Fully-developed Turbulent Channel Flow Research Articles

Particle deposition model for a fully developed turbulent channel flow

This study aims to develop a mathematical model for solid particle deposition under a fully-developed turbulent flow in a rectangular channel, considering the effect of the change in geometry over time. The present study introduces a mathematical approach to predict the equilibrium thickness/mass of the deposition, saturation and equilibrium times, and their corresponding non-dimensionalized parameters. Scaling analysis, and parametric study are reported. For a fixed Reynolds number Re, the particle deposition increases with non-dimensional relaxation time. In general, as more particles are deposited, the surface takes less time to become saturated and approach equilibrium faster. The saturation and equilibrium times decrease with an increase in non-dimensional particle relaxation time. For a fixed particle concentration, as the inlet velocity increases, the saturation and equilibrium time decreases, and the asymptotic deposited mass decreases.

A comparison of hydrodynamic and thermal properties of artificially generated against realistic rough surfaces

The mathematical roughness generation approaches enjoy outstanding flexibility in delivering desired roughness geometries to perform systematic research. However, whether an mathematically (artificially) generated roughness can be considered an adequate surrogate of a realistic surface in terms of its influence on the flow remains nonetheless an open question. Motivated by this, the present study discusses the possibility of reproducing flow properties over realistic roughness with artificial roughness. To this end, six types of artificial rough surfaces are generated through imitation of the realistic height probability density function (PDF) and the roughness power spectrum (PS) preserving the stochastic nature of the roughness structure. The flow properties of the artificial surfaces are assessed using direct numerical simulations (DNS) in a fully-developed turbulent channel flow at Reτ=500−2000. An excellent match in terms of global flow properties, mean velocity and temperature profiles, Reynolds stresses as well as equivalent sand grain sizes is found compared to their original counterpart with exception of a strongly anisotropic sample (surface anisotropy ratio SAR≈1.7). Additionally, some artificial surfaces are generated by matching only the PS, and it was shown that only at adequately low effective slopes this can lead to similar flow properties. Overall, the results suggest that artificial roughness generated using the employed method by mimicking realistic PDF and PS can be applied as a full-fledged surrogate for realistic roughness under the premise of surface isotropy.

Predictive accuracy of wall-modelled large-eddy simulation on unstructured grids

The predictive accuracy of wall-modelled LES is influenced by a combination of the subgrid model, the wall model, the numerical dissipation induced primarily by the convective numerical scheme, and also by the density and topology of the computational grid. The latter factor is of particular importance for industrial flow problems, where unstructured grids are typically employed due to the necessity to handle complex geometries. Here, a systematic simulation-based study is presented, investigating the effect of grid-cell type on the predictive accuracy of wall-modelled LES in the framework of a general-purpose finite-volume solver. Following standard practice for meshing near-wall regions, it is proposed to use prismatic cells. Three candidate shapes for the base of the prisms are considered: a triangle, a quadrilateral, and an arbitrary polygon. The cell-centre distance is proposed as a metric to determine the spatial resolution of grids with different cell types. The simulation campaign covers two test cases with attached boundary layers: fully-developed turbulent channel flow, and a zero-pressure-gradient flat-plate turbulent boundary layer. A grid construction strategy is employed, which adapts the grid metric to the outer length scale of the boundary layer. The results are compared with DNS data concerning mean wall shear stress and profiles of flow statistics. The principle outcome is that unstructured simulations may provide the same accuracy as simulations on structured orthogonal hexahedral grids. The choice of base shape of the near-wall cells has a significant impact on the computational cost, but in terms of accuracy appears to be a factor of secondary importance.

Development of machine learning techniques to enhance turbulence models

The implementation of the machine learning methods of convolutional neural networks to enhance RANS closure models is presented. The RANS models are not universal and accurate, however they are computationally affordable. Finding a way to improve the model predictability will be an advantage. For this, machine learning algorithms based on available high-fidelity data sets for canonical flow cases obtained from DNS and measurements can be helpful. The application of these algorithms for a fully-developed turbulent channel flows with periodic hills, in a square duct and for other cases is considered.

