Turbulent Heat Transfer

Recent applications of Computational Fluid Dynamics (CFD) to heat and fluid flow in the electric power generation industry are presented, with various turbulence models (including heat transfer) ranging from Reynolds Averaged Navier-Stokes Equations (RANS) with Eddy Viscosity or Second Moment Closures, to Direct and Large Eddy Simulation (DNS, LES). These simulations are clearly demonstrating the renewed importance of turbulence closure models and the need to combine all those approaches depending on the applications since the finer models require a priori estimates of the turbulence characteristics, if only to define the strategy for mesh generation. In order to address full scale industrial problems, recent developments are taking every advantage of very high performance computing facilities available. The Code_Saturne software coupled with SYRTHES for conjugated heat transfer proved to be very well suited to this kind of architecture. They are available as free software under GNU...

This paper presents an experimental investigation of turbulent flow inside square-sectioned channels connected with a square-ended bend using particle image velocimetry (PIV). Aluminium porous foam blocks of aspect ratio of 1.5 with 0.93 porosity and pore density per cm of 2, are attached to two opposite walls of the straight section normal to the turn axis, in a staggered manner. The spacing ratio of the blocks (S /D) is 1; whereas the height ratio (h/D) is 0.6. Water is used as the working fluid at Reynolds number of 36,000. The duct is either stationary or rotates orthogonally about an axis normal to that of the turn at a rotation number of 0.32. Results show the serpentine manner of the flow in the upstream and downstream channels due to the presence of the porous blocks. While in the straight sections there is no flow separation downstream of each block, turbulence levels are raised by the blocks' presence. Within the bend, in contrast to the case with a smooth upstream section, a single vortex dominates the flow. For the first time, the effects of orthogonal rotation are also highlighted. While rotation does not change the overall flow character, it does force more fluid through the blocks on the duct trailing (pressure) side.

In this study, the heat transfer and friction characteristics of four different rib geometries-45 angled, Vshaped, W-shaped and M-shaped ribs in a two-pass stationary channel have been numerically investigated. The aspect ratio (Height to Width) of the cooling channel was 1:1 (square). The rib pitch-to-rib height ratio (p/e) and the rib-height-to-channel hydraulic diameter ratio (e/D h) were 16 and 0.125 respectively. The Reynolds number was varied from 20,000 to 70,000. For the computations, the Reynolds averaged NaviereStokes (RANS) equations were solved with the commercial software ANSYS Fluent using the realizable version of k-ε (RKE) model. The heat transfer results were benchmarked with experiments on a test rig with similar geometries and flow conditions. Detailed analysis of the flow characteristics in the two-pass channel was carried out so as to understand the interaction of the ribinduced secondary flows and the bend-induced secondary flows and their contribution to heat transfer enhancement. The heat transfer enhancement provided by V-shaped ribs was 7% higher than 45 ribs, 28% higher than W-shaped ribs and 35% higher than M-shaped ribs. However, the pressure penalty for Vshaped ribs was 19% higher than 45 ribs, 24% higher than W-shaped ribs and 28% higher than M-shaped ribs. On comparing the overall thermal hydraulic performance, V-shaped and 45 ribs were observed to perform significantly better than W-shaped and M-shaped ribs.

In this study, the heat transfer and friction characteristics of four different rib geometries-45 angled, Vshaped, W-shaped and M-shaped ribs in a two-pass stationary channel have been numerically investigated. The aspect ratio (Height to Width) of the cooling channel was 1:1 (square). The rib pitch-to-rib height ratio (p/e) and the rib-height-to-channel hydraulic diameter ratio (e/D h) were 16 and 0.125 respectively. The Reynolds number was varied from 20,000 to 70,000. For the computations, the Reynolds averaged NaviereStokes (RANS) equations were solved with the commercial software ANSYS Fluent using the realizable version of k-ε (RKE) model. The heat transfer results were benchmarked with experiments on a test rig with similar geometries and flow conditions. Detailed analysis of the flow characteristics in the two-pass channel was carried out so as to understand the interaction of the ribinduced secondary flows and the bend-induced secondary flows and their contribution to heat transfer enhancement. The heat transfer enhancement provided by V-shaped ribs was 7% higher than 45 ribs, 28% higher than W-shaped ribs and 35% higher than M-shaped ribs. However, the pressure penalty for Vshaped ribs was 19% higher than 45 ribs, 24% higher than W-shaped ribs and 28% higher than M-shaped ribs. On comparing the overall thermal hydraulic performance, V-shaped and 45 ribs were observed to perform significantly better than W-shaped and M-shaped ribs.

Several low-Reynolds number k- turbulence models have been used to simulate the flow and heat transfer in slot confined and circular unconfined impinging jet configurations. Predictions for the velocity with its fluctuation and Nusselt number are compared to available experimental data. The relative performance of the models is assessed. It has been found that results obtained for the velocity parallel to the plate are in agreement with experimental data but none of models are entirely successful in predicting the radial Reynolds normal stress. For heat transfer, an additional source term in the equation of  was necessary for reducing near-wall length scales and improving the near-transfer predictions by means of the low-Reynolds number k- turbulence models.

