Reynolds analogy in combustor modeling

The Reynolds analogy concept has been used in almost all turbulent reacting flow RANS (Reynolds-averaged Navier–Stokes) simulations, where the turbulence scalar transfers in flow fields are calculated based on the modeled turbulence momentum transfer. This concept, applied to a diffusion flame model combustor, is assessed in this paper. Some of the numerical results, obtained from a flamelet combustion model with the turbulent Prandtl/Schmidt number varying from 0.25 to 0.85, are presented and compared with a benchmark experimental database. It is found that the turbulent Prandtl/Schmidt number has significant effects on the predicted temperature and species fields in the combustor. This is also true for the temperature profile along the combustor wall. In contrast, its effect on the velocity field is insignificant in the range considered. With an optimized turbulent Prandtl/Schmidt number, both velocity and scalar fields can be reasonably and quantitatively predicted. For the present configuration and operating conditions, the optimal Prandtl/Schmidt number is 0.5, lower than the traditionally used value of ～0.85. This study suggests that for accurate prediction of turbulence scalar transfers in practical reacting flows, the Reynolds analogy concept should be improved and new approaches should be developed.     

Lattice Boltzmann method simulation of backward-facing step on convective heat transfer with field synergy principle

The lattice Boltzmann method (LBM) is applied to simulate the two-dimensional incompressible steady low Reynolds number backward-facing step flows. In order to restrict the approach to the two-dimensional flow, the largest Reynolds number chosen was Re = 200. To increase the uniformity of the radial temperature profile for fluid flow in channel and consequently to enhance the heat transfer, the inserted square blockage is used and investigated numerically. In addition, the field synergy principle is also applied to demonstrate that an interruption within fluid results in decreased intersection angle between the velocity and temperature gradient. The numerical results of velocity and temperature field agree well with the available experimental and numerical results.     

Effect of magnetic field on near-wall coherent structures and heat transfer in magnetohydrodynamic turbulent channel flow of low Prandtl number fluids

A numerical study is carried out of the magnetic field effects on the coherent structures and the associated heat transfer in a turbulent channel flow with constant temperature at the bottom (cold) and top (hot) walls. Results from direct numerical simulations are conditionally sampled in order to extract the dominant coherent structures in the near-wall region for flows with and without a uniform external magnetic field in the wall-normal direction. The Reynolds number based on the bulk velocity and the wall distance is 5600, while only a representative small Stuart number of 0.01 is explored. Two fluids with Prandtl numbers of 0.01 and 0.71 are studied. It is shown that the conditionally averaged quasi-streamwise vortices are modified by the magnetic field with their size being increased and their strength decreased. The underlying organized fluid motions are damped by the Lorentz force and the turbulent heat transfer related to the action of quasi-streamwise vortices is decreased by the magnetic field. For the higher Prandtl number fluid, a similarity between the coherent temperature and the coherent streamwise velocity fluctuations is observed for both types of flow. This is diminished for the lower Prandtl number fluid, especially in the magnetohydrodynamic flow, inhibiting the intrusion of cold (hot) fluid from the cold (hot) wall towards the central region.     

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.     

Mixed convection from an isolated spherical particle

A numerical study on mixed convection around a hot spherical particle moving vertically downwards in a still fluid medium has been made. The flow field is considered to be axisymmetric for the range of Reynolds number (based on the diameter and the settling velocity of the particle) considered. A third-order accurate upwind scheme is employed to compute the flow field and the temperature distribution. The form of the wake and the thermal field is analyzed for several values of Grashof number and the Reynolds number. The influence of buoyancy on drag and the rate of heat transfer are studied. At moderate Reynolds number, recirculating eddy develops in the downstream of the sphere. With the rise of surface temperature this eddy collapses and the fluid adjacent to the heated surface develops into a buoyant plume above the sphere. The increase in surface temperature of the sphere delays the flow separation. Our results show that the drag force and the rate of heat transfer strongly depend on Grashof number for the moderate values of Reynolds number. The conjugate heat transfer from the moving sphere is also addressed in the present paper. We have compared our computed solution with several empirical and asymptotic expressions available in the literature and found them in good agreement.     

A numerical study of laminar convective heat transfer in microchannel with non-circular cross-section

Three-dimensional numerical simulations of the laminar flow and heat transfer of water in silicon microchannels with non-circular cross-sections (trapezoidal and triangular) were performed. The finite volume method was used to discretize the governing equations. Numerical results were compared with experimental data available in the literature, and good agreements were achieved. The effects of the geometric parameters of the microchannels were investigated, and the variations of Nusselt number with Reynolds number were discussed from the field synergy principle. The simulation results indicate that when the Reynolds numbers are less than 100, the synergy between velocity and temperature gradient is much better than the case with Reynolds number larger than 100. There is an abrupt change in the intersection angle between velocity and temperature gradient around Re=100. In the low Reynolds number region the Nusselt number is almost proportional to the Reynolds number, while in the high Reynolds number region, the increasing trend of Nusselt number with Reynolds number is much more mildly, which showed the applicability of the field synergy principle. In addition, for the cases studied the fully developed Nusselt number for the microchannels simulated increases with the increasing Reynolds number, rather than a constant.     

