Large-scale computer simulation of fully developed turbulent channel flow with heat transfer

Recently, with the advent of supercomputers, there has been considerable interest in the use of direct numerical simulation to obtain information about turbulent shear flow at low Reynolds number. This paper presents a pseudospectral technique to solve the full three-dimensional time-dependent Navier-Stokes and advection-diffusion equations without the use of subgrid-scale modelling. The technique has not been previously used for fully developed turbulent channel flow simulation and is based on methods applied in other contexts. The emphasis of this paper is to provide a reasonably detailed account of how the simulation is done rather than to present new calculations of turbulence. The details of an algorithm for turbulent channel flow simulation and the grid and time step sizes needed to integrate through transient behaviour to steady state turbulence have not been published before and are presented here. Results from a Cray-2 simulation of fully developed turbulent flow in a channel with heat transfer are presented along with a critical comparison between experiment and computation. The first- and second-order moments agree well with experimental measurements; the agreement is poor for higher-order moments such as the skewness and flatness near the walls of the channel. Detailed information given about the effects of spatial grid resolution on a computed results is important for estimating the size of the computation required to study various aspects of a turbulent flow.     

Direct numerical simulation of turbulent heat transfer in a square duct with transverse ribs mounted on one wall

Turbulent heat transfer in a ribbed square duct of three different blockage ratios are investigated using direct numerical simulation (DNS). The results of ribbed duct cases are compared with those of a heated smooth duct flow. It is observed that owing to the existence of the ribs and confinement of the duct, organized secondary flows appear as large streamwise-elongated vortices, which intensely interact with the rib elements and four sidewalls and have profound influences on the transport of momentum and thermal energy. This study also shows that the drag and heat transfer coefficients are highly sensitive to the rib height. It is observed that as the rib height increases, the impinging effect of the flow on the windward face of the rib strengthens, leading to enhanced rates of turbulent mixing and heat transfer. The influence of sidewalls and rib height on the turbulence structures associated with temperature fluctuations are analyzed based on multiple tools such as vortex swirling strengths, temporal auto-correlations, spatial two-point cross-correlations, joint probability density functions (JPDF) between the temperature and velocity fluctuations, statistical moments of different orders, and temperature spectra.     

Numerical simulation of flow and heat transfer in a random packed bed

Random packed beds have more complex interior structure than structured beds and are widely used in industry and engineering.CFD simulation was carried out to investigate and analyze the local flow and heat transfer in a 120-sphere random packed bed.3D Navier-Stokes equation was solved with a finite volume formulation based on the Chimera meshing technique.Investigation was focused on low Reynolds number flow(Re=4.6-56.2),which typically occurs in packed bed reactors in bio-chemical fields.Detailed temperature field information was obtained.Inhomogeneity of flow and heat transfer due to the non-uniform distribution of void fraction was discussed and analyzed.     

Direct numerical simulation of turbulent heat transfer in annuli: Effect of heat flux ratio

Fully developed turbulent flow and heat transfer in a concentric annular duct is investigated for the first time by using a direct numerical simulation (DNS) with isoflux conditions imposed at both walls. The Reynolds number based on the half-width between inner and outer walls, δ=(r₂-r₁)/2, and the laminar maximum velocity is Re_δ=3500. A Prandtl number Pr=0.71 and a radius ratio r^*=0.1 were retained. The main objective of this work is to examine the effect of the heat flux density ratio, q^*=q₁/q₂, on different thermal statistics (mean temperature profiles, root mean square (rms) of temperature fluctuations, turbulent heat fluxes, heat transfer, etc.). To validate the present DNS calculations, predictions of the flow and thermal fields with q^*=1 are compared to results recently reported in the archival literature. A good agreement with available DNS data is shown. The effect of heat flux ratio q^* on turbulent thermal statistics in annular duct with arbitrarily prescribed heat flux is discussed then. This investigation highlights that heat flux ratio has a marked influence on the thermal field. When q^* varies from 0 to 0.01, the rms of temperature fluctuations and the turbulent heat fluxes are more intense near the outer wall while changes in q^* from 1 to 100, lead to opposite trends.     

