Structure of mixed convective longitudinal vortex air flow driven by a heated circular plate embedded in the bottom of a horizontal flat duct

In this study experimental flow visualization combined with transient temperature measurement are conducted to investigate the structure of the buoyancy driven longitudinal vortex rolls in low Reynolds number mixed convective air flow through a horizontal flat duct with an isothermally heated circular disk embedded in the bottom plate of the duct for the Reynolds number ranging from 15.1 to 99.2 and Rayleigh number from 3506 to 29,493. How the circular geometry of the heated surface affects the longitudinal vortex flow characteristics is investigated in detail. The results indicate that the longitudinal vortex rolls (L-rolls) in the duct core are induced at more upstream locations than those near the duct sides, which is completely opposite to those induced in a duct with a uniformly heated bottom. Besides, the thermals driven by the circular heated surface are not evenly spaced in the spanwise direction and are slightly asymmetric. It is of interest to note that at a given Rayleigh number Ra the thermals are unstable at high Reynolds numbers, suggesting the existence of the inertia driven instability. Thus the L-rolls evolved from these thermals are also unstable with the presence of nonperiodic generation and disappearance of new L-rolls. But at slightly lower Re the thermals and L-rolls are steady and regular. The vortex flow becomes unstable and irregular for a further reduction in the Reynolds number, which obviously results from the buoyancy driven instability. The simultaneous presence of these two instability mechanisms explains the appearance of the reverse steady-unsteady transition in the vortex flow.Based on the present data, a flow regime map is given to delineate various L-roll patterns driven by the circular heated plate. In addition, the boundaries separating these patterns are empirically correlated. Empirical correlations for the onset points of the L-rolls are also provided.     

Buoyancy driven vortex flow and its stability in mixed convection of air through a blocked horizontal flat duct heated from below

Experimental flow visualization combined with transient temperature measurement are carried out here to explore the possible stabilization of the buoyancy drive vortex flow in mixed convection of air in a bottom heated horizontal flat duct by placing a rectangular solid block on the duct bottom. Two acrylic blocks having dimensions 40 × 20 × 5 mm³ (block A) and 40 × 20 × 10 mm³ (block B) are tested. The blocks are placed on the longitudinal centerline of the duct bottom at selected locations. How the location and orientation of the rectangular block affect the stability of the regular vortex flow is investigated in detail. Experiments are conducted for the Reynolds number varying from 3 to 30 and Rayleigh number from 3000 to 6000, covering a wide range of the buoyancy-to-inertia ratio. For longitudinal vortex flow, the presence of either block near the duct entry causes the onset points of the longitudinal rolls to move significantly upstream especially for the roll pair directly behind the block. Besides, the longitudinal vortex flow in the exit portion of the duct is destabilized by the block. The transverse vortex flow is found to be only slightly affected by the block when it is placed in the exit half of the duct. Significant deformation of the transverse rolls is noted as they pass over the block. However, they restore to their regular shape in a short distance. Substantial decay in the transient flow oscillation results in the region right behind the block. Elsewhere the flow oscillates at nearly the same frequency and amplitude as that in the unblocked duct. When the block is placed near the duct entry, stabilization of the vortex flow behind the block is more pronounced. This flow stabilization is more prominent for block B with its height being twice of block A. Placing the block with its long sides normal to the forced flow direction can also enhance the flow stabilization. For the mixed longitudinal and transverse vortex flow, placing the block near the duct inlet causes the transverse rolls to change to regular or deformed longitudinal rolls in the duct depending on the buoyancy-to-inertia ratio and orientation of the block. The flow stabilization by the block is substantial. Again the stabilization of the mixed vortex flow can be enhanced by increasing the block height and length and by placing the block with its long sides normal to the forced flow direction.     

