Identification of near-wall flow structures producing large wall transfer rates in turbulent mixed convection channel flow

In this paper, we analyze the influence of aiding and opposing buoyancy on the statistics of the wall transfer rates in a mixed convection turbulent flow at low Reynolds numbers in a vertical plane channel. The analysis is carried out using a database obtained from direct numerical simulations performed with a second-order finite volume code. The aiding/opposing buoyancy produces an overall decrease/increase of the intensities of the fluctuations of the wall shear stresses in comparison with the forced convection flow. The near wall structures responsible for the positive extreme values of the fluctuations of the wall shear stress, educed by a conditional sampling technique, consist in two quasi-parallel counterrotating streamwise vortices that convect high momentum fluid towards the wall in the region between them. Buoyancy produces an overall increase of the Reynolds stresses near the cold wall in comparison with the hot wall. This affects the streamwise length, the orientation, the velocity and the intensity of these flow structures near the two walls of the channel. It is found that the flow structures near the cold wall are shorter and produce more intense fluctuations than those near the hot wall.     

Direct numerical simulation of rarefied turbulent microchannel flow

Direct numerical simulation (DNS) has been carried out to investigate the effect of weak rarefaction on turbulent gas flow and heat transfer characteristics in microchannel. The Reynolds number based on the friction velocity and the channel half width is 150. Grid number is 64 × 128 × 64. Fractional time-step method is employed for the unsteady Navier–Stokes equations, and the governing equations are discretized with finite difference method. Statistical quantities such as turbulent intensity, Reynolds shear stress, turbulent heat flux and temperature variance are obtained under various Knudsen number from 0 to 0.05. The results show that rarefaction can influence the turbulent flow and heat transfer statistics. The streamwise mean velocity and temperature increase with increase of Kn number. In the near-wall-region rarefaction can increase the turbulent intensities and temperature variance. The effects of rarefaction on Reynolds shear stress and wall-normal heat flux are presented. The instantaneous velocity fluctuations in the vicinity of the wall are visualized and the influence of Kn number on the flow structure is discussed.     

An investigation of turbulent open channel flow with heat transfer by large eddy simulation

Large eddy simulation of fully developed turbulent open channel flow with heat transfer is performed. The three-dimensional filtered Navier-Stokes and energy equations are numerically solved using a fractional-step method. Dynamic subgrid-scale (SGS) models for the turbulent SGS stress and heat flux are employed to close the governing equations. Two typical temperature boundary conditions, i.e., constant temperature and constant heat flux being maintained at the free surface, respectively, are used. The objective of this study is to explore the behavior of heat transfer in the turbulent open channel flow for different temperature boundary conditions and to examine the reliability of the LES technique for predicting turbulent heat transfer at the free surface, in particular, for high Prandtl number. Calculated parameters are chosen as the Prandtl number (Pr) from 1 up to 100, the Reynolds number (Re_τ) 180 based on the wall friction velocity and the channel depth. Some typical quantities, including the mean velocity, temperature and their fluctuations, heat transfer coefficients, turbulent heat fluxes, and flow structures based on the velocity, vorticity and temperature fluctuations, are analyzed.     

Large-eddy simulation of streamwise-rotating turbulent channel flow

In many engineering and industrial applications the investigation of rotating turbulent flow is of great interest. Whereas some research has been done concerning channel flows with a spanwise rotation axis, only few investigations have been performed on channel flows with a rotation about the streamwise axis. In the present study an LES of a turbulent streamwise-rotating channel flow at Re_τ = 180 is performed using a moving grid method. The three-dimensional structures and the details of the secondary flow distribution are analyzed and compared with experimental data. The numerical-experimental comparison shows a convincing agreement as to the overall flow features. The results confirm the development of a secondary flow in the spanwise direction, which has been found to be correlated to the rotational speed. Furthermore, the findings show the distortion of the main flow velocity profile, the slight decrease of the streamwise Reynolds stresses in the vicinity of the walls, and the pronounced increase of the spanwise Reynolds stresses at higher rotation rates near the walls and particularly in the symmetry region. As to the numerical set-up it is shown that periodic boundary conditions in the spanwise direction suffice if the spanwise extent of the computational domain is larger than 10 times the channel half width.     

One-information suboptimal control repercussion on the fine structure of wall turbulence

The suboptimal control with the cost function directly connected to the wall shear and introduced for a while has been revisited through direct numerical simulations of high temporal and spatial resolution. Its effect on the fine structure of the wall turbulence has been analyzed in details, essentially through the spanwise vorticity transport mechanism. It is shown that only half of the viscous sublayer is mainly affected by the control. The actuation efficiency is limited in terms of the wall shear stress reduction, but is high as long as the turbulent wall activity is concerned. The wall shear stress is reduced due both to the reduction of the shear production in the viscous sublayer and to the contribution of the turbulent body force. The dissipation involving in the streamwise vorticity fluctuations transport equation increases significantly and overcomes the production in a thin layer near the wall leading to a drastic diminution of the turbulent wall shear stress fluctuations.     

