Effect of wall friction on oscillation of velocity at the head of the gravity current

Velocity oscillations at the head of the gravity current were investigated in experiments and numerical simulations of a locked-exchange flow. A comparison of the experimental and numerical simulations showed that the depth and volume of the released fluid affected the oscillations in the velocity of the gravity current. At the initial stage, the head moved forward at a constant velocity, and velocity oscillations occurred. The head maximum thickness increased at the same time as the head, which did not have a round, and accumulated buoyant fluid due to the buoyancy effect intrusion force. The period of accumulation and release of the buoyant fluid was almost the same as that observed for the head movement velocity; the head movement velocity was faster when the buoyant fluid accumulated and slower when it was released. At the viscous stage, the forward velocity decreased proportionally to the power of 1/2 of time, since the head was not disturbed from behind. As the mass concentration at the head decreased, the gravity current was slowed by the viscous stage in its effect. At the viscous stage, the mass concentration at the head was no longer present, and the velocity oscillations also decreased.     

Theoretical derivation of tangential velocity profiles in a flat vortex chamber-influence of turbulence and wall friction

Summary As part of a study on the hydrodynamics of a cyclone separator, a theoretical investigation of the flow pattern in a flat box cyclone (vortex chamber) has been carried out. Expressions have been derived for the tangential velocity profile as influenced by internal friction (eddy viscosity) and wall friction. The most important parameter controlling the tangential velocity profile is = –u ₀ R/(v+ ), where u ₀ is the radial velocity at the outer radius R of the cyclone, the kinematic liquid viscosity and is the kinematic eddy viscosity. For values of greater than about 10 the tangential velocity profile is nearly hyperbolic, for smaller than 1 the tangential velocity even decreases towards the centre. It is shown how and also the wall friction coefficient may be obtained from experimental velocity profiles with the aid of suitable graphs. Because of the close relation between eddy viscosity and eddy diffusion, measurements of velocity profiles in flat box cyclones will also provide information on the eddy motion of particles in a cyclone, a motion reducing its separation efficiency.List of symbols A cross-sectional area of cyclone inlet - h height of cyclone - p static pressure in cyclone - p static pressure difference in cyclone between two points on different radius - r radius in cyclone - r ₁ radius of cyclone outlet - R radius of cyclone circumference - u radial velocity in cyclone - u ₀ radial velocity at circumference of flat box cyclone - v tangential velocity - v ₀ tangential velocity at circumference of flat box cyclone - w axial velocity - z axial co-ordinate in cyclone - friction coefficient in flat box cyclone (for definition see § 5) - ₁ value of friction coefficient for ₁<< ₂ - ₂ value of friction coefficient for ₂<<1 - = - ₁ value of for ₁<< ₂ - ₂ value of for ₂<<1 - thickness of laminar boundary layer - =/h - turbulent kinematic viscosity - ratio of z to h - k ratio of height of cyclone to radius R of cyclone - parameter describing velocity profile in cyclone =–u ₀ R/(+) - kinematic viscosity of fluid - density of fluid - ratio of r to R - ₁ value of at outlet of cyclone - ₂ value of at inner radius of cyclone inlet - _w shear stress at cyclone wall - angular momentum in cyclone/angular momentum in cyclone inlet - ₁ value of at = ₁ - ₂ value of at = ₂     

Effect of air core on the shape and discharge of the outflow through a bottom outlet

Experiments were conducted to study the generation of air core and its effect on the outflow shape and discharge in a cylindrical water tank with a bottom well-designed outlet. Depending on the stages of the air core in the tank, the outflow shape can vary from a smooth water jet to a smooth spindle shape with air-core, and to water sprays. The diameter of the nozzle size also has influence on the outflow pattern. The existence of the penetrated air core can dramatically reduce the outflow discharge, with the discharge coefficient decreasing with the nozzle diameter.     

Reconstruction of velocity fields from wall pressure measurements in a shock wave/turbulent boundary layer interaction

We present here experimental results in a shock wave/turbulent boundary layer interaction at Mach number of 2.3 impinged by an oblique shock wave, with a deflection angle of 9.5°, as installed in the supersonic wind tunnel of the IUSTI laboratory, France. For such a shock intensity, strong unsteadiness are developing inside the separated zone involving very low frequencies associated with reflected shock motions.The present work consists in simultaneous PIV velocity fields and unsteady wall pressure measurements. The wall pressure and PIV measurements were used to characterize the pressure distribution at the wall in an axial direction, and the flow field associated. These results give access for the first time to the spatial-time correlation between wall pressure and velocity in a shock wave turbulent boundary layer interaction and show the feasibility of such coupling techniques in compressible flows. Linear Stochastic Estimation (LSE) coupled with Proper Orthogonal Decomposition (POD) has been applied to these measurements, and first results are presented here, showing the ability of these techniques to reproduce both the unsteady breathing of the recirculating bubble at low frequency and the Kelvin–Helmholtz instabilities developing at moderate frequency.     