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.     

A Numerical Study on the Forced Convection of Laminar Nanofluid in a Microchannel with Both Slip and No-Slip Conditions

This article provides numerically study of the thermal performance of a microchannel, cooled with either pure water or a Cu-water nanofluid, while considering the effects of both slip and no-slip boundary conditions on the flow field and heat transfer. The microchannel is partially heated at a constant temperature and cooled by forced convection of a laminar flow at a relatively lower temperature. The effects of pertinent parameters such as Reynolds number, solid volume fraction, and slip velocity coefficient on the thermal performance of the microchannel are studied. The results of the numerical simulation indicate that the heat transfer rate is significantly affected by the solid volume fraction and slip velocity coefficient at high Reynolds numbers.     

Numerical investigation of laminar forced convection of water upwards in a narrow annulus at supercritical pressure

In the present work, convection heat transfer of water at supercritical pressure in a narrow annulus at low Reynolds numbers (less than 1500) has been investigated numerically. The continuity, momentum and energy equations have been solved simultaneously using computational fluid dynamics techniques with the inlet Reynolds number ranging from 250 to 1000, Grashof number from 2.5 × 10⁵ to 1 × 10⁶ and the inlet fluid temperature from 360 °C to 380 °C. In all of the case studies, a sub-cooled water flow at supercritical pressure (25 MPa) and a temperature close to the pseudo-critical point enters the annular channel with constant heat flux at inner wall surface and insulated at outer wall. To calculate the velocity and temperature distributions of the flow, discretized form of the governing equations in the cylindrical coordinate system are obtained by the finite volume method and solved by the SIMPLE algorithm. It has been shown that the effect of buoyancy is strong and causes extensive increase in velocity near the inner wall, and consequently an increase in the convective heat transfer, which is desirable. Besides, the effects of inlet Reynolds number, Grashof number and inlet temperature on the velocity distribution and also on the heat transfer have been investigated.     

Subsonic compressible flow in two-sided lid-driven cavity. Part I: Equal walls temperatures

This paper presents a numerical study of the laminar, viscous, subsonic compressible flow in a two-dimensional, two-sided, lid-driven cavity using a multi-domain spectral element method. The flow is driven by steadily moving two opposite walls vertically in opposite directions. All the bounding walls have equal temperatures. The results of the simulations are used to investigate the effects of the cavity aspect ratio, the Reynolds number and the Mach number on the flow. At lower Reynolds numbers, the flow pattern consists of two separate co-rotating vortices contiguous to the moving walls. For higher Reynolds numbers, initially a two-vortex flow is formed, which eventually turns into a single elliptical vortex occupying most of the cavity. For a higher aspect ratio, the flow patterns are dissimilar in that the streamlines become more and more elliptic. For aspect ratios as high as 2.5, at high Reynolds numbers, a three-vortex stage is formed. It is found that the compressibility effects are not very significant for Mach numbers less than 0.4. Dissipation of kinetic energy into internal energy changes the temperature field especially near the boundaries. Boundary layer studies suggest that the velocity and temperature boundary layer thicknesses are lower for higher Reynolds numbers. For engineering purposes, these thicknesses can be approximated by the existing flat-plate solutions.     

Numerical study for laminar wavy motions of liquid film flow on vertical wall

Film flows are classified into non-wavy laminar, wavy laminar and turbulence along the Reynolds number or the flow stability. Since the wavy motions of the film flows are so intricate and nonlinear, the studies have largely been dependent upon the experimental way. The numerical approaches have been limited on the non-wavy flow regime. To track the free surface position, various numerical techniques such as the VOF (Volume of Fluids), the MAC (Marker and Cell) and the moving grid have been adopted. However those were for a more accurate estimation of the average film thickness and not for capturing the wavy motion. Because the wavy motion highly affects the heat transfer in the film flow, the profound concern for the wavy motion is significant. In this study, the wavy motions of the laminar wavy film flow with the Reynolds number 200–1000 are successfully found by the VOF and PLIC (Piecewise Linear Interface Calculation) method. The numerical results, including the average film thickness, and the wave’s amplitude, frequency and velocity, are compared with the experimental results.     

