CFD analysis of convective heat transfer at the surfaces of a cube immersed in a turbulent boundary layer

Steady Reynolds-Averaged Navier–Stokes (RANS) CFD is used to evaluate the forced convective heat transfer at the surfaces of a cube immersed in a turbulent boundary layer, for applications in atmospheric boundary layer (ABL) wind flow around surface-mounted obstacles such as buildings. Two specific configurations are analysed. First, a cube placed in turbulent channel flow at a Reynolds number of 4.6 × 10³ is considered to validate the numerical predictions by comparison with wind-tunnel measurements. The results obtained with low-Reynolds number modelling (LRNM) show a satisfactory agreement with the experimental data for the windward surface. Secondly, a cube exposed to high-Reynolds number ABL flow is considered. The heat transfer in the boundary layer is analysed in detail. The dimensionless parameter y¹, which takes into account turbulence, is found to be more appropriate for evaluating heat transfer than the commonly used y⁺ value. Standard wall functions, which are frequently used for high-Reynolds number flows, overestimate the convective heat transfer coefficient (CHTC) significantly (±50%) compared to LRNM. The distribution of the CHTC–U₁₀ correlation over the windward surface is reported for Reynolds numbers of 3.5 × 10⁴ to 3.5 × 10⁶ based on the cube height and U₁₀, where U₁₀ is the wind speed in the undisturbed flow at a height of 10 m.     

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.     

Transitional flow patterns behind a backstep with porous-based fluid injection

The flow structure downstream of a backstep with mass injection from a porous base was analyzed both qualitatively and quantitatively in the transitional flow regime of Re_h = 2009–3061. By increasing the wall injection velocity ratio gradually, four distinct flow patterns, shifted from pattern A to B, C and D, were categorized. Pressure distributions of these patterns were dominated by the wall injection velocity ratio, and various downstream-flowing tendencies were produced correspondingly. The effect of flow stabilization by decreasing the Reynolds number became more prominent if the wall injection velocity ratio was increased. Due to the existence of a shear layer, a large value of the Reynolds stress was measured near the tip of the step in pattern A. Once the wall injection was initiated, the local strength of Reynolds stress at the same location was decreased. By increasing the wall injection velocity ratio, the region with decreased level of Reynolds stress extended gradually from the tip of backstep to the streamwise location x = 0.45X_r. The turbulent kinetic energy in pattern A was mostly contributed by the horizontal fluctuation of flow near the backstep in the recirculation zone, and the region with maximum horizontal fluctuation was found to evolve toward the base as the flow moves downstream. However, the weighting of vertical fluctuation became more significant as the wall injection velocity ratio increased.     

Thermal protection with liquid film in turbulent mixed convection channel flows

In this numerical study, a channel flow of turbulent mixed convection of heat and mass transfer with film evaporation has been conducted. The turbulent hot air flows downward of the vertical channel and is cooled by the laminar liquid film on both sides of the channel with thermally insulated walls. The effect of gas–liquid phase coupling, variable thermophysical properties and film vaporization are considered in the analysis. In the air stream, the k–ε turbulent model has been utilized to formulate the turbulent flow. Parameters used in this study are the mass flow rate of the liquid film B, Reynolds number Re, and the free stream temperature of the hot air T_o. Results show that the heat flux was dramatically increases due to the evaporation of liquid water film. The heat transfer increases as the mass flow rate of the liquid film decreases, while the Reynolds number and inlet temperature increase, and the influences of the Re and T_o are more significant than that of the liquid flow rate. It is also found that liquid film helps lowering the heat and mass transfer rate from the hot gas in the turbulent channel, especially at the downstream.     

The calculation of turbulent boundary layers with foreign gas injection

Numerical solutions have been obtained for flat plate compressible turbulent boundary layers of air with foreign gas injection, on the hypothesis that the momentum equation is coupled to the species and energy equations only through spatial variations of the mean density and viscosity. The finite difference calculation procedure incorporates the “ω²” transformation with central differencing. The injected species include H₂, He, CH₄, H₂O, CO, Air, CO₂, Freon 12, Xe and CCl₄; temperature ratios T_s/T_e range from 0.2 to 2.0 while the Mach numbers range from 0 to 6. Thermodynamic properties are estimated allowing for variable specific heats; for the transport properties, kinetic theory with the Lennard-Jones potential is used. Thermal diffusion and diffusional conduction are ignored. Eddy viscosity models for the inner region were evaluated by comparison with experimental data for blown constant property flows, and a “best” model selected for the parametric calculations. The turbulent Schmidt and Prandtl numbers were taken as constants, respectively 0.8 and 0.9. The results show the important role played by density variations across the boundary layer; the mass and heat transfer Stanton numbers for the heaviest injectants actually increase with injection, and the light injectants are found to be more effective in reducing skin friction and heat transfer than experimental data indicate. Agreement with experiment for low speed flows is shown to be generally satisfactory; also, the predicted influence of Mach number on skin friction is found to be consistent with experiment.     

