Simulation Of Turbulent Channel Flow Research Articles

Identifying regions of importance in wall-bounded turbulence through explainable deep learning

Despite its great scientific and technological importance, wall-bounded turbulence is an unresolved problem in classical physics that requires new perspectives to be tackled. One of the key strategies has been to study interactions among the energy-containing coherent structures in the flow. Such interactions are explored in this study using an explainable deep-learning method. The instantaneous velocity field obtained from a turbulent channel flow simulation is used to predict the velocity field in time through a U-net architecture. Based on the predicted flow, we assess the importance of each structure for this prediction using the game-theoretic algorithm of SHapley Additive exPlanations (SHAP). This work provides results in agreement with previous observations in the literature and extends them by revealing that the most important structures in the flow are not necessarily the ones with the highest contribution to the Reynolds shear stress. We also apply the method to an experimental database, where we can identify structures based on their importance score. This framework has the potential to shed light on numerous fundamental phenomena of wall-bounded turbulence, including novel strategies for flow control.

Direct numerical simulation of compressible turbulent channel flows over porous boundaries

The impact of porous boundaries on skin friction and heat transfer in compressible turbulent channel flows is explored through direct numerical simulations. Utilizing the volume-averaged Navier–Stokes equations for the porous media, we examine flows at Mach numbers Mb=0.3 and Mb=1.5, with friction Reynolds numbers ranging from 176 to 220, across three permeability levels: 0 (impermeable), 1.6×10−5, and 1.0×10−4. Our findings reveal a dual impact of porous boundaries on skin friction: a direct reduction due to averaged slip velocity at the interface and an indirect increase from amplified Reynolds shear stress due to enhanced wall-normal permeability. This permeability weakens the wall-blocking effect, leading to intensified wall-normal velocity fluctuations and consequently higher Reynolds stress. Additionally, the Mach number significantly influences flow structures, particularly at higher permeabilities, where it disrupts near-wall streaks at Mb=0.3 but has a diminished effect at Mb=1.5. Thermal analysis confirms the validity of the generalized Reynolds analogy for the mean temperature in these flows, with the turbulent Prandtl number approximating 1, in line with the strong Reynolds analogy. Moreover, a strong spatial correlation between heat flux and wall shear stress fluctuations underscores the intertwined dynamics of momentum and thermal transport at the porous–fluid interface.

Causality between streaks and bursts in wall-bounded turbulence

We use an information-theoretic method, referred to as information flux, to quantify the causal relationships between streaks and bursts in a non-intrusive manner. Within this framework, causality is quantified as the flux of Shannon information from the present of the quantities of interest to their future. We also use the so-called information leak to measure the information that is not accounted for due to unobserved variables. We investigate data from a direct numerical simulation of turbulent channel flow at the friction Reynolds number Re τ ≈ 180. The spatial distribution of causality is investigated as two time scales based on 50% value of the information leak and maximum of the normalized cross-induced information flux. It is found that the most causal spatial configuration for streaks and bursts is always streamwise-aligned. Furthermore, four dominant causal spatial configurations between streaks and bursts are identified. At the short time scale around 10 viscous units (when information flux is 50%), streaks and bursts have comparable causality to one another. At the longer time scale (corresponding to the maximum cross-induced causality), there is greater causality from streaks to bursts.

Direct numerical simulations of high-enthalpy supersonic turbulent channel flows including finite-rate reactions

Direct numerical simulations of temporally evolving high-enthalpy supersonic turbulent channel flows are conducted at a Mach number of 3.0 and Reynolds number of 4880 under isothermal wall conditions. Air is assumed to behave as a five-species mixture, and chemical non-equilibrium and equilibrium assumptions are adopted to investigate the influence of finite-rate reactions on the turbulent statistics and large-scale structures. The two wall temperatures of 1733.2 and 3500 K are such that the mixture components undergo strong dissociation and recombination reactions along the channel. Investigation shows that the turbulent intensity is weakened and the mean and fluctuating temperatures are smaller when finite-rate reactions are considered. The mean dissociation degree is a quadratic function of the normal position, and its curvature under the chemical non-equilibrium assumption is greater than that under the chemical equilibrium assumption. The fluctuating mass fractions of the generated species seem to decrease slightly in the near-wall region, and their distributions are obviously different from those of the fluctuating velocity and fluctuating temperature. Finite-rate reactions increase the proportion of turbulent kinetic energy production in the skin friction decomposition, especially when the wall temperature is 3500 K. The large-scale structures visualized by the cross correlation between temperature and species mass fraction become stronger in the normal direction. The turbulent Schmidt number and several velocity–temperature correlations, including the recovery enthalpy and strong Reynolds analogy, are insensitive to the chemical reaction rate and wall temperature.