Visualization of mixed convective vortex rolls in an impinging jet flow of air through a cylindrical chamber

In this study a combined buoyancy and inertia driven vortex flow in an air jet impinging onto a heated circular plate confined in a cylindrical chamber simulating that in a vertical single-wafer rapid thermal processor for semiconductor manufacturing is investigated experimentally by flow visualization. A copper plate is used here to simulate the wafer for its better uniformity of the surface temperature and air is used to replace the inert gases. We concentrate on how the inlet gas flow rate, temperature difference between the wafer and air jet, and chamber pressure affect the vortex flow. The results show that typically the flow in the chamber is in the form of two-roll structure characterized by a circular vortex roll around the air jet along with another circular roll near the side wall of the chamber. Both rolls are somewhat deformed. The rolls are generated by the reflection of the jet from the wafer and by the deflection of the wall boundary layer flow along the wafer surface by the upward buoyancy due to the heated wafer. At low buoyancy and inertia the vortex rolls are steady and axisymmetric. At increasing buoyancy associated with the higher temperature difference and chamber pressure, the inner roll becomes slightly smaller and the outer roll becomes correspondingly bigger. Moreover, at a higher gas flow rate the inner roll is substantially bigger. Based on the present data, a correlation equation is provided to predict the location where the two rolls contact each other, providing the approximate size of the rolls. Moreover, at high buoyancy and inertia the flow becomes time dependent and does not evolve to a steady state.     

Characteristics for flow and heat transfer around a circular cylinder near a moving wall in wide range of low Reynolds number

The present study numerically investigates two-dimensional laminar fluid flow and heat transfer past a circular cylinder near a moving wall. Numerical simulations to calculate the fluid flow and heat transfer past a circular cylinder are performed for different Reynolds numbers varying in the range of 60–200 and a fixed Prandtl numbers of 0.7 (air) in the range of 0.1 ? G/D ? 4, where G/D is the ratio of the gap between the cylinder and a moving wall, G and the cylinder diameter, D. The flow and thermal fields become the steady state below the critical gap ratios of 0.8, 0.4 and 0.2 for the Reynolds numbers of 60, 80 and 100, respectively. As the gap ratio decreases, the magnitude of lift coefficient for all Reynolds numbers increased significantly with diminishing G/D due to the ground effect. The cases of Reynolds numbers of 60, 80 and 100 revealed the sharp slope of drag coefficient in the range of the gap ratio where the flow transfers from the unsteady state to the steady state. As the Reynolds number decreases, the variation of Nusselt is much significant and increases considerably with decreasing G/D.     

Steady mixed convective flow and heat transfer from tandem square cylinders in a horizontal channel

The two-dimensional laminar steady mixed convective flow and heat transfer around two identical tandem square cylinders confined in a horizontal channel are simulated by the high-accuracy multidomain pseudo-spectral method. The blockage ratio of the channel is chosen as 0.1, whereas the spacing between the cylinders is fixed with four widths of the cylinder. The Prandtl number is fixed at 0.7, the Reynolds number (Re) is studied in the range 5?≤?Re?≤?60, and the Richardson number (Ri) demonstrating the influence of thermal buoyancy ranges from 0 to 1. Numerical results reveal that, with the thermal buoyancy effect, the mixed convective flow remains steady. The variations of the overall drag and lift coefficients and the Nusselt numbers, are presented and discussed. Furthermore, the influence of thermal buoyancy on fluid flow and heat transfer is discussed and analyzed.     

A Solution for the Flow Between a Cone and a Plate at Low Reynolds Number

An analysis of the flow in the gap between a rotating cone and a stationary plate at low Reynolds numbers is presented. Using series expansions for the components of the mean velocity profile and the pressure gradient the Navier-Stokes equations and the continuity equation for a Newtonian fluid written in cylindrical coordinates are solved. It is found that the solution is stable and convergent for the local Reynolds numbers Re smaller than 1.2928. The computed angle of the wall streamlines is found to be in good agreement with experimental data.     

