Simulation Of Turbulent Channel Flow Research Articles

Statistical Descriptions of Inhomogeneous Anisotropic Turbulence

Descriptions are given of the Langevin and diffusion equation of passively marked fluid particles in turbulent flow with spatially varying and anisotropic statistical properties. The descriptions consist of the first two terms of an expansion in powers of C0−1, where C0 is an autonomous Lagrangian-based Kolmogorov constant: C0≈7. Solutions involve the application of methods of stochastic analysis while complying with the basic laws of physics. The Lagrangian-based descriptions are converted into Eulerian-based fixed-point expressions through asymptotic matching. This leads to novel descriptions for the mean values of the fluctuating convective terms of the conservation laws of continua. They can be directly implemented in CFD codes for calculating fluid flows in engineering and environmental analysis. The solutions are verified in detail through comparison with direct numerical simulations of turbulent channel flows at large Reynolds numbers.

Effects of Wall Topology on Statistics of Cube-Roughened Wall Turbulence

In this work, we carried out roughness-resolved direct numerical simulations of cube-roughened turbulent channel flows to investigate the effects of aligned and staggered arrangements, element spacings, and element orientations on the statistics of rough-wall turbulence. The results show that the equivalent sandgrain roughness, Reynolds stresses and dispersive stresses are affected by element spacings and arrangements in different ways depending on the cube orientations. Placing the roughness elements in a staggered way in general increases the equivalent sandgrain roughness, unless when the element–element interaction is insignificant for the cube orientation with wakes of short length. As for the Reynolds normal stresses and the streamwise component of the dispersive stresses (both are normalized by the total friction velocity), placing the cube elements in a staggered way decreases their maximal values when compared with the aligned arrangements. As for the effects of element spacing on the equivalent sandgrain roughness and the maximums of the Reynolds normal stresses, similar trends are observed for different element orientations and arrangements when increasing the element spacing l/r (where r is the cube height) from 2.0 to 2.8. When further increasing the element spacing l/r from 2.8 to 3.5, however, different trends are observed for different element orientations. As for the dispersive stresses, greater maximal values of their streamwise components are observed for larger element spacing for all the considered cube-roughened surfaces. For the turbulence statistics in the wake of the cube element, certain similarities are observed for different element spacings.

Improved modelling of interfacial terms in the second-moment closure for particle-laden flows based on interface-resolved simulation data

Correlations for the interfacial terms in the fluid dissipation rate equation and Reynolds stress equations are established for particle-laden flows, based on data from the interfaced-resolved direct numerical simulations of particle sedimentation in a periodic domain at a density ratio ranging from 0.01 to 1000, a particle concentration ranging from 2.3 % to 30.2 % and a particle Reynolds number below 250. The correlations for the mean drag and the pseudo-turbulent kinetic energy are also reported, which are used for the modelling of the interfacial term in the fluid dissipation rate equation. The interfacial term correlations obtained are then incorporated in the Reynolds stress model (RSM) (i.e. second-moment closure) for the simulation of vertical turbulent channel flows laden with the finite-size particles at relatively low particle volume fractions. The results show that the RSM with new interfacial term correlations can quantitatively predict particle-induced turbulence enhancement or suppression in vertical channel flows.

Artificial neural network-based wall-modeled large-eddy simulations of turbulent channel and separated boundary layer flows

Wall-models in a large-eddy simulation (LES) are essential to alleviate the large near-wall resolution requirements for high-Reynolds-number turbulent flow simulations. Among the existing wall-models for a LES, an equilibrium wall-stress model has the highest computational efficiency. Because this model has limitations, such as a lack of non-equilibrium effects and the assumption of a particular law of the wall in the mean velocity, we propose artificial neural network-based wall-stress models (AWMs). The input variables for the AWMs are extracted from the decomposition of the skin-friction coefficient proposed by Fukagata et al. [1], and the AWMs are shown to be able to predict the wall-shear stress in complex flows accurately. The performance of the AWMs is tested for two types of flows, a fully developed turbulent channel flow and a separated turbulent boundary layer flow. A direct comparison of the turbulence statistics with those obtained by previous wall-models (i.e., a log-law-based wall-stress model and a non-equilibrium wall-stress model) shows that better predictions are achieved using the AWMs for both flows, even with untrained Reynolds numbers. When using a coarse grid along the wall-normal direction in wall-modeled LESs (WMLESs) with the AWMs, an upward shift of the mean velocity profile (positive log-layer mismatch, LLM) compared to direct numerical simulation data is found, consistent with previous studies. However, this LLM problem can be overcome by imposing a filtered wall-normal velocity at the wall that is dynamically determined based on the continuity equation and the Taylor series expansion within wall-adjacent cells.

