Surface waves in a vertically excited circular cylindrical container

The nonlinear free surface amplitude equation, which has been derived from the inviscid fluid by solving the potential equation of water waves with a singular perturbation theory in a vertically oscillating rigid circular cylinder, is investigated successively in the fourth-order Runge-Kutta approach with an equivalent time-step. Computational results include the evolution of the amplitude with time, the characteristics of phase plane determined by the real and imaginary parts of the amplitude, the single-mode selection rules of the surface waves in different forced frequencies, contours of free surface displacement and corresponding three-dimensional evolution of surface waves, etc. In addition, the comparison of the surface wave modes is made between theoretical calculations and experimental measurements, and the results are reasonable although there are some differences in the forced frequency.

Instability of the vertically forced surface wave in a circular cylindrical container

The nonlinear amplitude equation, which was derived by Jian Yongjun employing expansion of two-time scales in inviscid fluids in a vertically oscillating circular cylindrical vessel, is modified by introducing a damping term due to the viscous dissipation of this system. Instability of the surface wave is analysed and properties of the solutions of the modified equation are determined together with phase-plane trajectories. A necessary condition of forming a stable surface wave is obtained and unstable regions are illustrated. Research results show that the stable pattern of surface wave will not lose its stability to an infinitesimal disturbance.

Two-phase flow patterns in a 90 degrees bend at microgravity

Bends are widely used in pipelines carrying single- and two-phase fluids in both ground and space applications. In particular, they play more important role in space applications due to the extreme spatial constraints. In the present study, a set of experimental data of two-phase flow patterns and their transitions in a 90degrees bend with inner diameter of 12.7 mm. and curvature radius of 76.5 mm at microgravity conditions are reported. Gas and liquid superficial velocities are found to range from (1.0 similar to 23.6) m/s for gas and (0.09 similar to 0.5) m/s for liquid, respectively. Three major flow patterns, namely slug, slug-annular transitional, and annular flows, are observed in this study. Focusing on the differences between flow patterns in bends and their counterparts in straight pipes, detailed analyses of their characteristics are made. The transitions between adjoining flow patterns are found to be more or less the same as those in straight pipes, and can be predicted using Weber number models satisfactorily. The reasons for such agreement are carefully examined.

Numerical estimate of the stability curve for the flow past a rotating cylinder

It is demonstrated that the primary instability of the wake of a two-dimensional circular cylinder rotating with constant angular velocity can be qualitatively well described by the Landau equation. The coefficients of the Landau equation are determined by means of numerical simulations for the Navier-Stokes equations. The critical Reynolds numbers, which depend on the angular velocity of the cylinder, are evaluated correctly by linear regression. (C) 2004 American Institute of Physics.

国内非牛顿流体力学进展

非牛顿流体;;本构方程;;流变测量;;流动稳定性;;收缩流动;;聚合物加工;;石油工业;;生物流体力学

Periodic vortex breakdown in wide spherical gaps

The flow field with vortex breakdown in wide spherical gaps was studied numerically by a finite difference method under the axisymmetric condition. The result shows that the flow bifurcates to periodic motion as the Reynolds number or the eccentricity of the spheres increases. (C) 1997 American Institute of Physics.

Hopf bifurcation in wakes behind a rotating and translating circular cylinder

A low-dimensional Galerkin method, initiated by Noack and Eckelmann [Physica D 56, 151 (1992)], for the prediction of the flow field around a stationary two-dimensional circular cylinder in a uniform stream at low Reynolds number is generalized to the case of a rotating and translating cylinder. The Hopf bifurcation describing the transition from steady to time-periodic solution is investigated. A curve indicating the transitional boundary is given in the two-dimensional parameter plane of Reynolds number Re and rotating parameter alpha. Our results show that rotation may delay the onset of vortex street and decrease the vortex-shedding frequency. (C) 1996 American Institute of Physics.

Numerical simulation of axisymmetric unsteady incompressible flow by a vorticity-velocity method

A new numerical method for solving the axisymmetric unsteady incompressible Navier-Stokes equations using vorticity-velocity variables and a staggered grid is presented. The solution is advanced in time with an explicit two-stage Runge-Kutta method. At each stage a vector Poisson equation for velocity is solved. Some important aspects of staggering of the variable location, divergence-free correction to the velocity held by means of a suitably chosen scalar potential and numerical treatment of the vorticity boundary condition are examined. The axisymmetric spherical Couette flow between two concentric differentially rotating spheres is computed as an initial value problem. Comparison of the computational results using a staggered grid with those using a non-staggered grid shows that the staggered grid is superior to the non-staggered grid. The computed scenario of the transition from zero-vortex to two-vortex flow at moderate Reynolds number agrees with that simulated using a pseudospectral method, thus validating the temporal accuracy of our method.

Study of the shock motion in a hypersonic shock system turbulent boundary-layer interaction

Wall pressure fluctuations and surface heat transfer signals have been measured in the hypersonic turbulent boundary layer over a number of compression-corner models. The distributions of the separation shock oscillation frequencies and periods have been calculated using a conditional sampling algorithm. In all cases the oscillation frequency distributions are of broad band, but the most probable frequencies are low. The VITA method is used for deducing large scale disturbances at the wall in the incoming boundary layer and the separated flow region. The results at present showed the existence of coherent structures in the two regions. The zero-cross frequencies of the large scale structures in the two regions are of the same order as that of the separation shock oscillation. The average amplitude of the large scale structures in the separated region is much higher than that in the incoming boundary layer. The length scale of the separation shock motion region is found to increase with the disturbance strength. The results show that the shock oscillation is of inherent nature in the shock wave/turbulent boundary layer interaction with separation. The shock oscillation is considered to be the consequence of the coherent structures in the separated region.

