Numerical Simulation of Turbulent Flow and Heat Transfer in a Three-Dimensional Channel Coupled with Flow Through Porous Structures

This study investigates numerically the turbulent flow and heat transfer characteristics of a T-junction mixing, where a porous media flow is vertically discharged in a 3D fully developed channel flow. The fluid equations for the porous medium are solved in a pore structure level using an Speziale, Sarkar and Gatski turbulence model and validated with open literature data. Overall, two types of porous structures, consisted of square pores, are investigated over a wide range of Reynolds numbers: an in-line and a staggered pore structure arrangement. The flow patterns, including the reattachment length in the channel, the velocity field inside the porous medium as well as the fluctuation velocity at the interface, are found to be strongly affected by the velocity ratio between the transversely interacting flow streams. In addition, the heat transfer examination of the flow domain reveals that the temperature distribution in the porous structure is more uniform for the staggered array. The local heat transfer distributions inside the porous structure are also studied, and the general heat transfer rates are correlated in terms of area-averaged Nusselt number accounting for the effects of Reynolds number, velocity ratio as well as the geometrical arrangement of the porous structures.     

Warm up of an automotive catalyst substrate by pulsating flow: a single channel modelling approach

Rapid warm up of an automotive catalyst substrate is important for early light off. This work considers the results from a model of warm up in a single channel. The mass flow is pulsating with high amplitude, about 75% of mean flow, but without flow reversal. The flow regime is laminar within the channel. Pulsations occur with frequency in the range 16–100 Hz, and are important in close-coupled systems where the catalyst is located near to the engine and where the rate of rise of gas inlet temperature with time is rapid, about 15 K/s. The use of a single channel model with conjugate heat transfer enables the heat transfer coefficient to be evaluated and compared with results from steady flow simulations. The value of the augmentation factor based on heat flux is found to be less than unity. The value of the augmentation factor based on heat transfer coefficient depends on the method for calculating the mean heat transfer coefficient, but is generally less than unity. The changes caused by pulsations will be small in practical systems. Changes in wall temperature found in the simulations are the result of the cumulative effect of changes in the mass flow rate.     

Jet impingement onto a tapered hole: Influence of jet velocity and hole wall velocities on heat transfer and skin friction

Jet impingement onto a hole with elevated wall temperature can be associated with the high‐temperature thermal drilling, where the gas jet is used for shielding the hole wall from the high‐temperature oxidation reactions as observed in the case of laser drilling. In laser processing, the molten flow from the hole wall occurs; and in the model study, the hole wall velocity resembling the molten flow should be accounted for. In the present study, gas jet impingement onto tapered hole with elevated temperature is considered and the heat transfer rates as well as skin friction at the hole wall surface are predicted. The velocity of molten flow from the hole wall determined from the previous study is adopted in the simulations and the effect of hole wall velocity on the heat transfer rates and skin friction is also examined. It is found that the Nusselt number and skin friction at the hole wall in the regions of hole inlet and exit attain high values. The influence of hole wall velocity on the Nusselt number and skin friction is found not to be very significant. Copyright © 2008 John Wiley & Sons, Ltd.     

Laminar flow heat transfer for simultaneously developing velocity and temperature profiles in ducts of rectangular cross section

Summary A numerical method is used to solve the heat transfer equations for laminar flow in ducts of rectangular cross section with simultaneously developing temperature and velocity profiles, both for constant wall temperature and for constant heat input per unit length of the duct. Like the solutions for a fully developed velocity profile, the Nusselt number for each aspect ratio is found to increase from a limiting value at large distances from the entry plane to a maximum at the entry plane. The results also show a strong effect of the Prandtl number on the heat transfer coefficients with uniform and fully developed velocity profiles representing the upper and lower limits respectively. Comparisons are made with analytical solutions for circular ducts and parallel plates and with experimental data.     

Skin friction and heat transfer in rapidly oscillating boundary layers

The influence of rapid oscillations in the outer part of a boundary layer upon the time-averaged skin friction and heat transfer is investigated analytically. The oscillations are taken to be harmonic. The only restriction on the oscillation amplitude is that it should be sufficiently small to permit the use of the boundary layer equations. The derived asymptotic formulae show the explicit dependence of momentum transfer on the frequency and the time-averaged boundary layer flow. For the heat transfer similar formulae can be derived in a number of limiting cases, viz. when the Prandtl number is either large or small.     

