Computation of a turbulent natural convection in a rectangular cavity with the elliptic-blending second-moment closure

A numerical study of a turbulent natural convection in an enclosure with the elliptic-blending second-moment closure (EBM) is presented. The primary emphasis of the study is placed on an investigation of the accuracy and numerical stability of the elliptic-blending second-moment closure for the turbulent natural convection flow. The turbulent heat fluxes in this model are treated by the general gradient diffusion hypothesis (GGDH). The model is applied to the prediction of a natural convection in a rectangular cavity and the computed results are compared with the experimental data commonly used for a validation of the turbulence models. The results are also compared with those by the two-layer model, the SST model, the V2-f model and the second-moment differential stress and flux model. It is shown that the elliptic blending model predicts as good as or better than the existing models for the mean velocity and turbulent quantities although this model employs a simpler GGDH for treating the turbulent heat fluxes.     

NUMERICAL INVESTIGATIONS OF HEAT TRANSFER OVER A MOVING SURFACE DUE TO IMPINGING KNIFE-JETS

Turbulent flow field and heat transfer from an array of impinging horizontal knife jets on a moving surface have been investigated using large eddy simulation (LES) with a dynamic subgrid stress model. The surface velocity directed perpendicular to the jet plane is varied up to two times the jet velocity at the nozzle exit. Performance of a horizontal knife jet with an exit angle of 60° is compared with the standard axial jet. It has been observed that increasing surface motion reduces heat transfer for both types of jets. However, the amount of heat transfer from the knife jets is more than that from the axial jets when the surface velocity is within the order of half the jet velocity at the nozzle exit. For further increase in surface velocity, heat transfer from the knife jets is, however, less than that in the case of axial jets if the Reynolds number (Re) is low. For higher Re and higher surface velocity, the heat transfer from either type of jets is of comparable magnitude.     

Numerical Analysis of Heat Transfer from a Moving Surface Due to Impingement of Slot Jets

Heat transfer from a moving surface with uniform wall temperature due to impingement of series of slot jets has been investigated numerically. In the present paper, transition–shear stress transport model has been used for numerical simulations, which can predict the heat transfer in laminar as well as turbulent flows. This model is adopted here to study the transport phenomenon and predict the transition from laminar to turbulent flow seamlessly under different surface velocities. The present model with stationary surface is validated with the correlation given by Martin for series of slot jets. It has also shown good agreement with existing data for both laminar and turbulent slot jets, and is further studied to understand the heat transfer under wide range of flow conditions and the effect of surface velocity on flow regime. The range of Reynolds number is from 100 to 5,000, whereas surface velocity varied up to six times the jet velocity at the nozzle exit. It has been observed that at high surface velocities the heat transfer from the moving wall is more than stationary case. The transition from laminar to turbulent regime is found to be starting at a Reynolds number of 400 and turns completely turbulent at a Reynolds number of 3,000. Q-criterion is used to confirm the transition zone by observing the breaking of vortices at higher Reynolds number.     

The role of jet inlet geometry in impinging jet heat transfer,modeling and experiments

Effects of jet inlet geometry and aspect ratio on local and average heat transfer characteristics of totally nine confined impinging jets have been investigated experimentally using thermochromic liquid crystals and numerically by using a 3-D low Reynolds number k–? model. Experimental study by using liquid crystals for temperature measurement was conducted for three different jet exit geometries (circular, elliptic, rectangular). In addition, simulations were performed at the same mass flow rate for totally nine jet exit geometries including circular, elliptic and rectangular jets with different aspect ratios for dimensionless jet to plate distances 2, 6, and 12.As the aspect ratio of equal cross-sectional area elliptic and rectangular jets increases, heat transfer enhancement in the stagnation region was obtained. As a result higher aspect ratio jets can be used as a passive enhancement technique for localized heating or cooling especially at small jet to plate distances. Wall jet region comprises very large portion of the impinging plate under study and generally lower heat transfer rates were attained for higher aspect ratio jets in this region especially at small jet to plate distances. Therefore as the aspect ratio increases, lower average heat transfer rates were acquired. The effect of aspect ratio on local and average heat transfer decreases with increasing jet to plate distance. Even though the mass flow rate is the same, heat transfer rate of rectangular jets were reduced with increasing the cross-sectional area. With increasing jet to plate distance very similar heat transfer characteristics were observed along the major and minor axis directions.     