A novel LES method for predicting drag reduction in viscoelastic fluid based on the time period of turbulence structures

Direct numerical simulations (DNS) of turbulent channel flow of viscoelastic fluid were performed with the Oldroyd-B model as a constitutive equation to identify the temporal characteristics of turbulence structures. First, using the results of the DNS in a minimal flow unit (MFU), temporal variations in the energy input and dissipation rates in fully developed wall turbulence of viscoelastic fluid were observed and compared with those of Newtonian fluid. Then, a modified time scale reflecting the local turbulence state was proposed by considering the temporal variation in the viscous stretching stress intensity. It was also found that the idea of the modified time scale could be extended and applied locally to viscoelastic fluid turbulence in a more significant computational domain than MFU to investigate the temporal characteristics of the turbulence structures. Finally, using the local modified time scale, a prediction method employing large eddy simulation for Newtonian fluid turbulence was extended for viscoelastic fluid turbulence. We proved that the drag reduction of viscoelastic fluid turbulence could be accurately predicted with a drag reduction ratio of approximately 40% by using the local modified time scale and the model in the constitutive equation. • The characteristics of viscoelastic fluid turbulence were observed from DNS results. • Active and hibernating turbulence states were compared with those in Newtonian fluid. • A local modified time scale which reflected the local turbulence state was proposed. • LES was extended using the modified time scale for viscoelastic fluid turbulence. • The proposed LES could predict the drag reduction of viscoelastic fluid turbulence.

Artificial neural network-based subgrid-scale models for LES of compressible turbulent channel flow

Fully connected neural networks (FCNNs) have been developed for the closure of subgrid-scale (SGS) stress and SGS heat flux in large-eddy simulations of compressible turbulent channel flow. The FCNN-based SGS model trained using data with Mach number Ma=3.0 and Reynolds number Re=3000 was applied to situations with different Mach numbers and Reynolds numbers. The input variables of the neural network model were the filtered velocity gradients and temperature gradients at a single spatial grid point. The a priori test showed that the FCNN model had a correlation coefficient larger than 0.91 and a relative error smaller than 0.43, with much better reconstructions of SGS unclosed terms than the dynamic Smagorinsky model (DSM). In a posteriori test, the behavior of the FCNN model was marginally better than that of the DSM in predicting the mean velocity profiles, mean temperature profiles, turbulent intensities, total Reynolds stress, total Reynolds heat flux, and mean SGS flux of kinetic energy, and outperformed the Smagorinsky model.

Numerical Investigation of Regime Transition in Canopy Flows

We have carried out highly resolved simulations of turbulent open channel flows. The channel wall is covered with different filamentous layers sharing the same thickness (h=0.1H, where H is the open channel height) and bulk Reynolds number (i.e., Re_b=U_bH/nu , , U_b is the bulk velocity and nu the kinematic fluid viscosity). The layers are composed of rigid, slender cylindrical filaments mounted perpendicular to the bottom wall. We have selected two layer configurations characterised by filament spacing ratios of Delta S/H=pi /24simeq 0.13 and Delta S/H=pi /32simeq 0.098. The geometrical features of the two layers, allow to classify them as transitional canopies (lambda =dh/Delta S^2simeq 0.15, where d is the filament diameter, i.e. dh is the filament frontal area) (Monti et al. 2020), which is defined as the separation between the sparse-dense asymptotic regimes, proposed by Nepf (2012). While the physical characterisation of the two asymptotic regimes is fairly understood, the transitional conditions remain an open question since the physical characteristics unique to the sparse and dense scenarios coexist in the transitional regime. By resolving every single filament with the aid of an immersed boundary technique in the framework of a Large Eddy formulation, we report the physical mechanisms that emerge at the onset of different regimes (chosen values of lambda fall on the verge between a dense and a sparse condition) and verify the criterion associated with the inception of the transition regime.

