Second-order corrections of the k-ε model to account for non-isotropic effects due to buoyancy

A new turbulence model which is a hybrid of the k-ε model and an algebraic Reynolds stress model (ASM) is developed. This model takes from an ASM that part of the non-isotropic Reynolds stress which is due to buoyancy, and the remaining part from the k-ε model. This concept is also applicable to flows with rotation where the Coriolis forces affect the turbulence by increasing its non-isotropy. The model is tested in a buoyancy-driven cavity flow. The contributions from the ASM corrections to the Reynolds stress and the turbulent heat flux are up to five and ten times, respectively, larger than those from the k-ε model.     

Analysis of heat transfer augmentation and flow characteristics due to rib roughness over absorber plate of a solar air heater

A computational analysis of heat transfer augmentation and flow characteristics due to artificial roughness in the form of ribs on a broad, heated wall of a rectangular duct for turbulent flow (Reynolds number range 3000–20,000, which is relevant in solar air heater) has been carried out. Shear stress transport k−ω turbulence model is selected by comparing the predictions of different turbulence models with experimental results available in the literature. A detailed analysis of heat transfer variation within inter rib region is done by using the selected turbulence model. The analysis shows that peak in local heat transfer coefficient occurs at the point of reattachment of the separated flow as observed experimentally. The results predict a significant enhancement of heat transfer in comparison to that for a smooth surface. There is a good matching between the predictions by SST k−ω and experimental results. In this work, nine different shapes of rib are examined using SST k−ω model and compared on the basis of heat transfer enhancement, friction characteristics and performance index considering heat transfer enhancement with the same pumping power.     

Heat Transfer and Fluid Flow over a Single Disk in a Fluid Rotating as a Rigid Body

Laminar heat transfer problem is analyzed for a disk rotating with the angular speed ωin a co-rotating fluid (with the angular speed Ω). The fluid is swirled in accordance with a forced-vortex law, it rotates as a solid body at β= Ω/ω= const. Radial variation of the disk's surface temperature follows a power law. An exact numerical solution of the problem is obtained basing on the self-similar profiles of the local temperature of fluid, its static pressure and velocity components. Numerical computations were done at the Prandtl numbers Pr = 1(?)0.71. It is shown that with increasing βboth radial and tangential components of shear stresses decrease, and to zero value at β= 1. Nusselt number is practically constant at β= 0(?) 0.3 (and even has a point of a maximum in this region); Nu decrease noticeably for larger βvalues.     

Conjugated heat transfer investigation with racetrack-shaped jet hole and double swirling chamber in rotating jet impingement

A numerical study is performed to investigate the effects of jet hole shape and channel geometry on impingement cooling for both stationary and rotating condition. Two hole shapes and two channel geometries are introduced to counteract the adverse effects of centrifugal force and Coriolis force which are induced by rotation. Both the fluid and solid part are considered for realizing the conjugate heat transfer simulation. The unsteady k-ω SST turbulence model was employed to obtain the time-averaged Nusselt number distributions, time-averaged temperature and temperature gradient fields and the turbulent flow structure. The results show that the cooling jet from the racetrack-shaped hole can effectively withstand the intensive streamwise crossflow to enhance the heat transfer. The double swirling chamber (DSC) channel significantly improves the heat transfer characteristics on the cambered surface and diminishes the adverse effects of the Coriolis force. The high Nu number region is expanded while the temperature uniformity is improved. The combination of the racetrack-shaped hole and DSC channel provides the highest heat transfer among the four cases. The averaged Nu numbers on both the leading and trailing sides for all tested cases show obvious downtrend as rotation number increases, especially at high Reynolds number.     

Features of convective heat transfer in heated helium channel flow

The aim of the present work is to choose an optimal method for thermohydraulic calculation of the gas flow in channels with intense heating at the flow Reynolds number below 10,000. These conditions are typical of the cooling channels of the High-Flux-Test Module of the International-Fusion-Materials-Irradiation-Facility (IFMIF/HFTM). A low Reynolds number and a high heating rate can result in partial relaminarization of the initially turbulent flow, and hence in a decrease in the heat transfer. A number of turbulence models offered by the commercial STAR-CD code were tested on the basis of the comparison of the numerical predictions with experimental data. This comparison showed that the low-Reynolds-number k-ε turbulence models predict the heat transfer characteristics close to the experimental data. The k-ε linear low Reynolds number turbulence model of Lien was applied as more appropriate for the thermohydraulic analysis of the IFMIF high flux test module.     