Direct numerical simulation of turbulent flow separation induced by a forward-facing step

Direct numerical simulation is used to investigate turbulent flow separations generated by a forward-facing step exposed to an incoming fully-developed turbulent plane channel flow at Reτ=180. The step height is 25% of the inlet channel height. The results are analyzed in terms of the topology of the Reynolds stresses, transport of turbulence kinetic energy (TKE) and unsteadiness of separation bubbles using a broad range of post-processing techniques, including the Lumley triangle, quadrant analysis, auto-correlation, joint probability density function, proper orthogonal decomposition and linear stochastic estimation. The incoming turbulence intensity is elevated as the step is approached and peaks along the mean separating streamline over the step. The topology of the Reynolds stresses switches from two-component to axisymmetric along the mean separating streamline over the step. The production term of TKE peaks in the separated shear layer, while the turbulent diffusion term tends to transport TKE away from the shear layer. An expanded separation bubble upstream of the step is typically associated with a contracted separation bubble over the step. This pattern is captured by the first proper orthogonal decomposition (POD) mode. In the first POD mode, the streamwise and vertical fluctuating velocities switch signs abruptly near the mean separating streamline over the step. This is characterized by two pairs of counter-rotating vortices: one pair of counter-rotating vortices leaning over the step and another pair of opposite-signed counter-rotating vortices near the top surface of the step.

Direct numerical simulation of spray droplet evaporation in hot turbulent channel flow

We perform a direct numerical simulation (DNS) of 14081 “cold” spherical droplets evaporating in a “hot” fully-developed turbulent channel flow. This effort is the first extensive computation that employs four-way coupling of the droplet motion with the turbulent carrier phase and interface-resolved evaporation dynamics, for a flow configuration that approaches conditions encountered in spray combustion applications. The complex interaction of momentum, heat, species transfer and phase change thermodynamics is explored. Large-scale droplet motion, modulation of the carrier phase turbulence, and influence of the mean and turbulent mass transport on the evaporation dynamics are observed and quantified. Based on the data set, phenomenological explanations of the shear-induced migration of the dispersed phase and of the effect of turbulent mass transport on the evaporation are provided. The transient nature of the DNS is exploited to generate a novel database that samples a range of turbulence and evaporation timescales, from which a model for the enhancement of the evaporation rate by the ambient turbulence is extracted.

Geometric Effects of Shallow Dimples in Turbulent Channel Flows at $$Re_{\tau }\approx 180$$: A Vorticity Transport Perspective

Shallow dimples have shown a great potential to reduce turbulent drag in several experiments. However, the mechanism underlying their effects on turbulence dynamics remains a subject of deliberation. In this numerical study, a vorticity transport perspective is adopted to elucidate the geometric effects of shallow dimples on the turbulence dynamics in a fully-developed turbulent channel flow. The geometric modifications considered in the present direct numerical simulation at a bulk Reynolds number of 2800 include changing the planform design and modulating the streamwise wall slope. The planform design had a significant impact on the mean flow topology and the drag property. Out of the five planform designs, diamond (shape) dimples produced the highest amount of total drag reduction of $$\approx 7\%$$, whereas symmetric circular dimples caused the greatest increase in total drag by $$\approx 6\%$$. Results revealed that geometric modifications of shallow dimples mainly affect the vorticity redistribution process that predominates in the inner region of a turbulent boundary layer, and in turn the generation of Reynolds stress. The drag property of a dimpled surface was found to scale with the velocity–vorticity correlation term representing the physical process of vorticity stretching and reorientation. The occurrence of flow separation near the leading edge of the dimple altered the vorticity dispersion process in the outer region, thereby modifying the generation of Reynolds stress in the bulk flow. On the other hand, the vortex dispersion process in the inner layer can be altered by modulating the streamwise wall slope. Accordingly, the vorticity redistribution process was modified but the near-wall generation of Reynolds stress was unaffected. Thus, only the form drag varied with the streamwise wall slope, while the viscous drag remained largely the same.

