Plane Channel Flow Research Articles

Microflow-based control of near-wall fluctuations for large viscous drag reduction

The stabilizing effect of microgroove surface morphology on viscous drag reduction was studied experimentally in the inlet region of a plane channel flow. The stabilization is thought to be due to the ability of a microgrooved surface pattern to suppress the velocity fluctuations in the spanwise direction on a restricted portion of the wetted surface, which prevents vorticity development at the wall and consequently across the entire flow field. This smart microflow control strategy, which works successfully only under very particular circumstances, was implemented in a microgroove-modified channel flow in which the front part has a microgrooved surface topology. The results of pressure drop measurements indicate that microgrooved surfaces can effectively stabilize laminar boundary layer development, leading to a significant reduction in the viscous drag. In the rear flat part of the microgroove-modified channel test section, a maximum drag reduction of \({\rm DR\simeq 35\%}\) was measured. This corresponds to an overall drag reduction of \({\rm DR\simeq 16\%}\) at a length Reynolds number of \(Re_x\simeq 10^6. \) The drag reduction effect persisted in a narrow range of flow velocities and for the reported experimental conditions corresponds to microgroove dimensions between 1.5 and 2.5 viscous length-scales.

Unsteady turbulence in plane channel flow

Direct numerical simulations were conducted for oscillating flow with zero time mean (reciprocating flow) in a plane channel subject to a harmonic forcing term of varying amplitude and frequency. The results confirmed the existence of four flow regimes (laminar, “disturbed laminar”, intermittently turbulent, and fully turbulent) depending on the above parameters. The flow behaviour was found to depend on the complex interplay of mean and turbulence quantities, as described by the closed loop formed by the streamwise Reynolds-averaged momentum equation in conjunction with the exact transport equations for the turbulent (Reynolds) stresses. A crucial role in this loop appeared to be played by the different time response of the mean flow to the applied forcing at different cross-stream locations, due to the laminar and turbulent diffusion of momentum from the walls and causing characteristic distortions of the cross-stream mean velocity profiles at different phases (i.e. acceleration vs. deceleration). The intrinsic inertia of turbulence quantities themselves played only a minor role, as confirmed by the fact that, in a broad range of conditions, turbulent stresses were roughly in phase with the respective production and dissipation terms. The structure of turbulence was found to depend largely on the instantaneous mean velocity profile, as confirmed by “frozen velocity” simulations.

Non-Newtonian fluid flow in plane channels: Heat transfer enhancement using porous blocks

A numerical investigation is performed for heat transfer enhancement in a parallel-plate channel. Porous blocks are inserted to partially fill the channel, which is crossed by a power-law fluid. The modified Brinkman–Forchheimer extended Darcy model for power-law fluids is used in the porous layer while the Navier–Stokes equation are employed in the clear region of the channel. Results are reported for two cases: (1) a channel with a single porous block and (2) a channel with two porous blocks mounted alternatively at the bottom and top walls of the channel. The combined effects of both the porous blocks and the non-Newtonian fluid properties on the hydrodynamic and thermal characteristics of the flow are analyzed. To this end, computations are performed to highlight the effect of parameters such as the Darcy number, the Reynolds number, and the power-law index. For the case of the single porous block, the heat transfer is enhanced and maximized at low permeability. In the second configuration as well, heat transfer improvement can also be obtained, even if the thermal conductivity ratio is equal to 1. This enhancement is maximized for particular values of the Darcy number that depend on the flow pattern and the power-law index. Concerning the rheological aspect, it is found that pseudo plastic fluids exhibit the highest Nusselt number and the lowest pressure loss. The presence of the porous inserts causes a significant increase in pressure drop, which is found to be more important with dilatant fluids.

Numerical Simulations of Heat Transfer in Plane Channel Flow

Reynolds-averaged Navier–Stokes “RANS” turbulence models (such as k-ε models) are still widely used for engineering applications because of their relatively simplicity and robustness. In fully developed plane channel flow (i.e. the flow between two infinitely large plates), even if available models and near-wall treatments provide adequate mean flow velocities, they fail to predict suitable turbulent kinetic energy “TKE” profiles near walls. TKE is involved in determination of eddy viscosity/diffusivity and could therefore provide inaccurate concentrations and temperatures. In order to improve TKE a User Defined Function “UDF” based on an analytical profile for TKE was developed and implemented in FLUENT. Mean streamwise velocity and TKE profiles were compared to DNS data for friction Reynolds number Reτ = 150. Simulation results for TKE show accurate profiles. Simulation results for horizontal heated channel flows obtained with FLUENT are presented. Numerical results are validated by direct numerical simulation “DNS” data for Reτ = 150.