Flow and heat transfer behaviors of phase change material slurries in a horizontal circular tube

The flow and convective heat transfer behaviors of microencapsulated phase change material (MPCM) slurries in a horizontal circular tube have been experimentally investigated. The slurry consisted of microencapsulated 1-bromohexadecane (C₁₆H₃₃Br) and water, with the mass fractions of MPCM varying from 5% to 27.6%. The pressure drop and local heat transfer coefficients were measured, and the influences of capsule fractions, heating rates, and flow structures on heat transfer performance were also studied. Heat transfer coefficients measured for MPCM slurry are significantly higher than for those for single-phase fluid flow in laminar flow conditions, but exhibit more complicated phenomena at low turbulent conditions. Moreover, a new simple heat transfer correlation equation was proposed that accurately predicts the local heat transfer coefficients of laminar MPCM slurry flow in a horizontal circular tube.     

Numerical simulation of separated flow transition and heat transfer around a two‐dimensional rib

Numerical simulations of separated flow transition and heat transfer around a two‐dimensional rib mounted in a laminar boundary layer were performed. The separated shear layer becomes unstable due to the Kelvin–Helmholtz instability and generates a two‐dimensional vortex. This vortex becomes three‐dimensional and collapses in the downstream part of the separation bubble. As a result, transition from laminar to turbulent flow occurs in the separated shear layer. Streamwise vortices exist downstream of the reattachment flow region. The low‐frequency flapping motion and transition of the separated shear layer are influenced by three‐dimensional dynamics upstream of the separation bubble. Large‐scale vortices around the reattachment flow region have substantial effects on heat transfer. Downstream of the reattachment point, the surface friction coefficient and Nusselt number are different from their profiles in the laminar boundary layer and approach the distributions seen in the turbulent boundary layer. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(8): 513–528, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20177     

Soret effect on the boundary layer flow regime in a vertical porous enclosure subject to horizontal heat and mass fluxes

The combined thermo- and double-diffusive convection in a vertical tall porous cavity subject to horizontal heat and mass fluxes was investigated analytically and numerically using the Darcy model with the Boussinesq approximation. The investigation focused on the effect of Soret diffusion on the boundary layer flow regime. The governing parameters were the thermal Rayleigh number, R_T, the Lewis number, Le, the buoyancy ratio, N, the Soret parameter, M, which characterized the Soret effect, and the aspect ratio of the enclosure, A_r. The results demonstrated the existence of a boundary layer flow solution for which the Soret parameter had a strong effect on the heat and mass transfer characteristics. For M ≠ 1 and M ≠ −1/Le, the profiles of the vertical velocity component, v, temperature, T, and solute concentration, S, exhibited boundary layer behaviors at high Rayleigh numbers. Furthermore, as R_T increased, the temperature and solute concentration became vertically and linearly stratified in the core region of the enclosure. The thermo-diffusion effect on the boundary layer thickness, δ, was discussed for a wide range of the governing parameters. It was demonstrated analytically that the thickness of the boundary layer could either increase or decrease when the Soret parameter was varied, depending on the sign of the buoyancy ratio. The effect of R_T on the fluid flow properties and heat and mass transfer characteristics was also investigated.     

Local heat transfer distribution on a smooth flat plate impinged by a slot jet

Experimental investigation of local heat transfer distribution on a smooth flat plate impinged by a normal slot jet is conducted. Present study concentrates on the influence of jet-to-plate spacing (z/b) and Reynolds number on the fluid flow and heat transfer distribution. A single slot jet with an aspect ratio (l/b) of about 50 is chosen to get the fully developed flow at the nozzle exit. Reynolds number based on slot width is varied from 4200 to 12,000 and jet-to-plate spacing (z/b) is varied from 0.5 to 12. The local heat transfer coefficients are estimated from the thermal images obtained from infrared thermal imaging camera. Measurement for the static wall pressure is carried out for various jet-to-plate spacings at a Reynolds number of 12,000. Normalized value of turbulence and velocity are measured using hot wire anemometer along the streamwise direction (x/b) for jet-to-plate spacings (z/b) of 1, 2, 4, 6, 8, 10 and 12. The entire flow field is divided into three regimes namely stagnation region (laminar boundary layer associated with favorable pressure gradient), transition region (associated with increase in turbulence intensities and heat transfer) and turbulent wall jet region. Semi-empirical correlation for the Nusselt number in the stagnation region is proposed. Heat transfer characteristics in the transition region are explained based on the fluid dynamic behavior from the hot wire measurements. Semi-empirical correlation for the Nusselt number in the wall jet region is presented using the velocity profile obtained from the hot wire measurements.     