Passive heat transfer in a turbulent channel flow simulation using large eddy simulation based on the lattice Boltzmann method framework

In this paper, a large eddy simulation based on the lattice Boltzmann framework is carried out to simulate the heat transfer in a turbulent channel flow, in which the temperature can be regarded as a passive scalar. A double multiple relaxation time (DMRT) thermal lattice Boltzmann model is employed. While applying DMRT, a multiple relaxation time D3Q19 model is used to simulate the flow field, and a multiple relaxation time D3Q7 model is used to simulate the temperature field. The dynamic subgrid stress model, in which the turbulent eddy viscosity and the turbulent Prandtl number are dynamically computed, is integrated to describe the subgrid effect. Not only the strain rate but also the temperature gradient is calculated locally by the non-equilibrium moments. The Reynolds number based on the shear velocity and channel half height is 180. The molecular Prandtl numbers are set to be 0.025 and 0.71. Statistical quantities, such as the average velocity, average temperature, Reynolds stress, root mean square (RMS) velocity fluctuations, RMS temperature and turbulent heat flux are obtained and compared with the available data. The results demonstrate great reliability of DMRT–LES in studying turbulence.     

Direct numerical simulation of turbulent heat transfer in a wall-normal rotating channel flow

Investigations into the characteristics of turbulent heat transfer and coherent flow structures in a plane-channel subjected to wall-normal system rotation are conducted using direct numerical simulation (DNS). In order to investigate the influence of system rotation on the temperature field, a wide range of rotation numbers are tested, with the flow pattern transitioning from being fully turbulent to being quasilaminar, and eventually, fully laminar. In response to the Coriolis force, secondary flows appear as large vortical structures, which interact intensely with the wall shear layers and have a significant impact on the distribution of turbulence kinetic energy (TKE), turbulence scalar energy (TSE), temperature statistics, and turbulent heat fluxes. The characteristic length scales of turbulence structures responsible for the transport of TSE are the largest at the quasilaminar state, which demands a very large computational domain in order to capture the two-dimensional spectra of temperature fluctuations. The effects of the Coriolis force on the turbulent transport processes of the temperature variance and turbulent heat fluxes are thoroughly examined in terms of their respective budget balances.     

Numerical simulation of heat transfer in a pipe with non-homogeneous thermal boundary conditions

Direct numerical simulations of heat transfer in a fully-developed turbulent pipe flow with circumferentially-varying thermal boundary conditions are reported. Three cases have been considered for friction Reynolds number in the range 180–360 and Prandtl number in the range 0.7–4. The temperature statistics under these heating conditions are characterized. Eddy diffusivities and turbulent Prandtl numbers for radial and circumferential directions are evaluated and compared to the values predicted by simple models. It is found that the usual assumptions made in these models provide reasonable predictions far from the wall and that corrections to the models are needed near the wall.     

Numerical analysis of swirling turbulent droplet-laden flow and heat transfer in a sudden pipe expansion

The effect of swirling intensity on the structure and heat transfer of a turbulent gas–droplet flow after a sudden pipe expansion has been numerically simulated. Air is used as the carrier phase, and water, ethanol, and acetone are used as the dispersed phase. The Eulerian approach is applied to simulate the dynamics and heat transfer in the dispersed phase. The gas phase is described by a system of Reynolds-averaged Navier-Stokes (RANS) equations, taking into account the effect of droplets on mean transport and turbulent characteristics in the carrier phase. Gas phase turbulence is predicted using the second-moment closure. A swirling droplet-laden flow is characterized by an increase in the number of small particles on the pipe axis due to their accumulation in the zone of flow recirculation and the action of the turbulent migration (turbophoresis) force. A rapid dispersion of fine droplets over the pipe cross-section is observed without swirling. With an increase in swirling intensity, a significant reduction in the length of the separation region occurs. The swirling of a two-phase flow with liquid droplets leads to an increase in the level of turbulence for all three types of liquid droplets investigated in this work due to their intensive evaporation. It is shown that the addition of droplets leads to a significant increase in heat transfer in comparison with a single-phase swirling flow. The greatest effect of flow swirling on heat transfer intensification in a two-phase gas-droplet flow is obtained for the droplets of ethanol and water and smallest effect is for the acetone droplets.     

