PIV for granular flows

 Particle image velocimetry (PIV) has been adapted for use in measuring particle displacement and velocity fields in granular flows. “Seeding” is achieved by using light and dark particles. The granular flow adjacent to a clear bounding wall is illuminated with a strobe, and the recorded images are analyzed using standard PIV techniques. The application is demonstrated by measuring convection rolls in a granular bed undergoing vertical oscillations. The PIV measured displacement is consistent with displacement of a marked layer of particles. Received: 29 January 1998/Accepted: 8 April 1999     

Influence of adverse pressure gradient on rough-wall turbulent flows

This paper presents an experimental investigation of adverse pressure gradient turbulent flow over two rough surfaces and a reference smooth surface. The adverse pressure gradient was produced in an asymmetric diffuser whose opening angle was 3°. The rough surfaces comprised sand grains and gravels of nominal mean diameters of 1.55 mm and 4.22 mm, respectively. The tests were conducted at an approach flow velocity of 0.5 m/s and the momentum thickness Reynolds number varied from 900 to 3000. A particle image velocimetry technique was used for the velocity measurements. Profiles of the mean velocity, turbulent intensities, Reynolds stress ratios, mixing length, eddy viscosity and the production terms were then obtained to document the effects of adverse pressure gradient (APG) on low Reynolds number rough-wall turbulent boundary layers. The results indicate that APG thickens the boundary layer and roughness sublayer. The APG and surface roughness also enhanced the production of turbulence as well as the turbulence level when compared with the smooth-wall data.     

Contaminant contraction in two-dimensional oscillatory flows

If the vertically-mixing time is comparable with that of period oscillatory current,the contaminant contraction may occur.The coefficient of shear dispersion is negative(singularity).According to the two-dimensional delay-diffusion equation derived by theauthor:where u(t),v(t)are vertically-averaged velocities,the equations for X(t),Y(t),central displacement,dispersion tensor,had been derived.αD_(ij)/τis positivewhenτis small.If theτis large,the memory functions may be negative.Also theexpressions for D_(ij)and X,Y had been obtained.     

Nonsimilar incompressible laminar boundary-layer flows in micropolar fluids

Summary The solution of the steady laminar incompressible nonsimilar boundary-layer problem for micropolar fluids over two-dimensional and axisymmetric bodies has been presented. The partial differential equations governing the flow have been transformed into new co-ordinates having finite range. The resulting equations have been solved numerically using implicit finite-difference scheme. The computations have been carried out for a cylinder and a sphere. The results indicate that the separation in micropolar fluids occurs at earlier streamwise locations as compared to Newtonian fluids. The skin friction and velocity profiles depend on the shape of the body and are almost insensitive to microrotation or coupling parameter, provided the coupling parameter is small. On the other hand, the microrotation profiles and microrotation gradient depend on the microrotation parameter and they are insensitive to the coupling parameter.

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Zusammenfassung Es wird die Lösung des stationären Grenzschichtproblems inkompressibler mikropolarer Flüssigkeiten für den Fall der Nichtähnlichkeit bei zweidimensionalen und achsensymmetrischen Körpern vorgelegt. Die dem Problem zugrunde liegenden partiellen Differentialgleichungen werden durch Einführung neuer Koordinaten auf ein endliches Gebiet transformiert. Die so erhaltenen Gleichungen werden mit Hilfe eines impliziten Differenzenverfahrens numerisch gelöst. Die Rechnung wird für den Zylinder und die Kugel durchgeführt. Die Ergebnisse zeigen, daß die Grenzschichtablösung früher erfolgt als bei vergleichbaren newtonschen Flüssigkeiten. Wandreibung und Geschwindigkeitsprofile hängen von der Gestalt des Körpers ab und sind nahezu unempfindlich gegen Mikrorotation und Kopplungsparameter, vorausgesetzt, daß der letztere klein ist. Dagegen hängen das Profil und der Gradient der Mikrorotation vom Parameter der Mikrorotation ab und sind ebenfalls unempfindlich gegen die Kopplungsparameter.

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With 6 figures     

The upper-branch stability of compressible boundary-layer flows

The upper-branch linear and nonlinear stability of compressible boundary-layer flows is studied using the approach of Smith and Bodonyi (1982) for a similar incompressible problem. Both pressure gradient boundary layers and Blasius flow are considered with and without heat transfer and the neutral eigenrelations incorporating compressibility effects are explicitly obtained. The compressible nonlinear viscous critical-layer equations are derived and solved numerically and the results indicate some solutions with positive phase shift across the critical layer. Various limiting cases are investigated including the case of much larger disturbance amplitudes and this indicates the structure for the strongly nonlinear critical layer of the Benney-Bergeron (1969) type. Finally, we also show how a match with the inviscid neutral inflexional modes arising from the generalized inflexion-point criterion is achieved.J. Cole is grateful to the Science and Engineering Research Council of Great Britain for financial support. J. Gajjar gratefully acknowledges the support of ICOMP, NASA Lewis Research Center, Cleveland, Ohio, where part of this work was done, and he is also grateful to the Computation Center at Iowa State University for a grant which enabled the numerical work in the paper to be completed. The permanent address of the authors is the Mathematics Department, Exeter University, Exeter EX4 4QE, England.     

