Numerical investigation of pulsating flow around a discrete heater in a channel

In this study, the forced convection heat transfer around a discrete heater located in a channel subjected to laminar pulsating air flow is numerically investigated. Simulations are conducted for six different frequencies and three different amplitudes, while the Reynolds number (Re = 125) and Prandtl number (Pr = 0.71) remain constant for all cases. The impact of the important governing parameters such as the Womersley number (Wo) and the amplitude of flow pulsation (A_o) on heat transfer rate from discrete heaters is examined in detail. The instant velocity and temperature profiles are obtained to determine of the role of dimensionless parameters for pulsating flow. The numerical results show that thermal transport from the heater is greatly affected by the frequency and amplitude of the flow pulsation. The results given are dimensionless parameters.     

Flow and heat transfer characteristics in pulsating pipe flows (effects of pulsation on internal heat transfer in a circular pipe flow)

Effects of pulsation on flow and heat transfer characteristics are experimentally examined in the pulsating pipe flows having sinusoidal velocity fluctuations around a nonzero mean. By systematically varying three pulsation parameters (the amplitude, frequency, and mean velocity), time-averaged and fluctuating temperature profiles are measured under the heating condition of constant wall temperature using saturated vapor. The mean Nusselt number, Nu_p, is calculated, and compared with that in ordinary turbulent pipe flows without pulsation. The results show that Nu_p, decreases initially as the pulsation amplitude increases, then recovers gradually, and finally becomes much greater than the original value. In pulsating pipe flows with a nonzero mean velocity, therefore, pulsation cannot always promote heat transfer, but sometimes suppresses it, depending mainly on the pulsation amplitude and mean velocity. It is also found that these heat transfer characteristics of a pulsating pipe flow are controlled by the transition of flow patterns with pulsation amplitude from a fully turbulent flow to a conditionally turbulent flow via a transitional flow. © 1997 Scripta Technica, Inc. Heat Trans Jpn Res, 25(5): 323–341, 1996     

Large eddy simulation of stably stratified turbulent open channel flows with low- to high-Prandtl number

Large eddy simulation of thermally stratified turbulent open channel flows with low- to high-Prandtl number is performed. The three-dimensional filtered Navier-Stokes and energy equations under the Boussinesq approximation are numerically solved using a fractional-step method. Dynamic subgrid-scale (SGS) models for the turbulent SGS stress and heat flux are employed to close the governing equations. The objective of this study is to reveal the effects of both the Prandtl number (Pr) and Richardson (Ri_τ) number on the characteristics of turbulent flow, heat transfer, and large-scale motions in weakly stratified turbulence. The stably stratified turbulent open channel flows are calculated for Pr from 0.1 up to 100, Ri_τ from 0 to 20, and the Reynolds number (Re_τ) 180 based on the wall friction velocity and the channel height. To elucidate the turbulent flow and heat transfer behaviors, some typical quantities, including the mean velocity, temperature and their fluctuations, turbulent heat fluxes, and the structures of the velocity and temperature fluctuations, are analyzed.     

Thermal protection with liquid film in turbulent mixed convection channel flows

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

A numerical study of turbulent flow and conjugate heat transfer in concentric annuli with moving inner rod

A numerical study is conducted to investigate turbulent flow and conjugate heat transfer in a concentric annulus with a heated inner cylinder moving in the streamwise direction. A modified two-equation k-ε model with low Reynolds number treatment near wall is employed to model the Reynolds stress and turbulent thermal field which are based on Boussinesq’s approximation. The governing equations are numerically resolved by means of a hybrid finite analysis method. A uniform inlet flow and thermal conditions are specified to consider the effects of entrance of both solid and fluid regions. For a constant Prandtl number of 6.99 of water flow, calculating results of the time-averaged streamwise velocity, turbulent viscosity and temperature field are obtained for the Reynolds numbers from 1.0 × 10⁴ to 5.0 × 10⁵, rod velocity ratio between 0 and 1.0, and the radius ratio ranging from 0.286 to 0.750. The parametric studies show that the bigger rod speed ratio or the radius ratio is, the temperature is higher within solid rod. For a certain absolute rod speed, temperature profile diminishes at both sides of solid rod and fluid as Reynolds number grows. Numerical results also show that compared with the case of β=0 where solid rod is stationary, for large rod speed ratio the averaged axial velocity and turbulent viscosity profiles have substantial deformations, that is, the gradient of averaged axial velocity and turbulent viscosity near rod surface greatly reduced by the axial movement of solid rod.     