Numerical simulation for laminar flow and heat transfer of gas in rectanglar micropassages with constant wall heat flux

Theoretical investigations were performed on the developed laminar flow and convective heat transfer characteristics for incompressible gases flow through rectanglar micropassages with constant wall heat flux. Mathematical models were proposed for considering the change in viscosity and thermal conductivity of gas in the wall-adjacent region from the kinetic theory. The dimensionless velocity distribution and corresponding pressure drop, the dimensionless temperature distribution and corresponding heat transfer characteristics were both simulated numerically, and the results were compared to other report simulations [10–12] with brief discussions.     

Nusselt number and friction factor in thermally stratified turbulent channel flow under Non-Oberbeck–Boussinesq conditions

In stably stratified turbulence, computations under Oberbeck–Boussinesq (OB) hypothesis of temperature-independent fluid properties may lead to inaccurate representation of the flow field and to wrong estimates of momentum/heat transfer coefficients. This is clearly assessed here comparing direct numerical simulations of stratified turbulence under OB conditions to simulations under NOB (Non-Oberbeck–Boussinesq) conditions of temperature-dependent fluid viscosity and thermal expansion coefficient. Compared to the OB case, NOB conditions may induce local flow relaminarization with significant variations (up to 30%) of heat and momentum transfer coefficients. Together with DNS results, we propose a phenomenological model (based on turbulent bursts) for heat transfer prediction in stratified turbulence under OB and NOB conditions. Implications of NOB assumptions on mixing efficiency (i.e. flux Richardson number Ri_f) and turbulent Prandtl number (Pr_t) are also discussed. These results are of specific importance in RANS modelling, where the condition Pr_t = 1 is usually assumed (Reynolds analogy). Although this assumption is valid in some situations (i.e. boundary layer, pipe flow) there is uncertainty about its validity for stably-stratified turbulence. We demonstrate that this assumption is inaccurate when NOB effects become significant.     

Numerical simulation of a low-Reynolds-number turbulent wake behind a flat plate

A numerical simulation of a plane turbulent wake at a very low Reynolds number has been performed using finite volume methods. The wake was produced by allowing two turbulent boundary layers, simulated separately in advance, to interact downstream of the trailing edge of a thin flat plate. A number of innovative numerical techniques were required in the simulation, such as the provision of fully turbulent time-dependent inflow data from a separate simulation, advective outflow boundary conditions and the approximate representation of an internal solid surface by a method which is computationally efficient. The resulting simulation successfully reproduced many of the statistical properties of the turbulent near-wake flow at low Reynolds number.     

A New modelling strategy for phase-change heat transfer in turbulent interfacial two-phase flow

The paper presents a modelling strategy for phase-change heat transfer in turbulent interfacial two-phase flow. The computational framework is based on interface tracking ITM (level set approach), combined with large-scale prediction of turbulence, a new methodology known as Large-Eddy & Interface Simulation (LEIS), where super-grid scale turbulence and interfaces are directly solved, whereas the sub-scale parts are modelled. Because steady-state flow conditions are difficult to attain, recourse is made of the Very Large-Eddy Simulation (V-LES) instead of LES, where the flow-dependent cut-off filter is larger and independent from the grid. The computational approach is completed by a DNS-based interfacial phase-change heat transfer model built within the Surface Divergence (SD) theory. The original SD model is found to return better results when modified to account for scale separation, i.e. to segregate low-Re from high-Re number flow portions in the same flow. The model was first validated for an experiment involving a smooth to wavy turbulent, stratified steam-water flow in a 2D channel (Lim et al., 1984, Condensation measurement of horizontal concurrent steam-water flow, ASME J. Heat Transfer 106, 425–432.), revealing that the original SD model performs better for high interfacial shear rates. This screening phase also demonstrated that the most critical issue is the accurate prediction of the interfacial shear using ITM. The model was then applied successfully to predict condensing steam in the event of emergency core cooling in a Pressurized Water Reactor (PWR), where water is injected into the cold leg during a postulated loss-of-coolant-accident. The simulation results agree fairly well with the COSI (short for COndensation at Safety Injections) data (Janicot and Bestion, 1993, Condensation modelling for ECC injection, Nucl. Eng. Des. 145, 37–45).     

