Numerical simulation of fluid flow and heat transfer characteristics in channel with V corrugated plates

A detailed numerical study is carried out to investigate fluid flow and heat transfer characteristics in a channel with heated V corrugated upper and lower plates. The parameters studied include the Reynolds number (Re = 2,000–5,500), angles of V corrugated plates (θ = 20°, 40°, 60°), and constant heat fluxs (q″ = 580, 830, 1,090 W/m²). Numerical results have been validated using the experimented data reported by Naphon, and a good agreement has been found. The angles of V corrugated plates (θ) and the Reynolds number are demonstrated to significantly affect the fluid flow and the heat transfer rate. Increasing the angles of V corrugated plates can make the heat transfer performance become better. The increasing Reynolds number leads to a more complex fluid flow and heat transfer rate. The numerical calculations with a non-equilibrium wall function have a better accuracy than with a standard wall function for solving high Reynolds numbers or complex flow problems.     

Numerical simulation of plate autorotation in a viscous fluid flow

A general formulation of the plane coupled dynamical and aerodynamical problem of the motion of a rigid body with a rotational degree of freedom in a viscous incompressible fluid flow is given. A computation technique for solving the Navier-Stokes equations based on the meshless viscous vortex domain method is used. The autorotation of a single plate and a pair of plates is investigated. The effect of the reduced moment of inertia and the Reynolds number on the angular rotation velocity is determined. The time dependences of the hydrodynamic loads are compared with the corresponding instantaneous flow patterns. The increased the autorotation velocity of two plates in tandem is detected.     

Flow development upstream of a fence

The effect of Reynolds number on the flow development upstream of a rigid, non-porous, static fence is investigated experimentally. The flow field is measured using time-resolved, two-component particle image velocimetry at Reynolds numbers based on fence height of 18000, 36000, and 54000. The results show that a laminar separation bubble forms upstream of the junction vortex at the base of the fence. The mean extent of the bubble decreases with increasing Reynolds number, with mean separation moving downstream and mean reattachment moving upstream. In the aft portion of the bubble, shear layer vortices form and are shed at scaled frequencies and wavelengths that are comparable to laminar separation bubble shedding in low Reynolds number airfoils and flat plates with an imposed adverse pressure gradient. The strong periodicity of the associated coherent structures and the proximity of shear layer roll-up relative to the fence should be taken into consideration in the relevant designs due to potential implications to structural loading. A simple flow separation prediction model combining inviscid fence flow solution with Thwaites’ method is introduced and shows good agreement with the experimental results for the Reynolds number range considered.     

Flow induced oscillation of two rigid rectangular plates in a side-by-side configuration

The present work is an experimental study of two oscillating rigid plates placed in side-by-side configuration, hinged at their leading edges, subjected to low subsonic flow. This problem is investigated using smoke-wire flow visualization, hot-wire anemometry, and time resolved particle image velocimetry. It is found that beyond a critical Reynolds number, the plates set into oscillatory motion. This critical Reynolds number depends on the gap between the plates. It is also seen that this value of Reynolds number, at lower values of gap to thickness ratio (<7) is significantly higher than that of the single plate configuration value. The frequency and amplitude of the oscillating plates at various gaps and Reynolds numbers have been studied and compared with the characteristics of an oscillating single plate. It is also found that depending on the gap and acceleration of the free-stream, there exist two modes of oscillation - (i) in-phase and (ii) out-of-phase. For gap to thickness ratio less than 10, only in-phase oscillations take place for all values of free-stream velocity considered in the present work, whereas, when this ratio is greater than 10, the mode of oscillation depends on the initial conditions up to a certain free-stream velocity, beyond which the plates switch to in-phase mode. Smoke wire flow visualization technique along with time resolved particle image velocimetry reveal that the vorticity distributions around the plates are responsible for the initiation of the two modes of oscillations.     

Modeling low Reynolds number incompressible flows with curved boundaries using SPH

In this paper, a method that can be used to model low Reynolds number incompressible flows with curved boundaries using SPH was presented. In contrast to that usually used for the flows with flat and straight boundaries, the hydrostatic pressure gradient is treated as a variable body force in this method, and thus, it can be applied to simulate the flows with curved boundaries. Three numerical examples of low Reynolds number incompressible flows, including Poiseuille flow, flow in a section of blood vessel with a local expansion, and flow between inclined plates were calculated to test the method. The results obtained with the proposed method were in good agreement with the analytical solutions. It implies that the method presented in this paper can be successfully used to simulate low Reynolds number incompressible flows not only with flat and straight boundaries but also with curved boundaries. Copyright © 2011 John Wiley & Sons, Ltd.     

