Convection in laminar three-dimensional separated flow

Distributions of the wall temperature, the Nusselt number, and the friction coefficient on all of the bounding walls of laminar three-dimensional forced convection flow adjacent to backward-facing step in a rectangular duct are reported. A uniform heat flux is imposed on the bounding walls (stepped wall, sidewalls, and flat wall) downstream from the step, while the walls of the duct upstream from the step and the step are treated as adiabatic surfaces. The flow upstream of the step is treated as hydrodynamically fully developed and isothermal, and the outlet flow downstream from the step is treated as being hydrodynamically and thermally fully developed. Local and average results are presented for a Reynolds numbers range of 150-450, and some results are compared with their equivalent from the two-dimensional case.     

Measurements in three-dimensional laminar separated flow

Velocity measurements are reported for three-dimensional laminar separated airflow adjacent to a backward-facing step using two-component laser Doppler velocimeter. The backward-facing step, with a height of S=1.0 cm, is mounted in a rectangular duct that has an upstream height of h=0.98 cm, downstream height of H=2 cm, and a width of W=8 cm. This geometry provides an aspect ratio of AR=8 and an expansion ratio of ER=2.02. The flow measurements covered a Reynolds number range between 98.5?Re?525. Measurements of velocity distributions reveal that a swirling “jet-like” flow develops near the sidewall in the separating shear layer, and the impingement of that flow on the stepped wall causes a minimum to develop in the spanwise distribution of the reattachment region. Reverse and recirculation flow regions develop adjacent to both the sidewall and the step, and these regions increase in size as the Reynolds number increases. Velocity distributions that were measured at various planes downstream from the step are presented, and predictions compare favorably with these measurements. The results show some interesting flow behaviors that could not be deduced from two-dimensional studies.     

Bifurcated three-dimensional forced convection in plane symmetric sudden expansion

Simulations of bifurcated three-dimensional laminar forced convection in horizontal duct with plane symmetric sudden expansion are presented to illustrate the effects of flow bifurcations on temperature and heat transfer distributions. The stable bifurcated flow that develops in this symmetric geometry leads to non-symmetric temperature and heat transfer distributions in the transverse direction, but symmetric distributions with respect to the center width of the duct in the spanwise directions for the Reynolds number of 400-800. A strong downwash develops at the corner of the step and a smaller reverse flow region develops adjacent to the lower stepped wall than the one that develops adjacent to the upper stepped wall. The downwash and the “jet-like” flow that develop near the sidewall create a strong swirling spanwise flow in the primary recirculating flow regions downstream from the sudden expansion. The magnitude of maximum Nusselt number that develops on the lower stepped walls is higher than the one that develops on the upper stepped wall. The locations of these maximum Nusselt numbers on the stepped walls are near the sidewalls and are upstream of the “jet-like” flow impingement regions. Results reveal that the locations where the streamwise component of wall shear stress is zero on the stepped walls do not coincide with the outer edge of the recirculation flow region near the sidewalls. Velocity, temperature, Nusselt number, and friction coefficient distributions are presented.     

Three-dimensional convective flow adjacent to backward-facing step - effects of step height

Three-dimensional simulations are presented for incompressible laminar forced convection flow adjacent to backward-facing step in rectangular duct and the effects of step height on the flow and heat transfer characteristics are investigated. Reynolds number, duct's width, and duct's height downstream from the step are kept constant at Re=343, W=0.08 m, and H=0.02 m, respectively. The selection of the values for these parameters is motivated by the fact that measurements are available for this geometry and they can be used to validate the flow simulation code. Uniform and constant heat flux is specified at the stepped wall downstream from the step, while other walls are treated as adiabatic. The size of the primary recirculation region and the maximum that develops in the Nusselt number distribution increase as the step height increases. The “jet-like” flow that develops near the sidewall within the separating shear layer impinges on the stepped wall causing a minimum to develop in the reattachment length and a maximum to develop in the Nusselt number near the sidewall. The maximum Nusselt number, in the spanwise distribution, develops generally in the same region where the reattachment length is minimum. The maximum in the friction coefficient distribution on the stepped wall increases with increasing step height inside the primary recirculation flow region, but that trend is reversed downstream from reattachment. The three-dimensional behavior and sidewall effects increase with increasing step height.     