Predictions of Flow and Heat Transfer in Low Emission Combustors

Flow and heat transfer predictions in modern low emission combustors are critical to maintaining the liner wall at reasonable temperatures. This study is the first to focus on a critical issue for combustor design. The objective of this paper is to understand the effect of different swirl angle for a dry low emission (DLE) combustor on flow and heat transfer distributions. This paper provides the effect of fuel nozzle swirl angle on velocity distributions, temperature, and surface heat transfer coefficients. A simple test model is investigated with flow through fuel nozzles without reactive flow. The fuel nozzle angle is varied to obtain different swirl conditions inside the combustor. The effect of flow Reynolds number and swirl number are investigated using FLUENT. Different RANS-based turbulence models are tested to determine the ability of these models to predict the swirling flow. For comparison, different turbulence models such as standard k ? ε, realizable k ? ε, and shear stress transport (SST) k?ω turbulence model were studied for non-reactive flow conditions. The results show that, for a high degree swirl flow, the SST k?ω model can provide more reasonable predictions for recirculation and high velocity gradients. With increasing swirl angle, the average surface heat transfer coefficient increases while the average static temperature will decrease. Preliminary analysis shows that the k?ω model is the best model for predicting swirling flows. Also critical is the effect of the swirling flows on the liner wall heat transfer. The strength and magnitude of the swirl determines the local heat transfer maxima location. This location needs to be cooled more effectively by various cooling schemes.     

Suitability of three different two-equation turbulence models in predicting film cooling performance over a rotating blade

The suitability of three different two-equation turbulence models in predicting film cooling effectiveness on a rotating blade was investigated and they are the commonly used standard k-ε model, the k-ω model and the shear stress transport k-ω model. To fulfill this target, both numerical simulation and the experimental investigation were carried out for a rotating blade having a flat test surface with a 4 mm diameter straight circular cooling hole in 30° inclined injection. The blade rotated at five different speeds of 0, 300, 500, 800 and 1000 rpm. The momentum ratio was set to be 0.285 and the Reynolds (Re_D) number based on the mainstream velocity and hydraulic diameter of the mainstream channel is 1.45 × 10⁵. The averaged density ratio was chosen to be 1.026 with air as both the coolant and the mainstream. Comparison between the numerical work and the experimental results indicated that (1) the rotating speed is the most critical parameter influencing the film cooling effectiveness distributions and the pressure surface could be remarkably different from the suction surface, (2) as for the algebraic averaged film cooling effectiveness, numerical predictions of the three turbulence models all overshoot compared with the experimental results, (3) among the three turbulence models, the standard k-ε model gave the poorest prediction.     

A κ—ε—PDF Two—Phase Turbulence Model for Simulating Sudden—Expansion Particle—Laden FLows

A κ-ε-PDF model based on statistical theory for turbulent gas-particle flows is proposed.and a numerical procedure combining the finite difference and finite fluctuaing-velocity-group methods is used.The obtained statistically averaged equations have the same form as those obtained by using the Reynolds averaging.Using the κ-ε-PDF model(PDF particle turbulence model combined with the κ-ε- gas turbulence model),amny terms,such as the diffusion term in particle Reynolds Stress equations,can be accurately calcuated for verifying the second-moment-closure model,the κ-ε-PDF model is used to simulate sudden-expansion particle-laden flow.comparison of the predictions using both κ-ε-PDF and the κ-ε- models with experimental results shows that the κ-ε-PDF model give more reasonable non-siotropic features of particle turbulence.     

Heat transfer predictions with a cubic k-ε model for axisymmetric turbulent jets impinging onto a flat plate

Local heat transfer in turbulent axisymmetric jets, impinging onto a flat plate, is predicted with a cubic k-ε model. Both the constitutive law for the Reynolds stresses and the transport equation for the dissipation rate ε contribute to improved heat transfer predictions. The stagnation point value and the shape of the profiles of the Nusselt number are well predicted for different distances between the nozzle and the flat plate. Accurate flow field predictions, obtained with the presented turbulence model, are the basis for the quality of the heat transfer results. The influence of the nozzle-plate distance on the stagnation point Nusselt number, is also correctly captured. For a fixed nozzle-plate distance, the influence of the Reynolds number on the stagnation point heat transfer is correctly reproduced. Comparisons are made to experimental data and to results from a low-Reynolds standard k-ε model [1] and the v²-f model [2].     