Thermal analysis of a flow of immiscible couple stress fluids in a channel

An analytical study of the entropy generation rate and heat transfer in a flow of immiscible couple stress fluids between two horizontal parallel plates under a constant pressure gradient is performed. Both plates are kept at different and constant temperatures higher than that of the fluid. The Stokes couple stress flow model is employed. The classical no-slip condition is prescribed at the plates, and continuity of the velocity, rotation, couple stress, shear stress, temperature, and heat flux is imposed at the interfaces. The velocity and temperature distributions are found analytically, and they are used to compute the entropy generation number and Bejan number. The effects of the couple stress parameter and Reynolds number on the velocity, temperature, entropy generation number, and Bejan number are investigated. It is observed that the friction near the plates in couple stress fluids decreases as the couple stress increases.     

Use of diverging or converging arrangement of plates for the control of chaotic mixing in symmetric sinusoidal plate channels

This paper presents an experimental flow visualization study of the effect that the variation of converging or diverging angles plays in the flow field of a symmetric sinusoidal channel. The experiments were performed in a water tunnel and the visualization technique was laser illumination of seeded particles whose traces were captured using long time exposure photography. Geometrical parameters such as wave amplitude, wavelength and distance between plates were kept constant, while the Reynolds number and divergence or convergence angles were varied. It was found from the experiments that the divergence of the plates is a good way to promote chaotic mixing in channel flows, as the flow becomes more unstable for diverging channels. For the case of converging channels, the flow becomes very stable even for large values of the Reynolds number. These results were compared with those of a channel formed by a pair of sinusoidal parallel plates.     

Perturbation solutions for asymmetric laminar flow in porous channel with expanding and contracting walls

The cases of large Reynolds number and small expansion ratio for the asym- metric laminar flow through a two-dimensional porous expanding channel are considered. The Navier-Stokes equations are reduced to a nonlinear fourth-order ordinary differential equation by introducing a time and space similar transformation. A singular perturbation method is used for the large suction Reynolds case to obtain an asymptotic solution by matching outer and inner solutions. For the case of small expansion ratios, we are able to obtain asymptotic solutions by double parameter expansion in either a small Reynolds number or a small asymmetric parameter. The asymptotic solutions indicate that the Reynolds number and expansion ratio play an important role in the flow behavior. Nu- merical methods are also designed to confirm the correctness of the present asymptotic solutions.     

Wake interference behind two flat plates normal to the flow: A finite-element study

A finite-element model of the Navier-Stokes equations is used for numerical simulation of flow past two normal flat plates arranged side by side at Reynolds number 80 and 160. The results from this simulation indicate that when the gap between the plates is twice the width of a single plate, the individual wakes of the plates behave independently, with the antiphase vortex shedding being dominant. At smaller gap sizes, the in-phase vortex shedding, with strong wake interaction, is favored. The gap flow in those cases becomes biased, with one of the wakes engulfing the other. The direction of the biased flow was found to be switching at irregular intervals, with the time histories of the indicative flow parameters and their power spectra resembling those of a chaotic system.This research was sponsored by NASA-Johnson Space Center under Grant NAG9-449, by NSF under Grant MSM-8796352, and by the U.S. Army under Contract DAAL03-89-C-0038.     

Instabilities of a gas-liquid flow between two inclined plates analyzed using the Navier–Stokes equations

The paper is devoted to a theoretical analysis of a counter-current gas-liquid flow between two inclined plates. We linearized the Navier–Stokes equations and carried out a stability analysis of the basic steady-state solution over a wide variation of the liquid Reynolds number and the gas superficial velocity. As a result, we found two modes of the unstable disturbances and computed the wavelength and phase velocity of their neutral disturbances varying the liquid and gas Reynolds number. The first mode is a “surface mode” that corresponds to the Kapitza's waves at small values of the gas superficial velocity. We found that the dependence of the neutral disturbance wavelength on the liquid Reynolds number strongly depends on the gas superficial velocity, the distance between the plates and the channel inclination angle for this mode. The second mode of the unstable disturbances corresponds to the transition to a turbulent flow in the gas phase and there is a critical value of the gas Reynolds number for this mode. We obtained that this critical Reynolds number weakly depends on both the channel inclination angle, the distance between the plates and the liquid flow parameters for the conditions considered in the paper. Despite a thorough search, we did not find the unstable modes that may correspond to the instability in frame of the viscous (or inviscid) Kelvin–Helmholtz heuristic analysis.     