Direct numerical simulation of turbulent channel flows using a stabilized finite element method

Direct numerical simulations (DNS) of incompressible turbulent channel flows at Re_τ = 180 and 395 (i.e., Reynolds number, based on the friction velocity and channel half-width) were performed using a stabilized finite element method (FEM). These simulations have been motivated by the fact that the use of stabilized finite element methods for DNS and LES is fairly recent and thus the question of how accurately these methods capture the wide range of scales in a turbulent flow remains open. To help address this question, we present converged results of turbulent channel flows under statistical equilibrium in terms of mean velocity, mean shear stresses, root mean square velocity fluctuations, autocorrelation coefficients, one-dimensional energy spectra and balances of the transport equation for turbulent kinetic energy. These results are consistent with previously published DNS results based on a pseudo-spectral method, thereby demonstrating the accuracy of the stabilized FEM for turbulence simulations.     

Large-eddy simulations of film cooling flows

Large-eddy simulations (LES) of a jet in a cross-flow (JICF) problem are carried out to investigate the turbulent flow structure and the vortex dynamics in gas turbine blade film cooling. A turbulent flat plate boundary layer at a Reynolds number of Re_∞ = 400,000 interacts with a jet issued from a pipe. To study the effect of the jet inclination angle α on the flow field, two angles are chosen, the perpendicular injection at 90° and the streamwise inclined injection at 30°. For the normal injection case a small blowing ratio of the jet velocity to the cross-stream velocity R = 0.1 is examined. For the streamwise inclined injection case two blowing ratios R = 0.1 and R = 0.48 are investigated to check the impact of the jet velocity on the cooling performance. The time-dependent turbulent inflow information for the cross-flow is provided by a simultaneously performed LES of a spatially developing turbulent boundary layer. Whereas in the perpendicular injection case a rather large separation region is found at the leading edge of the jet hole, in the streamwise inclined injection cases no separation is observed. Compared with the normal injection case at the same blowing ratio, the streamwise inclination weakens the jet-cross-flow interaction significantly. Thus, the first appearance of the counter-rotating vortex pair (CVP) is shifted downstream and its strength is reduced. The increase of the blowing ratio leads to a stronger penetration of the jet into the cross-flow, resulting in a more upstream located and more pronounced CVP. Downstream of the jet exit the streamwise vortices are so large that besides the jet fluid also the cross-stream is partially entrained into this zone, which yields the worst cooling performance.     

Analysis of the energy budget in turbulent channel flow using orthogonal wavelets

The spatial and scale statistics of turbulence kinetic energy are examined in turbulent channel flow at Re_τ = 300 using the orthonormal wavelet transform. The behaviour of the production, viscous and transfer terms is examined in terms of their variation with both space and scale. All terms are numerically large at wavenumbers at which a −5/3 slope is apparent in the velocity spectra, and they all exhibit significant spatial variability as evidenced by large flatnesses which increase with decreasing scale size. The flatness of terms involving transfer are particularly large. Attention focusses primarily on the sublayer and local-equilibrium regions: in the former, scale-to-scale flux is large and negative and consistent with conventional “backscatter” in Fourier space. In the linear sublayer, the flux is positive, consistent with Couette-like vortex stretching. The present work paves the way for close scrutiny of those components of the subgrid-scale stress that contribute most to the subgrid energy flux in large-eddy simulation of near-wall turbulent flows.     

Lattice Boltzmann computations of incompressible laminar flow and heat transfer in a constricted channel

A multi-population thermal lattice Boltzmann method (TLBM) is applied to simulate incompressible steady flow and heat transfer in a two-dimensional constricted channel. The method is validated for velocity and temperature profiles by comparing with a finite element method based commercial solver. The results indicate that, at various Reynolds numbers, the average flow resistance increases and the heat transfer rate decreases in a constricted channel in comparison to a straight channel. The effect of the constriction ratio is also investigated. The results show that the presented numerical model is a promising tool in analyzing simultaneous solution of fluid flow and heat transfer phenomena in complex geometries.     