Planar channel flow in Braginskii magnetohydrodynamics

Braginskii magnetohydrodynamics (MHD) is a single-fluid description of large-scale motions in strongly magnetised plasmas. The ion Larmor radius in these plasmas is much shorter than the mean free path between collisions, so momentum transport across magnetic field lines is strongly suppressed. The relation between the strain rate and the viscous stress becomes highly anisotropic, with the viscous stress being predominantly aligned parallel to the magnetic field. We present an analytical study of the steady planar flow across an imposed uniform magnetic field driven by a uniform pressure gradient along a straight channel, the configuration known as Hartmann flow, in Braginskii MHD. The global momentum balance cannot be satisfied by just the parallel viscous stress, so we include the viscous stress perpendicular to magnetic field lines as well. The ratio of perpendicular to parallel viscosities is the key small parameter in our analysis. When another parameter, the Hartmann number, is large the flow is uniform across most of the channel, with boundary layers on either wall that are modifications of the Hartmann layers in standard isotropic MHD. However, the Hartmann layer solution predicts an infinite current and infinite shear at the wall, consistent with a local series solution of the underlying differential equation that is valid for all Hartmann numbers. These singularities are resolved by inner boundary layers whose width scales as the three-quarters power of the viscosity ratio, while the maximum velocity scales as the inverse one-quarter power of the viscosity ratio. The inner wall layers fit between the Hartmann layers, if present, and the walls. The solution thus does not approach a limit as the viscosity ratio tends to zero. Essential features of the solution, such as the maximum current and maximum velocity, are determined by the size of the viscosity ratio, which is the regularising small parameter.

A wall-layer model for large-eddy simulations of turbulent flows with/out pressure gradient

In this work, modeling of the near-wall region in turbulent flows is addressed. A new wall-layer model is proposed with the goal to perform high-Reynolds number large-eddy simulations of wall bounded flows in the presence of a streamwise pressure gradient. The model applies both in the viscous sublayer and in the inertial region, without any parameter to switch from one region to the other. An analytical expression for the velocity field as a function of the distance from the wall is derived from the simplified thin-boundary equations and by using a turbulent eddy coefficient with a damping function. This damping function relies on a modified van Driest formula to define the mixing-length taking into account the presence of a streamwise pressure gradient. The model is first validated by a priori comparisons with direct numerical simulation data of various flows with and without streamwise pressure gradient and with eventual flow separation. Large-eddy simulations are then performed using the present wall model as wall boundary condition. A plane channel flow and the flow over a periodic arrangement of hills are successively considered. The present model predictions are compared with those obtained using the wall models previously proposed by Spalding, Trans. ASME, J. Appl. Mech 28, 243 (2008) and Manhart et al., Theor. Comput. Fluid Dyn. 22, 243 (2008). It is shown that the new wall model allows for a good prediction of the mean velocity profile both with and without streamwise pressure gradient. It is shown than, conversely to the previous models, the present model is able to predict flow separation even when a very coarse grid is used.

An improved near-wall treatment for turbulent channel flows

The success of predictions of wall-bounded turbulent flows requires an accurate description of the flow in the near-wall region. This article presents a comparative study between different near-wall treatments and presents an improved method. The study is applied to fully developed plane channel flow (i.e. the flow between two infinitely large plates). Simulations were performed using Fluent. Near-wall treatments available in Fluent were tested: standard wall functions, non-equilibrium wall function and enhanced wall treatment. A user defined function (UDF), based on an analytical profile for the turbulent kinetic energy (Absi, R., 2008. Analytical solutions for the modeled k-equation. ASME Journal of Applied Mechanics, 75 (4), 044501), is developed and implemented. Predicted turbulent kinetic energy profiles are presented and validated by DNS data.