Spatial and spectral characteristics of information flux between turbulent boundary layers and porous media

The interaction between boundary layer turbulence and a porous layer is the cornerstone of interface engineering. In this study, the spatial and spectral-resolved transfer entropy is used to assess the asymmetry of the causal interaction next to the permeable wall. The analysis is based on pore-resolved direct numerical simulation of turbulent channel flow over cylinder arrays. The spatial map of transfer entropy reveals the information flux between the porous medium and arbitrary nearby positions, and paths connecting locations with maximum information transfer are identified. The paths in the ‘top-down’ and ‘bottom-up’ directions, respectively, lean upstream and downstream, demonstrating that the coupling process is directionally dependent. The scale dependence of transfer entropy is inspected with a surrogate data strategy. As wall permeability increases, the active scale range in causal interaction shifts from near-wall vortices to Kelvin–Helmholtz type eddies. In addition, linear stochastic estimation is used to determine the statistical velocity field for a local informative event. In an average sense, the interaction between a convecting sweep or ejection event and the up/down-welling motions at the pore unit is the core mechanism that contributes to the causal coupling. The statistical findings derived from the transfer entropy are then validated using a neural network-based remote sensing model.

An ensemble Synthetic Eddy Method for accurate treatment of inhomogeneous turbulence

An ensemble approach to generating turbulent inflow boundary conditions using the Synthetic Eddy Method is proposed that improves signal accuracy in recovering target statistics for inhomogeneous turbulence while reducing the cost of generating an inflow signal. This is accomplished by eliminating typical restrictions related to the Synthetic Eddy Method such as homogeneous turbulence, limited shape functions, random eddy placement, and uniform synthetic eddy convection velocity. The approach gives flexibility and freedom to prescribe arbitrary synthetic eddy length scales, shape functions, eddy placement, and convective velocities while accurately reproducing input Reynolds stresses and maintaining the simplicity of the original method. Three examples of leveraging this flexibility to provide accurate turbulent length scale inhomogeneity and reduce the required number of generated synthetic eddies are provided. Turbulent inflow signals for a channel flow configuration are generated using six variations and the resulting signal accuracy and costs are compared. These inflow signals are applied to a set of Large Eddy Simulations of turbulent channel flow and show favorable results over the original method in terms of the skin friction coefficient convergence, Q-criterion plots, and computed Reynolds stresses. The ensemble approach is shown to be more accurate in reproducing desired turbulent characteristics compared to the original Synthetic Eddy Method, in a simpler manner compared to recent variants of the method.

Quasi-dynamic subgrid-scale kinetic energy equation model for large-eddy simulation of compressible flows

A quasi-dynamic subgrid-scale (SGS) kinetic energy one-equation eddy-viscosity model is introduced in this paper for large-eddy simulation (LES) of compressible flows. With the additional SGS kinetic energy equation, the SGS kinetic energy can be predicted properly. Then, using the dual constraints of SGS kinetic energy and the SGS kinetic energy flux, the eddy-viscosity model can be determined exactly. Taking a similar scheme as the expansion of the SGS stress, other unclosed quantities in the equations to be solved could be well modelled separately. Therefore, with the advance of the equations, all the model coefficients can be determined dynamically. Differing from the classic dynamic procedure, the new methodology needs no test filtering, and thus it could also be called a quasi-dynamic procedure. Using direct numerical simulation of compressible turbulent channel flow, the$a$ $priori$test shows that the key modelled quantities of the suggested model display high correlations with the real values. In LES of compressible turbulent channel flows of the Mach number being$1.5$and 3.0, the proposed model can precisely predict some important quantities, including the mean velocity, Reynolds stress and turbulent flux, and it can also supply more abundant turbulent structures. For the compressible flat-plate boundary layer, the new model can correctly predict the transition process, mean velocity and turbulence intensities in the turbulent region. The results show that the proposed model has the advantage of scale adaptivity. Finally, the new model is applied to LES of turbulent mixing in spherical converging Richtmyer–Meshkov instability, and the accurate results show that the new model has a good ability for LES of complex fluids.