Several low-Reynolds number k- turbulence models have been used to simulate the flow and heat transfer in slot confined and circular unconfined impinging jet configurations. Predictions for the velocity with its fluctuation and Nusselt number are compared to available experimental data. The relative performance of the models is assessed. It has been found that results obtained for the velocity parallel to the plate are in agreement with experimental data but none of models are entirely successful in predicting the radial Reynolds normal stress. For heat transfer, an additional source term in the equation of  was necessary for reducing near-wall length scales and improving the near-transfer predictions by means of the low-Reynolds number k- turbulence models.

We investigate the effect of the wall-scalar fluctuations on passive scalar turbulent fields for a moderate Reynolds number R τ = 395 and for several Prandtl numbers ranging from the very low value P r = 0.01 to the high value P r = 10 by means of DNS simulations. Several cases of plane channel flows are considered. Case I is a channel flow heated on both walls with a constant imposed heat flux q w. We consider for this case two different types of boundary conditions. For the first one, the isoscalar boundary condition θ w = 0 is imposed at the wall implying that its fluctuation and therefore its rms scalar fluctuations θ rms = θ ′ θ ′ is zero at the wall whereas in the second type, θ w is not prescribed to a fixed value so that it is fluctuating in time at the wall leading to non-zero rms fluctuations. In this latter case, as the heat flux is maintained constant in time at the wall, the fluctuating heat flux q ′ w reduces to zero at the wall. For illustration purpose, in addition to Case I, we also consider Case II which is a plane channel heated only from one wall but cooled from the other one at the same rate taking into account of the free-stream scalar boundary condition at the wall θ ′ w = 0 with q ′ w = 0. The distributions of the mean scalar field, root-mean-square fluctuations, turbulent heat flux, correlation coefficient, turbulent Prandtl number, and * Corresponding author. Nusselt number are examined in detail. Moreover, some insights into the flow structure of the scalar fields are provided. As a result of interest, it is found that the mean scalar field θ is not affected by the scalar fluctuations at the wall. But owing to the different boundary conditions applied at the wall, significant differences in the evolution of the rms scalar fluctuations θ rms are observed in the immediate vicinity of the wall. Surprisingly, the maximum rms intensity remains almost unchanged in the near wall region whatever the type of boundary condition is applied at the wall. In addition, the turbulent heat fluxes that play a major role in heat transfer are found to be independent of the wall scalar fluctuations. This study demonstrates that the impact of the wall scalar fluctuations is appreciable mainly in the near wall region. This outcome must be taken into account when simulating industrial flows with thermal boundary conditions involving different fluid/solid combinations.

AMIraet-An experimental investigation into turbulent heat transfer to pseudoplastic titanium dioxide suspensions in pipes has been carried out. Existing heat transfer correlations, including the analogy equations between heat and momentum transfer, generally predict higher Nusselt and Stanton numbers than those observed experimentally. However, a simplified heat transfer model based on the consideration of the laminar sub-layer at the wall and the turbulent core correlates the heat transfer results for heating as well as cooling. The limitations of the existing analogy equations between heat and momentum transfer are discussed.

An extension of the Taylor-Prandtl analogy for momentum and heat transfer is presented for time-independent non-New tonian fluids. The development given requires pressure drop-flowmte characteristics of the fluids in laminar as well as in turbulent flow in smooth tubes. There is thus no commitment to a specific fluid model. Linear velocity and temperature distributions are used for the viscous sub-layer and an effective viscosity pe, where c(~ = [7,/(8V/D)] L, is used for the momentum flux in the viscous sub-layer. In evaluating the Prandtl group F'r,, the effective viscosity ue is used. The effective viscosity used here is different from the apparent viscosity and the effective viscosity used by Metzner et al. and Petersen and Christiansen; the Reynoldsgroup ReB used is based on Bowen's pammeters. In evaluating Pr, for suspensions, the fluid properties used are those of the continuous phase which occupies the viscous sub-layer. The analysis has also been extended to power law fluids and to other fluids whose laminar flow properties have been obtained with rotational viscometers.

Forced convection is a special type of heat transfer in which fluids are forced to move, in order to increase the heat transfer. The aim of this study is to investigate in a numerical simulation of forced convection in a cubic cavity containing two cylindrical heat sources in the middle. The cavity is subjected to an inflow of air inlet from the left and an outlet flow from the right side with the same dimensions of the opening doors (0.1 H). The walls of the cavity are maintained adiabatic. The conservation equations governing the flow of forced convection are solved using the finite volume method that is used by FLUENT –ANSYS Software. Also, a comparison was performed shows good agreement between the numerical results with those available in the literature (numerical, analytical and experimental). The effect of the dimension of cavity (number of Rayleigh) and the velocity of ventilation of the air (number of Reynolds), as well as the dimension between sources cylindrical are prese...