Turbulent separated convection flow adjacent to backward-facing step—effects of step height

Simulations of turbulent convection flow adjacent to a two-dimensional backward-facing step are presented to explore the effects of step height on turbulent separated flow and heat transfer. Reynolds number and duct’s height downstream from the step are kept constant at Re₀ = 28,000 and H = 0.19 m, respectively. Uniform and constant heat flux of q_w = 270 W/m² is specified at the stepped wall downstream from the step, while other walls are treated as adiabatic. The selection of the values for these parameters is motivated by the fact that measurements are available for this geometry and they can be used to validate the flow and heat transfer simulation code. Two-equation low-Reynolds-number model is employed to achieve the turbulent Prandtl number. The primary and secondary recirculation regions increase in size as the step height increases. The bulk temperature increases more rapidly as the step height increases. Increasing the step height causes the magnitude of the maximum turbulent kinetic energy to increase. Near the step and below the step height, the turbulent kinetic energy becomes smaller as the step height increases. Inside the recirculation region, magnitude of the peak friction coefficient does not significantly change with the increase of step height. The friction coefficient becomes smaller in magnitude with the increase of the step height. The peak Stanton number becomes smaller as the step height increases.     

Three-dimensional convection flow adjacent to inclined backward-facing step

Simulations of three-dimensional laminar forced convection adjacent to inclined backward-facing step in rectangular duct are presented to examine effects of step inclination on flow and heat transfer distributions. The step height is maintained as constant while its inclination angle is changed from 15° to 90°. The inlet flow is hydrodynamically steady and fully developed with uniform temperature. The bottom wall is heated with constant heat flux, while other walls are maintained as being thermally adiabatic. Velocity, temperature, Nusselt number, and friction coefficient distributions are presented. The “jet-like” flow and its impingement do not appear as the inclination angle of backward-facing step is small (α = 15°). At the center width of the duct and close to the stepped wall, the location where the streamwise velocity component is zero changes from a saddle point to a nodal point as the step inclination angle decreases. The downwash adjacent to the sidewall becomes stronger as the step inclination angle increases. The maximum Nusselt number on the stepped wall is located near the sidewall for α  30° and it appears near the center width of duct for small step inclination angle (α = 15°). The friction coefficient inside the primary recirculation region increases with the increase of the step inclination angle. Downstream of the primary recirculation region, increase of the friction coefficient becomes slower as the step inclination angle increases.     

Heat transfer of a non-Newtonian fluid (Carbopol aqueous solution) in transitional pipe flow

An experimental study of the forced convection heat transfer for non-Newtonian fluid flow in a pipe is presented. We focus particularly on the transitional regime. A wall boundary heating condition of heat flux is imposed. The non-Newtonian fluid used is Carbopol (polyacrylic acid) aqueous solutions. Detailed rheology as well as the variation of the rheological parameters with temperature are reported. Newtonian and shear thinning fluids are also tested for comparative purposes. The characterization of the flow and the thermal convection is made via the pressure drop and the wall temperature measurements over a range of Reynolds number from laminar to turbulent regime. Our measurements show that the non-Newtonian character stabilizes the flow, i.e., the critical Reynolds number to transitional flow increases with shear thinning and yield stress. The heat transfer coefficients are given and compared with heat transfer laws for different regime flows. Details when the heat transfer coefficient loses rapidly its local dependence on the Reynolds number are analyzed.     

Fluid flow and mass transfer in a sinusoidal wavy‐walled tube at moderate Reynolds numbers

Fluid flow and mass transfer characteristics in an axisymmetric sinusoidal wavy‐walled tube are experimentally investigated in the Reynolds number range of 50 to 1000. Attention is paid to the transitional flow, which is observed in the Reynolds number range of 160 to 200. In the laminar flow regime, wall shear stress and mass transfer rate increase with the slopes of 1 and 1/3, respectively, whereas in the turbulent flow regime they increase with the slopes of 3/2 and 3/5, respectively. In the transitional flow regime they increase dramatically, with a sharp slope. It is found that in this flow regime, laminar‐like motion and turbulent‐like motion alternatively take place at different time intervals. This is quite different from the flow instability for the wavy‐walled channel, where Tollmien‐Schlichting waves are observed. The flow instability in the wavy‐walled tube in the transitional flow regime is considered to be responsible for a significant increase in the wall shear stress and mass transfer rate. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(7): 650–661, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10121     

