Large eddy simulation in Code_Saturne of thermal mixing in a T junction with brass walls

Following on from Kuhn et al (2010) we study the capability of large eddy simulation with conjugate heat transfer to predict thermal fluctuations with thermal mixing. Wall functions are used to model the wall heat transfer. Comparison with experimental results show that the temperature variance on the outer skin of the solid is well predicted by the simulation. It is shown that the variance of thermal flux in the fluid closely maps the temperature variance at the outer boundary of the solid. Since the variance of thermal flux is closely related to the dissipation of temperature variance it can be concluded that the dissipation of temperature variance in the fluid is linked to temperature variance in the solid. Analysis of the equation of the temperature variance in the solid confirms this is indeed the case. It is the dissipation of temperature variance in the fluid that characterizes how the temperature variance penetrates the solid. Thus RANS modelling can be used to predict thermal variance in solids provided that there is an accurate model for the dissipation of temperature variance at the wall and an equation for the thermal variance in the solid is solved.     

DNS,LES and RANS of turbulent heat transfer in boundary layer with suddenly changing wall thermal conditions

The objectives of this study are to investigate a thermal field in a turbulent boundary layer with suddenly changing wall thermal conditions by means of direct numerical simulation (DNS), and to evaluate predictions of a turbulence model in such a thermal field, in which DNS of spatially developing boundary layers with heat transfer can be conducted using the generation of turbulent inflow data as a method. In this study, two types of wall thermal condition are investigated using DNS and predicted by large eddy simulation (LES) and Reynolds-averaged Navier–Stokes equation simulation (RANS). In the first case, the velocity boundary layer only develops in the entrance of simulation, and the flat plate is heated from the halfway point, i.e., the adiabatic wall condition is adopted in the entrance, and the entrance region of thermal field in turbulence is simulated. Then, the thermal boundary layer develops along a constant temperature wall followed by adiabatic wall. In the second case, velocity and thermal boundary layers simultaneously develop, and the wall thermal condition is changed from a constant temperature to an adiabatic wall in the downstream region. DNS results clearly show the statistics and structure of turbulent heat transfer in a constant temperature wall followed by an adiabatic wall. In the first case, the entrance region of thermal field in turbulence can be also observed. Thus, both the development and the entrance regions in thermal fields can be explored, and the effects upstream of the thermal field on the adiabatic region are investigated. On the other hand, evaluations of predictions by LES and RANS are conducted using DNS results. The predictions of both LES and RANS almost agree with the DNS results in both cases, but the predicted temperature variances near the wall by RANS give different results as compared with DNS. This is because the dissipation rate of temperature variance is difficult to predict by the present RANS, which is found by the evaluation using DNS results.     

Forced convection heat transfer of Giesekus viscoelastic fluid in pipes and channels

A theoretical solution is presented for the convective heat transfer of Giesekus viscoelastic fluid in pipes and channels, under fully developed thermal and hydrodynamic flow conditions, for an imposed constant heat flux at the wall. The fluid properties are taken as constant and axial conduction is negligible. The effect of Weissenberg number (We), mobility parameter (α) and Brinkman number (Br) on the temperature profile and Nusselt number are investigated. The results emphasize the significant effect of viscous dissipation and fluid elasticity on the Nusselt number in all circumstances. For wall cooling and the Brinkman number exceeds a critical value (Br ₁), the heat generated by viscous dissipation overcomes the heat removed at the wall and fluid heats up longitudinally. Fluid elasticity shifts this critical Brinkman number to higher values.     

Stability of Flow with Viscous Dissipation in a Horizontal Porous Layer with an Open Boundary Having a Prescribed Temperature Gradient

A buoyancy-induced stationary flow with viscous dissipation in a horizontal porous layer is investigated. The lower boundary surface is impermeable and subject to a uniform heat flux. The upper open boundary has a prescribed, linearly varying, temperature distribution. The buoyancy-induced basic velocity profile is parallel and non-uniform. The linear stability of this basic solution is analysed numerically by solving the disturbance equations for oblique rolls arbitrarily oriented with respect to the basic velocity field. The onset conditions of thermal instability are governed by the Rayleigh number associated with the prescribed wall heat flux at the lower boundary, by the horizontal Rayleigh number associated with the imposed temperature gradient on the upper open boundary, and by the Gebhart number associated with the effect of viscous dissipation. The critical value of the Rayleigh number for the onset of the thermal instability is evaluated as a function of the horizontal Rayleigh number and of the Gebhart number. It is shown that the longitudinal rolls, having axis parallel to the basic velocity, are the most unstable in all the cases examined. Moreover, the imposed horizontal temperature gradient tends to stabilise the basic flow, while the viscous dissipation turns out to have a destabilising effect.     