Linear stability analysis of flow in a periodically grooved channel

We have conducted the linear stability analysis of flow in a channel with periodically grooved parts by using the spectral element method. The channel is composed of parallel plates with rectangular grooves on one side in a streamwise direction. The flow field is assumed to be two‐dimensional and fully developed. At a relatively small Reynolds number, the flow is in a steady‐state, whereas a self‐sustained oscillatory flow occurs at a critical Reynolds number as a result of Hopf bifurcation due to an oscillatory instability mode. In order to evaluate the critical Reynolds number, the linear stability theory is applied to the complex laminar flow in the periodically grooved channel by constituting the generalized eigenvalue problem of matrix form using a penalty‐function method. The critical Reynolds number can be determined by the sign of a linear growth rate of the eigenvalues. It is found that the bifurcation occurs due to the oscillatory instability mode which has a period two times as long as the channel period. Copyright © 2003 John Wiley & Sons, Ltd.     

Stability analysis of the onset of vortex shedding for wakes behind flat plates

Above a critical Reynolds number, wake flows behind flat plates become globally unstable, the leading modal instability in this case is known as Kelvin–Helmholtz mechanism. In this article, both local and BiGlobal linear instability analyses are performed numerically to study the onset of the shedding process. Flat plates with different base shapes are considered to assess geometry effects, and the relation between the critical shedding Reynolds number, \(Re_\mathrm{cr}\), and the boundary layer thickness is studied. Three types of base shapes are used: square, triangular and elliptic. It is found that the base shape has a great impact on the growth rate of least stable disturbance mode, thus would influence \(Re_\mathrm{cr}\) greatly, but it has little effect on the vortex shedding frequency. The shedding frequency is determined mainly by boundary layer thickness and has little dependence on the Reynolds number and base shape. We find that for a fixed Reynolds number, increasing boundary layer thickness acted in two ways to modify the global stability characteristics: It increases the length of the absolute unstable region and it makes the flow less locally absolutely unstable in the near-wake region, and these two effects work against each other to destabilize or stabilize the flow.     

Flow resistance and heat transfer characteristics in micro-cylinders-group

De-ionized water flows through in-line and staggered arrays micro-cylinders-group plates with different distances among micro-cylinders, and the resistance characteristic and the Nusselt numbers of micro plates are experimentally obtained. The investigations show that the distances among cylinders (S values) have slight influence on flow resistance and the experimental Nusselt number and they are far less than predictions of classical correlations at extremely low Reynolds number due to the appearance of the sluggish regions in micro cylinders-group plate. With the increase of Reynolds number, the influence of the S values on flow resistance becomes more apparent and the flow resistance and the experimental Nusselt number of micro-cylinders-group rapidly increases due to the decrease of sluggish regions in the micro-cylinders-group plate and the weakness of the variation of the thermophysical properties with temperature and the endwall effects.     

Flutter,Tumble and Vortex Induced Autorotation

The phenomenon of flutter and tumble of objects in free fall has been studied using two-dimensional numerical simulations of uniform flow past a plate which is free to rotate about a fixed axis through its centroid. Particular focus is on the effect of Reynolds number and plate thickness-to-length ratio on the flutter-to-tumble transition and on the observed frequency of the angular motions. Simulations indicate that the tendency to tumble increases with increasing Reynolds number and decreasing thickness ratio. A case is also made that the tumbling frequency for two-dimensional plates is governed by a Karman type vortex shedding process. These results for this pinned plate have also been verified by simulating a limited number of free-fall cases.     

