Unsteady mixed convection heat transfer from tandem square cylinders in cross flow at low Reynolds numbers

A two-dimensional numerical study is carried out to understand the influence of cross buoyancy on the vortex shedding processes behind two equal isothermal square cylinders placed in a tandem arrangement at low Reynolds numbers. The spacing between the cylinders is fixed with five widths of the cylinder dimension. The flow is considered in an unbounded medium, however, fictitious confining boundaries are chosen to make the problem computationally feasible. Numerical calculations are performed by using a finite volume method based on the PISO algorithm in a collocated grid system. The range of Reynolds number is chosen to be 50–150. The flow is unsteady laminar and two-dimensional in this Reynolds number range. The mixed convection effect is studied for Richardson number range of 0–2 and the Prandtl number is chosen constant as 0.71. The effect of superimposed thermal buoyancy on flow and isotherm patterns are presented and discussed. The global flow and heat transfer quantities such as overall drag and lift coefficients, local and surface average Nusselt numbers and Strouhal number are calculated and discussed for various Reynolds and Richardson numbers.     

An experimental study of the effect of wall temperature nonuniformity on natural convection in an enclosure heated from the side

An experimental study of natural convection in a parallelepipedal enclosure induced by a single vertical wall is described. The upper half of this wall was warm and the lower half cold. The other enclosure walls were insulated. The temperature and flow measurements were performed in the high Rayleigh number regime (10¹⁰<Ra<5×10¹⁰) by using water as the working fluid. The Rayleigh number was based on the enclosure height and the temperature difference between the warm and the cold part of the driving wall. The flow field featured two flat cells, one filled with warm fluid along the top horizontal wall, and the other filled with cold fluid along the bottom horizontal wall. Each of these cells was surrounded by an additional cell as tall as half the enclosure height. The above flow structure prohibited extensive thermal contact between warm and cold fluid, thus limiting the role of convection on the heat transfer process in the cavity. The findings of this study differ significantly from the findings of previous studies based on the ‘classical’ enclosure model possessing two isothermal vertical walls, the one warm and the other cold, and support the view that the use of ‘more realistic‘ temperature boundary conditions in enclosure natural convection needs careful examination.     

非对称槽道中涡旋波的特性研究

利用PIV流场显示技术，对振荡流体在非对称槽道中涡旋波的产生、发展和消失的规律进 行了实验研究和分析，测得了涡旋波流场的速度矢量图，阐明了涡旋波流场周期性变化的特 点. 结合涡动力学方程，深入分析并揭示了做周期性运动的流体能在槽道中产生波的特性这 一规律，从中发现：流体周期变化的非定常性和不对称的槽道结构是形成涡旋波流动的主要 因素. 本文对涡旋波流场中各个旋涡的速度分布和涡量进行了测量和计算，分析了涡旋波 强化传质的机理，并研究了Re数对涡旋波流动的影响     

Thermal stratification studies in a side heated water pool for advanced heavy water reactor applications

Strong heat source at the isolation condenser wall of an Advanced Heavy Water Reactor, results in natural convection in gravity driven water pool, which leads to a thermally stratified pool. Governing equations simulating fluid flow and heat distribution are solved numerically by a general purpose Computational Fluid Dynamics solver developed at Indian Institute of Technology, Kanpur. Incompressible finite volume method with non-staggered grid arrangement is used in this exercise. This algorithm is fully implicit and semi-coupled. Turbulent natural convection in a boundary layer for high Rayleigh numbers is analyzed by the Lam–Bremhorst k − ε turbulence model. Analysis of unsteady laminar natural convection in a side-heated water cavity is also done for different values of Rayleigh number. Results show a warm fluid layer floating on the top of gradually colder layer (along the vertical direction) that indicates the presence of thermal stratification phenomenon. This fact necessitates additional safety features in such a system so that the detrimental effect such as stratification is minimized.     