When the flow in a minichannel system passes around a bend, secondary flows develop and flow separation can also occur in the bend both of which can affect the flow, pressure drop and heat transfer rate in the bend and in the flow upstream and downstream of the bend. In order to investigate this, attention has been given to flow in a simple such system. In the system considered the channels have a trapezoidal crosssection with parallel top and bottom surfaces. The flow enters the channel with a uniform velocity and temperature and passes through a straight channel that has a length that is 10 times the size of the channel. The flow then passes around a sharp 90 bend, flows through a short straight channel and then flows through another sharp 90 bend. Following the two bends, the flow passes down another straight channel which also has a length 10 times the size of the channel. A uniform temperature exists over the entire surface of the channel. It has been assumed that the flow is s...

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Large-Eddy-Simulation of turbulent heat transfer for water flow in rotating pipe is performed, for various rotation ratios (0 B N B 14). The value of the Reynolds number, based on the bulk velocity and pipe diameter, is Re = 5,500. The aim of this study is to examine the effect of the rotating pipe on the turbulent heat transfer for water flow, as well as the reliability of the LES approach for predicting turbulent heat transfer in water flow. Some predictions for the case of non-rotating pipe are compared to the available results of literature for validation. To depict the influence of the rotation ratio on turbulent heat transfer, many statistical quantities are analyzed (distributions of mean temperature, rms of fluctuating temperature, turbulent heat fluxes, higher-order statistics). Some contours of instantaneous temperature fluctuations are examined. Keywords Large eddy simulation (LES) Á Rotating pipe flow Á Turbulent heat transfer Á Fully developed water flow Superscripts ð:Þ Statistically averaged (.) ? Normalized by u s , m and T s (.) 0 Fluctuation component

It is well known that turbulent transfer models can sometimes produce results that cannot be realised in nature. In this paper we develop simple rules to check the physical robustness of parameterisations of land-surface turbulent transfer for heterogeneous surfaces. The methodology draws upon areal-averaging by parameter aggregation and by flux aggregation. Both techniques have been demonstrated to be valid. Combining the two techniques enables one to determine the surface potential temperature and specific humidity, averaged over the grid-box. When this is done the implied turbulent transfer is sometimes counter-gradient. The implications of this result are discussed. The methodology presented is general and provides a complementary way of evaluating the role of coupling land-surface schemes to atmospheric host models to that

Since direct numerical simulations (DNS) of natural convection in a differentially heated cavity can not be performed at high Ra-numbers, a dynamically less complex mathematical formulation is sought. In the quest for such a formulation, we consider regularizations (smooth approximations) of the nonlinearity. The regularization method basically alters the convective terms to reduce the production of small scales of motion by means of vortex stretching. In doing so, we propose to preserve the symmetry and conservation properties of the convective terms exactly. This requirement yields a novel class of regularizations that restrain the convective production of smaller and smaller scales of motion by means of vortex stretching in an unconditional stable manner, meaning that the velocity can not blow up in the energy-norm (in 2D also: enstrophy-norm). The numerical algorithm used to solve the governing equations preserves the symmetry and conservation properties too. The regularization model is successfully tested for a 3D natural convection flow in a differentially heated cavity (Ra = 10 10 , P r = 0.71 and height aspect ratio 4)

It is well known that turbulent transfer models can sometimes produce results that cannot be realised in nature. In this paper we develop simple rules to check the physical robustness of parameterisations of land-surface turbulent transfer for heterogeneous surfaces. The methodology draws upon areal-averaging by parameter aggregation and by flux aggregation. Both techniques have been demonstrated to be valid. Combining the two techniques enables one to determine the surface potential temperature and specific humidity, averaged over the grid-box. When this is done the implied turbulent transfer is sometimes counter-gradient. The implications of this result are discussed. The methodology presented is general and provides a complementary way of evaluating the role of coupling land-surface schemes to atmospheric host models to that

We investigate the effect of the wall-scalar fluctuations on passive scalar turbulent fields for a moderate Reynolds number Rτ = 395 and for several Prandtl numbers ranging from the very low value Pr = 0.01 to the high value Pr = 10 by means of direct numerical simulation (DNS) simulations. Several cases of plane channel flows are considered. Case I is a channel flow heated on both walls with a constant imposed heat flux qw. We consider for this case two different types of boundary conditions. For the first one, the isoscalar boundary condition θw = 0 is imposed at the wall implying that its fluctuation and therefore its rms scalar fluctuations θrms=⟨θ′θ′⟩ is zero at the wall whereas in the second type, θw is not prescribed to a fixed value so that it is fluctuating in time at the wall leading to nonzero rms fluctuations. In this latter case, as the heat flux is maintained constant in time at the wall, the fluctuating heat flux q′w reduces to zero at the wall. For illustration purpo...