Jet impingement onto a tapered hole: Influence of jet velocity and hole wall velocities on heat transfer and skin friction

Jet impingement onto a hole with elevated wall temperature can be associated with the high‐temperature thermal drilling, where the gas jet is used for shielding the hole wall from the high‐temperature oxidation reactions as observed in the case of laser drilling. In laser processing, the molten flow from the hole wall occurs; and in the model study, the hole wall velocity resembling the molten flow should be accounted for. In the present study, gas jet impingement onto tapered hole with elevated temperature is considered and the heat transfer rates as well as skin friction at the hole wall surface are predicted. The velocity of molten flow from the hole wall determined from the previous study is adopted in the simulations and the effect of hole wall velocity on the heat transfer rates and skin friction is also examined. It is found that the Nusselt number and skin friction at the hole wall in the regions of hole inlet and exit attain high values. The influence of hole wall velocity on the Nusselt number and skin friction is found not to be very significant. Copyright © 2008 John Wiley & Sons, Ltd.     

筒仓泄料过程中阻塞现象的数值模拟

基于颗粒材料离散颗粒模型及颗粒流方案,通过数值试验研究了筒仓泄料过程中影响颗粒流发生阻塞的若干因素,给出了阻塞概率随筒仓底部开口半径及倾角、颗粒间摩擦系数及颗粒粒径分布的关系曲线.基于颗粒簇的概念,进一步研究了颗粒形状的影响,并对颗粒材料阻塞时的力链分布特征进行简要分析.     

Dynamics of a homogeneous ball on a horizontal plane with sliding,spinning, and rolling friction taken into account

We analyze the dynamics of a homogeneous ball on a horizontal plane with friction of all kinds, namely, sliding, spinning, and rolling friction, taken into account. The qualitative-analytic study of the ball dynamics is supplemented with numerical experiments.     

A method of computing skin friction and adiabatic wall temperature in a laminar boundary-layer without pressure gradient

Meccanica - A method of computing the shear stress in a laminar boundary-layer without pressure gradient is described. The non linear term in the Von Mises' equation is replaced by a suitable...     

Solution of the problem of outflow of fluid from a half-space through a partially permeable wall

An exact solution is obtained to the problem of outflow of a perfect incompressible fluid from a half-space through an opening, occupied by a permeable plate. It is shown that the flow rate Q of the fluid in the case of outflow through a permeable plate can exceed the flow rate Q₀ of the fluid in the case of jet outflow through a free space.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 174–176, September–October, 1985.     

Effect of wall friction and vortex generation on the radial distribution of different phases

Arguments are presented to prove the existence of rolling vortices in single-phase and two-phase flow. In the liquid phase, they appear in a boundary layer near a wall while in the continuous vapor phase they occur near the interface with a liquid film. The intensity and size of these vortices depend on the local velocity gradients normal to the wall. The interaction between the rotational field associated with such vortices and bubbles in liquid flow or droplets in vapor flow is discussed. This interaction may be called the wall-vortex effect. It appears that several, apparently unrelated, phenomena observed in two-phase flow systems may be interpreted in terms of this mechanism. Among these are: (i) radial void peaking near the walls (ii) vapor velocities less than liquid velocity observed also in vertical upward flow (iii) reduced droplet diffusion near the liquid film and (iv) reduced vapor mixing between subchannels at low steam qualities. The cause of secondary flows in non-circular channels may also be explained in terms of rolling vortices near the walls. Finally, a comparison is made with the well known Magnus effect.     

Effect of pressure gradient of friction and heat transfer in a dusty boundary layer

Approximate analytic expressions for the local friction and heat transfer coefficients in a dusty laminar boundary layer are obtained and tested in the case of an incompressible carrier phase, power-law variation of the external gas flow velocity and small velocity and temperature phase disequilibrium. These expressions supplement the numerical analysis of the dusty boundary layer on a blunt body [1, 2] and the asymptotic calculation of the friction and heat transfer in a quasiequilibrium dusty gas boundary layer on a plate [3]. The combined effect of dustiness and pressure gradient on the friction and heat transfer coefficients is discussed. The results obtained can be used for the practical calculation of the friction and heat transfer in a quasiequilibrium dusty laminar boundary layer and for interpreting the corresponding experimental data. Tomsk. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 105–108, September–October, 1988.     

Resonant vibrations of a cylindrical wall of a discharge chamber,induced by an electrical discharge in water

The influence of resonant modes of interaction of the vapor-gas cavity and the discharge chamber wall on energy exchange between them is studied. Mathematical modeling of electrodynamic, hydrodynamic, and elastoplastic wave processes in the discharge chamber is performed in a coupled, geometrically and physically nonlinear formulation. The dependence of the amount of energy transferred from the capacitor to the liquid and solid through their contact boundary on dynamic system parameters is determined.     

Hydrodynamic pressure during reflection of a bore from a vertical wall

This paper presents the results of experiments in which a nonlinear wave was reflected from a vertical wall. It is shown that the hydrodynamic pressure of the wave depends significantly on the shape of its leading edge. It is found that the highest pressure is reached during reflection of a wave with a cumulative jet at the leading edge.     

Reynolds stress, mean velocity, and dynamic static pressure measurement by a four-hole pressure probe

An improved version of the four-hole directional pressure probe, or Cobra probe, is described, in which the frequency response has been extended to 1.5 kHz. The probe measures all three orthogonal mean and turbulent velocity components at a point in the flow field. The probe also resolves the local mean and turbulent components of static pressure, allowing moments between the fluctuating velocity components and pressure to be determined. The techniques developed to allow the improved frequency response and the use of the probe in turbulent, developed pipe flow (a calibration flow) are described. Also given are the turbulent pressure-velocity correlations, which show a high degree of anticorrelation for one velocity component.