Fully-developed heat transfer in annuli for viscoelastic fluids with viscous dissipation

Analytical solutions are obtained for heat transfer in concentric annular flows of viscoelastic fluids modeled by the simplified Phan-Thien–Tanner constitutive equation. Solutions for thermal and dynamic fully developed flow are presented for both imposed constant wall heat fluxes and imposed constant wall temperatures, always taking into account viscous dissipation.Equations are presented for the normalized temperature profile, the bulk temperature, the inner and outer wall temperatures and, through their definitions for the inner and outer Nusselt numbers as a function of all relevant non-dimensional parameters. Some special results are discussed in detail. Given the complexity of the derived equations, for ease of use compact exact expressions are presented for the Nusselt numbers and programmes to calculate all quantities are made accessible on the internet. Generally speaking, fluid elasticity is found to increase the heat transfer for imposed heating at the wall, especially in combination with internal heat generation by viscous dissipation, whereas for imposed wall temperatures it reduces heat transfer when viscous dissipation is weak.     

Conjugate heat transfer in thermally developing laminar flow with viscous dissipation effects

In this study, thermally developing laminar forced convection in a pipe including viscous dissipation and wall conductance is investigated numerically. The constant heat flux is assumed to be imposed at the outer surface of the pipe wall. The finite volume method is used. The distributions for the developing temperature and local Nusselt number in the entrance region are obtained. The dependence of the results on the Brinkman number and the dimensionless thermal conductivity are shown. The viscous heating effect on the wall is shown. Significant viscous dissipation effects have been observed for large Br.     

Experimental study of pool temperature effects on nucleate pool boiling

Nucleate pool boiling experiments with constant wall temperature were performed using pure R113 for subcooled, saturated, and superheated pool conditions. A microscale heater array and Wheatstone bridge circuits were used to maintain the constant wall temperature and to measure the instantaneous heat flow rate accurately with high temporal and spatial resolutions. Images of bubble growth were taken at 5000 frames per second using a high-speed CCD camera synchronized with the heat flow rate measurements. The bubble geometry was obtained from the captured bubble images. The effect of the pool conditions on the bubble growth behavior was analyzed using dimensionless parameters for the initial and thermal growth regions. The effect of the pool conditions on the heat flow rate behavior was also examined. The bubble growth behaviors during subcooled, saturated, and superheated pool boiling were analyzed using a modified Jakob number that we newly defined. Dimensionless time and bubble radius parameters with the modified Jakob number characterized the bubble growth behavior well. These phenomena require further analysis for various pool temperature conditions, and this study will provide good experimental data with precise constant wall temperature boundary condition for such works.     

Analytical Investigation of the Effect of Viscous Dissipation on Couette Flow in a Channel Partially Filled with a Porous Medium

An analytical study of viscous dissipation effect on the fully developed forced convection Couette flow through a parallel plate channel partially filled with porous medium is presented. A uniform heat flux is imposed at the moving plate while the fixed plate is insulated. In the fluid-only region the flow field is governed by Navier–Stokes equation while the Brinkman-extended Darcy law relationship is considered in the fully saturated porous medium. The interface conditions are formulated with an empirical constant β due to the stress jump boundary condition. Fluid properties are assumed to be constant and the longitudinal heat conduction is neglected. A closed-form solution for the velocity and temperature distributions and also the Nusselt number in the channel are obtained and the viscous dissipation effect on these profiles is briefly investigated.     

Effects of pressure work and viscous dissipation on Graetz problem for gas flows in parallel-plate channels

The analytical solutions are obtained for the Graetz problem with pressure work and viscous dissipation in the thermal entrance region of the parallel-plate channels for two basic boundary conditions of uniform wall temperature and uniform wall heat flux involving fully developed laminar gas flows. The asymptotic Nusselt number is found to be zero instead of the conventionally accepted value of 7.54 for the uniform wall temperature case and (140/17)/ [1+(27/17) PrEc] for uniform wall heat flux case. The effects of pressure work and viscous dissipation contribute significantly to the asymptotic results for heat transfer and cannot be neglected under any circumstances in the case of uniform wall temperature. Sample results are presented to illustrate the effects of pressure work and viscous dissipation on heat transfer characteristics in the thermal entrance region.     