Non-equilibrium turbulent phenomena in transitional flat plate boundary-layer flows

Many recent laboratory experiments and numerical simulations support a non-equilibrium dissipation scaling in decaying turbulence before it reaches an equilibrium state. By analyzing a direct numerical simulation(DNS) database of a transitional boundary-layer flow, we show that the transition region and the non-equilibrium turbulence region, which are located in different streamwise zones, present different non-equilibrium scalings. Moreover, in the wall-normal direction, the viscous sublayer, l...     

An improved implicit finite-difference scheme for boundary-layer flows

The paper presents a modification to two well-known non-iterative implicit finite-difference schemes for confined and unconfined boundary-layer-type flows. The modification aims at improving the accuracy of these schemes by reducing the adverse effect of linearization, which is inherent in both of them. Using the present improved scheme, the same level of accuracy of the results could be obtained with large mesh sizes in the flow direction (coarse grid). The modification is done by adding a local iterative procedure at each computational step in the flow (marching) direction. As an example, to demonstrate the proposed modification, the simple case of developing forced convection in the entry region of concentric annuli has been considered. The results are presented, which prove the applicability of the proposed modification and show its effect on the obtained accuracy and on the required computer time.     

Investigations of wake flows of a flat plate in steady,oscillatory and combined flows

Numerical study on near wake flows of a flat plate in three kinds of oncoming flows is made by using the discrete vortex model and improved vorticity creation method. For steady oncoming flow, both gross and detailed features of the wake flow are calculated and discussed. Then, in harmonic oscillatory oncoming flow two different wake flow patterns withK _c=2,4 and 10 are obtained respectively. Our results present a new wake flow pattern for lowKc numbers (Kc<5) describing vortex shedding, pairing and moving in a period of the oscillatory flow starting from rest. The calculated drag and inertia force coefficients are closer to experimental data from the U-tube than the previous results of vortex simulation. For in-line combined oncoming flow the vortex lock-in and dynamic characteristics are simulated. The results are shown to be in good agreement with experiments. The project supported by National Natural Science Fundation of China and LNM of Institute of Mechanics. CAS     

FLAT-PLATE BOUNDARY-LAYER FLOWS INDUCED BY DUSTY SHOCK WAVE

ＦＬＡＴ－ＰＬＡＴＥＢＯＵＮＤＡＲＹ－ＬＡＹＥＲＦＬＯＷＳＩＮＤＵＣＥＤＢＹＤＵＳＴＹＳＨＯＣＫＷＡＶＥ（王柏懿）（陶锋）ＦＬＡＴ－ＰＬＡＴＥＢＯＵＮＤＡＲＹ－ＬＡＹＥＲＦＬＯＷＳＩＮＤＵＣＥＤＢＹＤＵＳＴＹＳＨＯＣＫＷＡＶＥ￥ＷａｎｇＢｏｙｉ；Ｔａ...     

Interpretation of PIV autocorrelation mesurements in complex particle-laden flows

Particle image velocimetry (PIV) was used to measure instantaneous and average particle velocity fields near the stagnation zone of a particle-laden impinging air jet. The results were compared with Lagrangian particle tracking measurements. Ensemble averages from the two methods agree well except in regions where particles have different histories, and a specific trajectory is dominant but not exclusive. The PIV autocorrelation method loses information regarding non-dominant particle trajectories. Thus, although instantaneous PIV measurements yield the dominant particle velocities correctly, the averaged measurements are biased in some regions.This work was supported by the Electric Power Research Institute under Contract RP 8034-01. We thank the 3M Corporation for their generous materials support.     

Prediction of turbulent oscillatory flows in complex systems

The economical prediction of a turbulent oscillatory isothermal flow at transitional Reynolds numbers is considered for an enclosure representative of an idealized electronics system. To assess the accuracy of numerical models, comparison is made with measurements. Normal wall distances, required in some turbulence models, are evaluated using a modified Poisson equation‐based technique. Solutions of the Poisson and fluid flow equations are accelerated using multi‐level schemes, giving valuable time‐savings. The Poisson equation‐based wall distance technique is shown to be effective. Zero‐ to two‐equation turbulence techniques are tested, including zonal and non‐linear eddy viscosity models. Of the nine models tested, the zonal models showed greatest potential. Copyright © 2000 John Wiley & Sons, Ltd.     