Direct numerical simulations of turbulent channel flow over ratchet roughness

The influence of the orientation of ratchet-type rough surfaces on their fluid dynamic roughness effect is investigated using direct numerical simulations of turbulent channel flow at Re_{tau }=395. The ratchet length-to-height ratio is varied from ell /k=2 to 16 for a fixed ratchet height of k/delta =0.1 where delta is the mean channel half-height. The results show that both roughness function and mean flow and turbulence statistics strongly depend on the ratchet orientation. Existing empirical formulae, which estimate the roughness function Delta U^+ or the equivalent sand-grain roughness k_s based on surface-slope related parameters such as the effective slope or the Sigal-Danberg parameter, fail to accurately predict the differences between ratchet surfaces with high windward slopes and ratchet surfaces with high leeward slopes.

Turbulent channel flow controlled by traveling-wave-like body force mimicking oscillating thin films

To improve energy efficiency, flow control techniques for skin-friction drag and heat transfer with regard to wall turbulence are essential. This study performs direct numerical simulation of turbulent channel flows. The traveling-wave-like body force is employed as the flow control technique to break the similarity between momentum and heat transfer. The traveling wave control mimics the self-excited thin film in the corresponding experimental study. When the wave traveled slowly along the downstream direction, the skin-friction drag, heat transfer, and analogy factor were found to increase. Moreover, these parameters increased with an increase in the reference height of the traveling wave (hw). Flow visualization shows turbulence enhancement owing to the increase in hw. Three-component decomposition elucidates the difference between the control effect on the Reynolds shear stress and the turbulent heat flux.

Predictive capability of the logarithmic law for roughness-modeled large-eddy simulation of turbulent channel flows with rough walls

Direct numerical simulation (DNS) and large-eddy simulation (LES) resolving roughness elements are computationally expensive. LES employing the logarithmic law as the wall model, without the need to resolve the flow at the roughness element scale, provides an efficient alternative for simulating turbulent flows over rough walls. In this work, we evaluate the predictive capability of the roughness-modeled LES by comparing its predictions with those from the roughness-resolved DNS for turbulent channel flows with rough walls. A good agreement is observed for the mean streamwise velocity. The Reynolds stresses predicted by the roughness-modeled LES also reasonably agree with the roughness-resolved predictions. Differences, on the other hand, are observed for the dispersive Reynolds stresses, integral scales, and space-time correlations. The roughness-modeled LES fails to predict the dispersive stresses as one can expect. In the outer layer, the integral length scale predicted by the roughness-modeled LES is lower than the roughness-resolved prediction, which cannot be improved by refining the grid. As for the space-time correlations, discrepancies are shown for the streamwise velocity fluctuations, with a faster decay of the correlation in the outer layer observed in the roughness-modeled predictions. Examination of the space-time correlation using the elliptic approximation model shows that the roughness-modeled LES underpredicts the convection velocity in the near wall region while overpredicting the sweeping velocity in the outer layer with no improvements observed when refining the grid.

Prediction of polymer extension, drag reduction, and vortex interaction in direct numerical simulation of turbulent channel flows