Three dimensional mixed convection in plane symmetric-sudden expansion: Symmetric flow regime

Three-dimensional simulations of laminar buoyancy assisting mixed convection in a vertical duct with a plane symmetric sudden expansion are presented to illustrate the effects of the buoyancy assisting force and the duct’s aspect ratio on the flow and heat transfer. This geometry and flow conditions appear in many engineering applications, but 3-D heat transfer results have not appeared in the literature. This study focuses on the regime where the flow and thermal fields are symmetric in this geometry. The buoyancy force is varied by changing the heat flux on the stepped walls that are downstream from the sudden expansion, and the duct’s aspect ratio is varied by changing the width of the duct while keeping the expansion ratio constant. Results are presented for duct’s aspect ratio of 4, 8, 12, 16, and ∞ (2-D flow), and for wall heat fluxes between 5–35 W/m². The Reynolds number and the range of wall heat flux are selected to insure that the flow remains laminar and symmetric in this geometry and reverse flow does not develop at the exit section of the duct. Results for the velocity, temperature, and the Nusselt number distributions are presented, and the effects of the buoyancy force and the duct’s aspect ratio on these results are discussed.     

Transitional flow patterns behind a backstep with porous-based fluid injection

The flow structure downstream of a backstep with mass injection from a porous base was analyzed both qualitatively and quantitatively in the transitional flow regime of Re_h = 2009–3061. By increasing the wall injection velocity ratio gradually, four distinct flow patterns, shifted from pattern A to B, C and D, were categorized. Pressure distributions of these patterns were dominated by the wall injection velocity ratio, and various downstream-flowing tendencies were produced correspondingly. The effect of flow stabilization by decreasing the Reynolds number became more prominent if the wall injection velocity ratio was increased. Due to the existence of a shear layer, a large value of the Reynolds stress was measured near the tip of the step in pattern A. Once the wall injection was initiated, the local strength of Reynolds stress at the same location was decreased. By increasing the wall injection velocity ratio, the region with decreased level of Reynolds stress extended gradually from the tip of backstep to the streamwise location x = 0.45X_r. The turbulent kinetic energy in pattern A was mostly contributed by the horizontal fluctuation of flow near the backstep in the recirculation zone, and the region with maximum horizontal fluctuation was found to evolve toward the base as the flow moves downstream. However, the weighting of vertical fluctuation became more significant as the wall injection velocity ratio increased.     

Sidewall effects on heat transfer in narrow backward facing step in transitional regime

In this work, we study numerically with large eddy simulation, the effects induced by the three-dimensional geometry of the channel on the flow topology that exists when the three-dimensional intrinsic instabilities appear in a backward facing step flow with low aspect ratio for Reynolds in the transitional regime (Re = 1,000–1,600), and its impact on the heat flux in the lower wall. Under the transitional regime, the three-dimensional instabilities begin to appear, but they can be masked by the flows due to the presence of the side walls. The study is carried out with two boundary conditions in the sidewalls, slip, and no-slip, to discriminate between the three-dimensionality induced by the geometry and the intrinsic three-dimensional instabilities. The results obtained are compared between the two boundary conditions, establishing what type of flow prevails and its influence on time-averaged mean Nusselt number for all Reynolds.     

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.     

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.     

Convection Heat Transfer Enhancement on Recirculating Flows in a Backward Facing Step: The Effects of a Small Square Turbulence Promoter

This work addresses the numerical simulation of incompressible turbulent recirculating channel flows in a backward-facing step. The effects of a small square turbulence promoter on convection heat transfer are evaluated through a parametric study. The governing equations comprise the time-averaged mass, linear momentum, and energy conservation principles in conjunction with the two-equation k–epsilon turbulence model. The study is focused on the assessment of the local and global Nusselt numbers at the channel stepped wall. The main results indicate that a maximum increment around 15% on the average Nusselt number can be achieved by using a small turbulence promoter to disturb the flow. Furthermore, it was found that the peak of the local Nusselt number on the stepped wall is located in the region where the turbulent diffusion is maximum in the near wall region.     