A novel split-dimple interrupted fin configuration for heat transfer augmentation

The use of an interrupted plate fin with surface roughness in the form of split-dimples is investigated. High-fidelity time-dependent calculations are performed for a wide range of Reynolds number ranging from Re_H = 240 to 4000, covering the laminar to fully turbulent flow regimes. The split-dimples provide an additional mechanism for augmenting heat transfer by perturbing continuous boundary layer formation on the fin surface and generating energetic shear layers. High heat transfer regions are observed at the fin and split-dimple leading edges as a result of boundary layer restarts, in regions of flow acceleration between protrusions, and flow impingement on the protrusion surface. While the protruding geometry of the split-dimple also aids in augmenting heat transfer from the fin surface by generating unsteady or turbulent wakes, it also increases pressure losses. The split-dimple fin results in a heat conductance that is 60–175% higher than a plain interrupted plate fin, but at a cost of 4–8 times the frictional losses.     

Theoretical analysis on flame dimension in turbulent ceiling fires

In this paper, theoretical analysis based on boundary layer theory on flame dimension in turbulent ceiling fires is carried out. The turbulent ceiling fire is developed from a downward round injection source beneath an unconfined inert ceiling. A correlation between the dimensionless flame diameter and the dimensionless heat release rate is obtained, C₁(S/d) ∼ C₂Q^13/4. This relation for turbulent ceiling fires is correlated to experimentally measured flame diameters for ceiling fires. Based on the limited data available, the agreement with experiments is very good. Additional experiments are needed to further verify the validity of this relation.     

Turbulent flow in a rectangular duct with a smooth-to-rough step change in surface roughness

Experimental study has been conducted on the response of turbulent flow in a rectangular duct to a smooth-to-rough step change in surface roughness on its short-side walls. The distributions of the primary flow velocity, secondary flow velocities, turbulence intensities, and turbulent shear stresses have been measured in seven cross-sections located from 2.0d_h to 37.5d_h downstream from the smooth-to-rough junction, and the relaxation process of this turbulent flow has been examined. It has been found that the relaxation process of this flow is considerably complex, but the flow characteristics except for the primary flow velocity in the core region as well as near the rough wall reach an almost equilibrium state, i.e., the fully developed rough-duct flow condition, within a distance of 37.5d_h from the change in the surface roughness.     

Determination of annular condensation heat transfer coefficient of steam in microchannels with trapezoidal cross sections

Experiments have been carried out to determine annular condensation heat transfer coefficient of steam in two silicon microchannels having trapezoidal cross sections with the same aspect ratio of 3.15 at 54 < G < 559 kg/m² s under 3-side cooling conditions. A semi-analytical method, based on turbulent flow boundary layer theory of liquid film with correlations of pressure drop and void fraction valid for microchannels, is used to derive the annular local condensation heat transfer coefficients. The predicted values based on the semi-analytical model are found within ±20% of 423 data points. It is shown that the annular condensation heat transfer coefficient in a microchannel increases with mass flux and quality and decreases with the hydraulic diameter.     

Fluid flow and heat transfer of natural convection around large horizontal cylinders: Experiments with air

Natural convective flows of air around large horizontal cylinders were investigated experimentally. The main concerns were the turbulent transition mechanisms and the heat transfer characteristics of turbulent flows. The cylinders were heated with uniform heat flux and their diameters were varied from 200 to 1200 mm to enable experiments over a wide range of modified Rayleigh numbers, Ra_D^* = 1.0 × 10⁸ to 5.5 × 10¹¹. The flow fields around the cylinders were visualized with smoke to investigate the turbulent transition mechanisms. The results show that three‐dimensional flow separations occur first at the trailing edge of the cylinder when Ra_D^* exceeds 3.5 × 10⁹, and the separation points shift upstream with increasing Rayleigh numbers. These separations become a trigger to the turbulent transition and transitional and turbulent flows appear downstream of the separations at higher Rayleigh numbers. However, they occupy a relatively small portion of the cylinder surfaces even at the maximum Rayleigh numbers of the present experiments. The local heat transfer coefficients were also measured. The results show that the coefficients are increased significantly in the transitional and turbulent regions compared with the laminar coefficients. Moreover, the present results for air were compared with previous results for water and the effects of Prandtl number on the flow and heat transfer were discussed. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(4): 293–305, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10080     

