100\,\%$ as compared to the pure water case. In contrast, for oleophobic walls, the enhancement is only of about $20\,\%$ as compared to pure water. The physical explanation of the heat transport increment for oleophilic walls is that thermal plumes detach from the oil-rich boundary layer and carry the heat with them. In the bulk, the oil–water interface prevents the plumes from mixing with the turbulent water bulk and to diffuse their heat. To confirm this physical picture, we show that the minimum amount of oil necessary to achieve the maximum heat transport is set by the volume fraction of the thermal plumes. Our findings provide guidelines of how to optimize heat transport in wall-bounded thermal turbulence. Moreover, the physical insight of how coherent structures are coupled with one of the phases of a two-phase system has very general applicability for controlling transport properties in other turbulent wall-bounded multiphase flows.

VISCOSITY IN SEAKEEPING

The paper addresses the issue of actuality in ship hydrodynamics: the estimation of ship’s linear and angular oscillations with respect to the state of equilibrium. The prediction of seakeeping properties raises a question about a relative importance of viscous and free-surface effects (Quérard et al. 2009), yet this question remains of more general importance in fluid mechanics, since it is related to the dynamic characteristics of objects/bodies immersed in a liquid. From a theoretical standpoint, the problem refers to flows with moving boundaries. It can also be considered in terms of fluid-structure interaction (FSI), however, not necessarily linked with the computation of the body deformation and stresses due to the flow. As the Author correctly notices, the computational solution to this problem in its full setup reveals to be extremely costly due to the 3D and unsteady nature of the fluid motion under turbulent flow conditions at nominally high Reynolds numbers (Re~109, as stated by the Author in Tab. 1) in presence of the free surface. For this reason, the full solution, or direct numerical simulation (DNS), of the governing Navier-Stokes (N-S) equations at these Re will remain unfeasible in the foreseeable future; see, e.g., Pozorski (2017) for an estimation of the DNS capability in simple wall-bounded turbulent flows. The situation gets even worse in ship hydrodynamics when a DNS of fluid flow would need to be coupled to the dynamics of the rigid body (of complex geometry, usually).

Settling strongly modifies particle concentrations in wall-bounded turbulent flows even when the settling parameter is asymptotically small

Using theory and Direct Numerical simulations, we show that gravitational settling can contribute strongly to particle concentrations in wall-bounded turbulent flows even when the settling number Sv is very small. This occurs because the other competing mechanisms, e.g. the turbophoretic drift velocity, become very small in certain regions of the flow, such as very close to the wall, which we demonstrate using asymptotic analysis.

Features of surface physical quantities and temporal-spatial evolution of wall-normal enstrophy flux in wall-bounded flows

This paper presents a concise derivation of the temporal-spatial evolution equation of the wall-normal enstrophy flux on a no-slip flat wall. Each contribution to the evolution is explicitly expressed using the two fundamental surface quantities: skin friction (or equivalently surface vorticity) and surface pressure which are coupled through the boundary enstrophy flux (BEF). The newly derived relation is then used to explore, in a preliminary manner, the physical features of surface quantities and their dynamical roles in wall-bounded laminar and turbulent flows. It is confirmed that the BEF usually changes its sign near the separation and attachment lines in the skin friction field. For the simulated incompressible turbulent channel flow at Reτ=180, violent variations of different terms in the derived formulation are observed in the regions below the strong wall-normal velocity events (SWNVEs) when compared to other common regions. Near the SWNVEs, the evolution of the wall-normal enstrophy flux is found to be dominated by the wall-normal diffusion of the vortex stretching term which is relatively weak or negligible for laminar flows. Combined with our previous research results, it is conjectured that the strong interaction between the quasi-streamwise vortex and the channel wall intensifies the temporal-spatial evolution of the wall-normal enstrophy flux on the wall, which accounts for the highly intermittent feature of the viscous sublayer.