Entropy analysis of unsteady magneto-nanofluid flow past accelerating stretching sheet with convective boundary condition

The unsteady laminar magnetohydrodynamics(MHD) boundary layer flow and heat transfer of nanofluids over an accelerating convectively heated stretching sheet are numerically studied in the presence of a transverse magnetic field with heat source/sink. The unsteady governing equations are solved by a shooting method with the Runge-KuttaFehlberg scheme. Three different types of water based nanofluids, containing copper, aluminium oxide, and titanium dioxide, are taken into consideration. The effects of the pertinent parameters on the fluid velocity, the temperature, the entropy generation number, the Bejan number, the shear stress, and the heat transfer rate at the sheet surface are graphically and quantitatively discussed in detail. A comparison of the entropy generation due to the heat transfer and the fluid friction is made with the help of the Bejan number. It is observed that the presence of the metallic nanoparticles creates more entropy in the nanofluid flow than in the regular fluid flow.     

Experimental investigation of turbulent entrainment in an annulus with moving sidewalls

The establishment of a turbulent mixed layer in a two-layer stratified shear flow, and the rate of entrainment into that layer were studied experimentally in a modified annulus. The modification of the conventional annulus was made by replacing the upper rotating screen with inner rotating sidewalls, extending over the upper half of the channel, so that the flow in the upper layer was nearly uniform and almost laminar, while the bottom layer was quiescent. Vertical density profile measurements were conducted using single electrode conductivity probes. The flow was visualized during the various stages of the experiment using the hydrogen bubble technique.After the start of the sidewalls rotation, the upper layer accelerates from rest, and consequently a transition process is taking place during which the initial density interface between the two layers is developed into a turbulent mixed layer. This turbulent layer is bounded by two sharp interfaces, each separating it from an outer non-turbulent zone. The generation of this five-layer structure seemed to be dominated by instabilities activated by the velocity difference between the upper and lower layer.Once a turbulent mixed layer is formed, entrainment of nonturbulent fluid into that layer is taking place causing its thickness to increase continuously. Depending on the overall Richardson number, based on the channel width, the slope of the entrainment law curve was found to have two different values, each indicating the dominance of a different source of turbulent energy production. For relatively low Richardson numbers, the slope is close to -1.8, implying that the velocity shear across each interface contributes significantly to the entrainment. On the other hand, for larger Richardson numbers the slope is about -1.25, in agreement with previous results of shear-free entrainment experiments.The measured velocity profiles indicate that as long as the mixed layer is not too thick, the radial inhomogeneities are small and the flow may be considered as nearly one-dimensional. It seems, therefore, that for the understanding of entrainment processes occurring in realistic stratified flows, the modified annulus is a more reliable tool than the conventional one.     

Effects of a barrier on temperature structure and mixing in thermally stratified water cooled from above

A Mach-Zehnder interferometer was used to study the unsteady temperature structure in radiation stratified water cooled from above. Temperature distribution measurements in a test cell filled with distilled water provide conclusive evidence that the thermal structure between the air-water interface and the stable region is controlled by buoyancy induced natural convection. The cooling from above produces a complex vertical temperature profile which can be divided into several distinct regimes. Introduction of a thin, rigid transparent (glass) plate into the water before thermal stratification by radiation and cooling confines the natural convection driven flow and reduces the intensity of mixing. As a result, the energy transport from the interior of the water layer to the interface is decreased. However, under the experimental conditions tested use of rigid, horizontal plates introduced in the fluid were not very effective in reducing the transport of heat from the warm interior to the cooler interface.     

Unsteady Couette flow in a rotating system

The unsteady Couette flow between two infinite horizontal plates induced by the non-torsional oscillations of one of the plates in a rotating system under the boundary layer approximations is investigated. An exact solution of the governing equations has been obtained by using Laplace transform technique. It is shown that when the oscillating plate situated at an infinite distance from stationary plate then the problem reduces to the unsteady boundary layer problem in a rotating system with non-torsional oscillations of the free-stream velocity.     