A study on the heat and mass transfer properties of multiple pulsating impinging jets

In order to explore the potential effect of unsteady intermittent pulsations on the heat and mass transfer rate of multiple impinging jets, a numerical study is performed on a two-dimensional pulsating impinging jet array under large temperature differences between jet flows and impingement wall when the thermo-physical properties can change significantly in the flow domain. Computational fluid dynamic approach is used to simulate the flow and thermal fields of multiple pulsating impinging jets. The numerical results indicate a significant heat transfer enhancement due to intermittent pulsation over a wide range of conditions. The oscillatory flow periodically alters the flow patterns in contrast to steady jets, which can eliminate the formation of a static stagnation point and enhance the local Nusselt number along the impingement wall between adjacent jets. Examination of the velocity field shows that the instantaneous heat transfer rate on the target surface is highly dependent on the hydrodynamic and thermal boundary layer development with time.     

Transient flow and heat transfer of liquid sodium coolant in the outlet plenum of a fast nuclear reactor

A calculation procedure for axisymmetric elliptic flows is applied to predict the transient velocity and temperature fields of a heavy fluid jet issuing vertically into a volume of relatively light fluid. This situation arises in the outlet plenum of a Liquid-Metal-Cooled Fast Breeder Reactor (LMFBR) during reactor transients. The time averaged conservation equations for momenta and heat transfer were solved on a CDC 6600 digital computer for various plenum inlet transients, along with a two-equation model of turbulence and proper modelling of the buoyancy terms. Predictions are presented of flow and heat transfer in the form of velocity vector plots and temperature contours. Predictions are in qualitative agreement with expectations, invariably establishing that the flow by-passes the outlet plenum.     

Confined swirling jet impingement onto an adiabatic wall

Impinging swirling jets generate interesting flow fields and depending on the magnitude of the swirl velocity, circulation cells develop in the region close to the solid wall. Moreover, axial momentum of the jet is influenced by the magnitude of the swirl velocity. This, in turn, results in considerable entropy generation in the flow field. In the present study, confined swirling jet impingement onto an adiabatic wall is investigated. The flow and temperature fields are computed numerically for various flow configurations. Different jet exit velocity profiles are considered and their effects on the flow field are examined. The entropy production due to different flow configurations is computed and the irreversibility ratios due to fluid friction and heat transfer are determined. It is found that the jet axis tilts towards the radial direction as swirl velocity increases and reducing the velocity profile number enhances the entropy generation due to heat transfer. The irreversibility ratio variation with the velocity profile number behaves opposite for the fluid friction and heat transfer.     

The effect of flow field and turbulence on heat transfer characteristics of confined circular and elliptic impinging jets

The flow field of confined circular and elliptic jets was studied experimentally with a Laser Doppler Anemometry (LDA) system. In addition, heat transfer characteristics were numerically investigated. Experiments were conducted with a circular jet and an elliptic jet of aspect ratio four, jet to target spacings of 2 and 6 jet diameters, and Reynolds number 10 000. The toroidal recirculation pattern was observed in the outflow region for both geometries at dimensionless jet to plate distance 2. Higher spreading rates in the minor axis direction of the elliptic jet have also been mapped. Along the target plate, different boundary layer profiles were obtained for circular and elliptic jets at H/d=2, but profiles became similar when dimensionless jet to plate distance was increased to 6. Positions of maximum radial and axial velocities and turbulence intensities have been determined for both geometries. For the confined circular and elliptic jet geometries, analysis of flow field measurements and numerical heat transfer results showed that inner peaks in local heat transfer closely relate to turbulence intensities in the jet and radial flow acceleration along the wall. Differences between the circular and elliptic jet, in terms of flow field and heat transfer characteristics, reduced with increase in the jet to plate distance.     

Forced Convection Laminar Film Condensation of Downward Flowing Vapor on a Single Horizontal Elliptic Cylinder or a Bank of Elliptical Tubes

A numerical study is performed on the laminar film condensation of pure saturated vapor flowing in the direction of gravity on a single horizontal elliptic cylinder or a bank of elliptical tubes. Temperature, velocity distribution, and heat transfer coefficient of the fully developed flow are carried out with a fully implicit finite difference scheme. The equality of shear stress at the liquid-vapor interface is used as the coupling condition between the two phases. The inertia and convection term are retained in the analysis. Outside of the vapor boundary layer, the vapor phase velocity is obtained from potential flow. The method of source density distribution on the body surface is used for determination of the external vapor velocity in elliptical tube banks. The effect of inundation produced by condensate on upper ellipses is taken into account by assuming that the vapor velocity field is not affected by the condensate flow from one elliptic cylinder to another. Based on the obtained solutions of flow field, the effect of surface tension, the interaction because of the ellipse spacing, and the inundation on the heat transfer coefficient and the boundary layer separation point have been evaluated. The results of this analysis are discussed especially in function of eccentricity e (effect of the surface tension). The heat transfer in interellipse space is analyzed and compared with the theoretical and experimental results of other authors. Good agreement is shown.     

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.     