Dynamic large eddy simulations of momentum and wall heat transfer in forced convection over wavy surfaces

The dynamic large eddy simulations (LES) of flow and heat transfer in a channel with heated wavy bottom walls are performed in the turbulent forced convection regime (Reb = 11, 200 and 30, 000, Pr = 7). Simulations provided physical insights into the momentum and heat transport over 2D and 3D wavy bottom walls. The numerical validation of the presented dynamic LES showed very good agreement with spectral direct numerical simulations and experimental particle image velocimetry data of both first- and second-order moments for the case with 2D waviness at Reb = 11, 200. Compared to a plane channel flow, bottom wall waviness generates streamwise and spanwise vortices that enhance heat transfer. The spanwise-oriented coherent structures occur in the separation zone, whereas streamwise-oriented coherent structures are present in the accelerated region of the flow field. For the 2D wavy horizontal wall configuration, the maximum in vertical profiles of the long-term averaged streamwise velocity component is shifted towards the upper flat wall. The instantaneous wall-temperature distribution exhibits a streaky character with high and low temperature regions. In contrast to that, for the 3D wavy wall configuration, reorganisation of the flow and turbulence structures takes place in the immediate proximity of the lower wall. Strong deviations from the standard log-law of the streamwise velocity component are observed for both configurations. At Reb = 11, 200, the 2D wavy wall configuration was more efficient in transporting heat than the 3D wavy wall – although the difference was relatively small ≈20%.

Lattice Boltzmann formulation for Braginskii magnetohydrodynamics

Braginskii magnetohydrodynamics is a single-fluid description of large-scale motions in a strongly magnetised plasma, one in which the ion gyroradius is much smaller than the mean free path between collisions in an unmagnetised plasma of the same density and temperature. The relation between stress and strain rate then becomes highly anisotropic, with the viscous stress being predominantly aligned parallel to the magnetic field lines. We modify an existing lattice Boltzmann formulation of isotropic resistive magnetohydrodynamics to simulate Braginskii magnetohydrodynamics by introducing an anisotropic collision operator for the hydrodynamic distribution functions. This collision operator applies a different relaxation time to the component of stress directed parallel to the magnetic field. The method is illustrated by comparison with independent numerical solutions for steady planar channel flows.

Influence of the reynolds number on the plane-channel turbulent flow of a fluid

Using the data on direct numerical simulation of the plane-channel fluid flow obtained by several authors, the influence of the Reynolds number on the location and maximal values of the tangential and normal Reynolds stresses is investigated. The flow in a viscous sublayer is studied. Deviations from the law of the wall are noted.

Smoothing algorithms for mean-flow extraction in large-eddy simulation of complex turbulent flows

Based on physical arguments, the importance of separating the mean-flow from turbulence in the modeling of the subgrid-scale eddy-viscosity is emphasized. Therefore, two distinct time-domain smoothing algorithms are proposed to estimate the mean-flow as the simulation progresses, namely, an exponentially weighted moving average (or exponential smoothing) and an adaptive low-pass Kalman filter. These algorithms highlight the longer-term evolution or cycles of the flow but erase short-term fluctuations. Indeed, it is our assumption that the mean-flow (in the statistical sense) may be approximated as the low-frequency component of the velocity field and that the turbulent part of the flow adds itself to this “unsteady mean.” The cutoff frequency separating these two components is fixed according to some characteristic time-scale of the flow in the exponential smoothing, but inferred dynamically from the recent history of the flow in the Kalman filter. In practice, these two algorithms are implemented in large-eddy simulations that rely on a shear-improved Smagorinsky’s model. In this model, the magnitude of mean-flow rate of strain is subtracted from the magnitude of the instantaneous rate of strain in the subgrid-scale eddy-viscosity. Two test-cases have been investigated: a turbulent plane-channel flow (Rew=395) and the flow past a circular cylinder in the subcritical turbulent regime (ReD=4.7×104). Comparisons with direct numerical simulation and experimental data demonstrate the good efficiency of the whole modeling. This allows us to address nonhomogeneous unsteady configurations without adding significant complication and computational cost to the standard Smagorinsky’s model. From a computational viewpoint, this modeling deserves interest since it is entirely local in space. It is therefore adapted for parallelization and convenient for boundary conditions.