On the stability of the natural convection flow in a square cavity heated from the side

The stability of the steady laminar natural-convection flow of air (Prandtl number 0.71) and water (Prandtl number 7.0) in a square cavity is calculated by numerically solving the unsteady, two-dimensional Navier-Stokes equations. The cavity has a hot and cold vertical wall and either conducting or adiabatic horizontal walls. The flow looses its stability at a lower Rayleigh number in the case of conducting horizontal walls than in the case of adiabatic horizontal walls. The flow of water is more stable than the flow of air. Directly above the critical Rayleigh number the unsteady flow shows a single-frequency oscillation. Air in the case of adiabatic horizontal walls is an exception and shows two frequencies. The instabilities in the cavity seem to be related to well-known elementary instability mechanisms. In the case of conducting and adiabatic horizontal walls the instability seems to be related to a Rayleigh/Bénard and a Tollmien-Schlichting instability respectively. The second instability for air in the case of adiabatic horizontal walls seems to be related to an instability after a hydraulic jump.     

稳定分层流密度界面处湍流混合与分形结构

采用室内混合箱研究稳定分层流(上层淡水、下层盐水) 无剪切密度界面处的湍流混合与分形结构. 湍流通过浸没在盐水层中的振动格栅产生, 密度界面结构通过在盐水层中添加荧光剂或染料可视化, 共进行12 组实验. 实验观测并记录了:(1) 淡、盐水密度界面距混合箱底部的平均高程(h);(2) 淡、盐水层的密度(ρ₀,ρ), (3) 淡、盐水密度界面. 其中, 淡、盐水密度界面通过照片、录像进行记录. 观测结果用于计算:(1) 盐水层密度;(2) 卷挟速度, (3) 整体理查孙数(Ri_o), (4) 二维、三维密度界面, (5) 二维、三维密度界面的分形维度. 结果分析发现:(1) 湍流卷挟率随Rio 增大而减小, 并且满足Ri_o的-3=2 或-7=4 幂律;表明随着湍流强度的减弱, 混合的速度也越来越缓慢;(2) 二维密度界面分形维度大于1, 三维密度界面分形维度大于2;表明二维、三维密度界面存在分形结构;(3) 分形维度随Ri_o的增大而减小;表明随着湍流强度的减弱, 密度界面也越来越趋于光滑.      

Instability threshold of a negatively buoyant fountain

Experimental simulations were carried out to investigate the onset of instability in negatively buoyant fountains by injecting glycerin–water mixtures into silicon oil. The transition from a stable to an unstable fountain structure is primarily governed by the Richardson number, and to a lesser extent, Reynolds number, viscosity ratio, Weber number and vent geometry. Transition nominally occurs at a Ri = 1.0. For a fountain issuing from a cylindrical pipe, the major effect of the Reynolds number is in determining whether or not the fountain is laminar or turbulent. The Reynolds number effect can be largely accounted for by basing a corrected Richardson number on the root mean square of the mean velocity. Viscosity ratio deviating from unity has the effect of stabilizing the flow structure and thereby reducing the transition Richardson number. Similarly, interfacial tension stabilizes the flow pattern resulting in a trend of increasing transition Richardson number with increasing Weber number. The results are valid in rectangular vents if the Richardson number and Reynolds number are based on the hydraulic diameter.     

Mixed convection boundary layer flow of a viscoelastic fluid over a horizontal circular cylinder

The steady mixed convection boundary layer flow of a viscoelastic fluid over a horizontal circular cylinder in a stream flowing vertically upwards is numerically studied for both cases of heated and cooled cylinders. The governing partial differential equations are transformed into dimensionless forms using an appropriate transformation and then solved numerically using the Keller-box method. The comparison between the solutions obtained and those for a Newtonian fluid is found to be very good. Effects of the mixed convection and elasticity parameters on the skin friction and heat transfer coefficients for a fluid having the Prandtl number equal to one are also discussed. It is found that for some values of the viscoelastic parameter and some negative values of the mixed convection parameter (opposing flow) the boundary layer separates from the cylinder. Heating the cylinder delays separation and can, if the cylinder is warm enough, suppress the separation completely. Similar to the case of a Newtonian fluid, cooling the cylinder brings the separation point nearer to the lower stagnation point. However, for a sufficiently cold cylinder there will not be a boundary layer.     