Numerical modeling of fluid flow and heat transfer in a narrow Taylor-Couette-Poiseuille system

We consider turbulent flows in a differentially heated Taylor-Couette system with an axial Poiseuille flow. The numerical approach is based on the Reynolds Stress Modeling (RSM) of [Elena and Schiestel, 1996] and [Schiestel and Elena, 1997] widely validated in various rotor-stator cavities with throughflow ( [Poncet, 2005], [Poncet et al., 2005] and [Haddadi and Poncet, 2008]) and heat transfer (Poncet and Schiestel, 2007). To show the capability of the present code, our numerical predictions are compared very favorably to the velocity measurements of Escudier and Gouldson (1995) in the isothermal case, for both the mean and turbulent fields. The RSM model improves, in particular, the predictions of the k-ε model of Naser (1997). Then, the second order model is applied for a large range of rotational Reynolds (3744 ? Re_i ? 37,443) and Prandtl numbers (0.01 ? Pr ? 12), flow rate coefficient (0 ? C_w ? 30,000) in a very narrow cavity of radius ratio s = R_i/R_o = 0.961 and aspect ratio L = (R_o − R_i)/h = 0.013, where R_i and R_o are the radii of the inner and outer cylinders respectively and h is the cavity height. Temperature gradients are imposed between the incoming fluid and the inner and outer cylinders. The mean hydrodynamic and thermal fields reveal three distinct regions across the radial gap with a central region of almost constant axial and tangential mean velocities and constant mean temperature. Turbulence, which is weakly anisotropic, is mainly concentrated in that region and vanishes towards the cylinders. The mean velocity distributions are not clearly affected by the rotational Reynolds number and the flow rate coefficient. The effects of the flow parameters on the thermal field are more noticeable and considered in details. Correlations for the averaged Nusselt numbers along both cylinders are finally provided according to the flow control parameters Re_i, C_w, and Pr.     

Thermal-field structure of a non-premixed turbulent flame formed in a strong pressure-gradient flow

Statistical characteristics of a non-premixed turbulent flame formed in a curved-rectangular duct and spatio-temporal structures of the thermal field were investigated experimentally. The flame was much affected by a strong pressure gradient in the radial direction of the duct curvature, which caused strong gradient diffusion in turbulent heat transfer on the inner-wall side of the flame and, in contrast, counter-gradient heat transfer on the outer-wall side. Two-point correlation measurement of temperature fields revealed that, in the strong gradient diffusion region, a spatial thermal pattern generated by turbulent mixing of high- and low-temperature fluid parcels was advected downstream with little diffusion. In contrast, the pattern was attenuated and diffused rapidly in the counter-gradient diffusion region. These results accurately correspond to the generation mechanism of the counter-gradient heat transport so far observed in stably stratified turbulent flows.     

DNS of heat transfer in turbulent and transitional channel flow obstructed by rectangular prisms

Direct numerical simulation (DNS) of heat transfer in a channel flow obstructed by rectangular prisms has been performed for Re_τ = 80–20, where Re_τ is based on the friction velocity, the channel half width and the kinematic viscosity. The molecular Prandtl number is set to be 0.71. The flow remains unsteady down to Re_τ = 40 owing to the disturbance induced by the prism. For Re_τ = 30 and 20, the flow results in a steady laminar flow. In the vicinity of the prism, the three-dimensional complex vortices are generated and heat transfer is enhanced. The Reynolds number effect on the time-averaged vortex structure and the local Nusselt number are investigated. The mechanism of the heat transfer enhancement is discussed. In addition, the mean flow parameters such as the friction factor and the Nusselt number are examined in comparison with existing DNS and experimental data.     