Study of the heat transfer characteristics in turbulent combined wall and offset jet flows

The heat transfer study of a combined wall jet and offset jet flow with different wall jet and offset jet flow velocities are considered. The flow is considered two-dimensional, steady, incompressible, turbulent at high Reynolds number with negligible body forces. The streamline curvature modification of the standard k–ε model is used to carry out the turbulence modeling. The Reynolds number is varied from 10⁴ to 4 × 10⁴ and Pr = 0.71 is taken for all computations. Constant wall temperature and constant wall heat flux boundary conditions are considered. The results are presented in the form of local Nusselt number, local heat flux, surface temperature in case of constant heat flux condition, average Nusselt number and total heat transfer.     

Turbulent heat transfer on the stationary disk in a rotor-stator system

A combined numerical and experimental study was performed to determine the turbulent heat transfer on a stationary disk, which is situated in a close distance from a rotating disk. The RNG k-ε model and the steady-state liquid crystal technique were employed respectively in the numerical simulation and the experiment. In the range of the rotational Reynolds number from 1.42×10⁵ to 3.33×10⁵, the heat transfer rate on the stator and the flow characteristics in the gap between the disks are presented. The results revealed that there exists an optimum rotor-stator distance for a given Reynolds number, at which the average heat transfer on the stator reaches maximum. When the Reynolds number increases, the maximum shifts towards smaller disk-distances.     

3-D Numerical simulation of swirling flow and convective heat transfer in a circular tube induced by means of loose-fit twisted tapes

The article presents the application of a mathematical model for simulation of the swirling flow in a tube induced by loose-fit twisted tape insertion. Effects of the clearance ratio defined as ratio of clearance between the edge of tape and tube wall to tube diameter (CR = c/D = 0.0 (tight-fit), 0.1, 0.2 and 0.3) on heat transfer enhancement (Nu), friction factor (f) and thermal performance factor (η) are numerically investigated for twisted tapes at two different twist ratios (y/w = 2.5 and 5.0). The simulation is conducted in order to gain an understanding of physical behavior of the thermal and fluid flow in the tube fitted with loose-fit twisted tape under constant wall temperature conditions in the turbulent flow regime for the Reynolds number ranging from 3000 to 10,000. The Navier–Stokes equation in common with a energy equation is solved using the SIMPLE technique with the standard k–ε turbulence model, the Renormalized Group (RNG) k–ε turbulence model, the standard k–ω turbulence model, and Shear Stress Transport (SST) k–ω turbulence model. The numerical results show that the predictions of heat transfer (Nu) and friction factor (f) based on the SST k–ω turbulence models are in better agreement with Manglik and Bergles [R.M. Manglik, A.E. Bergles, Heat transfer and pressure drop correlations for twisted-tape inserts in isothermal tubes, part II: Transition and turbulent flows, Transaction ASME, Journal of Heat Transfer, 115 (1993) 890–896.] than other turbulence models. The mean flow patterns in a tube with loose-fit twisted tapes in terms of contour plots of velocity, pathline, pressure, temperature and turbulent kinetics energy (TKE) are presented and compared with those in a tube fitted with tight-fit twisted tapes. It is visible that the twisted tape inserts for y/w = 2.5 with CR = 0.0 (tight-fit), 0.1, 0.2 and 0.3 can enhance heat transfer rates up to 73.6%, 46.6%, 17.5% and 20%, respectively and increase friction factors up to 330%, 262%, 189%, and 160%, respectively, in comparison with those of the plain tube. The tube with loose-fit twisted tape inserts with CR = 0.1, 0.2 and 0.3 provide heat transfer enhancement around 15.6%, 33.3% and 31.6% lower than those with CR = 0.0 (the tight-fit twisted tape). The heat transfer augmentation is expected to involve the swirl flow formation between the tape and a tube wall. In addition, the simulation for thermal performance factor (η) of a tube with the loose-fit twisted tape and the tight-fit twisted tape under the same pumping power is also conducted, for comparison.     