The effect of creep flow on two-dimensional isoflux microchannels

Microchannel convective heat transfer and friction loss characteristics are numerically evaluated for gaseous, two-dimensional, steady state, laminar, constant wall heat flux flows. The effects of Knudsen number, accommodation coefficients, second-order slip boundary conditions, creep flow, and hydrodynamically/thermally developing flow are considered. These effects are compared through the Poiseuille number and the Nusselt number. Numerical values for the Poiseuille and Nusselt numbers are obtained using a continuum based three-dimensional, unsteady, compressible computational fluid dynamics algorithm that has been modified with slip boundary conditions. To verify the numerical results, analytic solutions of the hydrodynamically and thermally fully developed momentum and energy equations have been derived subject to both first- and second-order slip velocity and temperature jump boundary conditions. The resulting velocity and temperature profiles are then utilized to obtain the microchannel Poiseuille and Nusselt numbers as a function of Knudsen number, first- and second-order velocity slip and temperature jump coefficients, Brinkman number, and the ratio of the thermal creep velocity to the mean velocity. Excellent agreement between the numerical and analytical data is demonstrated. Second-order slip terms and creep velocity are shown to have significant effects on microchannel Poiseuille and Nusselt numbers within the slip flow regime.     

An investigation of two-phase flow pressure drop in helical rectangular channel

Numerical simulations have been carried out to evaluate the two-phase frictional pressure drop for air-water two-phase flow in horizontal helical rectangular channels by varying configurations, inlet velocity and inlet sectional liquid holdup. The investigations performed using eight coils, five different inlet velocity and four different inlet sectional liquid holdups. The effects of curvature, torsion, fluid velocity and inlet sectional liquid holdup on two-phase frictional pressure drop have been illustrated. It is found that the two-phase frictional pressure drop relates strongly to the superficial velocities of air or water, and that the curvature and torsion have some effect on the pressure drop for higher Reynolds number flows in large-scale helical rectangular channel; the inlet sectional liquid holdup only increases the magnitude of pressure drop in helical channel and has no effect on the development of pressure drop. The correlation developed predicts the two-phase frictional pressure drop in helical rectangular channel with acceptable statistical accuracy.     

Numerical simulation of wall mass transfer rates in capillary-driven flow in microchannels

Microchannels are believed to open up the prospect of precise control of fluid flow and chemical reactions. The high surface to volume ratio of micro size channels allows efficient mass transfer rates. The capillary effect can be used to pump fluids in microchannels and the flow generated can dissolve chemicals previously deposited on the walls of the channel. The purpose of this work is to analyze the wall mass transfer rates generated by a capillary driven flow in a microchannel. The results have implications in the optimization and design of devices for biological assays. We performed simulations of the capillary-driven flow in two-dimensional rectangular and circular microchannels by solving numerically the governing momentum and mass transfer equations with a second order accuracy finite volume code. The effects of the Reynolds number, of the contact angle and of the channel geometry on the time evolution of the local and averaged wall mass transfer rates are reported and analyzed. The flow field behind the meniscus, viewed from a reference frame moving at the velocity of the meniscus, showed to have two recirculations that enhance the wall mass transfer rates close to the triple point. A correlation between the Sherwood number and the Reynolds number, the contact angle and the time is reported. The correlation can be a useful tool for design purposes of microfluidic devices with capillary driven flows in which a fast heterogeneous reaction occurs on the wall.     

Application of Hermite wavelet method for heat transfer in a porous media

In this article, the flow and heat transfer for non-Newtonian viscoelastic fluid in an axisymmetric channel with a porous wall is investigated. Convective boundary conditions have been used in the problem formulation. We obtain coupled, highly nonlinear ordinary differential equations from the fundamental governing equations via appropriate similarity variables. The solution for velocity and temperature are computed by applying the Hermite wavelet method (HWM). The comparison between the results from the HWM, differential transform method, and numerical method are well in agreement which proves the capacity of HWM for solving such problems. The effects of Reynolds number and Prandtl number on the velocity and temperature are illustrated through graphs and tables for different values of an independent variable.     

Research Needs in Low Reynolds Number Flow Heat Exchangers

Low Reynolds number flows prevail in some process, power, automotive, aircraft, and other industrial heat exchangers such as shell-and-tube, plate, and compact heat exchangers. Laminar or low Reynolds number turbulent flows are the results of either high viscosity fluids, compact flow passages (i.e., small hydraulic diameter), or low fluid velocities. Significant advancements have been made in the past 100 years in understanding and predicting flow and heat transfer in such internal flows. This paper summarizes the research needs to further advance the science of low Reynolds number flow heat exchangers. Emphasis is primarily given to the thermal design aspects; research needs related to mechanical design, manufacturing, material selection, and other nonthermal design aspects are not covered. Also the coverage is restricted primarily to single-phase applications. The outlined research needs are based on the input from invited lecturers and some participants, experts in the field, at the Fourth NATO Advanced Study Institure in Ankara, Turkey, July 1981.     