Hydrodynamic and viscoelastic interactions between the turbulent fluid within a channel at Reτ=180 and a polymeric phase are investigated numerically using a multiscale hybrid approach. Direct numerical simulations are performed to predict the continuous phase and Brownian dynamics simulations using the finitely extensible nonlinear elastic dumbbell approach are carried out to model the trajectories of polymer extension vectors within the flow, using parallel computations to achieve reasonable computation timeframes on large-scale flows. Upon validating the polymeric configuration solver against theoretical predictions in equilibrium conditions, with excellent agreement observed, the distributions of velocity gradient tensor components are analyzed throughout the channel flow wall-normal regions. Impact on polymer stretching is discussed, with streamwise extension dominant close to the wall, and wall-normal extension driven by high streamwise gradients of wall-normal velocity. In this case, it is shown that chains already possessing high wall-normal extensions may attempt to orientate more in the streamwise direction, causing a curling effect. These effects are observed in instantaneous snapshots of polymer extension, and the effects of the bulk Weissenberg number show that increased WeB leads to more stretched configurations and more streamwise orientated conformities close to the wall, whereas, in the bulk flow and log-law regions, the polymers tend to trace fluid turbulence structures. Chain orientation angles are also considered, with WeB demonstrating little influence on the isotropic distributions in the log-law and bulk flow regions. Polymer–fluid coupling is implemented through a polymer contribution to the viscoelastic stress tensor. The effect of the polymer relaxation time on the turbulent drag reduction is discussed, with greater Weissenberg numbers leading to more impactful reduction. Finally, the velocity gradient tensor invariants are calculated for the drag-reduced flows, with polymers having a significant impact on the Q–R phase diagrams, with the presence of polymers narrowing the range of R values in the wall regions and causing flow structures to become more two-dimensional.

Developed spatial turbulent channel flow simulation for acoustic wave propagation

When an acoustical object is tested in a duct, very often it is located downstream of a long rigid duct which creates a developed turbulent flow. This paper presents a strategy to reproduce the same situation numerically, in the subsonic case. The direct numerical simulation of a periodic precursor simulation is done, a plane of which is used to feed the spatial simulation where a developed flow is desired. The turbulence in the spatial channel is developed only if the correct source term is used in the precursor simulation, which has been discussed by Brun et al. (2008). The inflow/outflow section of the spatial channel are managed with the methods of characteristics including plane wave masking and relaxation terms. As a result plane acoustic waves are introduced with no distortion of the injected flow, and their propagation in the developed flow is computed and compared to predictions made by modal analysis. Some low frequencies are included, for which the damping rate is affected by turbulence.

Improved implicit potential method for incompressible flows on a fully collocated mesh

AbstractIn the present work, we present a new version of the pressure‐based implicit potential (IPOT) method for incompressible flows, which can be applied on a fully collocated mesh. The new version combines the IPOT algorithm with the Rhie and Chow (RC) technique, to produce solutions on collocated grids that are free of spurious pressure modes. The IPOT‐RC method retains all the benefits of the original algorithm, i.e. explicit velocity–pressure coupling, easy implementation and reduced iteration time, without requiring a special grid topology. The presentation of the IPOT‐RC method is accompanied by an extensive discussion on the cause of the spurious oscillations in zero‐div problems in general, and a possible cure that is linked to the RC technique. The IPOT‐RC method is validated through several benchmark problems including the lid‐driven cavity flow, flow over a backward facing step and direct numerical simulation of turbulent channel flow.

Direct numerical simulation of supersonic turbulent flows over rough surfaces

We perform direct numerical simulation of supersonic turbulent channel flow over cubical roughness elements, spanning bulk Mach numbers $M_b=0.3$ – $4$ , both in the transitional and fully rough regime. We propose a novel definition of roughness Reynolds number which is able to account for the viscosity variations at the roughness crest and should be used to compare rough-wall flows across different Mach numbers. As in the incompressible flow regime, the mean velocity profile shows a downward shift with respect to the baseline smooth wall cases, however, the magnitude of this velocity deficit is largely affected by the Mach number. Compressibility transformations are able to account for this effect, and data show a very good agreement with the incompressible fully rough asymptote, when the relevant roughness Reynolds number is used. Velocity statistics present outer layer similarity with the equivalent smooth wall cases, however, this does not hold for the thermal field, which is substantially affected by the roughness, even in the channel core. We show that this is a direct consequence of the quadratic temperature–velocity relation which is also valid for rough walls. Analysis of the heat transfer shows that the relative drag increase is always larger than the relative heat transfer enhancement, however, increasing the Mach number brings data closer to the Reynolds analogy line due to the rising relevance of the aerodynamic heating.