Untersuchung von Schwingungen einer Zweiphasenströmung durch Druckabfall und Dichtewellen mit Hilfe finiter Differenzen

The previous experimental analysis has indicated the existence to two major modes of oscillations, i.e., Density-Wave (high frequency) and Pressure-Drop (low frequency) Oscillations in single channel, electrically heated, forced convection upflow systems. In this work the stability of such a system is investigated theoretically and the results are compared with experimental findings obtained by the authors. The Homogeneous Phase Equilibrium model is used to describe the two-phase flow characteristics. The friction between the pipe wall and the expanding fluid is modeled using the Moody friction factor assuming an effective two-phase viscosity. Gravitational forces are included and heat transfer into the fluid is assumed to be the function of the wall temperature, fluid temperature and heat transfer coefficient which is also assumed to be a function of the flow rate. Though simple, this model is found to be very satisfactory in simulating both modes of oscillations with acceptable accuracy. The physical nature of each mode is different and distinct, therefore, separate solution methods are developed for each case. The Steady-State Flow Characteristics are obtained for various heat inputs and inlet temperatures by solving the conservation equations together with the equation of state by using an Implicit Finite- Difference technique. In the analysis of low frequency oscillations it is assumed that the quasi-steady state conditions prevail in the heater. The system equations obtained with this assumption are solved under constant exit pressure and constant container pressure boundary conditions using the finite-difference technique. Two methods of approach are adapted in solving the non-linear hyperbolic equations which describe the system at low mass flow rates where the density-wave type oscillations are observed. They are the Explicit Integral Momentum method (EIM) and the Explicit Finite-Difference method (EFD). A comparison of the results with experiments and other mathematical models is discussed.     

Heat transfer in laminar pulsating flows of fluids with temperature dependent viscosities

The effect of time-dependent pressure pulsations on heat transfer in a pipe flow with constant temperature boundaries is analysed numerically when the viscosity of the pulsating fluid is an inverse linear function of the temperature. The coupled differential equations are solved using Crank-Nicholson semi-implicit finite difference formulation with some modifications.The results indicate local variations in heat transfer due to pulsations. They are useful in the design of heat exchangers working under pulsating flow conditions. The analytical results are presented for both heating and cooling. The conditions under which pulsating flows can augment the heat transfer are discussed. The results are applicable for heat exchangers with fluids of high Prandtl number.     

Numerical solutions of pulsating flow and heat transfer characteristics in a pipe

Numerical studies are made of flow and heat transfer characteristics of a pulsating flow in a pipe. Complete time-dependent laminar boundary-layer equations are solved numerically over broad ranges of the parameter spaces, i.e., the frequency parameter β and the amplitude of oscillation A. Recently developed numerical solution procedures for unsteady boundary-layer equations are utilized. The capabilities of the present numerical model are satisfactorily tested by comparing the instantaenous axial velocities with the existing data in various parameters. The time-mean axial velocity profiles are substantially unaffected by the changes in β and A. For high frequencies, the prominent effect of pulsations is felt principally in a thin layer near the solid wall. Skin friction is generally greateer than that of a steady flow. The influence of oscillation on skin friction is appreciable both in terms of magnitude and phase relation. Numerical results for temperature are analyzed to reveal significant heat transfer characteristics. In the downstream fully established region, the Nusselt number either increases or decreases over the steady-flow value, depending on the frequency parameter, although the deviations from the steady values are rather small in magnitude for the parameter ranges computed. The Nusselt number trend is amplified as A increases and when the Prandtl number is low below unity. These heat transfer characteristics are qualitatively consistent with previous theoretical predictions.     

Influence of hall effect and ion slip on velocity and temperature fields in an MHD channel

The combined influence of viscosity, Hall effect and ion slip on hydrodynamic fields and on heat transfer is investigated. The exact solutions for velocity, induced magnetic field and temperature are derived for the laminar MHD flow in a flat channel assuming a small magnetic Reynolds number, finely segmented electrodes, fully developed flow and uniform heat flux at channel walls. The internal generation of heat is not considered. The Kantorowitsch method of variational calculus is employed to approximate the complicated velocity distribution.     

Migration of particles in a turbulent nonisothermic flow as a result of dependence of the viscosity of the gas on the temperature

The motion is considered of a Stokes-like spherical particle in a turbulent nonisothermic gas flow whose viscosity depends on the temperature. The field of the turbulent velocity is assumed to be homogeneous, isotropic, and steady. It is shown that if there is a mean temperature gradient in the gas, and, consequently, a heat flow due to turbulent pulsations, then there may be turbulent migration of particles in a direction collinear with the gradient of the mean temperature. The migration is due to statistical correlation of turbulent pulsations of velocity and temperature, and is not connected with the phenomenon of ordinary thermophoresis. Upon the introduction of a number of simplifying assumptions, the rate of migration is calculated in dependence on the characteristics of the particle and the flow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 53–58, November–December, 1986. The author is grateful to V. S. Galkin, V. A. Zharov, M. N. Kogan, and V. A. Sabel'nikov for discussions of the study.     