Effect of gas compressibility on the stability of a boundary layer above a permeable surface at subsonic velocities

In the present study we investigate the stability of a boundary layer for the condition that the velocity perturbations at the permeable surface are nonzero. The stability for the boundary layer of an incompressible liquid in such a formulation was considered in [1]. For the case of subsonic velocities the effect of compressibility on the flow inside the boundary layer is weak, and in the present article this effect was neglected. The unsteady flow in narrow pores of a permeable covering depends strongly on the compressibility of the gas. Therefore, in the derivation of the relation connecting the pressure oscillations at the permeable surface with the oscillations of the flow through it, the effect of the compressibility was taken into consideration. It is shown that the boundary conditions, and therefore also the stability of the boundary layer at the permeable surface, depend considerably on the Mach number, even for a subsonic exterior flow.     

Turbulent diffusion of a buoyant layer at a wall

Summary When a light fluid is injected at a steady rate at the roof of a tunnel in which there is a turbulent main flow of a heavier fluid, the turbulent diffusion of the light layer may be considerably reduced due to buoyancy. For large Richardson numbers turbulent mixing ceases altogether.The equations of motion and diffusion were solved by introducing an eddy diffusivity which is dependant on the Richardson number. Experiments were made on brine (floor) layers in a water flow, and on methane (roof) layers in an air flow. Results were essentially in agreement with theory.The motion and mixing of the layers depend mainly on the inclination of the tunnel and on a dimensionless combination of main-flow velocity, gravity, relative density difference, volume input rate of layer fluid, and tunnel width. Values of the dimensionless parameter are suggested to overcome the effects of buoyancy on mixing, and to prevent layers from moving up a slope against the main flow.     

Numerical simulation of glass fogging and defogging

A numerical procedure for the prediction of fogging and defogging phenomena is presented. The simulation involves the solution of an air flow field along a cold solid surface, the evaluation of the unsteady conduction through the solid itself, and a model for the heat and mass transfer within the thin water layer on the fogged surface. A suite of routines for the unsteady simulation of the water layer evolution is coupled with an equal order finite element Navier Stokes solver and a finite volume conduction code. The procedure is fully independent of the numerical details of the solid and fluid domain solvers. Two different coupling approaches may be followed: A loose one, where the Navier Stokes solution is used only for a steady state estimate of the heat transfer coefficient, or a close one, where the Navier Stokes, conduction and water layer codes are iterated simultaneously. The latter is required for the problem of natural convection, where temperature (and thus the energy balance of the water layer) and flow field are coupled. The water layer is modelled as a collection of closely packed tiny droplets, leaving a portion of dry area among them. The effect of the contact angle is taken into account, and physical assumptions allow to define the local ratio between wet and dry surface for both the fogging and defogging process. As a case study, a comparison with experimental data for a complete fogging and defogging cycle of a glass lens in natural convection is presented.     

Laboratory observations of interactions of forced plumes with stratified shear layers

Plumes of fluid are often observed in nature to interact with stratified shear layers. Examples of this include chimney plumes hitting inversion-layer ceilings; sewage plumes impinging on unmixed fresh/saltwater interfaces; descending plumes of cold water formed at ice-leads interacting with the oceanic thermocline; and volcano plumes interacting with atmospheric interfaces. Controlled laboratory studies of these phenomena have not previously been described in the literature, and as a result there is a lack of understanding regarding their morphology and dynamics. Thus, a novel set of experiments is described here in which the behaviour of a turbulent plume is observed in the presence of a two-layer ambient. The lower layer, into which the plume initially emerges, is quiescent and at a relatively high density. The upper layer is forced to flow uniformly across the top of the lower layer, and has a lower density. The flow of the resulting plume is characterised by (a) its vertical and lateral spreading in the lower layer; (b) the nature of its extension upstream and downstream at the interface; and (c) the extent to which it penetrates into the upper layer. The behaviour is found to be governed by three non-dimensional parameters: the initial gradient Richardson number of the interface Ri_G, the ratio of the upper layer crossflow speed to the speed of the plume when it first impinges on the interface U_F/U_PI, and the ratio of the plume Monin–Obukhov lengthscale to the lower layer depth L_MO/H_L. Regime diagrams are presented showing the effects of changing these parameters on the plume flow, quantitative relationships are determined, and practical applications of the results are considered.     