The laminar generalized Stokes layer and turbulent drag reduction

This paper considers plane channel flow modified by waves of spanwise velocity applied at the wall and travelling along the streamwise direction. Both laminar and turbulent regimes for the streamwise flow are studied. When the streamwise flow is laminar, it is unaffected by the spanwise flow induced by the waves. This flow is a thin, unsteady and streamwise-modulated boundary layer that can be expressed in terms of the Airy function of the first kind. We name it the generalized Stokes layer because it reduces to the classical oscillating Stokes layer in the limit of infinite wave speed. When the streamwise flow is turbulent, the laminar generalized Stokes layer solution describes well the space-averaged turbulent spanwise flow, provided that the phase speed of the waves is sufficiently different from the turbulent convection velocity, and that the time scale of the forcing is smaller than the life time of the near-wall turbulent structures. Under these conditions, the drag reduction is found to scale with the Stokes layer thickness, which renders the laminar solution instrumental for the analysis of the turbulent flow. A classification of the turbulent flow regimes induced by the waves is presented by comparing parameters related to the forcing conditions with the space and time scales of the turbulent flow.

Bingham fluid simulation with the incompressible lattice Boltzmann model

The Bingham fluid flow is numerically studied using the lattice Boltzmann method by incorporating the Papanastasiou exponential modification approach. The He–Luo incompressible lattice Boltzmann model is employed to avoid numerical instability usually encountered in non-Newtonian fluid simulations due to a strong non-linear relationship between the shear rate tensor and the rate-of-strain tensor. First, the value of the regularization parameter in Bingham fluid mimicking is analyzed and a method to determine the value is proposed. Then, the model is validated by pressure-driven planar channel flow and planar sudden expansion flow. The velocity profiles for the pressure-driven planar channel flow are in good agreement with analytical solutions. The calculated reattachment lengths for a 2:1 planar sudden expansion flow also agree well with the available data. Finally, the Bingham flow over a cavity is studied, and the streamlines and yielded/unyielded regions are discussed.

Direct numerical simulation of two-dimensional channel flows of electro-rheological fluids

Direct numerical simulation (DNS) of electro-rheological (ER) fluid flows in two-dimensional (2D) electrode channel has been performed by adopting a combined finite element method (FEM). Hydrodynamic interactions between the particles and the fluid are described by the Navier–Stokes equations for the fluid in combination with the equations of motion for the particles, while the multi-body electrostatic interaction is represented by the point-dipole model. ER effects on the plane channel flow for a given pressure gradient have been studied by varying the Mason number and volume fraction of the particles, and interrogating the motion of the particles in views of the formation of ER chain structures, the fluid velocity profile in the channel, and the shear stress versus the shear rate. As the Mason number decreases and volume fraction increases, the tendency that particles align to form chain structures becomes stronger. The yield stress of the ER fluid increases with the electric field intensity and the particle concentration. The quadratic correlation between the yield stress and the electric field intensity has been extracted from the present direct numerical simulation. Lastly, it has been shown that the yield stress linearly increases with the volume fraction in the intermediate range.

Large-eddy simulation of turbulent heat convection in a spanwise rotating channel flow

In this paper, we investigate the effects of the Coriolis force in a heated plane channel flow subjected to spanwise rotation using the method of large-eddy simulation. We present both the general and simplified transport equations for the resolved turbulent stresses, which are essential for understanding the unique pattern of turbulent kinetic energy production in a rotating system. Numerical simulations are performed using primarily two dynamic subgrid-scale stress models and one dynamic subgrid-scale heat flux model; namely, the conventional dynamic model (DM) and a novel dynamic nonlinear model (DNM) for closure of the filtered momentum equation, and an advanced dynamic full linear tensor thermal diffusivity model (DFLTDM) for closure of the filtered thermal energy equation. The turbulent flow field studied herein is characterized by a Reynolds number Re τ = 150 and various rotation numbers Ro τ ranging from 0 to 7.5. In order to validate the LES approach, turbulent statistics obtained from the simulations are thoroughly compared with the available experimental results and direct numerical simulation (DNS) data. A detailed comparative study has been conducted in order to evaluate the performance of the DM and DNM in terms of their prediction of characteristic features of the velocity and temperature fields and their capability of reflecting both forward and backward scatter of kinetic energy between the filtered and subgrid scales.