This experimental work investigates buoyant flow in a differentially heated vertical channel located inside a water cavity. The flow is found to be highly unsteady, and the key aspect of this study is to consider this unsteady behavior as a succession of states that turn out to be driven by the flow outside the channel. A conditional mean operator with respect to the average wall temperature is used to disentangle the different states through which the flow passes. Most of these states are characterized by a transition from laminar heat transfer in the bottom part of the channel to turbulent heat transfer, with a transition point that moves toward the exit as the average wall temperature increases. For the highest values of the average wall temperature, no transition is observed, and the heat exchange is found to be similar to that along a single vertical plate. For an intermediate range of wall temperature, a transition zone with turbulent heat transfer is observed in the upper part of the channel, and the heat transfer is found to follow the same laws as found for a symmetrically heated channel. For the lowest values of the wall temperature, the beginning of the turbulent zone is observed near the entry. The analysis is extended to several channel widths. The origin of the unsteady behavior is attributed to the flow in the whole cavity, and the conditional mean operator allows characterization of the flow inside the channel independently from the flow in the surroundings.

Large eddy simulation with an extended Smagorinsky model has been carried out to study a fully developed turbulent forced convection of thermally independent shear-thinning (n = 0.75) fluid through a heated axially rotating pipe. Uniform constant heat flux has been imposed at the wall as a thermal boundary condition. The Reynolds and Prandtl numbers of the simulation have been assumed to be Re s = 4000 and Pr s = 1, respectively, over a rotation rate range of 0 ≤ N ≤ 3. The computations procedure is based on a finite difference scheme, second-order accurate in space and time; the numeric resolution is 65 3 grid points in axial, radial and circumferential directions, respectively, with a computational domain length of 20R. The aim of the present study is to investigate the effects of the rotating pipe wall on the turbulent and thermal statistics. The emerged findings suggest that the centrifugal force induced by the rotating pipe wall results in a marked enhancement of the mean axial velocity and an attenuation of the temperature profiles along the radial coordinates; this trend is more pronounced as the rotation rate increases. The increased rotation rate also induces a significant reduction in the temperature fluctuations intensity and consequently, in the axial turbulent heat flux. The predictions also show that the friction factor and Nusselt number are reduced when the rotation rate varies from 0 to 0.5, while they are enhanced with increasing N for N ≥ 1.

Similarity analysis shows that Nu x varies as Gr x 1/4 for natural convection on an isothermal vertical surface but Nu x varies as Gr x 1/5 for isothermal horizontal surfaces. It is thus difficult to develop a rigorouslyderived, closed-form solution for Nu x on a surface with arbitrary inclination. In the present study we have formulated, for the first time, a unified integral theory for laminar natural convection on an arbitrarily inclined surface, both for specified variation in surface temperature (T w (x) ¼ T ∞ þ f 1 (x)) and surface heat flux (q w ¼ f 2 (x)), such that the Nusselt number matches with results obtained from the similarity analysis in the limiting cases of vertical and horizontal surfaces. The predictions of the present formulation also agree well with previous computational and experimental results at intermediate angles of inclination between the vertical and the horizontal. f 1 (x) or f 2 (x) can be any arbitrary function, including power law variation, and represents a differentially heated surface. Another important feature of the present integral theory is that the developed generalized equations can accommodate arbitrary orders of polynomials (l and c) representing the velocity and temperature profiles, and optimum values for l and c have been systematically determined for various boundary conditions (i.e. l ¼ 4, c ¼ 2 for isothermal case and l ¼ 3, c ¼ 2 for constant-heat-flux case). Because of the simplicity of the present theory, it is easy to generate results for combinations of Grashof number, Prandtl number and inclination angle not presented here. The different physical mechanisms for natural convection on vertical and horizontal surfaces (buoyancy versus indirect pressure difference) are explained with the help of the present analysis. It is shown that for moderate to high Prandtl number fluids, the natural convection mechanism for vertical surface is the dominating factor for a large range of inclination angles except for near horizontal configurations. The range of inclination angles for which the vertical solution predominates decreases as the Prandtl number decreases. For very low Prandtl number fluids at low Grashof number, the vertical mechanism applies only to nearly vertical surfaces. A physical explanation for such behaviour is discovered here, for the first time, in terms of the relative magnitudes of the buoyancy and indirect pressure difference. Compact scaling laws for significant data reduction are proposed and explained. New algebraic correlations have been developed that give Nusselt number as explicit functions of Grashof number, Prandtl number and inclination angle. A new methodology for the representation of the results brings out more powerfully the role of inclination angle in determining the heat transfer rate as well as the mechanism of natural convection.