High-fidelity reconstruction of turbulent flow from spatially limited data using enhanced super-resolution generative adversarial network

In this study, a deep learning-based approach is applied with the aim of reconstructing high-resolution turbulent flow fields using minimal flow field data. A multi-scale enhanced super-resolution generative adversarial network with a physics-based loss function is introduced as a model to reconstruct the high-resolution flow fields. The model capability to reconstruct high-resolution laminar flows is examined using direct numerical simulation data of laminar flow around a square cylinder. The results reveal that the model can accurately reproduce the high-resolution flow fields even when limited spatial information is provided. The DNS data of turbulent channel flow at two friction Reynolds numbers Reτ=180 and 550 are used to assess the ability of the model to reconstruct the high-resolution wall-bounded turbulent flow fields. The instantaneous and statistical results obtained from the model agree well with the ground truth data, indicating that the model can successfully learn to map the coarse flow fields to the high-resolution ones. Furthermore, the possibility of performing transfer learning for the case of turbulent channel flow is thoroughly examined. The results indicate that the amount of the training data and the time required for training can be effectively reduced without affecting the performance of the model. The computational cost of the proposed model is also found to be effectively low. These results demonstrate that using high-fidelity training data with physics-guided generative adversarial network-based models can be practically efficient in reconstructing high-resolution turbulent flow fields from extremely coarse data.

Shape and scaling of the mean-velocity profile in thermally-stratified plane-Couette flows

It has long been known from measurements that buoyant motions cause the mean-velocity profile (MVP) in thermally-stratified, wall-bounded turbulent flows to significantly deviate from its constant-density counterpart. Theoretical analysis has restricted attention to an ‘intermediate layer’ of the MVP, akin to the celebrated ‘log layer’ in the constant-density case. Here, for thermally-stratified plane-Couette flows, we study the shape and scaling of the whole MVP. We elucidate the mechanisms that dictate the shape of the MVP by using the framework of the spectral link (Gioia et al 2010 Phys. Rev. Lett. 105 184501), and obtain scaling laws for the whole MVP by generalizing the Monin-Obukhov similarity theory.

Asymptotics of streamwise Reynolds stress in wall turbulence

The scaling of different features of streamwise normal stress profiles$\langle uu\rangle ^+(y^+)$in turbulent wall-bounded flows is the subject of a long-running debate. Particular points of contention are the scaling of the ‘inner’ and ‘outer’ peaks of$\langle uu\rangle ^+$at$y^+\approxeq ~15$and$y^+ ={O}(10^3)$, respectively, their infinite Reynolds number limit, and the rate of logarithmic decay in the outer part of the flow. Inspired by the thought-provoking paper of Chen & Sreenivasan (J. Fluid Mech., vol. 908, 2021, p. R3), two terms of an inner asymptotic expansion of$\langle uu\rangle ^+$in the small parameter$Re_{\tau }^{-1/4}$are constructed from a set of direct numerical simulations (DNS) of channel flow. This inner expansion is for the first time matched through an overlap layer to an outer expansion, which not only fits the same set of channel DNS within 1.5 % of the peak stress, but also provides a good match of laboratory data in pipes and the near-wall part of boundary layers, up to the highest$Re_{\tau }$values of$10^5$. The salient features of the new composite expansion are first, an inner$\langle uu\rangle ^+$peak, which saturates at 11.3 and decreases as$Re_{\tau }^{-1/4}$. This inner peak is followed by a short ‘wall log law’ with a slope that becomes positive for$Re_{\tau }$beyond${O}(10^4)$, leading up to an outer peak, followed by the logarithmic overlap layer with a negative slope going continuously to zero for$Re_{\tau }\to \infty$.

Unsteady aerodynamic simulations by the lattice Boltzmann method with near-wall modeling on hierarchical Cartesian grids

Near-wall modeling for large-eddy simulation (LES) based on the lattice Boltzmann method (LBM) is applied to the unsteady aerodynamic simulations around the tandem cylinders and the 30P30N three-element high-lift airfoil using hierarchical Cartesian grids. The near-wall modeling of the inner turbulent boundary layer is essential for LES to accurately calculate the high Reynolds number wall-bounded turbulent flow with a reasonable calculation cost. Therefore, near-wall modeling for LES has been studied within the framework of the Navier–Stokes equations. However, LBM-based modeling is still in its early developing stage because of the LBM’s calculation algorithm using distribution functions on a non-body fitted Cartesian grid, and further developments are needed regarding the applicability to flow simulations around arbitrary complicated shapes that appear in the actual engineering field. In this study, aerodynamic simulations around tandem cylinders are conducted using the proposed near-wall modeling that reproduces the profiles of the turbulent boundary layer in turbulent channel flow simulations on a non-body-fitted Cartesian grid. The same benchmark problem is also calculated using the non-slip wall boundary condition (interpolated bounce-back scheme) for comparison. Those calculation results are validated through the comparisons with the available experimental measurements, and the effectiveness of the proposed near-wall modeling to high Reynolds number wall-bounded turbulent flow simulations around objects with curvilinear surfaces is demonstrated. Followed by the tandem cylinders, the aerodynamic simulation around the 30P30N three-element high-lift airfoil is also conducted in order to demonstrate the applicability to more complicated shapes. The simulation result shows that the proposed method can stably calculate the relatively complicated configuration such as the high-lift airfoil, and the potential of the proposed method to unsteady aerodynamic simulations around arbitrary complicated shapes is demonstrated.