Étude expérimentale d'une interaction de jets obliques avec un écoulement transversal compressible. I. Effets de la compressibilité en régime subsonique sur les champs aérothermiques

Experimental study of inclined jets cross flow interaction in compressible regime. I. Effect of compressibility in subsonic regime on velocity and temperature fields. The results of the investigation of the interaction of a row of jets with a compressible cross flow are compared with their counterpart obtained in incompressible regime. The comparison reported here focuses on the flow field resulting from the interaction above and at the wall. The velocity and temperature fields are measured respectively by laser Doppler velocimetry and thermocouple probes. The wall temperature distributions are measured using an infrared camera. The experiments are performed for cross flow Mach numbers of 0.72 and 0.1 for respectively the compressible and incompressible regimes with almost the same injection rate (R=0.50 and 0.6). Significant differences are noticed between the two flow fields in particular on the vertical development of the jets in the cross flow and on the turbulent diffusion. The jet penetration is found to be higher in the compressible regime with less interaction between the jets. The comparison also shows that the wall heat transfer modifications induced by the jets are less pronounced in the compressible case as a result of the higher penetration of the jets. These results show that neither the mass flux ratio nor the momentum ratio are good candidates for extrapolation of the cooling efficiency from the incompressible case to the real compressible case as encountered in the practical applications.     

Streamline upwind numerical simulation of two-dimensional confined impinging slot jets

In the present paper, flow and heat transfer characteristics of confined impinging slot jets have been numerically investigated using a SIMPLE-based segregated streamline upwind Petrov-Galerkin finite element method. For laminar jets, it is shown that the skin friction coefficient approaches the grid-independent Galerkin solution and that the present simulation induces negligible false diffusion in the flow field. For turbulent jets, the k-ω turbulence model is adopted. The streamwise mean velocity and the heat transfer coefficient respectively agree very well with existing experimental data within limited ranges of parameters.     

Effects of Variable Jet Nozzle Angles on Cross-Flow Suppression and Heat Transfer Enhancement of Swirl Chamber

This paper investigated the effects of variable jetting nozzle angles on the cross-flow suppression and heat transfer enhancement of swirl cooling in gas turbine leading edge. The swirl chamber with vertical jet nozzles was set as the baseline, and its flow fields and heat transfer characteristics were analyzed by 3D steady state Reynolds-averaged numerical methods to reveal the mechanism of cross-flow weakening the downstream jets and heat transfer. On this basis, the flow structure on different cross sections and heat transfer characteristics of swirl chamber with variable jetting nozzle angels were compared with the baseline swirl chamber. The results indicated that for the baseline swirl chamber the circumferential velocity gradually decreased and the axial velocity gradually increased, and the cross-flow gradually formed. The cross-flow deflected the downstream jets and drawn them to the center of the chamber, thus weakening the heat transfer. For swirl chamber with variable jetting nozzle angles, the air axial velocity is axial upstream, opposite to the mainstream, so that the impact effects of cross-flow on the jets were reduced, and the heat transfer was enhanced. Furthermore, with the increase of axial velocity along the swirl chamber, the jetting nozzle angle also gradually increased, as well as the effect of cross-flow suppression, which formed a relative balance. For all swirl chambers with variable jet nozzle angles, the thermal performance factors were all larger than 1, which indicated the heat transfer was enhanced with less friction increment.     

Stresses in radiative annular fin under thermal loading and its inverse modeling using sine cosine algorithm (SCA)

This work presents a novel mathematical model for the analysis of thermal stresses in a radiative annular fin with temperature-dependent thermal conductivity and radiative parameter. An approximate analytical solution for thermal stresses is derived using a homotopy perturbation method (HPM)-based closed-form solution of steady-state nonlinear heat transfer equation, coupled with classical elasticity theory. The effect of thermal parameters on the temperature field and the thermal stress fields are discussed. The various thermal parameters, such as a parameter describing the temperature-dependent thermal conductivity, coefficient of thermal expansion, coefficient of radiative parameter, and the variable radiative parameter, are inversely estimated for a given stress field. For inverse modeling, a population-based sine cosine algorithm (SCA) was employed to estimate the thermal parameters. The inverse modeling is verified by using the estimated thermal parameters in the closed-form solution of stress field. The reconstructed stress fields obtained from the inversely estimated parameters are then compared with the reference stress field. Results show a very good agreement between the reference stress field and the inversely estimated stress fields.     

