Analysis of mixed convection in transient laminar and turbulent flows in driven cavities

This work presents large eddy simulation of mixed convection in transient, two-dimensional laminar and turbulent flows in cavities. The Smagorinsky model is employed for the sub-grid treatment. The simulations are based on the finite element solution of the conservation equations, and are presented for Reynolds and Richardson numbers ranging from 400 to 10,000 and from 0.1 to 0.44, respectively. Results for both the laminar and turbulent are compared with those in the literature, leading to maximum deviations of about 5%. In general, the results show a strong dependence of the type of stratification with the fluid dynamics and heat transfer.     

Connecting dispersion models and wall temperature prediction for laminar and turbulent flows in channels

In a former paper, Drouin et al. [6] proposed a model for dispersion phenomena in heated channels that works for both laminar and turbulent regimes. This model, derived according to the double averaging procedure, leads to satisfactory predictions of mean temperature. In order to derive dispersion coefficients, the so called “closure problem” was solved, which gave us access to the temperature deviation at sub filter scale. We now propose to capitalize on this useful information in order to connect dispersion modeling to wall temperature prediction. As a first step, we use the temperature deviation modeling in order to connect wall to mean temperatures within the asymptotic limit of well established pipe flows. Since temperature in wall vicinity is mostly controlled by boundary conditions, it might evolve according to different time and length scales than averaged temperature. Hence, this asymptotic limit provides poor prediction of wall temperature when flow conditions encounter fast transients and stiff heat flux gradients. To overcome this limitation we derive a transport equation for temperature deviation $(T_w-〈{\overline{T}}_f{〉}_f)$. The resulting two-temperature model is then compared with fine scale simulations used as reference results. Wall temperature predictions are found to be in good agreement for various Prandtl and Reynolds numbers, from laminar to fully turbulent regimes and improvement with respect to classical models is noticeable.     

Numerical simulation of laminar and turbulent buoyancy-driven flows using a lattice Boltzmann based algorithm

The capability of simulating natural and forced convection has been recently developed and integrated into PowerFLOW, a general purpose CFD solver based on the lattice Boltzmann algorithm. Several benchmark tests have been performed to validate this buoyancy model. Two typical cases of Rayleigh-Bénard convection with the Rayleigh number slightly above (Ra=2000) and below (Ra=1500) the critical Rayleigh number of 1708 were tested to verify the conceptual and algorithmic correctness of the buoyancy model. Then simulations of turbulent natural convection in an enclosed tall cavity with two different Rayleigh numbers, Ra=0.86×10⁶ and Ra=1.43×10⁶, were carried out and found to be in a very good agreement with the experiments of Betts and Bokhari.     

Thermal performances of enhanced smooth and spiky twisted tapes for laminar and turbulent tubular flows

This experimental study investigates the heat transfer properties over developing and developed flow regimes, the pressure drop coefficients and the thermal performance factors (TPF) of tubular flows with the continuous and spiky twist tapes enhanced by perforated, jagged and notched winglets. The axial distributions of Nusselt number (Nu) and the mean Fanning friction factors (f) of the tubular flows at Reynolds numbers (Re) ranging from 500 to 40000 are comparatively examined for five different types of twisted tapes with three twist ratios (y) of 1.875, 2.186 and 2.815 for each type of twisted tapes. Through this comparative study, the favorable types of twisted tapes which generate the higher degrees of HTE impacts over the developing and developed flow regimes are respectively identified. These newly devised twist tapes enrich the varieties of passive heat transfer enhancement (HTE) devices, especially for retrofit applications. A set of selective Nu and f results illustrates the thermal characteristics of the enhanced tubular flows by these twisted tapes. The HTE and TPF properties for all the present types of twisted tapes are subsequently compared with those reported for other types of twisted tapes in the literature. Among these comparative groups, the present V-notched spiky twisted tape generally offers the highest HTE impacts with favorable TPF performances. Empirical correlations that evaluate the averaged Nu over the developing and developed flow regimes; as well as and tube-wise averaged f for the enhanced tubular flows fitted with all the present types of twisted tapes are generated.     