Coherent structures in trailing-edge cooling and the challenge for turbulent heat transfer modelling

The present paper tests the capability of a standard Reynolds-Averaged Navier–Stokes (RANS) turbulence model for predicting the turbulent heat transfer in a generic trailing-edge situation with a cutback on the pressure side of the blade. The model investigated uses a gradient-diffusion assumption with a scalar turbulent-diffusivity and constant turbulent Prandtl number. High-fidelity Large-Eddy Simulations (LES) were performed for three blowing ratios to provide reliable target data and the mean velocity and eddy viscosity as input for the heat transfer model testing. Reasonably good agreement between the LES and recent experiments was achieved for mean flow and turbulence statistics. The LES yielded coherent structures which were analysed, in particular with respect to their effect on the turbulent heat transfer. For increasing blowing ratio, the LES replicated an also experimentally observed counter-intuitive decrease of the cooling effectiveness caused by the coherent structures becoming stronger. In contrast, the RANS turbulent heat transfer model failed in predicting this behaviour and yielded significantly too high cooling effectiveness. It is shown that the model cannot predict the strong upstream and wall-directed turbulent heat fluxes caused by large coherent structures, which were found to be responsible for the counter-intuitive decrease of the cooling effectiveness.     

Numerical investigation of heat transfer and fluid flow characteristics inside a wavy channel

The periodically fully developed laminar heat transfer and fluid flow characteristics inside a two-dimensional wavy channel in a compact heat exchanger have been numerically investigated. Calculations were performed for Prandtl number 0.7, and Reynolds number ranging from 100 to 1,100 on non-orthogonal non-staggered grid systems, based on SIMPLER algorithm in the curvilinear body-fitted coordinates. Effects of wavy heights, lengths, wavy pitches and channel widths on fluid flow and heat transfer were studied. The results show that overall Nusselt numbers and friction factors increase with the increase of Reynolds numbers. According to the local Nusselt number distribution along channel wall, the heat transfer may be greatly enhanced due to the wavy characteristics. In the geometries parameters considered, friction factors and overall Nusselt number always increase with the increase of wavy heights or channel widths, and with the decrease of wavy lengths or wavy pitches. Especially the overall Nusselt number significantly increase with the increase of wavy heights or channel widths, where the flow may become into transition regime with a penalty of strongly increasing in pressure drop. An erratum to this article can be found at     

Direct numerical simulation of turbulent heat transfer on the Reynolds analogy over irregular rough surfaces

The effect of rough surface topography on heat and momentum transfer is studied by direct numerical simulations of turbulent heat transfer over uniformly heated three-dimensional irregular rough surfaces, where the effective slope and skewness values are systematically varied while maintaining a fixed root-mean-square roughness. The friction Reynolds number is fixed at 450, and the temperature is treated as a passive scalar with a Prandtl number of unity. Both the skin friction coefficient and Stanton number are enhanced by the wall roughness. However, the Reynolds analogy factor for the rough surface is lower than that for the smooth surface. The semi-analytical expression for the Reynolds analogy factor suggests that the Reynolds analogy factor is related to the skin friction coefficient and the difference between the temperature and velocity roughness functions, and the Reynolds analogy factor for the present rough surfaces is found to be predicted solely based on the equivalent sand-grain roughness. This suggests that the relationship between the Reynolds analogy factor and the equivalent sand-grain roughness is not affected by the effective slope and skewness values. Analysis of the heat and momentum transfer mechanisms based on the spatial- and time-averaged equations suggests that two factors decrease the Reynolds analogy factor. One is the increased effective Prandtl number within the rough surface in which the momentum diffusivity due to the combined effects of turbulence and dispersion is larger than the corresponding thermal diffusivity. The other is the significant increase in the pressure drag force term above the mean roughness height.