Turbulent Channel Flow: Direct Numerical Simulation-Data-Driven Modeling

Turbulent Channel Flow: Direct Numerical Simulation-Data-Driven Modeling

Reynolds-number scaling of wall-pressure–velocity correlations in wall-bounded turbulence

Wall-pressure fluctuations are a practically robust input for real-time control systems aimed at modifying wall-bounded turbulence. The scaling behaviour of the wall-pressure–velocity coupling requires investigation to properly design a controller with such input data so that it can actuate upon the desired turbulent structures. A comprehensive database from direct numerical simulations (DNS) of turbulent channel flow is used for this purpose, spanning a Reynolds-number range $Re_\tau \approx 550\unicode{x2013}5200$ . Spectral analysis reveals that the streamwise velocity is most strongly coupled to the linear term of the wall pressure, at a Reynolds-number invariant distance-from-the-wall scaling of $\lambda _x/y \approx 14$ (and $\lambda _x/y \approx 8$ for the wall-normal velocity). When extending the analysis to both homogeneous directions in $x$ and $y$ , the peak coherence is centred at $\lambda _x/\lambda _z \approx 2$ and $\lambda _x/\lambda _z \approx 1$ for $p_w$ and $u$ , and $p_w$ and $v$ , respectively. A stronger coherence is retrieved when the quadratic term of the wall pressure is concerned, but there is only little evidence for a wall-attached-eddy type of scaling. An experimental dataset comprising simultaneous measurements of wall pressure and velocity complements the DNS-based findings at one value of $Re_\tau \approx 2$ k, with ample evidence that the DNS-inferred correlations can be replicated with experimental pressure data subject to significant levels of (acoustic) facility noise. It is furthermore shown that velocity-state estimations can be achieved with good accuracy by including both the linear and quadratic terms of the wall pressure. An accuracy of up to 72 % in the binary state of the streamwise velocity fluctuations in the logarithmic region is achieved; this corresponds to a correlation coefficient of $\approx$ 0.6. This thus demonstrates that wall-pressure sensing for velocity-state estimation – e.g. for use in real-time control of wall-bounded turbulence – has merit in terms of its realization at a range of Reynolds numbers.

Direct numerical simulations of turbulent channel flow with a rib-roughened porous wall

To describe the effects of porous roughness on turbulence, we have carried out direct numerical simulations using the lattice Boltzmann method. The simulated flows are fully developed turbulent flows in channels consisting of a solid smooth top wall and a porous bottom wall with transverse porous ribs whose heights are 10 % of the channel height. The considered ratios of the rib spacing to the rib height are $w/k\simeq 1$ and 9. The Kelvin-cell structure is applied to construct faithfully the porous media whose porosities are $\varphi \ge 0.79$ . Three kinds of porous media having different permeabilities are considered. The most permeable one has an approximately one order higher permeability than that of the least permeable one. The higher permeability case is designed to have a pore scale that is the same as the rib height so that it is the most permeable case for the rib roughness with the designed porosity. In the simulations, the bulk Reynolds number is set to $Re_b=5500$ , and the corresponding permeability Reynolds numbers are $Re_K=2.2\unicode{x2013}7.5$ . The simulated field data and the drag coefficient, which includes both the pressure drag by the ribs and the frictional drag over the porous wall, are analysed to understand the characteristics of the permeable roughness in terms of permeability. The decomposition of the drag coefficient into the integrated laminar, rib-drag, dispersion and turbulence parts elucidates the transition mechanism between the typical d-type to k-type roughness depending on $Re_K$ . By the double (time and space) averaged budget equations for the dispersion and Reynolds stresses, we explain how the energy generated by the roughness transfers to turbulence through dispersion resulting in the k-type characteristics. The nominal roughness sublayer thickness and the characteristic roughness height are introduced with the parameters obtained by fitting the velocity data to Best's and Nikuradse's logarithmic velocity formulae. Along with data in the literature, it is suggested that the ratio of the characteristic roughness height to the nominal roughness sublayer thickness becomes constant irrespective of the rib spacing in the full permeable-wall turbulence at $Re_K> 7$ .