On the application of en-methods to three-dimensional boundary-layer flows

Extension of the eⁿ-method from two-dimensional to three-dimensional boundary-layer flows has not been straightforward. Confusion has centred on whether to use temporal or spatial stability theories, conversion between the two approaches, and the choice of integration path. The aim of this study is to clarify the confusion about the direction and magnitude of maximum growth in convectively unstable three-dimensional non-parallel boundary layers. To this end, the time-asymptotic response of the boundary layer to an impulsive point excitation is considered. Since all frequencies and all wavenumbers are excited by an impulsive point source, the most amplified component of the response is equivalent to the result of maximizing the growth over arbitrary choices of harmonic point excitation; the standard eⁿ-approach. The impulse response is calculated using a spatial steepest-descent method, which is distinct from the earlier Cebeci–Stewartson method. It is necessary to allow both time and spanwise distance to become complex during integration, but with the constraint that both are real at the end point. This method has been applied to the two-dimensional Blasius boundary layer, for which validation of the method is more straightforward, and also to a three-dimensional Falkner–Skan–Cooke (with non-zero pressure gradient and sweep) boundary layer. Dimensional frequencies and spanwise wavenumbers of propagating components are kept constant (although not necessarily real), as is physically relevant to steady flows with spatial inhomogeneity in the chordwise direction only. With this method a spatial approach is taken without having to make a priori choices about the value of disturbance frequency or wavenumber. Further, purely by choosing a downstream observation point, it is possible to find the maximum-amplitude component directly without having to calculate the entire impulse response (or wave packet). If the flow is susceptible to more than one convective instability mode, provided the modes are separated in the frequency–wavenumber space, separate n-factors can be calculated for each mode. Wave-packet propagation in the Ekman layer (a strictly parallel three-dimensional boundary layer) is also discussed to draw comparisons between the conditions for maximum growth in parallel and non-parallel boundary layers.     

Calculation of separated flows by means of boundary-layer equations

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 46–54, November–December, 1990.     

Radiative heat transfer in absorbing, emitting, and anisotropically scattering boundary-layer flows with reflecting boundary

The heat transfer in absorbing, emitting, and anisotropically scattering boundary-layer flows with reflecting boundary over a flat plate, over a 90-deg wedge, and in stagnation flow is solved by application of the Galerkin method with the particular solution boundary condition I _p (τ₀,ξ,?μ) of the equation of radiative transfer for an inhomogeneous term and the Box method. The exact integral expressions for the radiation part of this problem are developed. The coupling between convective and radiative heat transfer in boundary-layer flows is described by a set of nonlinear simultaneous equations including differential equations and integrodifferential equations. The Galerkin method and the particular solution boundary condition I _p (τ₀,ξ,?μ) are used to analyze the radiation part of the problem. The nonsimilar boundary-layer equations are solved by the Box method. The present numerical procedure solutions are compared in tables with the other exact treating results, the P-3, and P-1 approximation methods for the case of isotropically scattering boundary-layer flows. The effects of linearly anistropically scattering and reflecting surface are taken into account. It is found that the present method is a reliable and efficient numerical procedure and scattering leads to a reduction in the total heat flux. The influence of the forward-backward scattering parameter on the total heat flux decreases with the increase of the surface reflectivity.     

2-D PIV measurements of oscillatory flow around parallel plates

Oscillatory flow in stacks of parallel plates is essential for the working of “standing wave” thermo-acoustic devices. In this paper, the flow in the transition from stack to open tube is studied experimentally using particle image velocimetry. When the flow is directed outwards of the stack, vortices originate behind the stack plates. The Strouhal to Reynolds ratio determines the vortex pattern behind the stack plates, varying from a single vortex pair to a complete vortex street. The influence of different plate-end shapes and porosities are also studied. The streaming velocity is measured using two different methods.     

Mobile bed thickness in skewed asymmetric oscillatory sheet flows

A new instantaneous mobile bed thickness model is presented for sediment transport in skewed asymmetric oscillatory sheet flows. The proposed model includes a basic bed load part and a suspended load part related to the Shields parameter, and takes into account the effects of mass conservation, phase-lag, and asymmetric boundary layer development, which are important in skewed asymmetric flows but usually absent in classical models. The proposed model is validated by erosion depth and sheet flow layer thickness data in both steady and unsteady flows, and applied to a new instantaneous sediment transport rate formula. With higher accuracy than classical empirical models in steady flows, the new formula can also be used for instantaneous sediment transport rate prediction in skewed asymmetric oscillatory sheet flows.     

Series solutions of boundary-layer flows in porous media with lateral mass flux

Approximate analytical solutions for free convection boundary layers on a heated vertical plate with lateral mass flux embedded in a saturated porous medium are presented using the modified Adomian decomposition method and Padé technique. Several values of the wall temperature exponent for illustrating the effects of suction/injection parameter on the flow and heat transfer are considered. This study also includes the influence of the exponent on an impermeable surface. The results obtained are comparable to the exact analytical solutions and elucidate reliability and efficiency of the technique.