Numerical study of the intensified heat transfer of an internally longitudinal ridged finned tube under pulsating flow

The turbulent pulsating flow and heat transfer in an internally longitudinal protuberant finned tube was numerically investigated by solving unsteady three‐dimensional elliptical Navier–Stokes equations. The realized k–? turbulent model was adopted. The dynamic behaviors of velocity field, average Nusselt number, and friction number of the internally longitudinal protuberant finned tube were numerically analyzed in a pulsating period, and it was further investigated by changing the frequency of the pulsating flow. It was found that the intensity of heat transfer enhancement increases with an increase of pulsating frequency, while the pressure drop will be increased simultaneously, the intensification of heat transfer in internally longitudinal protuberant finned tubes are gradually better than the pressure drop with an increase of pulsating frequency. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20253     

Turbulent natural convection in a vertical parallel-plate channel with asymmetric heating

Turbulent natural convection in a vertical parallel plate channel has been investigated both experimentally and numerically. The experimental channel is formed of a uniform temperature heater wall and an opposing glass wall. A fibre flow laser doppler anemometer (LDA) is used to measure velocity profiles along the channel. Simultaneous velocity and temperature profile measurements are made at the channel outlet. A commercial computational fluid dynamics (CFD) code is used to simulate heat transfer and fluid flow in the channel numerically. The code is customised building in some low Reynolds number (LRN) k–ε turbulence models. The numerical method used in this study is found to predict heat transfer and flow rate fairly accurately. It is also capable of capturing velocity and temperature profiles with some accuracy. Experimental and numerical data are presented comparatively in the form of velocity, temperature, and turbulent kinetic energy profiles along the channel for a case. Correlating equations are obtained from the numerical results for heat transfer and induced flow rate and, are presented graphically comparing with other studies available in the literature.     

Prevision numérique de la convection forcée turbulente dans une cavité bidimensionnelle entrainée

Turbulent flow and associated heat transfer in confined geometry (driven closed cavity flow in two dimensions) has been studied using a finite-difference numerical method in primitive variables. Turbulence modelling is based on one point closures derived from the classicalk-ε model. Calculated mean velocity and turbulent kinetic energy are compared with available experimental data. In spite of its limitations, the k-ε model proved to be a useful tool for prediction of global quantities. The case of forced heat convection with fixed wall temperature is considered. Mean temperature field and overall thermal properties of the cavity flow are studied. Correlations giving Nusselt numbers at each face of the cavity versus Reynolds number are deduced from numerical results, they sum up mean transfer properties of such a flow configuration.     

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.     

Direct numerical simulation of wall-normal rotating turbulent channel flow with heat transfer

Direct numerical simulation of wall-normal rotating channel flow with heat transfer has been performed for the rotation number N_τ from 0 to 0.1, the Reynolds number 194 based on the friction velocity of non-rotating case and the half-height of the channel, and the Prandtl number 1. The objective of this study is to reveal the effects of rotation on the characteristics of turbulence and heat transfer. Some statistical turbulence and heat transfer quantities, including the mean velocity, temperature and their fluctuations, turbulent heat fluxes, and turbulence structures, are investigated. Based on the present calculated results, two typical rotation regimes are identified. When 0 < N_τ < 0.06, the turbulence statistics correlated with the spanwise velocity fluctuation are enhanced since the shear rate of spanwise mean flow induced by Coriolis force increases; however, the other statistics are suppressed. When N_τ > 0.06, all the turbulence statistics are suppressed significantly. To elucidate the effects of rotation on the turbulent heat transfer, the budget terms in the transport equation of turbulent heat fluxes are analyzed. Remarkable change of the direction of near-wall streak structures of the velocity and temperature fluctuations, nearly in alignment with the absolute mean flow direction, is revealed. An attempt to evaluate the mean spacing and the direction of streaky structures near the wall has been examined based on the two-point correlations of the velocity and temperature fluctuations.     