Numerical simulation of three-dimensional turbulent separated and reattaching flows using a modified turbulence model

A modified version of k-ε model is proposed through modification of the damping function of eddy viscosity that incorporates the effect of wall proximity in the near the wall region and the effect of non-equilibrium away from the wall together with the simple model functions in the ε equation. The proposed turbulence model is validated with the available experimental data of reattachment length, mean streamwise velocity distribution, turbulence intensity profile, and wall static pressure coefficient in the turbulent backward-facing step flows. The predicted results with the present model are in good agreement with the experiments. Computed results reveal that the reattachment length (recirculation zone) and the wall static pressure are decreased with increasing inlet velocity. And the asymmetric distributions of the reattachment point, cross-section view of velocity vector, streamwise skin friction coefficient, and turbulent kinetic energy demonstrate the important three-dimensional side-wall effect in an insufficient aspect ratio channel flow.     

A zonal RANS-LES method to determine the flow over a high-lift configuration

High Reynolds number flows are particularly challenging problems for large-eddy simulations (LES) since small-scale structures in thin and often transitional boundary layers are to be resolved. The range of the turbulent scales is enormous, especially when high-lift configuration flows are considered. For this reason, the prediction of high Reynolds number flow over the entire airfoil using LES requires huge computer resources. To remedy this problem a zonal RANS-LES method for the flow over an airfoil in high-lift configuration at Re_c=1.0×10⁶ is presented. In a first step, a 2D RANS solution is sought, from which boundary conditions are formulated for an embedded LES domain, which comprises the flap and a sub-part of the main airfoil. The turbulent fluctuations in the boundary layers at the inflow region of the LES domain are generated by controlled forcing terms, which use the turbulent shear stress profiles obtained from the RANS solution. The comparison with an LES solution for the full domain and with experimental data shows likewise results for the velocity profiles and wall pressure distributions. The zonal RANS-LES method reduces the computational effort of a full domain LES by approx. 50%.     

Transient response analysis and modeling of near wall flow conditions in a micro channel: evidence of slip flow

An experimental tool for determination of the near wall transport parameters in a micro channel, supported by flow simulation, is presented. The method is based on the transient flow response due to convective diffusion, in absence of specific adsorption. An approximately step-function type temporal solute concentration variation serves as the input signal. The associated response signal of a surface plasmon resonance sensor, acting as an integral part of a micro channel, has been taken as the output signal. It provides the flow-dependent change of the NaOH solute concentration in the channel within the optical detection and near wall distance interval 0 < d < 0.5 μm. The temporal signal evolution and response time, until an initially plain aqueous solution is replaced by the solute, varies inversely with solute concentration and flow rate. In the asymptotic limits, the near wall forced convective and diffusive channel transit times, along with the associated velocities, can be extracted and separated. A low convective near wall flow speed would account for 100% adsorption efficiency. The validity of the scaling relation for Fickian diffusive transport has been confirmed by experiments. Convective near wall flow reveals a distorted parabolic flow profile. This indicates relaxation of the no-slip condition, and presence of slip flow. Neither boundary layer formation, nor near wall micro turbulences have been observed. Eventually, a compact mathematical transient flow model, outlined in the Laplace domain for the electrical equivalent analogue circuit and applicable to the convective diffusion equation, has been developed for the flow transients.     

On restraining the production of small scales of motion in a turbulent channel flow

Since most turbulent flows cannot be computed directly from the incompressible Navier-Stokes equations, a dynamically less complex mathematical formulation is sought. In the quest for such a formulation, we consider nonlinear approximations of the convective term that preserve the symmetry and conservation properties. In particularly, the energy, enstrophy (in 2D) and helicity are conserved. The underlying idea is to restrain the convective production of small scales in an unconditional stable manner, meaning that the approximate solution cannot blow up in the energy-norm (in 2D also: enstrophy-norm). The numerical algorithm used to solve the governing equations preserves the symmetry and conservation properties too. The resulting simulation method is successfully tested for a turbulent channel flow (Re_τ = 180 and 395).     

A numerical investigation of turbulent flows in a spanwise rotating channel

A numerical investigation of fully developed turbulent flow in a spanwise rotating channel is performed to study turbulence characteristics subject to system rotation. The work provides insight into several salient features of the spanwise rotating turbulent channel flows, including the near-wall vortical structures, turbulence energy cascade and redistribution, and vortex stretching. The influence of system rotation on the near-wall vortical structures is investigated based on the vorticity fluctuations and their probability density functions (PDF). The properties of the Lamb vector fluctuation and the corresponding PDF are examined to reveal the effect of rotation on the turbulence energy cascade and production in the rotating channel. The budgets of Reynolds stresses and fluctuating enstrophy are analyzed to elucidate the role of the Coriolis force on turbulence energy redistribution between the streamwise and wall-normal directions and the mechanisms of vortex stretching for the generation of the vorticity fluctuations near the pressure and suction walls.     