Boundary layer in the vicinity of the stagnation point of a body of axial symmetry in a turbulent stream

The flow in the boundary layer in the vicinity of the stagnation point of a flat plate is examined. The outer stream consists of turbulent flow of the jet type, directed normally to the plate. Assumptions concerning the connection between the pulsations in velocity and temperature in the boundary layer and the average parameters chosen on the basis of experimental data made it possible to obtain an isomorphic solution of the boundary layer equations. Equations are obtained for the friction and heat transfer at the wall in the region of gradient flow taking into account the effect of the turbulence of the impinging stream. It is shown that the friction at the wall is insensitive to the turbulence of the impinging stream, while the heat transfer is significantly increased with an increase in the pulsations of the outer flow. These properties are confirmed by the results of experimental studies [1–4].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 83–87, September–October, 1973.     

A transient natural convection of micropolar fluids over a vertical cylinder

A transient free convective boundary layer flow of micropolar fluids past a semi-infinite cylinder is analysed in the present study. The transformed dimensionless governing equations for the flow, microrotation and heat transfer are solved by using the implicit scheme. For the validation of the current numerical method heat transfer results for a Newtonian fluid case where the vortex viscosity is zero are compared with those available in the existing literature, and an excellent agreement is obtained. The obtained results concerning velocity, microrotation and temperature across the boundary layer are illustrated graphically for different values of various parameters and the dependence of the flow and temperature fields on these parameters is discussed. An increase in the vortex viscosity tends to increase the magnitude of microrotation and thus decreases the peak velocity of fluid flow. An increase in the vortex viscosity in micropolar fluids is shown to decrease the heat transfer rate.     

Momentum and heat transfer of a special case of the unsteady stagnation-point flow

This paper investigates the unsteady stagnation-point flow and heat transfer over a moving plate with mass transfer,which is also an exact solution to the unsteady Navier-Stokes(NS)equations.The boundary layer energy equation is solved with the closed form solutions for prescribed wall temperature and prescribed wall heat flux conditions.The wall temperature and heat flux have power dependence on both time and spatial distance.The solution domain,the velocity distribution,the flow field,and the temperature distribution in the fluids are studied for different controlling parameters.These parameters include the Prandtl number,the mass transfer parameter at the wall,the wall moving parameter,the time power index,and the spatial power index.It is found that two solution branches exist for certain combinations of the controlling parameters for the flow and heat transfer problems.The heat transfer solutions are given by the confluent hypergeometric function of the first kind,which can be simplified into the incomplete gamma functions for special conditions.The wall heat flux and temperature profiles show very complicated variation behaviors.The wall heat flux can have multiple poles under certain given controlling parameters,and the temperature can have significant oscillations with overshoot and negative values in the boundary layers.The relationship between the number of poles in the wall heat flux and the number of zero-crossing points is identified.The difference in the results of the prescribed wall temperature case and the prescribed wall heat flux case is analyzed.Results given in this paper provide a rare closed form analytical solution to the entire unsteady NS equations,which can be used as a benchmark problem for numerical code validation.     

Study on transient local entropy generation in pulsating fully developed laminar flow through an externally heated pipe

This study presents the investigation of transient local entropy generation rate in pulsating fully developed laminar flow through an externally heated pipe. The flow inlet to the pipe is considered as pulsating at a constant period and amplitude (only the velocity oscillates). The simulations are extended to include different pulsating flow cases (sinusoidal flow, step flow, and saw-down flow). To determine the effects of the mean velocity, the period and the amplitude of the pulsating flow on the entropy generation rate, the pulsating flow is examined for various cases of these parameters. Two-dimensional flow and temperature fields are computed numerically with the help of the fluent computational fluid dynamics (CFD) code. In addition to this CFD code, a computer program has been developed to calculate numerically the entropy generation and other thermodynamic parameters by using the results of the calculations performed for the flow and temperature fields. In all investigated cases, the irreversibility due to the heat transfer dominates. The step flow constitutes the highest temperature (about 919 K) and generates the highest total entropy rate (about 0.033 W/K) within the pipe. The results of this study indicate that in the considered situations, the inverse of square of temperature (1/T ²) is more dominant on the entropy generation than the temperature gradients, and that the increase of the mean velocity of the pulsating flow has an adverse effect on the ratio of the useful energy transfer rate to irreversibility rate.     