Calculation of turbulent flow and heat transfer in a porous-baffled channel

This study presents the numerical predictions on the turbulent fluid flow and heat transfer characteristics for rectangular channel with porous baffles which are arranged on the bottom and top channel walls in a periodically staggered way. The turbulent governing equations are solved by a control volume-based finite difference method with power-law scheme and the k-ε turbulence model associated with wall function to describe the turbulent structure. The velocity and pressure terms of momentum equations are solved by SIMPLE (semi-implicit method for pressure-linked equation) method.The parameters studied include the entrance Reynolds number Re (1×10⁴-5×10⁴), the baffle height (h=10, 20 and 30 mm) and kind of baffles (solid and porous); whereas the baffle spacing S/H are fixed at 1.0 and the working medium is air. The numerical calculations of the flow field indicate that the flow patterns around the porous- and solid-type baffles are entirely different due to different transport phenomena and it significantly influences the local heat transfer coefficient distributions. Relative to the solid-type baffle channel, the porous-type baffle channel has a lower friction factor due to less channel blockage.Concerning the heat transfer effect, both the solid-type and porous-type baffles walls enhanced the heat transfer relative to the smooth channel. It is further found that at the higher baffle height, the level of heat transfer augmentation is nearly the same for the porous-type baffle, the only difference being the Reynolds number dependence. As expected, the centerline-averaged Nusselt number ratio increases with increasing the baffle height because of the flow acceleration.     

Parametric study of turbulent slot-jet impingement heat transfer from concave cylindrical surfaces

Numerical investigation of convective heat transfer process from concave cylindrical surfaces due to turbulent slot-jet impingement is performed. Constant heat flux condition is specified at the concave surfaces. The flow and thermal fields in the vicinity of the surfaces are computed using the RNG k–? turbulence model with a two-layer near wall treatment. Parametric studies are carried out for various jet-exit Reynolds numbers, surface curvature, and nozzle-to-surface spacing. Results presented include streamlines, isotherms, velocity and temperature profiles in the wall-jet region, and the local Nusselt number distribution on the impingement concave wall for various parameter values in the study. The results indicate that while the jet-exit Reynolds number and the surface curvature have a significant effect on the heat transfer process, it is relatively insensitive to the jet-to-target spacing. A correlation for the average Nusselt number at the concave surface as a function of the parameters considered in the study is also derived.     

Thermal transport phenomena over a slot-perforated flat surface in pulsating free stream

A theoretical study is performed to investigate unsteady, two-dimensional, incompressible thermal-fluid flow over both sides of a slot-perforated flat surface, which is placed in a pulsating free stream. The effects of the pulsating Strouhal number, the Reynolds number Re, and the ratio of the slot width, d, to the plate thickness, δ, on the heat transfer performance and the velocity and thermal fields are disclosed. It is found from the study that: (i) when the free stream is pulsated, the alternating change in the fluid flow disturbs the thermal boundary layer formed along the plate and induces mixing of the upper and lower streams of the plate downstream from the slot, resulting in an amplification of heat-transfer performance; (ii) heat-transfer performance at the rear plate is induced with an increase in d/δ and Re; and (iii) heat transfer performance is intensified with an increase in fSr.     

Turbulent impinging jet heat transfer enhancement due to intermittent pulsation

A numerical study was carried out of heat transfer under a pulsating turbulent slot impinging jet. The jet velocity was varied in an intermittent (on–off) fashion. The effects of the time-mean jet Reynolds number, temperature difference between the jet flow and the impinging surface, nozzle-to-target distance as well as the frequency on heat and mass transfer were examined. The numerical results indicate significant heat transfer enhancement due to intermittent pulsation of the jet flow over a wide range of conditions for both cooling and heating cases. Simulations of the flow and temperature fields show that the instantaneous heat transfer rate on the target surface is highly dependent on the hydrodynamic and thermal boundary layer development with time.     

Heat transfer with laminar pulsating flow in a channel or tube in rolling motion

The heat transfer model of laminar pulsating flow in a channel or tube in rolling motion is established. The correlations of velocity, temperature and Nusselt number are obtained. And the effects of several parameters on Nusselt number are investigated. The results are evaluated with Nield & Kuznetsov's work. It is found that Nield & Kuznetsov's results are not applicable for the laminar pulsating flow in nuclear power systems in ocean environments.     