Heat Transfer Effects on a Fully Premixed Methane Impinging Flame

A numerical assessment of different thermal conditions for an impinging flame configuration is investigated using large-eddy simulation. The cases of study correspond to a turbulent methane flame at equivalence ratio ER = 0.8 and temperature T = 298 K exiting at 30 m/s with a nozzle-to-plate distance over diameter of H/D = 2. Computational cases based on different thermal conditions are compared to a conjugate case, in which fluid and solid domains are solved simultaneously. A solid material defined with enhanced conductivity properties is used to represent the wall in the conjugate case, so that the characteristic time scales of the solid are reduced. The results indicate that the heat transfer condition influences not only the mean temperature and gradients, but also the temperature fluctuations in the near-wall region. It is found that adiabatic, isothermal and more sophisticated Robin-type boundary conditions contribute to underpredict/overpredict the temperature field near the wall. As the time scales of fluid and solid are of the same order, the use of conjugate approaches is required to predict the correct flow fields near the wall and the skin temperature.     

Laminar forced convection with viscous dissipation in a concentric annular ductConvection laminaire forcée avec dissipation visqueuse dans un conduit annulaire concentrique

Forced convection heat transfer in fully developed flows of viscous dissipating fluids in concentric annular ducts is analyzed analytically. Special attention has been paid to the effect of the viscous dissipation. Two different cases of the thermal boundary conditions are considered: uniform heat flux at the outer wall and adiabatic inner wall (Case A) and uniform heat flux at the inner wall and adiabatic outer wall (Case B). Solutions for the velocity and temperature distributions and the Nusselt number are obtained for different values of the aspect ratio and the Brinkman number. The present analytical results for the case without the viscous dissipation effect are compared with those available in the literature and an excellent agreement is observed. To cite this article: M. Avc?, O. Ayd?n, C. R. Mecanique 334 (2006).     

Analysis of a laminar boundary layer flow over a flat plate with injection or suction

An analysis is performed to study a laminar boundary layer flow over a porous flat plate with injection or suction imposed at the wall. The basic equations of this problem are reduced to a system of nonlinear ordinary differential equations by means of appropriate transformations. These equations are solved analytically by the optimal homotopy asymptotic method (OHAM), and the solutions are compared with the numerical solution (NS). The effect of uniform suction/injection on the heat transfer and velocity profile is discussed. A constant surface temperature in thermal boundary conditions is used for the horizontal flat plate.     

Unsteady-state temperature distribution in a convecting fin of constant area

A solution for the unsteady-state temperature distribution in a fin of constant area dissipating heat only by convection to an environment of constant temperature, is obtained. The partial differential equation is separated into an ordinary differential equation with position as the independent variable, and a partial differential equation with position and time as the independent variables. The problem is solved for either a step function in temperature or a step function in heat flow rate, for zero time, at one boundary while the other boundary is insulated. The initial condition is taken as an arbitrary constant. The unspecified boundary values (temperature or heat flow rate) are presented for both cases by utilizing dimensionless plots. Experimental verification is presented for the case of constant heat flow rate boundary condition.     

Analysis of viscous dissipation effect on thermal entrance heat transfer in laminar pipe flows with convective boundary conditions

Consideration is given to the influence of viscous dissipation on the thermal entrance region laminar pipe flow heat transfer with convective boundary condition. The Eigenfunction series expansion technique is employed to solve the governing energy equation. The results for axial distributions of dimensionless bulk and wall temperatures, local Nusselt number as well as modified local Nusselt number are presented graphically forNu ₀ =0.1, 2, and 100. The complicated variations of conventional local Nusselt number is due to the inappropriate definition of conventional heat transfer coefficient in this problem. A modified local heat transfer coefficient, based on the difference of bulk fluid temperature and wall temperature, is introduced. Its value can clearly indicate the extent and the direction of heat exchange between the fluid in the pipe and the ambient. The effects of outside Nusselt number are also investigated. Significant viscous dissipation effects have been observed for large Br.     

On the viscous dissipation modeling of thermal fluid flow in a porous medium

The problem of viscous dissipation and thermal dispersion in saturated porous medium is numerically investigated for the case of non-Darcy flow regime. The fluid is induced to flow upward by natural convection as a result of a semi-infinite vertical wall that is immersed in the porous medium and is kept at constant higher temperature. The boundary layer approximations were used to simplify the set of the governing, nonlinear partial differential equations, which were then non-dimensionalized and solved using the finite elements method. The results for the details of the governing parameters are presented and investigated. It is found that the irreversible process of transforming the kinetic energy of the moving fluid to heat energy via the viscosity of the moving fluid (i.e., viscous dissipation) resulted in insignificant generation of heat for the range of parameters considered in this study. On the other hand, thermal dispersion has shown to disperse heat energy normal to the wall more effectively compared with the normal diffusion mechanism.     