Effect of temperature gradient orientation on the characteristics of mixed convection flow in a lid-driven square cavity

The effect of temperature gradient orientation on the fluid flow and heat transfer in a lid-driven differentially heated square cavity is investigated numerically. The transport equations are solved using the high-order compact scheme. Four cases are considered depending on the direction of temperature gradient imposed. The differentially heated top and bottom walls result in gravitationally stable and unstable temperature gradients. While the differentially heated left and right side walls lead to assisting and opposing buoyancy effects. The governing parameters are Pr = 0.7 and Ri = 0.1, 1, and 10. It is found that both Richardson number and direction of temperature gradient affect the flow patterns, heat transport processes, and heat transfer rates in the cavity. Computed average Nusselt number indicates that the heat transfer rate increases with decreasing Ri regardless the orientation of temperature gradient imposed. And the assisting buoyancy flows have best performance on heat transport over the other three cases.     

Modeling of fluid flow in a tube with a moving indentation

The time-dependent flow in a tube with a moving indentation is numerically simulated using a dynamic mesh model. The model was used to simulate the flow in a tube with an indentation moving at different frequencies. The model was validated for a two-dimensional channel with a moving indentation. The results exhibited good agreement with the available experimental results. The results show that a single vortex was formed at a wall frequency of 0.1 Hz and was swept out of the tube at the end of the period. At a higher frequency of 1 Hz, vortex doubling occurred with reverse flow dominating downstream of the indentation. The results also show that the wall shear stress was larger for the higher frequency case of the moving indentation.     

Turbulent natural convection between inclined isothermal plates

Steady two-dimensional turbulent natural convection between inclined isothermal plates has been investigated numerically. Validations for the present computational procedure were carried out utilizing experimental and numerical data published in the literature. The comparisons with published data indicate very good agreement. The present calculations were conducted for a single aspect ratio, L/b = 24, over the range of modified Rayleigh number Ra′ of 10⁴ ? Ra′ ? 10⁶ and angle of inclination 0° ? θ ? 90°. The results indicate that the channel overall average Nusselt number is reduced, the rate of reduction increases as the inclination angle is increased and that the overall average Nusselt number at different inclination angles can be presented by a single correlation if plotted versus the product of the modified Rayleigh number and (Cos θ)^0.5. For the case of horizontal channel (θ = 90°), the results indicate that the local Nusselt number along the lower wall is much higher than that along the upper wall.     

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.     

A new model for Brownian force and the application to simulating nanofluid flow

A new expression is proposed to simulate Brownian force based on the experimental measurement results of Brownian motion, which follows white Gaussian noise process. As the time t → 0 and the particle density is equal to the fluid density, the new expression approaches the classical formula of the model used by many researchers. The modified model is validated by theoretical and experimental data. On the other hand, as it origins from the unbalanced force exerted by surrounding fluid molecules, the drag analogy force model is constructed describing the Brownian force, which depends on size-related statistical velocity. Thus, a different expression for the Langevin equation is presented. The present model is applied in simulating flow and heat transfer in a channel utilizing alumina–water nanofluid. Navier–Stokes equations with modified source terms for the continuous flow have been discretized using finite element method. The velocities and temperatures of nanoparticles are determined in the Lagrangian reference frame. The simulation results show that the distribution of nanoparticles inside the channel is obviously unsteady and nonuniform. The fluid velocity and temperature profiles show significant fluctuation feature at low Reynolds numbers (Re). The impact of Brownian motion on the fluid flow is analyzed quantitatively. We have found that for Re < 0.06, the affected intensity increases rapidly.     

Numerical analysis of confined turbulent flow

This work outlines a second order accurate, coupled, conservative new numerical scheme for solving a two dimensional incompressible turbulent flow filed. Mean vorticity, ω, and mean stream function, ψ, are used as the mean flow dependent variables. The turbulent kinetic energy $\text{k}$ and the turbulent energy decay rate, ?, are used to define the turbulent state. In the present computational scheme two systems of equations and variables are considered: the mean flow system, ψ-ω, and the turbulent state system, $\text{k-?}$. Every system is solved implicity in a coupled double loop manner, and all the flow equations are solved iteratively in the global sense. Since the turbulence boundary conditions have a non-regular variation near a solid wall, they are coupled to the equations implicitly in both systems. In this way the numerical instabilities due to the irregular form of the equations near the solid walls are suppressed. The rate of convergence of the new numerical scheme of the coupled systems ψ-ω and $\text{k-?}$ is twice that realized when solving these equations separately. The necessary conditions for convergence of the numerical equations are investigated as well as the rate of convergence features. The detailed stability conditions are derived. As an example, the axisymmetric mixing of two confined jets with an internal heat source is considered with this numerical scheme.