Heat transfer in all pipe flow regimes: laminar,transitional/intermittent,and turbulent

A predictive theory is presented which is capable of providing quantitative results for the heat transfer coefficients in round pipes for the three possible flow regimes: laminar, transitional, and turbulent. The theory is based on a model of laminar-to-turbulent transition which is also viable for purely laminar and purely turbulent flow. Fully developed heat transfer coefficients were predicted for the three regimes. The present predictions were brought together with the most accurate experimental data known to the authors as well as with several algebraic formulas which are purported to be able to provide fully developed heat transfer coefficients in the so-called transition regime between Re = 2300 and 10,000. It was found that over the range Re > 4800, both the present predictions and those of the Gnielinski formula [V. Gnielinski, New equations for heat and mass transfer in turbulent pipe and channel flow, Int. Chem. Eng. 16 (1976) 359–367] are very well supported by the experimental data. However, the Gnielinski model is less successful in the range from 2300 to 3100. In that range, the present predictions and those of Churchill [S. Churchill, Comprehensive correlating equations for heat, mass, and momentum transfer in fully developed flow in smooth tubes, Ind. Eng. Chem. Fundam. 16 (1977) 109–116] are mutually reinforcing. Heat transfer results in the development region have also been obtained. Typically, regardless of the Reynolds number, the region immediately downstream of the inlet is characterized by laminar heat transfer. After the breakdown of laminar flow, a region characterized by intermittent heat transfer occurs. Subsequently, the flow may become turbulent and fully developed or the intermittent state may persist as a fully developed regime. The investigation covered both of the basic thermal boundary conditions of uniform heat flux (UHF) and uniform wall temperature (UWT). In the development region, the difference between the respective heat transfer coefficients for the two cases was approximately 25% (UHF > UWT). For the fully developed case, the respective heat transfer coefficients are essentially equal in the turbulent regime but differ by about 25% in the intermittent regime. The reported results are for a turbulence intensity of 5% and flat velocity and temperature profiles at the inlet.     

The effect of wall conduction for the extended Graetz problem for laminar and turbulent channel flows

Axial heat conduction effects within the fluid can be important for duct flows if either the Prandtl number is relatively low (liquid metals) or if the dimensions of the duct are small (micro heat exchanger). In addition, axial heat conduction effects in the wall of the duct might be of importance. The present paper shows an entirely analytical solution to the extended Graetz problem including wall conduction (conjugate extended Graetz problem). The solution is based on a selfadjoint formalism resulting from a decomposition of the convective diffusion equation into a pair of first order partial differential equations. The obtained analytical solution is relatively simple to compute and valid for all Péclet numbers. The analytical results are compared to own numerical calculations with FLUENT and good agreement is found.     

Nonreacting turbulent mixing flows

This paper provides a comprehensive review of available data on turbulent nonreacting flows which could be of use in the evaluation of turbulence modeling schemes. The review is limited to parabolic, stationary shear flows with well-defined boundary conditions; these flows have many of the characteristics of flows found in combustion devices and are typical of laboratory flames for which model evaluation data are most likely to be available. This report is an outgrowth of a study conducted under the direction of the Air Force Office of Scientific Research. A bound volume containing, in detail, the results of that study will be available in the near future.     

Chaotic analysis of mixing enhancement in steady laminar flows through multiple pipe bends

Using numerical simulations, properties of the flow and heat transfer in multiple pipe bends composed of 90°-bends are investigated for various switching angles, and the mixing performance is compared by means of various trajectory-based analyses. Although the behavior of both the secondary flow and Nusselt number show a periodic feature, they do not completely correspond with each other. The Lyapunov exponent quantitatively exhibits a distinct difference in the mixing depending on the switching angle, while the Poincaré map depicts a specific aspect even in a long-term. The residence time distribution is a potential indicator reflecting the flow structure with time-information.     

An experimental investigation of flow and heat transfer characteristics over blocked surfaces in laminar and turbulent flows

Flow and heat transfer measurements were obtained over a blocked surface mounted on a low speed wind tunnel in order to investigate the combined the effects of free stream velocities and the different size of rectangular blocks on the flow and heat transfer characteristics. Mean velocity and turbulence intensities were measured by a constant temperature anemometer and wall temperatures by copper-constant thermocouple and static pressures by a micro-manometer, respectively. It was found that the flow separations and reattachments were occurred before the first blocks, on the first blocks, between blocks and after the last blocks. The blocked surface area and flow separation caused not only heat transfer enhancement but higher turbulence levels as well. The average Stanton numbers, for block heights of 10, 15 and 20 mm, were higher than those of flat surface by 82%, 95%, 113% in laminar and 27%, 38%, 50% in turbulent, respectively. These results showed that heat transfer enhancement on the blocked surface increased with block heights and become more pronounced in laminar than that of turbulent flows.     