A non‐Fourier heat flux model for magnetohydrodynamic micropolar liquid flow across a coagulated sheet

In this analysis, a heat transfer extrusion system was made by using a modified heat flux model, namely, the Cattaneo‐Christov heat flux. In the present study, we examined the effect of Arrhenius activation energy on magnetohydrodynamic mixed convection stagnation point flow of a micropolar fluid over a variable thickened surface in the attendance of Brownian motion. The fluid motion is assumed to be steady and laminar. The combined influence of heat and mass transfer aspects are scrutinized. First, suitable transformations are considered to modify the governing partial differential equations as ordinary differential equations and revealed by the consecutive application of numerical procedures like shooting and Runge‐Kutta‐Fehlberg. Graphs are delineated to scrutinize the effects of sundry dimensionless parameters on the flow fields. We found that, the present results made a good agreement with the existing results. We observed that there is an enhancement in the fields of concentration with thermophoresis and activation energy parameters but an opposite trend is noticed for the Brownian motion parameter. Also, it is interesting to note that the buoyancy and the primary slip parameters are increasing functions of velocity fields.     

活塞组-气缸套耦合传热模拟

将柴油机缸内燃气、活塞组-气缸套、冷却介质作为一个耦合体,考虑相应的物理场及各部件间的耦合传热关系,建立了活塞组-气缸套的耦合传热模型。并用该模型实机模拟了6110型柴油机活塞组-气缸套的耦合传热过程．预测出活塞组润滑油膜-气缸套的耦合传热过程。实验表明数值结果合理可信。     

Modeling of the microconvective contribution to wall heat transfer in subcooled boiling flow

In the present work, the two-phase turbulent boundary layer in subcooled boiling flow is investigated. The bubbles in the near-wall region have a significant effect on the dynamics of the underlying liquid flow, as well as on the heat transfer. The present work develops a single-fluid model capable of accounting for the interactions between the bubbles and the liquid phase, such that the two-phase convective contribution to the total wall heat transfer can be described appropriately even in the framework of single-fluid modeling. To this end, subcooled boiling channel flow was experimentally investigated using a laser-Doppler anemometer to gain insight into the bubble-laden near-wall velocity field. It was generally observed that the streamwise velocity component was considerably reduced compared to the single-phase case, while the near-wall turbulence was increased due to the presence of the bubbles. Since the experimentally observed characteristics of the liquid velocity field turned out to be very similar to turbulent flows along rough surfaces, it is proposed to model the near-wall effect of the bubbles on the liquid flow analogously to the effect of a surface roughness. Incorporating the proposed approach as a dynamic boundary condition into a well-established mechanistic flow boiling model makes it possible to reflect adequately the contribution of the microconvection to the total wall heat transfer. A comparison against the experimental data shows good agreement for the predicted wall shear stress as well as for the wall heat flux for a wide range of wall temperatures and Reynolds numbers.     

A Numerical Study for Heat Transfer Characteristics of a Micro Combustor by Large Eddy Simulation

The characteristics of heat transfer in confined multiple jet flows of a micro can combustor is investigated by means of large eddy simulation (LES). The micro combustor can be employed for a hybrid system, which consists of a micro gas turbine and a solid oxide fuel cell. In the present study, the focus is brought into heat transfer, which has a great effect on combustion stability as heat loss to the outside of combustor. The study is made for the three cases of different baffle plate configurations with changing the velocity ratio between fuel and oxidant jets. Downstream of the baffle plate, the flow recirculation regions appear and they can affect the enhancement of the turbulent heat transfer to the wall. In particular, the near-wall flow recirculation region formed between the oxidant jet and the combustor wall plays an important role for wall heat transfer. We study the turbulent thermal fields and conjugate heat transfer which show peculiar characteristics corresponding to the three different baffle plate shapes and different velocity ratios.     

Approximate solution to the natural convection heat transfer from a vertical plate

A new model for laminar natural convection heat transfer between an isothermal vertical plate to a power-law fluid is proposed. The difficulty caused by the fact that the momentum and energy equations are coupled is avoided by introducing an approximation based on the partial similarity between the velocity fields for forced and natural convections. The model proposed in this work agrees well with the available experimental data and correlations. Further, we have extended the analysis to turbulent natural convection heat transfer. The predicted turbulent heat transfer rates are in satisfactory agreement with the data and the correlations published in the literature.     

Heat transfer analysis of blast furnace stave

The three-dimensional mathematical model of temperature and thermal stress field of the blast furnace stave is built. The radiation heat transmitted from solid materials (coke and ore) to inner surface of the stave, which has been neglected by other studies, is taken into account. The cast steel stave is studied and the finite element method is used to perform the computational analysis with soft ANSYS. Numerical calculations show very good agreement with the results of experiment. Heat transfer analysis is made of the effect of the cooling water velocity and temperature, the cooling channel inter-distance and diameter, the lining material, the cooling water scale, the coating layer on the external surface of the cooling water pipe as well as the gas clearance on the maximum temperature and thermal stress of the stave hot surface. It is found that reducing the water temperature and increasing the water velocity would be uneconomical. The heat transfer and hence the maximum temperature and thermal stress in the stave can be controlled by properly adjusting operating conditions of the blast furnace, such as the gas flow, cooling channel inter-distance and diameter, lining material, coating layer and gas clearance.