CALCULATION OF HEAT TRANSFER IN A RADIALLY ROTATING COOLANT PASSAGE

The three-dimensional flow field and heat transfer in a radially rotating coolant passage are studied numerically. The passage chosen has a square cross section with smooth isothermal walls of finite length. The axis of rotation is normal to the flow direction with the flow radially outward. The effects of Coriolis forces, centrifugal buoyancy, and fluid Reynolds number on the flow and heat transfer have all been considered. The analysis has been performed by using a fully elliptic, three-dimensional, body-fitted computational fluid dynamics code based on pressure correction techniques. The numerical technique employs a multigrid iterative solution procedure and the standard κ ? ε turbulence model for both the hydrodynamics and heat transfer. The effect of rotation is included by considering the governing equations of motion in a relative frame of reference that moves with the passage. The consequence of rotation is to bring higher velocity fluid from the core to the trailing surface, thereby increasing both the friction and heat transfer at this face. At the same time, the heat transfer is predicted to decrease along the leading surface. The effect of buoyancy is to increase the radial velocity of the fluid, thus generally increasing the heat transfer along both the leading and trailing surfaces. These effects and trends that have been predicted are in agreement with experimental heat transfer data available in the literature [1,2]. The quantitative agreement with the data was also found to be quite satisfactory.     

A Tomo‐PIV study of the effects of freestream turbulence on stall delay of the blade of a horizontal‐axis wind turbine

Volumetric velocity fields were measured using tomographic particle image velocimetry on a model of the blade of a 5 kW horizontal‐axis wind turbine to study the effects of freestream turbulence levels (FTLs) at 0.4%, 4% and 13% on stall delay phenomenon at two different global tip speed ratios of 3 and 5 with Reynolds number (Re) ? 5000. Static pressures were measured, and results illustrated that FTL has stronger effect on the surface pressures of the static airfoil. Magnitudes of the absolute velocities within the separated flows above the static airfoil's suction surface increase significantly with higher FTL, while the changes of these velocities above the rotating blade's surface are less obvious. Radial flows from rotating blade's root to tip were also observed with strong spanwise velocity component located in the vicinities of the vortices. At the root and middle sections of the rotating blade, the flows with strong radial velocity component, w, become wider with higher FTL near to the rotating blade's leading edge when the angles of attack (AOAs) are large. At large AOAs, the strength and size of the vortices shed from the rotating blade's leading and trailing edges decrease significantly with higher FTL. However, at small AOAs, the size and coherence of the vortices near the rotating blade's trailing edge increase significantly with higher FTL. Surface streamlines of the rotating blade illustrated that at the rotating blade's root region and at large AOAs, the streamlines tend to lean toward the rotating blade's trailing edge at higher FTL. Copyright © 2014 John Wiley & Sons, Ltd.     

Effect of rib height on heat transfer in a two pass rectangular channel (AR = 1:4) with a sharp entrance at high rotation numbers

Blockage ratio effects on heat transfer in 1:4 AR channels with developing flow is experimentally determined. The blockage ratios (e/D_h) were 0.078 and 0.156. Reynolds numbers up to 40 K and rotational speeds up to 400 rpm were considered. The rotation number (Ro) and local buoyancy parameter (Bo_x) were extended to 0.65 and 1.5, respectively. The entrance dominates over rotation on the trailing surface first pass. The leading surface is dominated by rotation. Rotation effects are reduced by the ribs and heat transfer is similar for both walls in the second pass. Rotation effects were similar for both blockage ratios. The correlations show that the buoyancy parameter is useful to predict heat transfer in the extended range.     

Experimental and numerical investigation of convection heat transfer of CO2 at supercritical pressures in a vertical mini-tube

Convection heat transfer of CO₂ at supercritical pressures in a 0.27 mm diameter vertical mini-tube was investigated experimentally and numerically for inlet Reynolds numbers exceeding 4.0 × 10³. The tests investigated the effects of heat flux, flow direction, buoyancy and flow acceleration on the convection heat transfer. The experimental results indicate that the flow direction, buoyancy and flow acceleration have little influence on the local wall temperature, with no deterioration of the convection heat transfer observed in either flow direction for the studied conditions. The heat transfer coefficient initially increases with increasing heat flux and then decreases with further increases in the heat flux for both upward and downward flows. These phenomena are due to the variation of the thermophysical properties, especially c_p. The numerical results correspond well with the experimental data using several turbulence models, especially the Realizable k–ε turbulence model.     