Wall shear rate in the Taylor-Couette-Poiseuille flow at low axial Reynolds number

An experimental investigation was done by the use of visual observations and the electrochemical technique in order to study the appearance of hydrodynamic instabilities at low Re_axg in the gap between two coaxial cylinders, with radius ratio R_r/R_s=0.615 and aspect ratio L/e=24. A motor drove the inner cylinder and the outer cylinder was fixed. A Newtonian fluid (Emkarox HV45) and two non-Newtonian fluids (aqueous solutions of guar and CMC) have been used. The analysis of the evolution of the size of the Taylor vortices is carried out for Re_axg<4.0. For Re_axg<2 we showed that the vortices underwent a contraction phase up to Ta_g≈80, and a stretching phase for Ta_g>80. For higher Re_axg, the contraction phase vanished and the vortices progressively stretched with increasing Ta_g. A dimensionless representation was also proposed for wall friction generalized to non-Newtonian fluids following the Ostwald law.     

Heat transfer on a horizontal rotating cylinder near a flat plate in a cross‐flow

An experimental study of heat transfer on a horizontal rotating cylinder near a flat plate was performed. The cylinder and plate were set in a cross‐flow. Temperature distribution and coefficients of local heat transfer were measured by a Mach–Zehnder interferometer. Flow visualization was made using smoke. Rotating Reynolds numbers (Re_r) and cross‐flow Reynolds numbers (Re_d) were varied from 0 to 2000. The spaces between cylinder and plate were varied from 1 × 10^?3 m to 5 × 10^?3 m. The rotating direction of cylinder was changed clockwise or counterclockwise. The following results are obtained: When the space between the rotating cylinder and flat plate is the same as the displacement thickness on the plate, the heat transfer on the cylinder near the plate has the best performance. We have procured the empirical equation of heat transfer from a rotating cylinder near the flat plate in the cross‐flow. 8 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20329     

Simulation of a high Reynolds number reactive transverse jet and the formation of a triple flame

This paper briefly describes a hybrid Eulerian–Lagrangian approach for the numerical simulation of turbulent combustion and its application to the study of transverse reactive jets. Because of their interesting mixing properties, transverse jets are important to a variety of industrial applications such as film cooling, primary or dilution jets in gas turbines, and flame stabilization in high speed combustion. To capture the jet complex structure and the associated reaction dynamics, we developed a fast, multiscale and parallel 3D code using a Lagrangian particle method to solve the vorticity transport equation and an Eulerian adaptive grid-based method to solve the reactive transport equations.     

Vortex shedding and heat transfer dependence on effective Reynolds number for mixed convection around a cylinder in cross flow

The influence of surface heating of a circular cylinder on the wake structure and heat transfer in the range of Reynolds number (Re) for which parallel vortex shedding occurs, is investigated numerically for different values of the buoyancy parameter, Gr. The role of buoyancy induced baroclinic vorticity on the wake formation is addressed in the present study. The variation of Strouhal number and Nusselt number with the ’effective Reynolds number’, is analyzed for different values of cylinder to free stream temperature ratio. Both Strouhal number and the rate of heat transfer increases monotonically with the increase of the effective Reynolds number. The validity of the correlations, which have been established by several authors, between the effective Reynolds number and Strouhal/ Nusselt number for forced convection, is examined in the mixed convection regime. The curves between the effective Reynolds number and the computed data for Strouhal number and Nusselt number do not collapse for the range of temperature ratio considered here. The flow field is found to be asymmetric and the cylinder experiences a negative lift. The drag coefficient increases steadily with the rise of surface temperature.     

Computations of Newtonian fluid flow around a square cylinder near an adiabatic wall at low and intermediate Reynolds numbers: Effects of cross-buoyancy mixed convection

ABSTRACT

The effects of cross-buoyancy mixed convection from a square cylinder in the proximity of a plane wall are studied for Reynolds number (Re) = 1–100, Richardson number (Ri) = 0–2, and gap ratio (G) = 0.25–1 at Prandtl number (Pr) = 0.7. The flow observed is steady for G = 0.25 and 0.5. The transition from a steady to a time-periodic system is observed for G = 1, and it is found at Re = 56, 60, and 74 for Ri = 0, 1, and 2, respectively. With increasing G and/or Ri, the drag coefficient and average Nusselt number increase for all Re values studied and the lift coefficient decreases with increasing Ri except at Re = 1. Maximum heat transfer augmentation is found about 89% at G = 0.5 (Re = 20, Pr = 0.7, Ri = 0) with respect to the corresponding value at G = 0.25 (Re = 20, Pr = 0.7, Ri = 0). Lastly, the correlations of drag coefficient and heat transfer have been obtained.     