A mixture differential quadrature method for solving two-dimensional incompressible Navier-Stokes equations

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Confined impinging twin air jets at high Reynolds numbers

An experimental study is carried out to investigate flow characteristics of confined twin jets issuing from the lower surface and impinging normally on the upper surface. Pressure distributions on the impingement and confinement plates were obtained for Reynolds numbers ranging from 30,000 to 50,000, nozzle-to-plate spacing (H/D) in the range of 0.5-4 and jet-to-jet spacing (L/D) in the range of 0.5-2. Smoke-wire technique was used to visualize the flow behavior. The effects of Reynolds number, nozzle-to-plate spacing and jet-to-jet spacing on the flow structure are examined. The subatmospheric regions occur on both impingement and confinement plates at the nozzle-to-plate spacing up to 1 for all studied Reynolds numbers and jet-to-jet spacings in consideration. They lie nearly up to the same radial location at both surfaces and move radially outward from the stagnation points with increasing nozzle-to-plate spacing and jet-to-jet spacing. It is concluded that there exists a relation between the subatmospheric regions and peaks in heat transfer coefficients for low spacings in the impinging jets.     

Experimental study of three-dimensional vortex structures in translating and rotating plates

Motivated by the unsteady force generation of flying animals, vortex formation and vorticity transport processes around small aspect-ratio translating and rotating plates with a high angle of attack are investigated. Defocusing Digital Particle Image Velocimetry was employed to explore the structure and dynamics of the vortex generated by the plates. For both translating and rotating cases, we observe the presence of a spanwise flow over the plate and the consequent effect of vorticity transport due to the tilting of the leading-edge vortex. While the spanwise flow is confined inside the leading-edge vortex for the translating case, it is widely present over the plate and the wake region of the rotating case. The distribution of the spanwise flow is a prominent distinction between the vortex structures of these two cases. As the Reynolds number decreases, due to the increase in viscosity, the leading-edge and tip vortices tend to spread inside the area swept by the rotating plate. The different vorticity distributions of the low and high Reynolds number cases are consistent with the difference in measured lift forces, which is confirmed using the vorticity moment theory.     

Radiation effects on combined convection over a vertical flat plate embedded in a porous medium of variable porosity

The present paper is concerned with the study of radiation effects on the combined (forced-free) convection flow of an optically dense viscous incompressible fluid over a vertical surface embedded in a fluid saturated porous medium of variable porosity with heat generation or absorption. The effects of radiation heat transfer from a porous wall on convection flow are very important in high temperature processes. The inclusion of radiation effects in the energy equation leads to a highly non-linear partial differential equations which are transformed to a system of ordinary differential equations using non-similarity transformation. These equations are then solved numerically using implicit finite-difference method subject to appropriate boundary and matching conditions. A parametric study of the physical parameters such as the particle diameter-based Reynolds number, the flow based Reynolds number, the Grashof number, the heat generation or absorption co-efficient and radiation parameter is conducted on temperature distribution. The effects of radiation and other physical parameters on the local skin friction and on local Nusselt number are shown graphically. It is interesting to observe that the momentum and thermal boundary layer thickness increases with the radiation and decrease with increase in the Prandtl number.     

MHD flow and heat transfer of micropolar fluid between two porous disks

A numerical study is carried out for the axisymmetric steady laminar incompressible flow of an electrically conducting micropolar fluid between two infinite parallel porous disks with the constant uniform injection through the surface of the disks. The fluid is subjected to an external transverse magnetic field. The governing nonlinear equations of motion are transformed into a dimensionless form through von Karman’s similarity transformation. An algorithm based on a finite difference scheme is used to solve the reduced coupled ordinary differential equations under associated boundary conditions. The effects of the Reynolds number, the magnetic parameter, the micropolar parameter, and the Prandtl number on the flow velocity and temperature distributions are discussed. The results agree well with those of the previously published work for special cases. The investigation predicts that the heat transfer rate at the surfaces of the disks increases with the increases in the Reynolds number, the magnetic parameter, and the Prandtl number. The shear stresses decrease with the increase in the injection while increase with the increase in the applied magnetic field. The shear stress factor is lower for micropolar fluids than for Newtonian fluids, which may be beneficial in the flow and thermal control in the polymeric processing.     

应用有限差分法的轴向流作用下叠层板的稳定性和模态分析

分析了轴向流作用下两端简支和固支叠层板的稳定性。基于势流理论建立轴向流作用下叠层板的流固耦合系统连续型运动方程,基于有限差分法建立了流场网格和结构网格统一的离散化格式,流场势函数用板的横向振动位移变量来表示,得到关于叠层板的横向振动位移变量的控制方程。求解控制方程的广义特征值,计算分析结果表明,两端简支和两端固支模型发生屈曲失稳,且得到了屈曲失稳临界速度与叠层板的层数和无量纲板间距的关系。此外,轴向流作用下叠层板的一阶模态并不是叠层板的同相弯曲模态。