Analysis of the numerical dissipation rate of different Runge–Kutta and velocity interpolation methods in an unstructured collocated finite volume method in OpenFOAM®

The approach used for computation of the convecting face fluxes and the cell face velocities results in different underlying numerical algorithms in finite volume collocated grid solvers for the incompressible Navier–Stokes equations. In this study, the effect of the following five numerical algorithms on the numerical dissipation rate and on the temporal consistency of a selection of Runge–Kutta schemes is analysed: (1) the original algorithm of Rhie and Chow (1983), (2) the standard OpenFOAM method, (3) the algorithm used by Vuorinen et al. (2014), (4) the Kazemi-Kamyab et al. (2015) method, and (5) the D’Alessandro et al. (2018) approach. The last three algorithms refer to recent implementations of low dissipative numerical methods in OpenFOAM®.No new computational methods are presented in this paper. Instead, the main scientific contributions of this paper are: (1) the systematic assessment of the effect of the considered five numerical approaches on the numerical dissipation rate and on the temporal consistency of the selected Runge–Kutta schemes within one unified framework which we have implemented in OpenFOAM, and (2) the application of the method of Komen et al. (2017) in order to quantify the numerical dissipation rate introduced by three of the five numerical methods in quasi-DNS and under-resolved DNS of fully-developed turbulent channel flow. In addition, we explain the effects of the introduced numerical dissipation on the observed trends in the corresponding numerical results.As one of the major conclusions, we found that the pressure error, which is introduced due to the application of a compact stencil in the pressure Poisson equation, causes a reduction of the order of accuracy of the temporal schemes for the test cases in this study. Consequently, application of higher order temporal schemes is not useful from an accuracy point of view, and the application of a second order temporal scheme appears to be sufficient.

Development of k-R turbulence model for wall-bounded flows

A new low-Reynolds-number turbulence model is formulated based on the turbulent kinetic energy k and eddy-viscosity parameter R=k2/ϵ. In the derivation, most of the diffusion terms emerging from the transformation have been preserved in the proposed model, maintaining the closest relationship with its parent k-ϵ model; the near-wall viscous balance is guaranteed by including a far-wall damping function. The turbulent structure parameter (i.e., Bradshaw-relation) that may enhance the predicted accuracy for non-equilibrium flows, is incorporated into the current model. The coefficients and functions are constructed such as to preserve the anisotropic characteristics of turbulence, encountered in rotational and irrotational flows. Fully-developed turbulent channel and flat-plate flows are computed to validate the model ability in replicating the near-wall turbulence. Two-dimensional asymmetric plane diffuser and airfoil flows are simulated to verify the model accuracy in capturing non-equilibrium flows with separation and reattachment. Computation of a three-dimensional wing with shock-wave is presented, rectifying the model competency in predicting large adverse-pressure-gradient flows. Furthermore, model predictions are compared with other two frequently-used turbulence models; a good correlation is obtained between the current model and experimental data.

Developing code-friendly variant of V2F turbulence model

Relevant modifications to the code-friendly variant of v¯2−f turbulence model is proposed that accounts for the distinct effects of low-Reynolds number and near-wall turbulence. It incorporates compatible formulations for inter-dependent coefficients Cϵ(1,2) and σ(k,ϵ) to amplify the level of dissipation in non-equilibrium flow regions, thus reducing the turbulent kinetic energy and time/length scale magnitudes to improve prediction of adverse pressure gradient flows, involving flow separation and reattachment. A non-linear eddy-viscosity coefficient with a realizable eddy-viscosity bound that may enhance the predicted accuracy for complex flows, is introduced with the present model. Coefficients of the elliptic-relaxation equation are constructed such as to preserve the anisotropic characteristics of turbulence, encountered in rotational and irrotational flows. Fully-developed turbulent channel and flat-plate flows are computed to validate the model ability in replicating the near-wall turbulence. An asymmetric plane diffuser flow is simulated to verify the model accuracy in capturing non-equilibrium flows with separation and reattachment. The Computation of flow over a three-dimensional (3D) axisymmetric hill is presented, rectifying the model competency in predicting an adverse-pressure-gradient flow with 3D turbulent separation. Model predictions are compared with the widely used SST (shear stress transport) k−ω model; a good correlation is obtained between the current model and DNS/experimental data.