Unstable vortex flow and new inertia-driven vortex rolls resulting from an air jet impinging onto a confined heated horizontal disk

An experiment combining flow visualization and temperature measurement is carried out here to investigate the possible presence of new inertia-driven vortex rolls and some unique characteristics of the time-dependent mixed convective vortex flow in a high-speed round air jet impinging onto a heated horizontal circular disk confined in a vertical cylindrical chamber. How the jet Reynolds and Rayleigh numbers and jet-to-disk separation distance affect the unique vortex flow characteristics is examined in detail. Specifically, the experiment is conducted for the jet Reynolds number varying from 0 to 1623 and Rayleigh number from 0 to 63,420 for the jet-to-disk separation distance fixed at 10.0, 20.0 and 30.0 mm. The results indicate that at sufficiently high Re_j the inertia-driven tertiary and quaternary rolls can be induced aside from the primary and secondary rolls. At an even higher Re_j the vortex flow becomes unstable due to the inertia-driven flow instability. Only for H = 20.0 mm the flow is also subjected to the buoyancy-driven instability for the ranges of the parameters covered here. Because of the simultaneous presence of the inertia- and buoyancy-driven flow instabilities, a reverse flow transition can take place in the chamber with H = 20.0 mm. At the large H of 30.0 mm the flow unsteadiness results from the mutual pushing and squeezing of the inertia- and buoyancy-driven rolls since they are relatively large and contact with each other. It is also noted that the critical Re_j for the onset of unsteady flow increases with ΔT for H = 10.0 and 20.0 mm. But for H = 30.0 mm the opposite is true and raising ΔT can destabilize the vortex flow. Based on the present data, flow regime maps delineating the temporal state of the flow are provided and correlating equations for the boundaries separating various flow regimes are proposed.     

Numerical investigation of low Prandtl number effect on mixed convection in a horizontal channel by the lattice Boltzmann method

The main purpose of this study is to numerically investigate the Prandtl number effect on mixed convection in a horizontal channel heated from below using the thermal lattice Boltzmann method (TLBM). The double-population model with two different lattices is used, in particular, the D2Q9 for the velocity field and D2Q5 for the thermal field. The developed lattice Boltzmann method code to simulate the fluid flow and heat transfer in the channel was validated with available literature results based on classical numerical methods, especially the finite volume method for Pr = 6.4 and the finite difference method for Pr = 0.667. The results obtained with the TLBM have shown good agreement with the conventional methods cited. The dynamic and thermal characteristics of the fluid flow were examined in the field of low Prandtl number, such that 0.05 ≤ Pr ≤ 0.667, and also compared to Pr = 6.4; for Ra = 2420 and 7400, the Reynolds number was fixed at 1. The results showed that the influence is relatively significant for the dynamic structure of flow convection for Pr ≤ 0.3 and is little influential beyond this value.     

Flow separation in a diverging conical duct: Effect of Reynolds number and divergence angle

Fluid flows in passages whose cross-sectional area increases in the streamwise direction are prone to separation. Here, the flow in a conical diffuser fed by a fully developed velocity at its inlet and mated at its downstream end to a long circular pipe is investigated by means of numerical simulation. A universal flow-regime model was used to accommodate possible laminarization of flows having moderate-turbulent and transitional Reynolds numbers at the diffuser inlet. It was found that flow separation occurred for a diffuser expansion angle of 5° for inlet Reynolds numbers less than about 2000. This finding invalidates a prior rule-of-thumb that flow separation first occurs at a divergence angle of seven degrees. Results from the 10 and 30° simulations showed separation at all investigated Reynolds numbers. The largest streamwise length of the separation zones occurred at the lower Reynolds numbers.     