Large eddy simulation with an extended Smagorinsky model has been carried out to study a fully developed turbulent forced convection of thermally independent shear-thinning (n = 0.75) fluid through a heated axially rotating pipe. Uniform constant heat flux has been imposed at the wall as a thermal boundary condition. The Reynolds and Prandtl numbers of the simulation have been assumed to be Re s = 4000 and Pr s = 1, respectively, over a rotation rate range of 0 ≤ N ≤ 3. The computations procedure is based on a finite difference scheme, second-order accurate in space and time; the numeric resolution is 65 3 grid points in axial, radial and circumferential directions, respectively, with a computational domain length of 20R. The aim of the present study is to investigate the effects of the rotating pipe wall on the turbulent and thermal statistics. The emerged findings suggest that the centrifugal force induced by the rotating pipe wall results in a marked enhancement of the mean axial velocity and an attenuation of the temperature profiles along the radial coordinates; this trend is more pronounced as the rotation rate increases. The increased rotation rate also induces a significant reduction in the temperature fluctuations intensity and consequently, in the axial turbulent heat flux. The predictions also show that the friction factor and Nusselt number are reduced when the rotation rate varies from 0 to 0.5, while they are enhanced with increasing N for N ≥ 1.

 A numerical study of the turbulent heat transfer in a two-dimensional rectangular air-cooled ventilated room with a human being as a discrete heat source was carried out in order to determine the best ventilation configuration. The results were obtained for a cavity of 2.5 m of height and 3.0 m of width. The right and left vertical walls of the cavity were kept at 35°C and 25°C respectively, whereas the remaining walls were adiabatic. Three cases for the air inlet and outlet locations were considered for the analysis. The air enters to the cavity at 15°C with speeds between 0.2 m/s and 2.0 m/s. The emissivity of the cavity walls was considered as 0, 0.5 and 1. The results indicate that the configuration (A) (inlet on the lower part of the right vertical wall and outlet on the upper part of the left vertical wall) offers the lowest average temperatures inside the room and the highest temperature distribution effectiveness.

Large eddy simulation with an extended Smagorinsky model has been carried out to study a fully developed turbulent forced convection of thermally independent shear-thinning (n = 0.75) fluid through a heated axially rotating pipe. Uniform constant heat flux has been imposed at the wall as a thermal boundary condition. The Reynolds and Prandtl numbers of the simulation have been assumed to be Re s = 4000 and Pr s = 1, respectively, over a rotation rate range of 0 ≤ N ≤ 3. The computations procedure is based on a finite difference scheme, second-order accurate in space and time; the numeric resolution is 65 3 grid points in axial, radial and circumferential directions, respectively, with a computational domain length of 20R. The aim of the present study is to investigate the effects of the rotating pipe wall on the turbulent and thermal statistics. The emerged findings suggest that the centrifugal force induced by the rotating pipe wall results in a marked enhancement of the mean axial velocity and an attenuation of the temperature profiles along the radial coordinates; this trend is more pronounced as the rotation rate increases. The increased rotation rate also induces a significant reduction in the temperature fluctuations intensity and consequently, in the axial turbulent heat flux. The predictions also show that the friction factor and Nusselt number are reduced when the rotation rate varies from 0 to 0.5, while they are enhanced with increasing N for N ≥ 1.

Time-developing thermally-driven boundary layers created by imposing aiding and opposing freestreams on the natural-convection boundary layer in water along a heated vertical flat plate have been examined with a direct numerical simulation to clarify their transition and turbulence behaviors. The numerical results for aiding flow reveal that the transition begins at a thick laminar boundary layer due to the delay of the transition and large-scale vortexes centering on the spanwise direction are followed, while, for opposing flow, the transition begins at a thin laminar boundary layer due to the quickening of the transition and relatively small-scale vortexes are generated with the progress of transition. To improve the significance of the present numerical results, the association of turbulence statistics between timeand space-developing flows has been investigated. Consequently, the numerical results for timedeveloping flow are converted to those for space-developing flow through the integral thickness of the velocity boundary layer for pure natural convection, and thus the regimes of boundary layer flows can be quantitatively assessed. Moreover, the turbulence statistics and the flow structures in the thermally-driven boundary layers are also presented.

Wall functions are widely used and offer significant computational savings compared with low-Reynolds-number formulations. However, existing schemes are based on assumed nearwall profiles of velocity, turbulence parameters, and temperature which are inapplicable in complex, nonequilibrium flows. A new wall function has therefore been developed which solves boundary-layer-type transport equations across a locally defined subgrid. This approach has been applied to a plane channel flow, an axisymmetric impinging jet, and flow near a spinning disc using linear and nonlinear k-e turbulence models. Computational costs are an order of magnitude less than low-Reynolds-number calculations, while a clear improvement is shown in reproducing low-Re predictions over standard wall functions.