Buoyant Flow with Viscous Heating in a Vertical Circular Duct Filled with a Porous Medium

Combined, forced, and free flow in a vertical circular duct filled with a porous medium is investigated according to the Darcy–Boussinesq model. The effect of viscous dissipation is taken into account. It is shown that a thermal boundary condition compatible with fully developed and axisymmetric flow is either a linearly varying wall temperature in the axial direction or, only in the case of uniform velocity profile, an axial linear-exponential wall temperature change. The case of a linearly varying wall temperature corresponds to a uniform wall heat flux and includes the uniform wall temperature as a special case. A general analytical solution procedure is performed, by expressing the seepage velocity profile as a power series with respect to the radial coordinate. It is shown that, for a fixed thermal boundary condition, i.e., for a prescribed slope of the wall temperature, and for a given flow rate, there exist two solutions of the governing balance equations provided that the flow rate is lower than a maximum value. When the maximum value is reached, the dual solutions coincide. When the flow rate is higher than its maximum, no axisymmetric solutions exist. E. Magyari is on leave from the Institute of Building Technology, ETH—Zürich.     

EXPERIMENTAL STUDY OF MEASUREMENT FOR DISSIPATION RATE SCALING EXPONENT IN HEATED WALL TURBULENCE

Experimental investigations have been devoted to the study of scaling law of coarse-grained dissipation rate structure function for velocity and temperature fluctuation of non-isotropic and inhomogeneous turbulent flows at moderate Reynolds number. Much attention has been paid to the case of turbulent boundary layer, which is typically the non-istropic and inhomogeneous trubulence because of the dynamically important existence of organized coherent structure burst process in the near wall region . Longitudinal velocity and temperature have been measured at different vertical positions in turbulent boundary layer over a heated and unheated flat plate in a wind tunnel using hot wire anemometer. The influence of non-isotropy and inhomogeneity and heating the wall on the scaling law of the dissipation rate structure function is studied because of the existence of organized coherent structure burst process in the near wall region . The scaling law of coarse-grained dissipation rate structure function is foun     

Laminar mixing and heat transfer for constant heat flux boundary condition

In a recent paper we have investigated mixing and heat transfer enhancement in a mixer composed of two circular rods maintained vertically in a cylindrical tank. The rods and tank can rotate around their revolution axes while their surfaces were maintained at a constant temperature. In the present study we investigate the differences in the thermal mixing process arising from the utilization of a constant heat flux as a boundary condition. The study concerns a highly viscous fluid with a high Prandtl number for which this chaotic mixer is suitable. By solving numerically the flow and energy equations, and using different statistical tools we characterize the evolution of the fluid temperature and its homogenization. Fundamental differences are reported between these two modes of heating or cooling: while the mixing with an imposed temperature results in a homogeneous temperature field, with a fixed heat flux we observe a constant difference between the maximal and minimal temperatures that establish in the fluid; the extent of this difference is governed by the efficiency of the mixing protocol.     

Transient natural convection in a cavity with heat input and a constant temperature wall on opposite sides

The transient natural convection of a fluid with Prandtl number of order 200 in a two-dimensional square cavity has been numerically studied. One of the vertical walls of the cavity is kept at a constant (ambient) temperature and a constant heat flux is applied on the opposite wall. The other walls are adiabatic. Initially, a boundary layer is formed near the heated wall; subsequently, a large vortical structure is generated, together with an upper intrusion layer. As time progresses, the average temperature in the cavity increases, and a descending boundary layer is formed near the constant temperature wall. During the transition to the steady-state regime, a thermal stratification pattern is formed. The results are compared with the scale analysis presented by Patterson and Imberger (1980).     

Steady and Unsteady Heat Transfer in a Channel Partially Filled with Porous Media Under Thermal Non-Equilibrium Condition

Steady and pulsatile flow and heat transfer in a channel lined with two porous layers subject to constant wall heat flux under local thermal non-equilibrium (LTNE) condition is numerically investigated. To do this, a physical boundary condition in the interface of porous media and clear region of the channel is derived. The objective of this work is, first, to assess the effects of local solid-to-fluid heat transfer (a criterion indicating on departure from local thermal equilibrium (LTE) condition), solid-to-fluid thermal conductivity ratio and porous layer thickness on convective heat transfer in steady condition inside a channel partially filled with porous media; second, to examine the impact of pulsatile flow on heat transfer in the same channel. The effects of LTNE condition and thermal conductivity ratio in pulsatile flow are also briefly discussed. It is observed that Nusselt number inside the channel increases when the problem is tending to LTE condition. Therefore, careless consideration of LTE may lead to overestimation of heat transfer. Solid-to-fluid thermal conductivity ratio is also shown to enhance heat transfer in constant porous media thickness. It is also revealed that an increase in the amplitude of pulsation may result in enhancement of Nusselt number, while Nusselt number has a minimum in a certain frequency for each value of amplitude.