Unsteady RANS simulation of turbulent flow and heat transfer in ribbed coolant passages of different aspect ratios

The flow and heat transfer in ribbed coolant passages of aspect ratios (AR) 1:1, 4:1, and 1:4 are numerically studied through the solution of the unsteady Reynolds averaged Navier–Stokes (URANS) equations. The URANS procedure, which utilizes a two equation k–ε model for the turbulent stresses, is shown to resolve large-scale bulk unsteadiness. The computations are carried out for a fixed Reynolds number of 25,000 and density ratio of 0.13, while the Rotation number is varied between 0.12 and 0.50.At higher rotation numbers (⩾0.5) at least three inter-rib modules are required to ensure periodicity in the streamwise direction. The flow exhibits unsteadiness in the Coriolis-driven secondary flow and in the separated shear layer. The average duct heat transfer is the highest for the 4:1 AR case. For this case, the secondary flow structures consist of multiple roll cells that direct flow both to the trailing and leading surfaces. The 1:4 AR duct shows flow reversal along the leading surface at high rotation numbers. For this AR, the potential for conduction-limited heat transfer along the leading surface is identified. The friction factor reveals an increase with the rotation number, and shows a significant increase at higher rotation numbers (∼Ro = 0.5).     

Heat/mass transfer in rotating impingement/effusion cooling with rib turbulators

A detailed measurement of the heat/mass transfer coefficients on the ribbed surfaces for the rotating impingement/effusion cooling system has been conducted. Three different jet orientations (front, leading, and trailing) were investigated at the same rotating speed and impinging jet Reynolds number of 3000. A naphthalene sublimation method was used to obtain local heat/mass transfer coefficients. Regardless of rib turbulators, the leading and trailing orientations lead to totally changed heat/mass transfer distributions due to the jet deflection, while the Sh distributions of the front orientation were similar to those of the stationary case. For leading and trailing orientations, the influence of crossflow, which deflected wall jets, decreased due to the blockage effect of the rib turbulators. Therefore, the wall jets spread more widely and the interaction between adjacent wall jets along spanwise direction became stronger, enhancing the heat/mass transfer compared to that on smooth surface.     

Numerical study of mixed convective heat transfer in a lid‐driven enclosure with rotating cylinders

A numerical simulation is performed to characterize the mixed convective transport in a three‐dimensional square lid‐driven enclosure with two rotating cylinders. The top wall is moving in the positive x‐direction, and the bottom wall is at a higher fixed temperature compared with all other isothermal walls. Both cylinders are rotating in its own plane about their centroidal axis. On the basis of rotation of both cylinders in clockwise or counter‐clockwise directions, four rotational models are studied. Various controlling parameters considered in the present study are Grashof number (10 ³ < Gr < 10 ⁵), rotating speed of the cylinder (5 < ω < 50), and the Reynolds number based on top wall movement is fixed to 100. The effect of cylinder rotation on the heat transfer of bottom wall is reported with the help of streamlines, contour plots of z‐component of vorticity, averaged and local Nusselt number, ratios of secondary flow and drag coefficient. It is observed that the heat transfer at the bottom wall is substantially dependent on the rotational model and rotational speed of the cylinder.     

Effect of rotation on heat transfer in two-pass square channels with five different orientations of 45° angled rib turbulators

The effect of various 45° angled rib turbulator arrangements on the Nusselt number ratio in a rotating, two-pass, square channel is investigated for three Reynolds numbers (5000, 10,000, 25,000), with rotation number up to 0.11, and two channel orientations with respect to the axis of rotation (β=90° and 135°). Five different arrangements of rib turbulators are placed on the leading and trailing surfaces at an angle of +45° or −45° to the main stream flow. The rib height-to-hydraulic diameter ratio (e/D) is 0.125; the rib pitch-to-height ratio (P/e) is 10; and the inlet coolant-to-wall density ratio (Δρ/ρ) is maintained around 0.11. The results show that the rotating ribbed surface Nusselt number ratios increase by a factor of 2 compared to the rotating smooth surface results. The results also show that the heat transfer enhancement depends on the rib-angle orientation (+45° or −45°) to the main stream flow in the first or second pass of the channel for both rotating and non-rotating conditions. Overall, the parallel rib cases show better heat transfer enhancement than the crossed rib case for both rotating and non-rotating conditions. The 90° channel orientation with respect to the axis of rotation produces greater rotating effect on heat transfer over the 135° channel orientation.