Synthetic turbulent inflow generator using machine learning

We propose a methodology for generating time-dependent turbulent inflow data with the aid of machine learning (ML), which has a possibility to replace conventional driver simulations or synthetic turbulent inflow generators. As for the ML model, we use an auto-encoder type convolutional neural network (CNN) with a multi-layer perceptron (MLP). For the test case, we study a fully-developed turbulent channel flow at the friction Reynolds number of ${\rm Re}_{\tau} = 180$ for easiness of assessment. The ML models are trained using a time series of instantaneous velocity fields in a single cross-section obtained by direct numerical simulation (DNS) so as to output the cross-sectional velocity field at a specified future time instant. From the a priori test in which the output from the trained ML model are recycled to the input, the spatio-temporal evolution of cross-sectional structure is found to be reasonably well reproduced by the proposed method. The turbulence statistics obtained in the a priori test are also, in general, in reasonable agreement with the DNS data, although some deviation in the flow rate was found. It is also found that the present machine-learned inflow generator is free from the spurious periodicity, unlike the conventional driver DNS in a periodic domain. As an a posteriori test, we perform DNS of inflow-outflow turbulent channel flow with the trained ML model used as a machine-learned turbulent inflow generator (MLTG) at the inlet. It is shown that the present MLTG can maintain the turbulent channel flow for a long time period sufficient to accumulate turbulent statistics, with much lower computational cost than the corresponding driver simulation. It is also demonstrated that we can obtain accurate turbulent statistics by properly correcting the deviation in the flow rate.

Eddy Viscosity and Velocity Profiles in Fully-Developed Turbulent Channel Flows

In this study, we present eddy viscosity formulations based on analytical solutions for turbulent kinetic energy (TKE) in fully-developed turbulent channel flows. Mean streamwise velocities are obtained by solving the momentum equation with the proposed analytical eddy viscosity formulations. Our results were validated by comparisons with DNS data of fully-developed turbulent channel flows for 300 < Reτ < 2000 (where Reτ denotes the friction Reynolds number defined by the friction velocity uτ, kinematic viscosity ν and the channel half-width δ). Our method allows accurate description of mean streamwise velocity profiles and turbulent shear stress outside the log-law layer, in the viscous and buffer layers and in the outer region. The aim of this study is to provide simple analytical tools for turbulent channel flow applications.

Effects of numerical dissipation on the predictive accuracy of wall-modelled large-eddy simulation

The effect of numerical dissipation on the predictive accuracy of wall-modelled large-eddy simulation is investigated via systematic simulations of fully-developed turbulent channel flow. A total of 16 simulations are conducted using the open-source computational fluid dynamics software OpenFOAM®. Four densities of the computational mesh are considered, with four simulations performed on each, in turn varying in the amount of numerical dissipation introduced by the numerical scheme used for interpolating the convective fluxes. The results are compared to publicly-available data from direct numerical simulation of the same flow. Computed error profiles of all the considered flow quantities are shown to vary monotonically with the amount of dissipation introduced by the numerical schemes. As expected, increased dissipation leads to damping of high-frequency motions, which is clearly observed in the computed energy spectra. But it also results in increased energy of the large-scale motions, and a significant over-prediction of the turbulent kinetic energy in the inner region of the boundary layer. On the other hand, dissipation benefits the accuracy of the mean velocity profile, which in turn improves the prediction of the wall shear stress given by the wall model. Thus, in the current framework, the optimal choice for the dissipation of the numerical schemes may depend on the primary quantity of interest for the conducted simulation. With respect to the resolution of the grid, the change in the accuracy is much less predictable, and the optimal resolution depends on the considered quantity and the amount of dissipation introduced by the numerical schemes.