A computational study of unsteady radiative magnetohydrodynamic Blasius and Sakiadis flow with leading‐edge accretion (ablation)

The present study investigates the influence of the magnetic field, thermal radiation, Prandtl number, and leading‐edge accretion/ablation on Blasius and Sakiadis flow. The convective boundary condition is employed to investigate the heat transfer. The nondimensional governing boundary layer equations have been solved by the homotopy analysis method for different values of the pertinent parameters. The effects of these parameters on the dimensionless velocity, temperature, skin friction, and Nusselt number are also investigated for various values of relevant parameters affecting the flow and heat transfer phenomena. The most relevant outcomes of the present study are that enhancement in magnetic field strength undermines the flow velocity establishing thinner velocity boundary layer for both Blasius and Sakiadis flows while an increase in accretion/ablation effect at leading‐edge manifests in a deceleration in velocity for Blasius case and the opposite trend is observed for Sakiadis flow. Another important outcome is that an increase in radiation and accretion/ablation at leading‐edge upsurges the fluid temperature leading to enhancement in the thermal boundary layer. For both Blasius and Sakiadis flow, the skin friction coefficient and the heat transfer rate decline with the enhancement of the leading‐edge accretion parameter. The results are compared with the existing data and are found in good agreement.     

Compressibility and rarefaction effect on heat transfer in rough microchannels

High pressure drop and high length to hydraulic diameter ratios yield significant compressibility effects in microchannel flows, which compete with rarefaction phenomena at the smaller scale. In such regimes, flow field and temperature field are no longer decoupled. In presence of significant heat transfer, and combined with the effect of viscous dissipation, this yields to a quite complex thermo-fluid dynamic problem. A finite volume compressible solver, including generalized Maxwell slip flow and temperature jump boundary conditions suitable for arbitrary geometries, is adopted. Roughness geometry is modeled as a series of triangular shaped obstructions, and relative roughness from 0% to 2.65% were considered. The chosen geometry allows for direct comparison with pressure drop computations carried out, in a previous paper, under adiabatic conditions. A wide range of Mach number is considered, from nearly incompressible to chocked flow conditions. Flow conditions with Reynolds number up to around 300 were computed. The outlet Knudsen number corresponding to the chosen range of Mach and Reynolds number ranges from very low value to around 0.05, and the competing effects of rarefaction, compressibility and roughness are investigated in detail. Compressibility is found to be the most dominant effect at high Mach number, yielding even inversion of heat flux, while roughness has a strong effect in the case of rarefied flow. Furthermore, the mutual interaction between heat transfer and pressure drop is highlighted, comparing Poiseuille number values for both cooled and heated flows with previous adiabatic computations.     

Heat transfer and hydromagnetic electroosmotic Von Kármán swirling flow from a rotating porous disc to a permeable medium with viscous heating and Joule dissipation

Magnetohydrodynamic flow and heat transfer in an ionic viscous fluid in a porous medium induced by a stretching spinning disc and modulated by electroosmosis under an axial magnetic field and radial electrical field is presented in this study. The effects of convective wall boundary conditions, Joule heating and viscous dissipation are incorporated. The governing partial differential conservation equations are transformed into a system of self-similar coupled, nonlinear ordinary differential equations with associated boundary conditions. The Matlab bvp4c solver featuring a shooting technique and the fourth-order Runge–Kutta–Fehlberg method are used to numerically solve the governing dimensionless boundary value problem. Multivariate analysis is also performed to examine the thermal characteristics. An increase in rotation parameter induces a reduction in the radial velocity, whereas it elevates the tangential velocity. Greater electrical field parameter strongly damps the radial velocity whereas it slightly decreases the tangential velocity. Increasing magnetic parameter also damps both the radial and tangential velocities. An increment in electroosmotic parameter substantially decelerates the radial flow but has a weak effect on the tangential velocity field. Increasing permeability parameter (inversely proportional to permeability) markedly damps both radial and tangential velocities. The pressure gradient is initially enhanced near the disk surface but reduced further from the disk surface with increasing magnetic parameter and electrical field parameter, whereas the opposite effect is produced with increasing Joule dissipation. Increasing magnetic and rotational parameters generate a strong heating effect and boost temperature and thermal boundary layer thickness. Nusselt number is boosted with increasing Brinkman number (viscous heating effect) and Reynolds number. The simulations are relevant to electromagnetic coating flows, bioreactors and electrochemical sensing technologies in medicine.     

Numerical study of flow and thermal oscillations in buoyant twin jets

Non-isothermal twin parallel jets in horizontal orientation, are studied numerically to ascertain the mean flow structure and the oscillation characteristics of temperature and velocity fields. The analysis is carried out for Reynolds number ranging between 9000 and 12,000 and Grashof number between 50 and 1000. The simulated results compare well with available experimental data on axial velocity distribution and jet merger distance. Subsequently, a parametric study is presented to bring out the effects of Reynolds number, nozzle spacing and jet inlet temperature.