Direct numerical simulation (DNS) of turbulent flow and heat transfer involves directly solving the unsteady Navier-Stokes and thermal energy equations without considering any assumptions about the physics and resolve all the scales of the flow, including the energy and dissipation spectral peaks. Data from DNS of fully developed turbulent pipe flows subjected to a constant surface heat-flux are used to validate with the existing DNS database. The present validation process involves matching of first and second order turbulence statistics. However, accurate comparison of DNS data sets requires satisfying the conformity of necessary and sufficient computational parameters. This paper will address the influence of the computational conditions on the thermal statistics, which affect the comparison of the matching statistics from different DNS data sets. It was observed that apart from the governing parameters (Kármán and Prandtl numbers), computational mesh and domain size significantly influence the resulting thermal statistics, which must be considered while performing validation of DNS data.

We present results from direct numerical simulation of turbulent heat transfer in pipe flow at a bulk flow Reynolds number of 5000 and Prandtl numbers ranging from 0.025 to 2.0 in order to examine the effect of streamwise pipe length (pd pD/2 6 L 6 12pd) on the convergence of thermal turbulence statistics. Various lower and higher order thermal statistics such as mean temperature, rms of fluctuating temperature, turbulent heat fluxes, two-point auto and cross-correlations, skewness and flatness were computed and it is found that the value of L required for convergence of the statistics depends on the Prandtl number: larger Prandtl numbers requires comparatively shorter pipe length for convergence of most of the thermal statistics.

Direct numerical simulations (DNS) are carried out to investigate fully developed turbulent heat transfer in a pipe at low Kármán number (Re τ = 171) and different Prandtl numbers (Pr = 0.026, 0.1, 0.2, 0.4, 0.71 and 1.0) using spectral element method. The isoflux boundary condition is applied on the pipe walls and temperature is considered as a passive scalar. The grid resolution used in the present computation in terms of wall units are [Δz + , Δr + , RΔθ + ] = [14.3, 0.5-3.6, 8.4]. Important turbulent quantities such as the mean temperature, rms of temperature fluctuations, and both streamwise and radial turbulent heat fluxes are calculated to analyse the effect of Prandtl number. Numerical data from the current computation shows good agreement with other available DNS data, validating the current numerical model.

A numerical study of the turbulent heat transfer in a two-dimensional rectangular air-cooled ventilated room with a human being as a discrete heat source was carried out in order to determine the best ventilation configuration. The results were obtained for a cavity of 2.5 m of height and 3.0 m of width. The right and left vertical walls of the cavity were kept at 35°C and 25°C respectively, whereas the remaining walls were adiabatic. Three cases for the air inlet and outlet locations were considered for the analysis. The air enters to the cavity at 15°C with speeds between 0.2 m/s and 2.0 m/s. The emissivity of the cavity walls was considered as 0, 0.5 and 1. The results indicate that the configuration (A) (inlet on the lower part of the right vertical wall and outlet on the upper part of the left vertical wall) offers the lowest average temperatures inside the room and the highest temperature distribution effectiveness.

Aim of this study is to evaluate a new three-equation turbulence model applied to flow and heat transfer through a pipe. Uncertainty is approximated by comparing with published direct numerical simulation results for fully-developed flow. Error in the mean axial velocity, temperature, friction, and heat transfer is found to be negligible. Keywords—Heat Transfer, Nusselt number, Skin friction, Turbulence.

A combined convective heat transfer and fluid dynamics investigation in a turbulent round jet impinging on a flat surface is presented. The experimental study uses a high resolution liquid crystal technique for the determination of the convective heat transfer coefficients on the impingement plate. The heat transfer experiments are performed using a transient heat transfer method. The mean flow and the character of turbulent flow in the free jet is presented through five hole probe and hot wire measurements, respectively. The flow field character of the region near the impingement plate plays an important role in the amount of convective heat transfer. Detailed surveys obtained from five hole probe and hot wire measurements are provided. An extensive validation of the liquid crystal based heat transfer method against a conventional technique is also presented. After a complete documentation of the mean and turbulent flow field, the convective heat transfer coefficient distributions ...

The present work is concerned with a comprehensive analysis of hydrodynamic forces, under MHD and forced convection thermal flow over a heated cylinder in presence of insulated plates installed at walls. The magnetic field is imposed in the transverse direction of flow. The Galerkin finite element (GFE) scheme has been used to discretize the two-dimensional system of nonlinear partial different equations. The study is executed for the varying range of flow behavior index n from 0.4 to 1.6, Hartmann number Ha from 0 to 100, Reynolds number Re from 10 to 50, Grashof number Gr from 1 to 10, thickness ratio e from 0.5 to 1.0, and Prandtl number Pr from 1 to 10, respectively. A coarse hybrid computational grid is developed, and further refinement is carried out for obtaining the highly accurate solution. The optimum case selection is based on flow patterns, drag and lift coefficients, and pressure drop reduction against cylinder thickness ratios and average Nusselt numbers. Drag coeffici...