Analysis of the flow and heat transfer characteristics for assisting incompressible laminar flow past an open cavity

A numerical study has been carried out to analyze the effects of mixed convective assisting flow past three-dimensional open cavity over a wide range of Reynolds (100–1000) and Richardson (0.001–10) numbers. The vertical walls in the inflow and outflow sides are isothermal while all other walls are adiabatic. The cavity is assumed to be cubic in geometry and the flow is laminar. A direct numerical simulation is undertaken to investigate the flow structure, the heat transfer characteristics and the complex interaction between the induced stream flow at ambient temperature and the buoyancy-induced flow from the heated wall. It is found that the flow becomes stable at moderate Grashof number and exhibits a three-dimensional structure, while for high Richardson number the mixed convection effects come into play and push the recirculating zone further upstream and the flow may becomes unstable.     

Stability of two-phase stratified flow as controlled by laminar/turbulent transition

Flow pattern transition from stratified-smooth to stratified-wavy has been usually identified with a condition of neutral stability, where destabilizing effects are due to the inertia of the two-phases. It is shown that this is indeed the case when instability is approached with laminar gas phase. However, when the upper gas phase is turbulent, a destabilizing term appears due to dynamic interaction of the turbulent flow with the perturbed free interface. At the transitional range from laminar to turbulent flow regime the evolution of wavy pattern is not predicted by stability condition and coincides with the laminar/turbulent flow regime transition.     

Evaluation and modification of gas-particle covariance models by Large Eddy Simulation of a particle-laden turbulent flows over a backward-facing step

Three-dimensional numerical investigation of a low speed particle-laden turbulent flow over a backward-facing step has been carried out. An assumption of incompressibility of the flow is used due to low Mach number of the flow. The gas phase is performed by Large Eddy Simulation (LES) and the particle phase is solved by a Lagrangian particle tracking model. The simulation results such as mean streamwise velocities and fluctuation velocities for the both phase are validated by experimental results performed by Fessler and Eaton (1999) [1]. Reynolds number of the gas phase over the backward-facing step with an expansion ratio of 5:3 is 18,400, based on the maximum inlet velocity and step height. The flow is considered as dilute. Hence a one-way coupling method is applied, in which we only consider the effect of fluid on the particle. Particle–particle collisions are also neglected. The success of simulation in predicting a particle-laden turbulent flow using LES and Lagrangian trajectory model provides a numerical basis for revisiting the gas-particle correlations models. Four second-order closure models for gas-particles covariance are evaluated in the present study. A modified better gas-particle covariance model is proposed in this paper.     

Experimental study on the unsteady laminar heat transfer downstream of a backwards facing step

The objective of this work is to study experimentally the unsteady heat transfer downstream of a backward-facing step in the 2-D laminar regime when the inlet flow is pulsated. To this aim, an experimental set-up has been prepared with water as the working fluid. The Reynolds number based on the hydraulic diameter of the inlet channel and average inlet velocity is 300. Inlet flow temperature is 30 °C and a region downstream of the step is heated up to 74 °C. Pulsation is achieved using a piston pump and heat transfer is studied up to a maximum pulsation Strouhal number of 1.2. The results obtained confirm previous numerical simulation work in the sense that pulsation could be used to partially recover the heat transfer efficiency that is lost in steady flow conditions downstream of a backward-facing step. It has also been confirmed that the behaviour of the averaged Nusselt number versus pulsation Strouhal number is of the resonant type. That is: the Nusselt number increases from the steady situation up to a certain value of the Strouhal number (0.41 in our case) and, then, it degrades as the frequency of the pulsation is further increased.     

Numerical study of three recirculation zones in the unilateral sudden expansion flow

Numerical simulations of the two-dimensional laminar flow over a backward-facing step channel using two commercially-available Computational Fluid Dynamics (CFD) code are reported. The subject is to analyze the three recirculation regions of the flow in a unilateral sudden expansion. Results are presented for laminar air flow for Reynolds number lower than 2500. The mathematical model equations (mass conservation and momentum) were solved with finite element (FEM) and finite volume (FVM) methods and a segregated approach. To get the grid independent, intensive refinement studies were carried out. Results obtained are compared to experimental data presenting a good agreement. The numerical results of this work show a non-linear increase of the reattachment length as also shown by the experimental results extracted from literature.