New development of the turbulent Prandtl number models for the computation of film cooling effectiveness

This paper presents the new development on the turbulent Prandtl number distribution models which are used to improve the computation accuracy of film cooling effectiveness distribution in the frame of the isotropic turbulence models. In the new developed turbulent Prandtl number distribution models, the turbulent Prandtl number varies with some characteristic quantity of the film cooling to make the models applicable for more film cooling cases effectively. A new VTG-Pr_t model is developed for the computation of film cooling cases in which the wall is mainly influenced by the mixing layer region between the jet core and the mainstream. The Pr_t value in this model varies with dimensionless temperature gradient which is suggested to be the characteristic quantity of the mixing layer region. The VTG-Pr_t model has been used in the computations of long cylindrical hole film cooling, short cylindrical hole film cooling, compound angle cylindrical hole film cooling and expansion shaped hole film cooling in the present paper. And it is validated to be an effective and easy way to obtain accurate film cooling effectiveness distributions for this kind of film cooling. But for the kind of film cooling, in which the wall is mainly influenced by the jet core region and the influence of heat diffusion in the mixing layer region on the cooling effectiveness is very small, the VTG-Pr_t model is disabled. Another turbulent Prandtl number distribution model, named VT-Pr_t model, is developed for this kind of film cooling in the present paper. The Pr_t value in this model varies with dimensionless temperature which is suggested to be the characteristic quantity of the jet core region. Good agreement between the computed and measured results is obtained through the use of VT-Pr_t model in the computation of converging slot hole film cooling.     

Effect of suction/injection on the flow of a micropolar fluid past a continuously moving plate in the presence of radiation

An analysis is carried out to study the effect of suction and injection on the flow and heat transfer characteristics for a continuous moving plate in a micropolar fluid in the presence of radiation. The boundary layer equations are transformed to non-linear ordinary differential equations. Numerical results are presented for the distribution of velocity, microrotation and temperature profiles within the boundary layer. The effects of varying the Prandtl number, Pr, the radiation parameter, N and porosity parameter, F_w, are determined.     

Analysis of voltage-drop near cold-electrodes of a combustion MHD generator

In this paper turbulent compressible boundary layer equations for mass, momentum and energy are solved near the cold electrode wall of a combustion MHD generator. Arcs are simulated by freezing the electron temperature (and hence electrical conductivity) to a temperature called T_arc when gas temperature is less than T_arc. Theoretical neare electrode drop for various current densities along the flow direction is analysed for various T_arc temperatures and compared with experimentally obtained near electrode drop. It is found that the T_arc temperature increases as a square root along the flow direction and has linear dependency on current density.     

Fluid flow and heat transfer of natural convection adjacent to upward‐facing inclined heated plates

Turbulent transition mechanism and local heat transfer characteristics of the natural convective flows over upward‐facing inclined plates were investigated experimentally. The experiments were performed in the range of modified local Rayleigh numbers from 10⁴ to 8 × 10¹⁴ and of inclination angles θ from 0 to 90°. The flow fields over the plate and the surface temperatures of the plate were visualized with dye and liquid crystal thermometry. The results showed that longitudinal vortices play a main role in the turbulent transition over the plate of θ < 72°. These vortices appear first in the laminar boundary layer, then detach from the plate and, finally become distorted. It is found that the heat transfer is enhanced markedly by the detachment and the distortion of these vortices. The local heat transfer coefficients were measured in the laminar, transitional, and turbulent regions. The results show that the coefficients in the turbulent region become identical and independent of inclination angles. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(3): 278–291, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10091     

The numerical computation of the evaporative cooling of falling water film in turbulent mixed convection inside a vertical tube

An analysis has been developed for studying the evaporative cooling of liquid film falling inside a vertical insulated tube in turbulent gas stream is presented. Heat and mass transfer characteristics in air–water system are mainly considered. A low Reynolds number turbulence model of Launder and Sharma is used to simulate the turbulent gas stream and a modified Van Driest model suggested by Yih and Liu is adopted to simulate the turbulent liquid film. The model predictions are first compared with available experimental data for the purpose of validating the model. Parametric computations were performed to investigate the effects of Reynolds number, inlet liquid temperature and inlet liquid mass flow rate on the liquid film cooling mechanism. Results show that significant liquid cooling results for the system with a higher gas flow Reynolds number Re, a lower liquid flow rate Γ₀ or a higher inlet liquid temperature T_L0.