Preferential accumulation of finite-size particles in near-wall streaks

The preference for particles to accumulate at specific regions in the near-wall part is a widely observed phenomenon in wall-bounded turbulence. Unlike small particles more frequently found in low-speed streaks, finite-size particles can accumulate in either low-speed or high-speed streaks. However, mechanisms and influencing factors leading to the different preferential concentration locations still need to be clarified. The present study conducts particle-resolved direct numerical simulations of particle-laden turbulent channel flows to provide a better understanding of this seemingly puzzling behaviour of preferential accumulation. These simulations cover different particle-to-fluid density ratios, particle volume fractions, particle sizes and degrees of sedimentation intensity. We find that the large particle size is the crucial factor that results in particles accumulating in high-speed streaks. Large particles not only are difficult to be conveyed by the quasi-streamwise vortices to low-speed streaks but also can escape from the near-wall region before moving spanwisely out from high-speed streaks. The sedimentation effect allows particles to gather closer to the channel wall and stay longer in the near-wall regions, reinforcing the sweeping mechanism of quasi-streamwise vortices that transport particles from high- to low-speed streaks. As a result, sedimenting particles tend to accumulate in the low-speed streaks.

Direct numerical simulation of momentum and scalar internal boundary layers

Direct numerical simulations (DNS) of turbulent open channel flow are performed to study and compare momentum and scalar internal boundary layers (IBL). An internal boundary layer (IBL) forms when a turbulent boundary layer is subjected to heterogeneous surface conditions. For example, a momentum IBL forms with a change in surface roughness and a scalar IBL forms due to a localised heat flux. Momentum IBLs are simulated using both a streamwise-varying roughness body forcing technique and a streamwise-varying wall shear stress. Passive scalar IBLs are simulated using both streamwise-varying scalar wall values and wall fluxes, for a homogeneous smooth wall. The roughness body forcing model is shown to reproduce the same IBL features as with the explicitly resolved roughness study of Rouhi et al. (2019), but at a reduced cost. Three common IBL detection methods are employed to estimate the power-law exponents in the growth rates of the IBL. The exponents for the momentum IBL cases are typically less than 0.7 for these methods, smaller than for the scalar-analogues of these methods. Furthermore, we analyse the streamwise variation of the root-mean-square wall-normal (vertical) velocity. We find that the ‘diffusion analogy’, or that momentum and scalar IBLs behave similarly, may not be an appropriate assumption, especially for rough-to-smooth transitions for momentum IBLs.

Direct numerical simulations of the drag degradation mechanism in channel flow over trapezoidal riblets

Direct numerical simulations of turbulent channel flows with trapezoidal riblets were conducted to analyze the characteristics of the near-wall flow structures in the drag reduction, drag neutral, and drag increase regimes. The trapezoidal riblets possess a tip angle of α =15°and a height–to-width ratio of k/s = 0.335 for cross-section-area based sizes lg+=Ag+= 11.7, 17, 23.2, and 29 at a friction Reynolds number of Reτ=395. The Reynolds stresses are compared with the smooth wall case, and it is observed that the intensity of the turbulent activities in the boundary layer is diminished for drag reduction riblet and enhanced for drag increase riblets. The roughness sublayer indicates that riblet only directly affect the near-wall region of the flow. By applying the Fukagata, Iwamoto, and Kasagi (FIK) identity in Phys. Fluids, vol. 14, 2002, L73, it is found that the modification of the overall drag is mainly due to the turbulent shear stress. The variation of the dispersive stress is only evident within the roughness sublayer for the drag increasing riblets. The enhanced mean wall-shear stress in the valley is responsible for the drag increase for oversized riblets. The production and convection terms of the turbulent stress reveal that although the total drag contribution is trivial, the convection inside the riblet valleys caused by secondary flow is crucial for the redistribution of the turbulent stress and drag increase of oversized riblets.

Sessile super-droplets as quasi-static wall deformations in direct numerical simulation of turbulent channel flow

Condensation is an important aspect of many flow applications due to the ubiquitous presence of humidity in the air at ambient conditions. For direct numerical simulations of such flows, simulating the gas phase as a mixture characterized by temperature and humidity coupled by the latent heat release and absorption has been shown to yield results consistent with multiphase direct numerical simulations at reduced cost. In the case of surface condensation, the deposition of condensate droplets represents an additional mechanism for flow modification. Extending the single-phase approach by tracking the mean deposition rates and consolidating the condensate mass into static super-droplets reintroduces the effects of surface droplets on the flow while retaining the computational advantages of simulating only the gas phase. Results of simulations of turbulent flow through a cooled, vertical channel with and without such droplets illustrate the additional effects captured compared to the original approach. In the immediate vicinity of a super-droplet, turbulent heat and vapor transport towards the cooled wall is enhanced. Direct impingement and deflection of the flow on the super-droplet cause a qualitative change in the distribution of the condensation rates, increasing on the surface of the super-droplets and decreasing in the surrounding regions. This modification of the near-wall transport leads to increased global cooling and drying efficiency compared to a smooth channel.