Synthetic turbulence generator for lattice Boltzmann method at the interface between RANS and LES

The paper presents a synthetic turbulence generator (STG) for the lattice Boltzmann method (LBM) at the interface of the Reynolds averaged Navier–Stokes (RANS) equations and the LBM large eddy simulation (LES). We first obtain the RANS velocity field from a finite volume solver at the interface. Then, we apply a numerical interpolation from the RANS velocity field to the LBM velocity field due to the different grid types of RANS and LBM. The STG method generates the velocity fluctuations, and the regularized LBM reconstructs the particle distribution functions at the interface. We perform a turbulent channel flow simulation at Reτ=180 with the STG at the inlet and the pressure-free boundary condition at the outlet. The velocity field is quantitatively compared with the periodic lattice Boltzmann based LES (LES-LBM) channel flow and the direct numerical simulation (DNS) channel flow. Both the adaptation length and time for the STG method are evaluated. Also, we compare the STG-LBM channel flow results with the existing LBM synthetic eddy method (SEM-LBM) results. Our numerical investigations show good agreement with the DNS and periodic LES-LBM channel flow within a short adaptation length. The adaptation time for the turbulent channel flow is quantitatively analyzed and matches the DNS around 1.5–3 domain flow-through time. Finally, we check the auto-correlation for the velocity components at different cross sections of the streamwise direction. The proposed STG-LBM is observed to be both fast and robust. The findings show good potential for the hybrid RANS/LES-LBM based solver on the aerodynamics simulations and a broad spectrum of engineering applications.

An uncertainty-quantification framework for assessing accuracy, sensitivity, and robustness in computational fluid dynamics

Combining different existing uncertainty quantification (UQ) techniques, a framework is obtained to assess a set of metrics in computational physics problems, in general, and computational fluid dynamics (CFD), in particular. The metrics include accuracy, sensitivity and robustness of the simulator’s outputs with respect to uncertain inputs and parameters. These inputs and parameters are divided into two groups: based on the variation of the first group (e.g. numerical/computational parameters such as grid resolution), a computer experiment is designed, the data of which may become uncertain due to the parameters of the second group (e.g. finite time-averaging). To construct a surrogate model based on uncertain data, Gaussian process regression (GPR) with observation-dependent (heteroscedastic) noise is used. To estimate the propagated uncertainties in the simulator’s outputs from the first group of parameters, a probabilistic version of the polynomial chaos expansion (PCE) is employed Global sensitivity analysis is performed using probabilistic Sobol indices. To illustrate its capabilities, the framework is applied to the scale-resolving simulations of turbulent channel and lid-driven cavity flows using the open-source CFD solver Nek5000. It is shown that at wall distances where the time-averaging uncertainty is high, the quantities of interest are also more sensitive to numerical/computational parameters. In particular for high-fidelity codes such as Nek5000, a thorough assessment of the results’ accuracy and reliability is crucial. The detailed analyses and the resulting conclusions can enhance our insight into the influence of different factors on physics simulations, in particular the simulations of high-Reynolds-number turbulent flows including wall turbulence.

Comparative analysis of drag reduction characteristics of two-type riblets based on numerical simulation

Turbulent drag reduction has always been a hot issue in fluid mechanics. Among various turbulent drag reduction methods, riblets has attracted wide attention due to its simple structure and convenient application. In order to investigate the effect of the riblets shape on the drag reduction, the effect of the triangular and trapezoidal riblets on the turbulent boundary layer flow field and drag reduction characteristics has been studied numerically by adopting the CFD method and based on the large eddy simulation (LES). The numerical simulation of turbulent channel flow was conducted by RANS, DES and LES methods respectively, and their results were compared with the results of direct numerical simulation (DNS) to verify the accuracy and feasibility of the large eddy simulation method. According to the experimental results in references, the flow field parameters such as integral statistics, first-order statistics and second-order statistics of the triangular and trapezoidal riblets on the turbulent boundary layer flow fields were compared and analyzed. The drag reduction characteristics of two-type riblets were investigated by studying the variation in physical parameters such as drag reduction rate, time-averaged velocity, root mean square velocity fluctuation, shear stress, turbulent kinetic energy generation and contour of spanwise velocity fluctuation, and it was concluded that the trapezoidal riblets have better drag reduction effect than the triangular riblets under the same dimensionless condition.