A pressure-based algorithm for internal compressible turbulent flows through a geometrical singularity

Compressible turbulent flow through the abrupt enlargement in pipes is studied numerically by means of Advection Upstream Splitting Method (AUSM+-up). In low Mach numbers, a pressure correction equation of elliptic type is derived. This equation is compatible with the nature of governing equations and retrieves hyperbolic characteristic at higher Mach numbers. It is shown that the proposed numerical algorithm is computationally more efficient than the preconditioned density-based methods. The flow parameters such as reattachment length, pressure loss coefficient and wall shear stress are predicted. It is found that the loss coefficient of the compressible flow rises drastically with increasing Reynolds number while it is constant for incompressible flows. Furthermore, the total-pressure ratio drops with increasing Reynolds number and expansion ratio where it approaches an asymptotic curve. In compressible flow, the pressure is minimum and constant after the enlargement section up to the axial position of the recirculation center.     

Heat transfer from a cylinder in axial turbulent flows

Local convective heat transfer coefficients were measured on a two-diameter long cylinder in axial flows of air at conditions unexplored so far, by using thermochromic liquid crystals (TLC) coated on an electrically heated strip-foil consisting bonded to the external surfaces. The Reynolds numbers (Re) based on the cylinder diameter were between 8.9 × 10⁴ and 6.17 × 10⁵, and the flow in front of the cylinder was modified in some cases by the use of a turbulence generating grid, or by circular disc inserts of two sizes placed upstream of the cylinder. These created a major change in the local convective heat transfer coefficient distribution on the cylinder. Increase of the turbulence intensity from Tu < 0.1% to Tu = 6.7% at the same Re increased the average calculated Nusselt number Nu over the cylinder by 25%, and decreased the Nu non-uniformity over the surface. One of the flow modification inserts also reduced significantly the Nu non-uniformity. The position of flow reattachment was measured using tufts. Our heat transfer data agree well with the small amount if data published of others, when extrapolated to their conditions. Correlations between the Nu and Re in the form Nu = CRe^e were established and presented for the average Nu on the front, middle and rear cylinder surfaces, and the variation of the local exponent e was shown along the cylinder. Introducing a new technique, a TLC-coated heated flat plate mounted in the flow above the cylinder in the meridional plane was demonstrated to help visualize the flow field above the cylinder. A track of maximum convective coefficients on this plate was found similar in position to the stream line dividing the forward and backward flows in a case measured for the separated flow in a past study.     

Modelling of roughness effects on heat transfer in thermally fully-developed laminar flows through microchannels

In this paper, roughness was modelled as a pattern of parallelepipedic elements of height k periodically distributed on the plane walls of a microchannel of height H and of infinite span. Two different approaches were used to predict the influence of roughness on heat transfer in laminar flows through this microchannel. Three-dimensional numerical simulations were conducted in a computational domain based on the wavelength λ. A one-dimensional model (RLM model) was also developed on the basis of a discrete-element approach and the volume averaging technique. The numerical simulations and the rough-layer model agree to show that the Poiseuille number Po and the Nusselt number Nu increase with the relative roughness. The RLM model shows that the roughness effect may be interpreted by using effective roughness heights k_eff and k_effθ for predicting Po and Nu respectively. k_eff and k_effθ depend on two dimensionless local parameters: the porosity of the rough-layer and the roughness height normalized with the distance between the rough elements. The present results show that roughness increases the friction factor more than the heat transfer coefficient (performance evaluation criteria < 1), for a relative roughness height expected in the fabrication of microchannels (k/(H/2) < 0.46) or k/D_h < 0.11).     

Progress in particle resuspension from rough surfaces by turbulent flows

This article deals with the resuspension phenomenon whereby particles adhering on a wall surface can be re-entrained by a flowing fluid. This is an area where significant progress has been achieved over the last years from an experimental, theoretical and numerical point of view. A first purpose of the present work is to report on the advances that have clarified our understanding of the physics of particle resuspension. It will be seen that new pictures have emerged about the physical processes involved in particle resuspension and, correspondingly, that new models have been proposed. A second purpose of the review is to put forward a general framework that allows both experimental analysis and new modelling ideas to be developed in terms of the fundamental interactions at play. These interactions are made up by the particle–fluid, particle–surface and particle–particle forces which are, in turn, related to the three specific fields of fluid dynamics, interface chemistry and surface roughness. Such a separation is helpful to highlight the actual physical processes while emphasising their relative importance in different situations and to provide useful guidelines for the necessary modelling efforts. In particular, it is stressed that new models which capture particle motion along a wall and simulate the complete particle dynamics represent an improvement over more classical static approaches. It is proposed that these new approaches be pursued and brought to higher levels of maturity.In this paper, attention is first focussed on the case where only a single layer of particles is sticking on the surface and, thus, can be re-entrained. A detailed review of the experimental works brings out the essential mechanisms and particle resuspension is shown to result from a balance between particle–fluid interactions and particle–surface interactions influenced by surface heterogeneities (roughness). The numerical models which have been proposed are then thoroughly discussed with respect to a new hierarchy of modelling approaches which is introduced. The present paper also outlines the mechanisms of multilayer particle resuspension which is still an open subject and where our present understanding remains preliminary. In this situation, resuspension is shown to be also governed by particle–fluid and particle–surface interactions but with the addition of particle–particle interactions (through cohesion forces or impaction). Finally, suggestions about the areas that still need to be addressed as well as about the issues that remain to be improved are addressed.     