Direct numerical simulations of premixed and stratified flame propagation in turbulent channel flow

Direct numerical simulations are performed to investigate the transient upstream flame propagation (flashback) through homogeneous and fuel-stratified hydrogen-air mixtures transported in fully-developed turbulent channel flows. Results indicate that, for both cases, the flame maintains steady propagation against the bulk flow direction and the global flame shape and the local flame characteristics are both affected by the occurrence of fuel stratification. Globally, the mean flame shape undergoes an abrupt change when the approaching reactants transition from an homogeneous to a stratified mixing configuration. A V-shaped flame surface, whose leading-edge is located in the near-wall region, characterizes the non-stratified, homogeneous mixture case while a U-shaped flame surface, whose leading-edge propagates upstream at the channel centreline, distinguishes the case with fuel stratification (fuel-lean in the near-wall region and fuel-rich away from the wall). The characteristic thickness, wrinkling and displacement speed of the turbulent flame brush are subject to considerable changes across the channel due to the dependence of the turbulence and mixture properties on the distance from the channel walls. More specifically, the flame transitions from a moderately wrinkled, thin-flamelet combustion regime in the homogeneous mixture case to a strongly wrinkled flame brush more representative of a thickened-flame combustion regime in the near-wall region of the fuel-stratified case. The combustion regime may be related to Karlovitz number and it is shown that a nominal channel-flow Karlovitz number, Kachin, based on the wallnormal variation of canonical turbulence (tη = (ν/e) 1/2) and chemistry (tl = δl/Sl) time scales in fully-developed channel flow, compares well with an effective Karlovitz number, Kachfl, extracted from the present DNS datasets using conditionally sampled values of tη and tl in the immediate vicinity of the flame (0.1 < C < 0.3).

Linear estimation of coherent structures in wall-bounded turbulence at Reτ = 2000

The estimation problem for a fully-developed turbulent channel flow at Reτ = 2000 is considered. Specifically, a Kalman filter is designed using a Navier–Stokes-based linear model. The estimator uses time-resolved velocity measurements at a single wall-normal location (provided by DNS) to estimate the time-resolved velocity field at other wall-normal locations. The estimator is able to reproduce the largest scales with reasonable accuracy for a range of wavenumber pairs, measurement locations and estimation locations. Importantly, the linear model is also able to predict with reasonable accuracy the performance that will be achieved by the estimator when applied to the DNS. A more practical estimation scheme using the shear stress at the wall as measurement is also considered. The estimator is still able to estimate the largest scales with reasonable accuracy, although the estimator’s performance is reduced.

Visibility graph analysis of wall turbulence time-series

The spatio-temporal features of the velocity field of a fully-developed turbulent channel flow are investigated through the natural visibility graph (NVG) method, which is able to fully map the intrinsic structure of the time-series into complex networks. Time-series of the three velocity components, (u,v,w), are analyzed at fixed grid-points of the whole three-dimensional domain. Each time-series was mapped into a network by means of the NVG algorithm, so that each network corresponds to a grid-point of the simulation. The degree centrality, the transitivity and the here proposed mean link-length were evaluated as indicators of the global visibility, inter-visibility, and mean temporal distance among nodes, respectively. The metrics were averaged along the directions of homogeneity (x,z) of the flow, so they only depend on the wall-normal coordinate, y+. The visibility-based networks, inheriting the flow field features, unveil key temporal properties of the turbulent time-series and their changes moving along y+. Although intrinsically simple to be implemented, the visibility graph-based approach offers a promising and effective support to the classical methods for accurate time-series analyses of inhomogeneous turbulent flows.

Can large-scale oblique undulations on a solid wall reduce the turbulent drag?

Direct numerical simulations of fully developed turbulent channel flows with wavy walls are undertaken. The wavy walls, skewed with respect to the mean flow direction, are introduced as a means of emulating a Spatial Stokes Layer (SSL) induced by in-plane wall motion. The transverse shear strain above the wavy wall is shown to be similar to that of a SSL, thereby affecting the turbulent flow and leading to a reduction in the turbulent skin-friction drag. However, some important differences with respect to the SSL case are brought to light too. In particular, the phase variations of the turbulent properties are accentuated and, unlike in the SSL case, there is a region of increased turbulence production over a portion of the wall, above the leeward side of the wave, thus giving rise to a local increase in dissipation. The pressure- and friction-drag levels are carefully quantified for various flow configurations, exhibiting a combined maximum overall-drag reduction of about 0.6%. The friction-drag reduction is shown to behave approximately quadratically for small wave slopes and then linearly for higher slopes, whilst the pressure-drag penalty increases quadratically. The transverse shear-strain layer is shown to be approximately Reynolds-number independent when the wave geometry is scaled in wall units.