Convective heat transfer to water near the critical region in a horizontal square duct

Numerical analysis has been carried out to investigate forced convective heat transfer to water near the critical region in a horizontal square duct. Near the critical point convective heat transfer in the duct is strongly coupled with large variation of thermophysical properties such as density and specific heat. Buoyancy force parameter has also severe variation with fluid temperature and pressure in the duct. There is flow acceleration along the horizontal duct resulted from fluid density decrease due to the heat transfer from the wall. Local heat transfer coefficient has large variation along the inner surface of the duct section and it depends on pressure. Nusselt number on the center of the bottom surface also has a peak where bulk fluid temperature is higher than the pseudocritical temperature and the peak decreases with the increase of pressure. Flow characteristics of velocity, temperature, and local heat transfer coefficient with water properties are presented and analyzed. Nusselt number distributions are also compared with other correlations for various pressures in the duct.     

Free convection boundary layer flow over vertical and horizontal flat plates embedded in a porous medium under mixed thermal boundary conditions

A similarity analysis of the steady free convection boundary layer over vertical and horizontal surfaces embedded in a fluid-saturated porous medium with mixed thermal boundary conditions is performed in this paper. New variables relating the similarity solutions of the Darcian velocity and temperature profiles associated with different values of the mixed thermal boundary condition parameter have been obtained. Boundary layer velocity and temperature profiles have been determined numerically for some values of the mixed thermal boundary condition parameter ε and the similarity exponent m.     

Effects of Prandtl number on three‐dimensional mixed convection in a horizontal square duct with heated and cooled side walls

We examined the effects of Prandtl number on three‐dimensional mixed convection in a horizontal square duct with heated and cooled side walls numerically. Non‐dimensional governing equations were solved for Re = 100, Pr = 0.1–10, and Ri = 36.44 by the SIMPLE method. The numerical results show that the swirl flow was generated along the flow direction, and its pitch lengthened with the increase of Pr. We also examined the strength of swirl flow using the swirl number, S, and we discuss heat transfer behavior as it corresponded to the flow. Heat transfer was promoted by the swirl flow with all Pr, and the optimum value existed within these Pr. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20319     

Fluid flow and heat transfer of mixed convection adjacent to vertical heated plates placed in uniform horizontal flow of air

Experiments have been carried out for mixed convective flows of air adjacent to the vertical heated plates in uniform horizontal forced flows to investigate relationships between the flow and the heat transfer. The experiments cover the ranges of the Reynolds and modified Rayleigh numbers: Re_L = 160 to 2300 and Ra_L^* = 4.3 × 10⁵ to 2.0 × 10⁸. The flow fields over the plates are visualized with particles and smoke. The results show that a stagnation point moves downward away from the center of the plate when the surface heat flux is beyond a critical value. The condition where the stagnation point begins to move is expressed with non‐dimensional parameters as: Gr_L^*/Re_L^2.5 = 0.15. Profiles of measured local heat transfer coefficients are smooth even at the stagnation points in all the cases examined. When buoyancy effect is sufficiently weak, the coefficients agree well with those of the wedge flow. With increasing the surface heat flux, the coefficients are augmented to approach asymptotically the boundary layer solution of natural convection along a vertical heated plate. Finally, forced, mixed, and natural convection regimes are classified by the non‐dimensional parameter (Gr_L^*/Re_L^2.5). © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20256     

Numerical investigation of the bowed stator effects in a transonic fan at low Reynolds number

The performance of fan stage in a small turbofan engines is significantly affected at high-altitude low Reynolds number. In order to examine the effect of low Reynolds number on the fan stage, 3D numerical simulation method was employed to analyse the performance variations and the underlying flow structure in the fan stage. For the sake of decreasing the influence of low Reynolds number, the different bowed stator airfoils were redesigned and the effect of the modified design was evaluated.