Detailed understanding of hot gas path flow and heat transfer characteristics in gas turbine systems is imperative in order to design cooling strategies to meet the stringent requirements in terms of coolant usage to maintain critical components below a certain temperature. To this end, extensive research has been carried out over the past four decades on advanced thermal diagnostic methods to accurately measure heat transfer quantities such as Nusselt number and adiabatic film cooling effectiveness. The need to capture local heat transfer characteristics of these complex flow systems drives the development of measurement techniques and the experimental test facilities to support such measurements. This article provides a comprehensive overview of the state-of-the-art thermal diagnostic efforts pertaining to heat transfer measurements in rotating gas turbine blade internal and external cooling and rotor-stator disc cavity, all under rotating environments. The major investigation eff...

We performed direct numerical simulation of fully developed turbulent velocity and temperature fields in a flume, for Reynolds number, based on the wall shear velocity and the height of the flume, Reϭ171 and Prandtl numbers Prϭ1.0 and Prϭ5.4. To elucidate exactly the role of the wall boundary condition for passive scalar, the system considered was the flow at constant properties of the fluid. Two types of thermal wall boundary conditions ͑BCs͒ for the dimensionless temperature equation were studied: isothermal wall boundary condition-H1, and isoflux wall boundary condition-H2. The profile of the mean temperature was not affected by the type of BC. However, the type of BC has a profound effect on the statistics of the temperature fluctuations in the near-wall region y ϩ Ͻ10. Comparison of near-wall statistics of temperature fluctuations shows that at Pr ϭ1 the buffer part of the turbulent boundary layer significantly influences the scalar transfer in the conductive sublayer, whereas at Prϭ5.4 the near-wall temperature field may be associated with predominant motion in the viscous sublayer.

A new correlation is presented to describe heat and mass transfer a t large Prandtl or Schmidt numbers to power l o r fluids in fully developed turbulent flow in a pipe. The resulting expression for the Stanton number differs from earlier semiempirical correlations in that it is based on a continuous eddy viscosity distribution from the woll to the center of the pipe and contains no adjustable parameters to be determined from heat transfer data. Nusselt numbers determined by the new correlation are in excellent agreement with data on heat transfer to both pseudoplastic and dilatant fluids. N~~ = (0. 0 2 3) 5 (n + 2) / 1 3 (4 n + 1) 1 (N R B) 4 (n + 2) / C 3 (4 n + l) 1 (N p r) 1/3 (7) Recently, Hughmark (10) has extended Longwell's (15) equation to power law fluids. The mean velocity profile is

The current numerical/analytical effort is a continuation of the experimented study described in "Fluid Dynamics and Convective Heat Transfer in Impinging Jets Through Implementation of a High Resolution Liquid Crystal Technique-Part I". The Navier Stokes predictions

Heat and mass transfer in laminar and turbulent non-Newtonian fluids is investigated in this work using the power function velocity profiles. Analytical solutions are presented for cases of mass transfer in laminar non-Newtonian fluid flows, namely for a flat velocity profile (plug flow), for the case of a constant velocity gradient at the solid boundary (Couette flow), and for the velocity distribution within a laminar boundary layer on a flat plate, and these are illustrated by rotating disks and cylinders in laminar Ostwald-de Waele fluids. Further, turbulent mass transfer processes (tubular flow, rotating disk, and rotating cylinder) in non-Newtonian fluids (Ostwald-de Waele fluid and drag-reducing fluid) at low and large Schmidt numbers are also discussed using the solutions of mass transfer in flows with power function velocity profiles. Reasonable agreement is found between the predictions of this work and the available experimental data and correlations. On ttudie, dans le prtsent travail, le transfert de chaleur et de matitre dans des tcoulements laminaires et turbulents de fluides non-newtoniens; on utilise, a cette fin, des profils de vitesse en loi de puissance. On prtsente des solutions analytiques pour le transfert de matitre dans trois cas d'tcoulement laminaire de fluides non-newtoniens: (a) un profil de vitesse plat (tcoulement piston), (b) un gradient de vitesse constant ti la paroi solide (tcoulement de Couette) et (c) une distribution de vitesse I'inttrieur d'une couche limite laminaire sur une plaque plane; ces cas sont illustds au moyen de disques et cylindres en rotation dans des fluides d'Ostwald-de-Waele en dgime laminaire. On discute en outre des processus de transfert de matitre en rtgime turbulent (tcoulements tubulaires, disque et cylindre en rotation) dans des fluides non-newtoniens (fluide d'Ostwald-de-Waele et fluide rtducteur de traPnte) des nombres de Schmidt faibles et tlevCs; on a employ6 pour cela, les solutions de transfert de matitre dans des tcoulements a profils de vitesse en loi de puissance. On a constatt qu'il y avait une concordance raisonnable entre les prtvisions du prksent travail et les donnks exp6rimentales et les cordations disponibles.