The influence of particle density and diameter on the interactions between the finite-size particles and the turbulent channel flow

Understanding the influence of different particle parameters on the two-way interactions between the particles and wall-bounded turbulence is important in many natural phenomena and engineering applications. In this work, particle-resolved direct simulation of particle-laden turbulent channel flow is performed based on the mesoscopic lattice Boltzmann method (LBM), and the particle–fluid interface is treated using the interpolated bounce back scheme. The friction Reynolds number (Reτ) of the single phase turbulent channel flow is 180, and the particle volume fraction is fixed at 1%. Three particle–fluid density ratios and three particle diameters are considered, and five particle-laden simulations are performed to investigate the influence of particle density and diameter on the interactions between the particles and the carrier turbulence. Results show that the streamwise velocity of the solid phase is larger than that of the fluid phase in the near-wall region, and the velocity difference between the two phases decreases with increasing particle density, but increases with increasing particle diameter. The probability density functions (PDFs) of particle velocity and angular velocity depend on the distance between the particles and the wall, but the PDFs of particle acceleration and angular acceleration are not spatially dependent. The distribution of particle Reynolds number follows the Gamma distribution within the buffer region and viscous sublayer. The solid phase concentration is high in the near-wall region, and the largest solid-phase concentration in this region occurs in the case with particles of intermediate density. Particles with different parameters would lead to different modulation to the carrier flow. Then, two aspects of the turbulence modulation are explored, i.e., the streamwise velocity and the turbulent kinetic energy (TKE). The presence of finite-size particles typically increases the streamwise velocity in the near-wall region and reduce the streamwise velocity outside this region. The trend is similar for TKE, but the TKE attenuation mainly occurs in the buffer region. The modulation to the streamwise velocity is analyzed using the streamwise momentum balance equation. It is found that the streamwise velocity modulation is dominated by the weighted Reynolds stress, but the different modulation in the near-wall region is due to the difference in weighted particle-induced stress, whereas the different modulation outside the near-wall region is due to the change in weighted Reynolds stress. Through TKE budget analysis, it is found that the enhancement of the total TKE source in the viscous sublayer increases with increasing particle density and diameter and the attenuation of total TKE source in the buffer region increases with increasing particle density and diameter, which is consistent with the TKE modulation for different cases.

Effect of Stokes number and particle-to-fluid density ratio on turbulence modification in channel flows

Two-way momentum-coupled direct numerical simulations of a particle-laden turbulent channel flow are addressed to investigate the effect of the particle Stokes number and of the particle-to-fluid density ratio on the turbulence modification. The exact regularised point-particle method is used to model the interphase momentum exchange in presence of solid boundaries, allowing the exploration of an extensive region of the parameter space. Results show that the particles increase the friction drag in the parameter space region considered, namely the Stokes number $St_+ \in [2,80]$ , and the particle-to-fluid density ratio $\rho _p/\rho _f \in [90,5760]$ at a fixed mass loading $\phi =0.4$ . It is noteworthy that the highest drag occurs for small Stokes number particles. A measurable drag increase occurs for all particle-to-fluid density ratios, the effect being reduced significantly only at the highest value of $\rho _p/\rho _f$ . The modified stress budget and turbulent kinetic energy equation provide the rationale behind the observed behaviour. The particles’ extra stress causes an additional momentum flux towards the wall that modifies the structure of the buffer and of the viscous sublayer where the streamwise and wall-normal velocity fluctuations are increased. Indeed, in the viscous sublayer, additional turbulent kinetic energy is produced by the particles’ back-reaction, resulting in a strong augmentation of the spatial energy flux towards the wall where the energy is ultimately dissipated. This behaviour explains the increase of friction drag in particle-laden wall-bounded flows.