Estimation of the turbulent mixing rate for low Prandtl number flows through rod bundles

The prediction of the turbulent mixing rate is very important in the thermal-hydraulic design of nuclear reactors. In this study, the turbulent mixing rate for low Prandtl number fluid flow through rod bundles is estimated with the scale analysis on the flow pulsation phenomenon which is pointed out as a main cause of the mixing in rod bundles. Based upon the assumption that the turbulent mixing is composed of molecular motion, isotropic turbulent motion (turbulent motion without the flow pulsation), and flow pulsation, the scale relation is derived as a function of P/D, Re, and Pr. The derived scale relation is compared with published experimental results and shows good agreements.     

Numerical simulation and optimization of turbulent flows through perforated circular pin fin heat sinks

In this study, the fluid flow and heat transfer characteristics of turbulent forced convection of air flow through perforated circular pin fin heat sinks with constant heat flux are investigated numerically. Circular perforated pin fins are shown to have 8% larger averaged Nusselt numbers than the corresponding solid pin cases. In addition, after the validation of the numerical results, the numerical optimization of this problem is also presented by using the response surface methodology (RSM) coupled with genetic algorithm (GA). The difference between the optimal thermal performance factor (η) which is calculated by regression function and obtained by using computational fluid dynamics (CFD) is less than 2%, and the numerical optimization shows that the enhancement of the objective function (η) can achieve 34%.     

Using porous inserts to enhance heat transfer in laminar fully-developed flows

The objective of this work is to investigate if it is possible to use porous inserts to enhance heat transfer in rectangular channels. A mathematical model that includes inertia and viscous effects is used to determined the velocity profile in the porous region. For the fluid region, momentum transfer is modeled using the Navier-Stokes equation. These equations and the energy equations are solved numerically via a finite-difference method. Heat transfer between the channel walls and the fluid is determined as a function of Darcy number, inertia parameter, ratio of the fluid and porous medium thermal conductivities, and the porous insert thickness. It is shown that heat transfer could be enhanced by placing a porous insert in the channel. Moreover, for some conditions heat transfer is maximized by using a porous insert thinner than the channel height while a porous insert that completely fills the channel is needed for other conditions.     

A method to dynamically estimate the diffusion boundary layer from local velocity conditions in laminar flows

The differential equation for dilute species transport next to a planar interface within the hydrodynamic boundary layer is transformed into a differential equation for the diffusion boundary layer. This differential equation contains two coefficients, which depend explicitly on the concentration profile. We show that these coefficients can be taken as identical constants, in a number of limiting cases. Using these constants, we show that this equation reproduces very well the temporal and spatial profile of the diffusion boundary layer determined from numerical simulations in some more complex intermediate cases. The final differential equation depends only on the diffusion coefficient and on local velocity and velocity gradients next to the interface, and not explicitly on concentration. Therefore this equation can be used to estimate the mass transfer coefficient from the local velocity profile when conditions are not fixed in space or time, and especially in transient computational fluid dynamics calculations. It can also be used to estimate new correlations for the mass transfer coefficient, in cases where the spatial velocity profile at the interface is known.     

3D unsteady numerical analysis of conjugate heat transport and turbulent/laminar flows in LEC growth of GaAs crystals

We present the conjugated 3D unsteady numerical analysis of industrial-scale LEC GaAs crystal growth, including the calculation of heat transfer in the crystal and crucibles, melt convection, and the encapsulant flow. The analysis of unsteady turbulent melt convection is performed in terms of the large eddy simulation approach. A special procedure was introduced into the calculations to predict the geometry of the crystallization front. The results of the 3D unsteady calculations are compared to the results obtained in terms of the conventional steady-state Reynolds averaged approach with respect to the calculation of the geometry of the crystallization front. The effect of convective heat transfer in the encapsulant is specially studied using the 3D unsteady analysis. To investigate details of dynamic interaction between two immiscible liquids having a plane interface, preliminary computational tests were performed in a model setup.