Effect of flow pulsation on laminar heat transfer between two parallel plates

The problem of heat transfer in viscous laminar pulsatile flow between two parallel plates is solved by means of a finite difference method. Boundary conditions of constant wall temperature and constant wall heat flux are considered separately. The numerical results show that flow pulsations change the instantaneous Nusselt number, but do not have any significant effect on the time-averaged values. A trend in reduction of timeaveraged Nusselt number is observed when the amplitude of flow pulsation increases and the frequency decreases. The validity of the result is limited to the case when no flow reversal exists.     

Experimental analysis of the local heat transfer coefficient of falling film evaporation with and without co-current air flow velocity

This paper presents the experimental results of the local heat transfer for falling film evaporation of water sheet by solving the inverse heat conduction problem. It is shown that the local heat transfer coefficients increase by increasing the air flow velocity, the film liquid flow rate or decreasing the inlet bulk film temperature. Correlations for the mean heat transfer coefficients in the absence of superimposed flow for the stagnation region, the thermally developed region and the bottom of the heated cylinder are proposed.     

Investigations of heat transfer and friction characteristics of compact cross-corrugated recuperators

As one of the key devices in the high temperature gas turbine system, cross-corrugated recuperators provide high heat transfer capabilities with compact size, light weight, strong mechanical strength and are mandatory to achieve 30 % electrical efficiency or higher for micro turbine engines. Flow in such geometries is usually laminar with lower Reynolds numbers. In order to understand mechanisms of flowing and heat transfer, periodic fully developed fluid flow and heat transfer in two types of cross-corrugated structures with inclination angle at 90° are investigated numerically and experimentally. Periodicity was used to reduce the complexity of the channel geometry and enables the smallest possible segment of the flow channel to be modeled. The velocity and temperature distributions were obtained in the three-dimensional complex domain. Besides a detailed flow analysis, comparison of the local heat and mass transfer and the pressure losses for these geometries are presented. It is shown that the flow phenomena caused by the different geometries were of significant influence on the homogeneity and on the quantity of the local heat and mass transfer as well as on the pressure drop. As a recuperator for micro turbine engines, cross-corrugated sinusoidal channels are more preferable to triangular channels.     

Unsteady two-fluid flow and heat transfer in a horizontal channel

The problem of unsteady oscillatory flow and heat transfer of two viscous immiscible fluids through a horizontal channel with isothermal permeable walls has been considered. The partial differential equations governing the flow and heat transfer are solved analytically using two-term harmonic and non-harmonic functions in both fluid regions of the channel. Effects of physical parameters such as viscosity ratio, conductivity ratio, Prandtl number and frequency parameter on the velocity and temperature fields are shown graphically. It is observed that the velocity and temperature decrease as the viscosity ratio increases, while they increase with increases in frequency parameter. The effect of increasing the thermal conductivity ratio also suppresses the temperature in both fluid regions. The effect of periodic frequency on the flow is depicted in tabular form. It is predicted that both the velocity and temperature profiles decrease as the periodic frequency increases.     

Direct numerical simulation of turbulent flow and heat transfer in a square duct with natural convection

In this paper, a direct numerical simulation of a fully developed turbulent flow and heat transfer are studied in a square duct with an imposed temperature difference between the vertical walls and the perfectly insulated horizontal walls. The natural convection is considered on the cross section in the duct. The numerical scheme employs a time-splitting method to integrate the three dimensional incompressible Navier-Stokes equation. The unsteady flow field was simulated at a Reynolds number of 400 based on the Mean friction velocity and the hydraulic diameter (Re _m = 6200), while the Prandtl number (Pr) is assumed 0.71. Four different Grashof numbers (Gr = 10⁴, 10⁵, 10⁶ and 10⁷) are considered. The results show that the secondary flow and turbulent characteristics are not affected obviously at lower Grashof number (Gr ≤ 10⁵) cases, while for the higher Grashof number cases, natural convection has an important effect, but the mean flow and mean temperature at the cross section are also affected strongly by Reynolds stresses. Compared with the laminar heat transfer at the same Grashof number, the intensity of the combined heat transfer is somewhat decreased.     

Heat transfer by Hagen-Poiseuille flow in the thermal development region with axial conduction

The heat transfer in the region of circular pipes close to the beginning of the heating section is investigated for low-Péclet-number flows with fully developed laminar velocity profile. Axial heat conduction is included and its effect on the temperature distribution is studied not only for the region downstream of the start of heating but also for that upstream. The energy equation is solved numerically by a finite difference method. Results are presented graphically for various Péclet numbers between 1 and 50. The boundary conditions are uniform wall temperature and uniform wall heat flux with step change at a certain cross-section. For the latter case, also some results for the region near the end of the heating section are reported. The solutions are applicable for the corresponding mass transfer situations where axial diffusion is important if the temperature is replaced by the concentration andPe byReSc.