Direct numerical simulation of turbulent flow and combined convective heat transfer in a square duct with axial rotation

Direct numerical simulations (DNS) of turbulent flow and convective heat transfer in a square duct with axial rotation were carried out. The pressure-driven flow is assumed to be hydrodynamically and thermally fully developed, for which the Reynolds number based on the friction velocity and hydraulic diameter is kept at constant (Re_τ = 400). In the finite length duct, two opposite walls are perfectly insulated and another two opposite walls are kept at constant but different temperatures. Four thermal boundary conditions were chosen in combination with axial rotation to study the effects of rotation and Grashof number on mean flow, turbulent quantities and momentum budget. The results show that thermal boundary conditions have significant effects on the topology of secondary flows, profiles of streamwise velocity, distribution of temperature and other turbulent statistic quantities but have marginal effects on the bulk-averaged quantities; Coriolis force affects the statistical results very slightly because it exerts on the plane normal to main flow direction and the rotation rate is low; Buoyancy effects on the turbulent flow and heat transfer increase with the increase of Grashof number (Gr), and become the major mechanism of the development of secondary flow, turbulence increase, and momentum and energy transport at high Grashof number.     

Study of Variable Turbulent Prandtl Number Model for Heat Transfer to Supercritical Fluids in Vertical Tubes

In order to improve the prediction performance of the numerical simulations for heat transfer of supercritical pressure fluids, a variable turbulent Prandtl number (Pr_t) model for vertical upward flow at supercritical pressures was developed in this study. The effects of Pr_t on the numerical simulation were analyzed, especially for the heat transfer deterioration conditions. Based on the analyses, the turbulent Prandtl number was modeled as a function of the turbulent viscosity ratio and molecular Prandtl number. The model was evaluated using experimental heat transfer data of CO₂, water and Freon. The wall temperatures, including the heat transfer deterioration cases, were more accurately predicted by this model than by traditional numerical calculations with a constant Pr_t. By analyzing the predicted results with and without the variable Pr_t model, it was found that the predicted velocity distribution and turbulent mixing characteristics with the variable Pr_t model are quite different from that predicted by a constant Pr_t. When heat transfer deterioration occurs, the radial velocity profile deviates from the log-law profile and the restrained turbulent mixing then leads to the deteriorated heat transfer.     

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

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

Unsteady turbulent heat transfer of mixed convection in a reciprocating circular ribbed channel

The SIMPLE-C scheme is used to solve the mass, momentum, energy conservation equations and turbulent k-ε equations with a two-layer model near wall for a fluid past a reciprocating circular ribbed channel when changing Reynolds number (4250-10,000), Grashof number (0-400,000,000), pulsating number (0-9.3) and cooling mediums. The average time-mean Nusselt number for the reciprocating circular ribbed channel can be 45-182% larger than that for the equivalent stationary smooth channel. The heat transfer enhancement produced by buoyancy for the reciprocating circular ribbed channel decreases as the pulsating number increases. The oscillating amplitude of Nusselt number with crank angle in the oil-cooling is less than in the water-cooling.     

Experiments on heat transfer enhancement from a heated square cylinder in a pulsating channel flow

Experiments have been performed to investigate heat transfer enhancement from a heated square cylinder in a channel by pulsating flow. For all the experiments, the amplitude of the pulsating flow is fixed at A = 0.05. The effects of the Reynolds number based on the mean flow velocity (Re = 350 and 540), the pulsating frequency (0 Hz < f_p < 60 Hz) and the blockage ratio of the square cylinder (β = 1/10, 1/8, and 1/6) on convective heat transfer are examined. The measured Strouhal numbers of shedding vortices for non-pulsating (A = 0) steady inlet flow are compared with the previously published data, and good agreement is found. The “lock-on” phenomenon is clearly observed for a square cylinder in the present flow pulsation. When the pulsating frequency is within the lock-on regime, heat transfer from the square cylinder is substantially enhanced. In addition, the influence of the Reynolds number and the blockage ratio on the lock-on occurrence is discussed in detail.