Squeezing flow between parallel plates

Summary The flow between two parallel plates (rectangular or circular) approaching or receding from each other symmetrically is analysed. The Xavier-Stokes equations have been transformed into an ordinary differential equation using a similarity transformation and the resulting equations are solved numerically. Results for the velocity components, pressure distribution and shearing stress on the wall are presented. In the case of squeezing flow between two circular plates the load supporting capacity of the upper plate has been calculated.

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Quetschströmung zwischen parallelen Platten

Übersicht Untersucht wird die Strömung zwischen zwei parallelen Rechteck- bzw. Kreisplatten, die sich einander nähern oder entfernen. Die Navier-Stokes-Gleichungen werden durch eine Ähnlichkeitstransformation in eine gewöhnliche Differentialgleichung überführt. Die Lösung erfolgt numerisch. Ergebnisse für die Geschwindigkeitskomponenten, die Druckverteilung und die Wandschubspannung werden vorgestellt. Für die Quetschströmung zwischen zwei Kreisplatten wird die Tragkraft bestimmt.

     

Compression of a plastic porous material between rotating plates

The problem of a plane flow of a rigid-plastic porous material between two rotating rough plates with no material flux through the point of their rotation and with a uniform distribution of porosity at the initial instant is considered under the assumption that the material behavior follows the cylindrical yield condition and the associated flow rule. The solution reduces to consecutive calculation of several ordinary integrals. It is demonstrated that the solution behavior depends on the angle between the plates, and the value of porosity at a certain stage of the deformation process can be equal to zero. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 128–135, July–August, 2009.     

On fluid flow between rotating surfaces

Viscous fluid flow in the space between a spherical and an ellipsoidal surfaces rotating with different angular velocities was studied. The conditions of the occurrence and features of radial fluid flows are discussed. The results can be used to study a number of geophysical phenomena related to the dynamics of the flow of fluid.     

Oscillating radial flow between parallel plates

An analysis is presented for laminar radial flow due to an oscillating source between parallel plates. The source strength varies according to Q=Q ₀ cos ωt, and the solution is in the form of an infinite series in terms of a reduced Reynolds number, R _a ^* =Q ₀/4πνa/(r/a)². (Q ₀ = amplitude of source strength, ω = frequency, a = half distance between plates, r = radial coordinate, t = time, and ν = kinematic viscosity.) The results are valid for small values of R _a ^* and all values of the frequency Reynolds number, α=ωa ²/ν. The effects of the parameters R _a ^* and α are discussed.     

Flow of viscoelastic fluids between plates rotating about distinct axes

We discuss the flow of BKZ fluids in an orthogonal rheometer. Some analytical results are proved, and numerical solutions are obtained for the Currie model. These solutions show a boundary layer behavior at high Reynolds numbers and the possibility of discontinuous solutions or nonexistence at high Weissenberg numbers.     

Viscous fluid flow between moving parallel plates

The problem of two-dimensional time-dependent viscous fluid flow in a clearance between transversely and longitudinally moving rigid planes is considered. Non-self-similar solutions of this problem are found within the framework of the Hiemenz class of exact solutions of hydrodynamic equations and the admissible laws of motion of a movable plane are described.     

Compressible gas flow between closely spaced plates

A theoretical analysis is presented to solve numerically the steady state Navier–Stokes equations, continuity equation and energy equation for a compressible ideal gas flow between two closely spaced, in general nonparallel, infinitely wide plates (siider bearing). The analysis includes the gas inertia effect and covers both non-choked and choked flows. The results of the present analysis compare very well with both analytical and experimental results of compressible flow in a slider bearing comprised of two parallel and stationary plates. It was found that for choked flow the gas inertia effect is important, while the consideration of the energy equation does not affect the accuracy of the calculated flow substantially. Finally, the stiffness of a slider bearing is presented for different geometrical characteristics of the bearing.     

Swirling flow structures in electrostatic precipitator

Stereoscopic digital Particle Image Velocimetry (PIV) has been used to make a three-dimensional flow mapping of a volume of approximately 0.1 × 0.1 × 0.15 m in a laboratory model electrostatic precipitator (ESP). The mapped volume covers about two unit cells determined by the 100 mm electrode spacing in the 0.2 × 0.2 × 1.0 m ESP test section of the negative corona, barbed wire, smooth-plate kind. The barbs act as corona fix points, yielding a three-dimensional electrostatic field. The induced large-scale secondary gas velocity structures in the form of unsteadily undulating axial rolls have been analyzed for swirlnumber and location of instantaneous swirl center in 11 axial planes. The flow possesses high levels of turbulence and axial vorticity. Measured particle velocities are corrected for electrical drift to produce gas velocities. Subsequently experimental results are compared to Large Eddy Simulation (LES) results.     

Convergent laminar fluid flow between two rotating disks

A stationary flow from the periphery to the center in a hollow between two coaxial, closely located rotating disks is studied by the iterative method of solving a system of equations of the dynamics of a viscous incompressible fluid. The existence and uniqueness of the approximate solution are shown. Moscow State University of the Food Industry, Moscow 125080. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 77–83, March–April, 2000.     

Stability of liquid flow between heated rotating cylinders

The effect of a radial temperature gradient on stability of steady-state flow of a viscous liquid between two solid concentric cylinders both rotating in the same direction is considered. The linear stability problem is considered in the Boussinesq approximation. Sufficient stability and instability conditions for the flow relative to rotationally symmetric perturbation are obtained. Neutral curves are computed for a wide range of problem parameters.     

Stability of Couette flow between two rotating cylinders

We investigate the stability in the large of Couette flow between two cylinders rotating in the same direction. For the case of infinitesimally small perturbations, a sufficient condition for stability of the Couette flow (the Synge condition) was obtained in [1, 2]. In [3] for an investigation of the stability in the nonlinear case, to this condition we must add certain constraints on the initial energy and the angular velocities. In the proposed study, using the second method of Lyapunov, sufficient conditions for stability in the large are obtained, which differ little from the Synge condition. In this case these conditions approach the Synge condition as the distance between the cylinders is decreased.