Reynolds Number Dependency of Wall-Bounded Turbulence Over a Surface Partially Covered by Barnacle Clusters

The settlement of barnacles on a ship hull is a common form of marine biofouling. In this study, the Reynolds number dependency of turbulent flow over a surface partially covered by barnacle clusters is investigated using direct numerical simulations of turbulent channel flow at friction Reynolds numbers ranging from 180 to 720. Mean flow, Reynolds and dispersive stress statistics are evaluated and compared to the corresponding results for a generic irregular rough surface with a Gaussian height distribution. For the barnacle surface, distinctive features emerge in the velocity statistics due to the interplay between the barnacle clusters and the large, connected smooth-wall sections surrounding them. This aspect is further investigated by applying a rough-smooth decomposition to the local time-averaged flow statistics for the barnacle surface. Using this decomposition, the partial recovery of smooth-wall behaviour over the smooth sections of the barnacle surface can be observed in the Reynolds stress statistics with the streamwise Reynolds stresses exhibiting a similar behaviour as previously found for boundary layers over surfaces with a rough to smooth transition.

Development of an Interpolated RANS-LES solver for wall-bounded turbulent fluid flows

Scale-resolving hybrid RANS-LES models are being increasingly used to numerically simulate wall-bounded turbulent flows since they are computationally efficient compared to LES (Large Eddy Simulation) while also being more accurate compared to RANS (Reynolds-Averaged Navier–Stokes) models. Existing hybrid RANS-LES models typically either suffer from modeled stress depletion or they can introduce a sharp jump in the mean Reynolds stress across the RANS-LES zone. We present a novel interpolated RANS-LES (IRL) solver implemented in OpenFOAM, in which the RANS equations (for eddy-viscosity) and LES equations (for filtered velocity) are evolved simultaneously on the same computational grid. Based on the distance from the no-slip wall, the flow domain is demarcated into a near-wall, free-stream, and a “hybrid” region, sandwiched between the near-wall and free-stream regions. Spalart Allmaras (S-A) model has been used to evolve the RANS eddy viscosity, while the Wall Adapting Local Eddy Viscosity (WALE) model is used for evolving the filtered LES velocity. Using a novel scheme based on solving a partial differential equation, the turbulent eddy-viscosity is interpolated between the RANS eddy viscosity in the near wall region and the effective eddy viscosity from the resolved LES fluctuations in the free-stream region. The mean subgrid stress in the LES momentum equation is then corrected in the near-wall and hybrid regions using the interpolated turbulent eddy-viscosity. IRL’s grid resolution requirements are the same as DES’s (Detached Eddy Simulation). Grid convergence and sensitivity studies have been carried out for two canonical flow geometries. For turbulent channel flow simulations, the IRL solver does not display the typical mean stress depletion observed in DES while also predicting resolved Reynolds stresses accurately in the free-stream region. For simulations of flow over backward facing step, the IRL solver can predict the friction factor and coefficient of pressure better than that DES, especially after the reattachment point.

Large-eddy simulation of turbulent channel flows with antifouling-featured bionic microstructures

The large-eddy simulation of a shark skin surface at Reynolds numbers of Reτ=1200, 2400, and 4500 is carried out in a fully turbulent flow channel to investigate the antifouling mechanism of shark skin from the perspective of hydrodynamics. The antifouling properties are validated through the confocal laser scanning microscopy of microorganism settlement and a measurement of the reduction in pollutant mass. A large-eddy simulation database is then analyzed, focusing on mean and turbulent statistics, to explain the flow characteristics of time-varying fields of the flow that surrounds and skims over the shark skin. A phenomenological scenario based on instantaneous visualizations of vortical events using the Q-criterion is put forward to identify the spatiotemporal evolution of turbulent coherent structures in the outer region. Subsequently, the proposed scenario is accessed by analyzing two-point correlation coefficients, the conditional averaging of vortical events, the wall friction coefficient distribution, and the spatiotemporal evolution of vortices. The flow patterns are predominantly driven by the periodic emission of hairpin-type vortices, which form a strong shear layer and exacerbate shear stress and momentum exchange. Furthermore, these vortices are associated with the generation of a bicyclical system involving an unsteady propagation of turbulent fluids, which develops separately near the front and back of each shark scale. These modes elaborate the antifouling mechanism of shark skin. Analysis of the probability density function and the spatiotemporal map reveals that these strong events have high levels of intermittency in time and space, which vitally contributes to the antifouling properties manifested in the evolution of periodic shear friction over different surfaces.