Measured wavenumber: Frequency spectrum associated with acoustic and aerodynamic wall pressure fluctuations

Direct measurements of the wavenumber-frequency spectrum of wall pressure fluctuations beneath a turbulent plane channel flow have been performed in an anechoic wind tunnel. A rotative array has been designed that allows the measurement of a complete map, 63×63 measuring points, of cross-power spectral densities over a large area. An original post-processing has been developed to separate the acoustic and the aerodynamic exciting loadings by transforming space-frequency data into wavenumber-frequency spectra. The acoustic part has also been estimated from a simple Corcos-like model including the contribution of a diffuse sound field. The measured acoustic contribution to the surface pressure fluctuations is 5% of the measured aerodynamic surface pressure fluctuations for a velocity and boundary layer thickness relevant for automotive interior noise applications. This shows that for aerodynamically induced car interior noise, both contributions to the surface pressure fluctuations on car windows have to be taken into account.

Modeling of the motion of light-weight particles and bubbles in turbulent flows

The aim of the paper is to present a statistical model of motion and dispersion of light-weight particles and bubbles in turbulent flows. The model is based on a kinetic equation for the probability density function of particle velocities. The results of modeling the parameters of particles and bubbles in a plane-channel flow are compared with known data of direct numerical simulation.

Dynamic mode decomposition of numerical and experimental data

The description of coherent features of fluid flow is essential to our understanding of fluid-dynamical and transport processes. A method is introduced that is able to extract dynamic information from flow fields that are either generated by a (direct) numerical simulation or visualized/measured in a physical experiment. The extracted dynamic modes, which can be interpreted as a generalization of global stability modes, can be used to describe the underlying physical mechanisms captured in the data sequence or to project large-scale problems onto a dynamical system of significantly fewer degrees of freedom. The concentration on subdomains of the flow field where relevant dynamics is expected allows the dissection of a complex flow into regions of localized instability phenomena and further illustrates the flexibility of the method, as does the description of the dynamics within a spatial framework. Demonstrations of the method are presented consisting of a plane channel flow, flow over a two-dimensional cavity, wake flow behind a flexible membrane and a jet passing between two cylinders.

A comparison of flow boiling heat-transfer in in-line mini pin fin and plane channel flows

The use of a boiling fluid as a coolant is an attractive option for electronic devices as electrical power densities increase. However, for systems working at the micro-scale, design methods developed for evaluating heat transfer in macro-scale evaporators are not appropriate for passages with hydraulic diameter of the order of 1 mm and below. Heat-transfer coefficients and pressure drops are reported for two surfaces, a pin-fin and a plate surface, each with 50 mm square base area. The pin-fin surface comprised of 1 mm square pin fins that were 1 mm high and located on a 2 mm square pitch array covering the base. The channel was 1 mm high and had a glass top plate. The data were produced while boiling R113 at atmospheric pressure. For both surfaces, the mass flux range was 50–250 kg/m2s and the heat flux range was 5–140 kW/m2. The results obtained have been compared with standard correlations for tube bundles. The measured heat-transfer coefficients for the pin-fin surface are slightly higher than those for the plate surface. Both are dependent on heat flux and reasonably independent of mass flux and vapour quality. Thus, heat transfer is probably dominated by nucleate boiling and is increased by the pin fins due to the increase in area and heat-transfer coefficient. The pin-fin pressure drops were typically 7 times larger than the plate values. The pin-fin heat-transfer coefficients and pressure drops are compared to macro-scale tube bundle correlations. At low vapour qualities the heat-transfer coefficients are in reasonable agreement with the correlations, but, as the vapour quality increases, they do not show the convective enhancement which would be expected for a conventionally-sized tube bundle. Measured two–phase pressure drops are in reasonable agreement with the tube bundle correlation.

Numerical simulations of a second-order chemical reaction in a plane turbulent channel flow

We analyze numerical simulations of a second-order chemical reaction ( Da = 1) in a fully developed turbulent plane channel flow at a low Reynolds number ( Re τ = 180). The reactive plume is formed when a reactant A is released through a line source into the channel flow doped with reactant B. Two different inlet pre-mixing conditions and line source heights are considered. Direct Numerical Simulations (DNS) and Stochastic Fields (SF) methods have been used and compared for these different conditions. The results obtained using SF are sensitive to the particular value of the turbulent Schmidt number ( Sc T ) selected to model the turbulent dispersion. It has been found that if a representative value of Sc T extracted from DNS is used in the SF method, both DNS and SF, give similar results.