On the Mechanism of Drag Reduction in Fully-Developed Turbulent Channel Flow with a Streamwise Micro-featured Superhydrophobic Wall

The superhydrophobic drag reduction changes the structures of turbulent flow. However, the underlying mechanism is not clear. The aim of this study is to determine the alternations of turbulent flow due to applying a streamwise micro-featured superhydrophobic wall. Large eddy simulations are performed to explore the effect of micro-features on near-wall behaviors. The results indicate that the outward motion of the lifted low-speed streaks is restricted to the lower wall layers, and the region of maximum production of streamwise vorticities is shifted toward the micro-featured wall. The quadrant analysis of Reynolds stress shows that there is a stronger increase in outward motion of high-speed fluid and inward motion of low-speed fluid than ejection and sweep.

Mean equation based scaling analysis of fully-developed turbulent channel flow with uniform heat generation

Multi-scale analysis of the mean equation for passive scalar transport is used to investigate the asymptotic scaling structure of fully developed turbulent channel flow subjected to uniform heat generation. Unlike previous studies of channel flow heat transport with fixed surface temperature or constant inward surface flux, the present flow has a constant outward wall flux that accommodates for the volumetrically uniform heat generation. This configuration has distinct analytical advantages relative to precisely elucidating the underlying self-similar structure admitted by the mean transport equation. The present analyses are advanced using direct numerical simulations (Pirozzoli et al., 2016) that cover friction Reynolds numbers up to δ+=4088 and Prandtl numbers ranging from Pr=0.2–1.0. The leading balances of terms in the mean equation are determined empirically and then analytically described. Consistent with its asymptotic universality, the logarithmic mean temperature profile is shown analytically to arise as a similarity solution to the mean scalar equation, with this solution emerging (as δ+→∞) on an interior domain where molecular diffusion effects are negligible. In addition to clarifying the Reynolds and Prandtl number influences on the von Kármán constant for temperature, kθ, the present theory also provides a couple of self-consistent ways to estimate, kθ. As with previous empirical observations, the present analytical predictions for kθ indicate values that are larger than found for the mean velocity von Kármán constant. The potential origin of this is briefly discussed.

A quantification method for numerical dissipation in quasi-DNS and under-resolved DNS, and effects of numerical dissipation in quasi-DNS and under-resolved DNS of turbulent channel flows

LES for industrial applications with complex geometries is mostly characterised by: a) a finite volume CFD method using a non-staggered arrangement of the flow variables and second order accurate spatial and temporal discretisation schemes, b) an implicit top-hat filter, where the filter length is equal to the local computational cell size, and c) eddy-viscosity type LES models. LES based on these three main characteristics is indicated as industrial LES in this paper.It becomes increasingly clear that the numerical dissipation in CFD codes typically used in industrial applications with complex geometries may inhibit the predictive capabilities of explicit LES. Therefore, there is a need to quantify the numerical dissipation rate in such CFD codes. In this paper, we quantify the numerical dissipation rate in physical space based on an analysis of the transport equation for the mean turbulent kinetic energy. Using this method, we quantify the numerical dissipation rate in a quasi-Direct Numerical Simulation (DNS) and in under-resolved DNS of, as a basic demonstration case, fully-developed turbulent channel flow. With quasi-DNS, we indicate a DNS performed using a second order accurate finite volume method typically used in industrial applications. Furthermore, we determine and explain the trends in the performance of industrial LES for fully-developed turbulent channel flow for four different Reynolds numbers for three different LES mesh resolutions. The presented explanation of the mechanisms behind the observed trends is based on an analysis of the turbulent kinetic energy budgets.The presented quantitative analyses demonstrate that the numerical errors in the industrial LES computations of the considered turbulent channel flows result in a net numerical dissipation rate which is larger than the subgrid-scale dissipation rate.No new computational methods are presented in this paper. Instead, the main new elements in this paper are our detailed quantification method for the numerical dissipation rate, the application of this method to a quasi-DNS and under-resolved DNS of fully-developed turbulent channel flow, and the explanation of the effects of the numerical dissipation on the observed trends in the performance of industrial LES for fully-developed turbulent channel flows.