Reynolds number effect on the concentration and preferential orientation of inertial ellipsoids

Direct numerical simulations are performed to study the influence of the flow Reynolds number (Re) on the dynamics of inertial, ellipsoidal particles in a turbulent wall-bounded flow. In wall units, the time required for the particle distribution to reach a statistically steady state increases with Re. Once the distribution reached a statistically steady-state, a more uniform concentration profile is observed for higher values of Re, regardless of particle shape, but with a noticeable influence of particle inertia. Finally, in the near-wall region, preferential orientation of all ellipsoids is modified when Re increases, with a strong dependence on the ellipsoids characteristics.

Reformulation and improvement of a universal subgrid eddy viscosity model based on the multiscale framework

A universal multiscale Smagorinsky model (UMSM) is established for the large eddy simulation (LES) of wall-bounded turbulent flows by reformulating a universal subgrid eddy viscosity model presented by Gu et al. (Europhysics Letter 94(3):34003,2011). The UMSM is adapted to the LES of wall-bounded turbulent flows by integrating the “small-all” form of the multiscale Smagorinsky model with the dynamic subgrid characteristic length, controlled by subgrid-scale (SGS) motions. The dynamic subgrid characteristic length is determined by the characteristic wave number, which is calculated from a new energy-weighted-mean method when the SGS turbulent kinetic energy and the dissipation wave number are known. The dissipation wave number is derived from the SGS turbulent kinetic energy spectrum equation and the total dissipation rate spectrum equation. The UMSM is used to simulate the fully developed channel flow and the turbulent flow past a square cylinder. The dynamic subgrid characteristic length, as a counterpart of Germano’s procedure, evaluates the rapidly fluctuating small-scale behavior and spatial variations of turbulent characteristics. The results for fully developed channel flow show that the errors in the streamwise velocity and the velocity fluctuations change slowly. The flat nature of the UMSM error across different multiscale Smagorinsky coefficients (Cs’) indicates that the model is relatively insensitive to the value of Cs′. Additionally, the UMSM is less sensitive to grid resolution since more details of turbulence fluctuations are captured on the same grid-points compared to the RVBMM (Journal of Computational Physics, 234:79-107,2013) and DSM (Journal of Fluid Mechanics 319:353-385,1996). Overall, the proposed model and the DSM exhibit similar behavior, and both LES formulations provide good agreement with reference data from direct numerical simulations. However, the UMSM is more computationally efficient, being 17% faster than the dynamic Smagorinsky model.

Pinhole measurements of hydroacoustic pressure fluctuations beneath wall-bounded turbulent flows

The common flush-mounted-transducer measurement method for underwater surface pressure fluctuations results in transducer-size-limited spatial resolution, which may be inadequate for the fluctuations produced beneath a turbulent boundary layer (TBL). For water moving over a smooth surface at speeds of a few meters per second, the relevant length scales may be less than 100 mm with fluctuation magnitudes far less than 1% of the free-stream dynamic pressure. Unfortunately, such size and sensitivity requirements cannot simultaneously be met with common instrumentation. However, mounting microphones behind pinholes is a possible solution for wall-bounded airflows. This presentation covers the effect of pinhole mounting pressure transducers for measuring surface pressure fluctuations in wall-bounded turbulent flows in water. The experimental work is conducted in a turbulent channel flow at varying flow speeds (0.5 to 7 m/s) using pressure transducers with a 5-mm-diameter sensitive area that are flush mounted and mounted behind variable size pinhole openings. The measured pressure-fluctuation power spectra are compared to each other and to results from past direct numerical simulations, in the 10 Hz to 10 kHz frequency range, to determine the utility of pinhole mounting for underwater TBL pressure-fluctuation measurements. [Sponsored by ONR.]