Numerical investigation of dynamic stall of an oscillating aerofoil

The flow structure around an NACA 0012 aerofoil oscillating in pitch around the quarter-chord is numerically investigated by solving the two-dimensional compressible N-S equations using a special matrix-splitting scheme. This scheme is of second-order accuracy in time and space and is computationally more efficient than the conventional flux-splitting scheme. A 'rigid' C-grid with 149 x 51 points is used for the computation of unsteady flow. The freestream Mach number varies from 0.2 to 0.6 and the Reynolds number from 5000 to 20,000. The reduced frequency equals 0.25-0.5. The basic flow structure of dynamic stall is described and the Reynolds number effect on dynamic stall is briefly discussed. The influence of the compressibility on dynamic stall is analysed in detail. Numerical results show that there is a significant influence of the compressibility on the formation and convection of the dynamic stall vortex. There is a certain influence of the Reynolds number on the flow structure. The average convection velocity of the dynamic stall vortex is approximately 0.348 times the freestream velocity.

Computation of turbulent-flow in a square duct - aspects of the secondary flow and its origin

A numerical study of turbulent flow in a straight duct of square cross-section is made. An order-of-magnitude analysis of the 3-D, time-averaged Navier-Stokes equations resulted in a parabolic form of the Navier-Stokes equations. The governing equations, expressed in terms of a new vector-potential formulation, are expanded as a multi-deck structure with each deck characterized by its dominant physical forces. The resulting equations are solved using a finite-element approach with a bicubic element representation on each cross-sectional plane. The numerical integration along the streamwise direction is carried out with finite-difference approximations until a fully-developed state is reached. The computed results agree well with other numerical studies and compare very favorably with the available experimental data. One important outcome of the current investigation is the interpretation analytically that the driving force of the secondary flow in a square duct comes mainly from the second-order terms of the difference in the gradients of the normal and transverse Reynolds stresses in the axial vorticity equation.

Magnetohydrodynamics equilibrium of a self-confined elliptic plasma ball

A variational principle is applied to the problem of magnetohydrodynamics (MHD) equilibrium of a self-contained elliptical plasma ball, such as elliptical ball lightning. The principle is appropriate for an approximate solution of partial differential equations with arbitrary boundary shape. The method reduces the partial differential equation to a series of ordinary differential equations and is especially valuable for treating boundaries with nonlinear deformations. The calculations conclude that the pressure distribution and the poloidal current are more uniform in an oblate self-confined plasma ball than that of an elongated plasma ball. The ellipticity of the plasma ball is obviously restricted by its internal pressure, magnetic field, and ambient pressure. Qualitative evidence is presented for the absence of sighting of elongated ball lightning.

Influence of suspended particles and particle cover over the density interface

The effect of the particle cover over the density interface between two layers of fluids and of the suspended solid particles in the upper turbulcnt layer on the turbulent entrainment has been studied experimentally. The entrainment distance D is a function of the time of power: D=kt, where =0.200-0.130p. For suspended particles in the upper layer and pure 2-layer fluid is equal to 0.200, but the value of k for the suspended particles is smaller than that for the pure 2-layer fluid. The non-dimensional entrainment velocity is E=KRiln, where n=1.50+0.93 p. It is shown that the particle cover over the interface changes the power of Ril in the entrainment and hinders the turbulent entrainment. The variation rule of E for the suspended particles is the same as that for the pure 2-layer fluid, but the K value of the former is smaller than that of the latter. The turbulent mixing mechanism has been discussed.

Standing wave of finite-amplitude in an circular basin with uneven bottom

The effect of the particle cover over the density interface between two layers of fluids and of the suspended solid particles in the upper turbulcnt layer on the turbulent entrainment has been studied experimentally. The entrainment distance D is a function of the time of power: D=kt, where =0.200-0.130p. For suspended particles in the upper layer and pure 2-layer fluid is equal to 0.200, but the value of k for the suspended particles is smaller than that for the pure 2-layer fluid. The non-dimensional entrainment velocity is E=KRiln, where n=1.50+0.93 p. It is shown that the particle cover over the interface changes the power of Ril in the entrainment and hinders the turbulent entrainment. The variation rule of E for the suspended particles is the same as that for the pure 2-layer fluid, but the K value of the former is smaller than that of the latter. The turbulent mixing mechanism has been discussed.

Simultaneous measurement of temperature, density and velocity in gas-flows by modulated photoluminescence

A novel possibility to determine the temperature, density and velocity simultaneously in gas flows by measuring the average value, amplitude of modulation and phase shift of the photoluminescence excited by a temporally or spatially modulated light source is investigated. Time-dependent equations taking the flow, diffusion, excitation and decay into account are solved analytically. Different experimental arrangements are proposed. Measurements of velocity with two components, and temporal and spatial resolutions in the measurements are investigated. Numerical examples are given for N z with biacetyl as the seed gas. Practical considerations for the measurements and the relation between this method and some existing methods of lifetime measurement are discussed.