Effect of Large Scale 3-D Structures on the Flow Around a Heated Cylinder at Low Reynolds Number

This work presents results of flow around a heated circular cylinder in mixed convection regime and demonstrates that Prandtl number and angle of attack of the incoming flow have a large influence on the characterisation of the flow transition from 2-D to 3-D. Previous studies show that heat transfer can enhance the formation of large 3-D structures in the wake of the cylinder for Reynolds numbers between 75 and 127 and a Richardson number larger than 0.35. This transitional mode is generally identified as “mode E”. In this work, we compare the results for water-based flow (large Prandtl number) with the ones for air-based flows (low Prandtl number). The comparison is carried out at two Reynolds numbers (100 and 150) and at a fixed Richardson number of 1. It shows that at the low Reynolds number of 100 the low Prandtl number flow does not enter into transition. This is caused by the impairment of the baroclinic vorticity production provoked by the spanwise temperature gradient. At low Prandtl number temperature gradients are less steep. For an air-based flow at Reynolds number 150, several Richardson numbers have been simulated. In this situation, the flow enters into transition and exhibits the characteristics of “mode E”, with the development of Λ-shaped structures in the near wake and mushroom-like structures in the far wake. It is also observed that the transition is delayed at Richardson number of 0.5. Simulations are also carried to investigate the effect of the angle of attack on the incoming flow on the development of large coherent structures. When the angle of attack is positive, the development of the wake tends to return to a more bi-dimensional configuration, where large scale coherent structures are impaired. In contrast, when the angle of attack is negative, large scale tri-dimensional structures dominate the flow in the wake, but with a very chaotic behaviour and the regular pattern of zero angle of attack is destroyed. The different behaviour of the flow with the variation of the angle of attack is also related to the baroclinic vorticity production, where new terms appear in the equations, leading to a positive effect of the vorticity production in case of a negative angle of attack and the opposite for a positive angle of attack.     

基于PIV测量的超声波流量计内流场特性研究

采用PIV(Particle Image Velocimetry)测量手段,考察了小口径超声波流量计的流动特性。首先针对前端安装直管段时,不同流量条件下的流场特性建立基本认识,实验结果表明,在低流量条件下,流量计内流场存在明显的不稳定演变和非定常流动特征。进一步以上游前端安装球阀为典型案例,考察了安装条件对超声波流量计响应特性和测量偏差的影响。结合直管段的实验观测结果,发现此种结构超声波流量计的适应性与其流场非定常性的关系具有很好的一致性,即流场结构稳定则适应性强。此外,综合多参数的实验结果表明,雷诺数是判断小口径超声波流量计测量准确性的重要无量纲参数。     

Characteristic Regimes of Transitional Separation Bubbles in Unsteady Flow

This experimental investigation deals with transition phenomena of a separated boundary layer under unsteady inlet flow conditions. The main purpose of this investigation is to understand the influence of the rotor-stator interaction in turbomachinery on the subsequent, highly loaded boundary layer. The research project is divided into two phases. In the first phase, which has been completed recently, only the variation of mean velocity caused by upstream blades was simulated in the experiments while the free-stream turbulence intensity was retained at a constant low level. The experiments are carried out in an Eifel-type wind tunnel to investigate the laminar separated boundary layer of a flat plate under oscillating inlet conditions. The adverse pressure gradient, similar to that of turbomachines, is generated by the contoured upper wall. The unsteadiness is produced by a rotating flap located downstream of the test section. The reduced frequency, the amplitude and the mean Reynolds number are varied to simulate the conditions prevailing in turbomachines. In addition to the Kelvin–Helmholtz instability of the separated shear layer, a lower frequency instability was observed. This is frequently referred to as `free shear layer flapping' and results in two distinctly different ways of re-attachment, depending primarily on the Reynolds number. For low momentum thickness Reynolds numbers at the separation point, large-scale vortices locked to the frequency of the unsteady main flow are identified. They originate nearly at the top of the separation bubble and are ejected downstream. A fully turbulent boundary layer develops after these vortices mix out. For higher Reynolds numbers, transition is completed within a short length of the free shear layer and there-attachment region. The characteristic momentum thickness Reynolds number separating these two regimes in unsteady flow is about 125. The Strouhal number (reduced frequency) does not appear to have any significant effect. Based on the experimental results, this behaviour is discussed in some detail. This revised version was published online in July 2006 with corrections to the Cover Date.