Levich developed a theoretical expression for mass transfer in turbulent Newtonian flows that he called a "three-zone" model.' Later, Davies discussed this approach in detail and derived an equation that is somewhat different numerically from Levich's.' We have used this type of modeling to develop expressions for the heat and mass transport in turbulent non-Newtonian flows. Two distinct cases have been treated: high Schmidt number flows and flows for which the turbulent drag is reduced by additives. When the Schmidt number is fairly high, as is the case in viscous polymer solutions and fermentation broths, the concentration boundary layer is very thin; therefore, mass transfer is controlled by a region close to the wall. When the power law is employed to portray the shear-dependent viscosity, then

A new correlation is presented to describe heat and mass transfer a t large Prandtl or Schmidt numbers to power l o r fluids in fully developed turbulent flow in a pipe. The resulting expression for the Stanton number differs from earlier semiempirical correlations in that it is based on a continuous eddy viscosity distribution from the woll to the center of the pipe and contains no adjustable parameters to be determined from heat transfer data. Nusselt numbers determined by the new correlation are in excellent agreement with data on heat transfer to both pseudoplastic and dilatant fluids. N~~ = (0. 0 2 3) 5 (n + 2) / 1 3 (4 n + 1) 1 (N R B) 4 (n + 2) / C 3 (4 n + l) 1 (N p r) 1/3 (7) Recently, Hughmark (10) has extended Longwell's (15) equation to power law fluids. The mean velocity profile is

In this work we investigate properties of the mean thermal energy balance equation using a multiscaling analysis approach. The analysis of the mean thermal energy balance (MHB) equation and the mean momentum balance (MMB) equation are presented side by side to better demonstrate the similarities and differences between the two. The main findings of this work include, first, the multiscaling for the MHB equation are similar to those for the MMB equation in the outer layer, mesolayer, and log layer. Péclet number Pe τ = PrRe τ in the MHB equation is the counterpart of Re τ in the MMB equation. Here Pr ≡ ν/α denotes the Prandtl number of the fluid, which is the ratio between the kinematic viscosity ν and the molecular thermal diffusivity α. Re τ = δu τ /ν is the Reynolds number of the flow defined with the channel half-height δ and the friction velocity u τ . In the outer layer, mesolayer, and log layer, the shapes of the mean temperature and the mean velocity are very similar, and the shapes of the wall-normal turbulent transport of heat and momentum are also similar. Second, the molecular thermal diffusion sublayer is strongly influenced by the Prandtl number. At low Prandtl number (Pr < 1), the thickness of the molecular thermal diffusion sublayer is y It = O( 1

This article reports the experimental and DNS database that has been generated, within the framework of the EU SESAME and MYRTE projects, for various low-Prandtl flow configurations in different flow regimes. This includes three experiments: confined and unconfined backward facing steps with low-Prandtl fluids, and a forced convection planar jet case with two different Prandtl fluids. In terms of numerical data, seven different flow configurations are considered: a wall-bounded mixed convection flow at low-Prandtl number with varying Richardson number (Ri) values; a wall-bounded mixed and forced convection flow in a bare rod bundle configuration ; a forced convection confined backward facing step (BFS) with conjugate heat transfer; a forced convection impinging jet for three different Prandtl fluids corresponding to two different Reynolds numbers of the fully developed planar turbulent jet; a mixed-convection cold-hot-cold triple jet configuration corresponding to Ri = 0.25; an unconfined free shear layer for three different Prandtl fluids; and a forced convection infinite wire-wrapped fuel assembly. This wide range of reference data is used to evaluate, validate and/or further develop different turbulent heat flux modelling approaches, namely simple gradient diffusion hypothesis (SGDH) based on constant and variable turbulent Prandtl number; explicit and implicit algebraic heat flux models; and a second order turbulent heat flux model. Lastly, this article will highlight the current challenges and perspectives of the available turbulence models, in different codes, for the accurate prediction of flow and heat transfer in low-Prandtl fluids.

This paper presents a technique that collapses existing experimental data of heat transfer in pipe flow of Newtonian and power law fluids into a single master curve. It also discusses the theoretical basis of heat, mass and momentum analogies and the implications of the present analysis to visualisations of turbulence.

On the basis of second-order transport equations of velocity and temperature fluctuations, we present a numerical analysis of axial and radial turbulent heat flux for pipe flows with different Prandtl numbers. Distributions of different additives in the balance equations of axial and radial heat fluxes were analyzed under the effects of Re and Pr. Predicted parameter distributions were in a good agreement with experimental data of different authors over wide ranges of the operation parameters.

Second-order transport equations of velocity and temperature fluctuations are employed in a numerical analysis of axial and radial turbulent heat flux for pipe flows with different Prandtl numbers. Distributions of different additives in the balance equations of axial and radial heat fluxes are analyzed under the effects of Re and Pr. Predicted parameter distributions are in a good agreement with

On the basis of second-order transport equations of velocity and temperature fluctuations, we present a numerical analysis of axial and radial turbulent heat flux for pipe flows with different Prandtl numbers. Distributions of different additives in the balance equations of axial and radial heat fluxes were analyzed under the effects of Re and Pr. Predicted parameter distributions were in a good agreement with experimental data of different authors over wide ranges of the operation parameters.