Influence of Ridge Spacing, Ridge Width, and Reynolds Number on Secondary Currents in Turbulent Channel Flow Over Triangular Ridges

Most studies of secondary currents (SCs) over streamwise aligned ridges have been performed for rectangular ridge cross-sections. In this study, secondary currents above triangular ridges are systematically studied using direct numerical simulations of turbulent channel flow. The influence of ridge spacing on flow topology, mean flow, and turbulence statistics is investigated at two friction Reynolds numbers, 550 and 1000. In addition, the effects of ridge width on SCs, which have not previously been considered for this ridge shape, are explored. The influence of SCs on shear stress statistics increases with increased ridge spacing until SCs fill the entire channel. One of the primary findings is that, for ridge configurations with pronounced secondary currents, shear stress statistics exhibit clear Reynolds number sensitivity with a significant growth of dispersive shear stress levels with Reynolds number. In contrast to rectangular ridges, no above-ridge tertiary flows are observed for the tested range of ridge widths. Flow visualisations of SCs reveal the existence of corner vortices that form at the intersection of the lateral ridge sides and the smooth-wall sections. These are found to gradually disappear as ridges increase in width. Premultiplied spectra of streamwise velocity fluctuations show strong dependency on the spanwise sampling location. Whereas spanwise averaged spectra show no strong modifications by SCs, a significant increase of energy levels emerges at higher wavelengths for spectra sampled at the spanwise locations that correspond to the centres of the secondary currents.

Interface Splitting Algorithm: A Parallel Solution to Diagonally Dominant Tridiagonal Systems

We present an interface-splitting algorithm (ITS) for solving diagonally dominant tridiagonal systems in parallel. The construction of the ITS algorithm profits from bidirectional links in modern networks, and it only needs one synchronization step to solve the system. The algorithm trades some necessary accuracy for better parallel performance. The accuracy and the performance of the ITS algorithm are evaluated on four different parallel machines of up to 2048 processors. The proposed algorithm scales very well, and it is significantly faster than the algorithm used in ScaLAPACK. The applicability of the algorithm is demonstrated in the three-dimensional simulations of turbulent channel flow at Reynolds number 41,430.

Large-eddy simulation of free-surface turbulent channel flow over square bars

The results of large-eddy simulations of free-surface turbulent channel flow over spanwise-aligned square bars are used to investigate the effects of bed roughness and water surface deformations on the root-mean-squared velocity fluctuations, dispersive shear stress, double-averaged Reynolds shear stress, wake kinetic energy and double-averaged turbulent kinetic energy. Two bar spacings, corresponding to transitional and k-type roughness, at similar Reynolds and Froude numbers are considered. The main peak of all statistical quantities occurs at the bar crest height. The effects of a standing wave at the water surface in flow over k-type roughness is marked by a local peak under the water surface for all statistical quantities considered here except wall-normal and spanwise velocity fluctuations. Quadrant analysis shows that sweeps and ejections are the strongest events contributing to both dispersive and double-averaged Reynolds shear stress but their contributions are different for the two bar spacings. Examining the budgets of dispersive and double-averaged Reynolds shear stress reveals that the dominant terms of these stresses are pressure–strain correlation and pressure transport and the contribution of wake production is similar for both of these stresses but with opposite sign. In addition to the main role of the bars in consuming or producing wake kinetic energy through production and transport and convection, the standing wave at the water surface in flow over k-type roughness induces large convection in the bulk flow too. The dominant terms in the double-averaged turbulent kinetic energy budget are similarly production, transport and convection. Large shear production renders large temporal fluctuations than spatial fluctuations of flow variables. The interaction of bars, bed and water surface is seen in the convection term in flow over k-type roughness.

Models of interphase drag force from direct numerical simulations of upward turbulent particle-laden channel flows

Data from the interfaced-resolved direct numerical simulations (IR-DNSs) of upward turbulent channel flow laden with finite-size heavy particles at particle concentration ranging from 0.84% to 2.36% are used to develop improved drag correlations which account for the effect of turbulence on drag enhancement. First, the contribution of drag nonlinearity to drag enhancement for the turbulent flow over a fixed sphere is analyzed with the consideration of velocity fluctuation anisotropy. The nonlinear drag enhancement is generally smaller than the actual drag enhancement in our numerical simulations. Second, several models for turbulence correction are presented with different choice of model parameters, and it is found that the turbulent intensity normalized by the mean slip velocity and the particle size normalized by the Kolmogorov scale are most important for modeling the effect of turbulence on particle drag, while the anisotropy of fluctuating velocity and the particle Reynolds number are less important.