Slow motions of a solid spherical particle close to a viscous interface

In order to investigate the hydrodynamic interaction between an interface and a spherical particle and its dependence on the type of interface, it is essential to compute the drag and torque exerted on the sphere in the vicinity of the interface. In this paper, the problem of all slow elementary motions (relative translation and rotation) and stationary movement of a spherical particle next to a solid, viscous or free interface is considered. For low capillary numbers and different values of surface dilatational and shear viscosities in a curvilinear co-ordinate system of revolution with bicylindrical co-ordinates in meridian planes, the problem reduces from three to two dimensions. The model equations and boundary conditions, which contain second-order derivatives of the velocities, transform to an equivalent well-defined system of second-order partial differential equations which is solved numerically for medium and small values of the dimensionless distance to the interface. Very good agreement with the asymptotic equation for a translating sphere close to a solid interface could be achieved. The numerical results reveal in all cases the strong influence of the surface viscosity on the motion of the solid sphere. For small distances from the interface, the drag and torque coefficients change significantly depending on the surface viscosity.     

Subsonic electrically quasi-neutralweakly-ionized gas flow past a spherical probe

The electric characteristics of a sphere located in a flow of viscous, electrically quasi-neutral weakly-ionized gas containing electrons and monovalent ions are investigated theoretically and numerically. As in the majority of applications, the electrogasdynamic (EGD) interaction parameter is assumed to be small. This makes it possible to solve the gasdynamic and electric equations successively. The spherical surface is assumed to be conducting and heat-insulated. At low free-stream Mach numbers the gas temperature is almost constant in the region of flow past the sphere. This makes it possible to use the model of a viscous incompressible medium. The flow past a sphere is analyzed for gasdynamic Reynolds numbers varying over the interval 0 ≤ Re ≤ 1000. The electrodynamic equations in which the convection and diffusion of the electrons and ions and their electrical drift are taken into account are reduced to three elliptic equations for the electron and ion concentrations and the electric potential. A constant potential is assigned on the boundary of the computation region simulating infinity. The entire problem is simulated numerically using specially constructed grids. The charged-component, potential, and electric current fields are determined and the volt-ampere characteristics of the sphere are constructed for various gas velocities. The results obtained generalize the available data on the voltampere characteristics of a sphere (probe) in a weakly-ionized medium at rest.     

On Thermal Contact of Two Axially Symmetric Elastic Solids

A contact problem of two elastic convex and axially symmetric solids heated (or cooled) to temperatures of different values is considered. Pertinent formulae have been derived for relations between the contact pressure, geometrical characteristics of the solids and distributions of heat flux over the contacting region. We have analysed: 1. The problem of the loss of the contact between two solids pressed together with active heat fluxes. We discuss the cases for which the contact of the axially symmetric solids can take the form of a circle, or an annulus. 2. The problem of a paradox when the mathematically well posed contact problem of thermoelasticity leads to a physically unacceptable solution with a region of overlapping materials. Here we discuss a generalization of the cooled sphere paradox. The heat flux functions are continuously differentiable, of constant sign. The conditions have been derived for the cases when the paradox can be avoided.     

Slow flow of gas past a strongly heated sphere in the presence of blowing and evaporation from its surface

A solution is obtained to the problem of the simultaneous influence of blowing (evaporation) and large temperature differences on the flow past a sphere and on the force acting on it with allowance for the Burnett thermal stresses in the momentum equation. It is assumed that the Reynolds numbers calculated using the blowing velocity and the velocity of the oncoming flow, respectively, have the order Re_w 1 and Re 1. The temperature difference is determined by the boundary conditions, namely, a constant temperature T_w T on the surface of the sphere (VT/T 1). The problem is solved by the method of matched asymptotic expansions with respect to the small parameter Re. The equations reduce to a system of ordinary differential equations, which are solved numerically by the orthogonal sweep method [1]. It is found that under certain conditions the drag of the sphere can become negative.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 128–134, July–August, 1982.I thank O. G. Fridlender for valuable advice and interest in the work.     

Jet methods of gas injection into fluid boundary layer for drag reduction

Two jet methods for saturating the fluid boundary layer with microbubbles for drag reduction in contrust with gas injection through porous materials are considered. The first method is the gas injection through the slot under a special fluid wall jet. The second method is the saturation of boundary layer by microbubbles via the gas-water mixture injection through the slot. Experimental data, reflecting the skin friction drag reduction on the flat plate and total drag reduction of axisymmetric bodies, are presented. The comparison between a jet methods of gas injection and gas injection through porous materials is made.Nomenclature v free-stream velocity - v _j mean velocity of a water through slot - v _g mean velocity of a gas through slot - h width of slot for realizing water jet - h ₁ width of slot for gas injection - incidence angle - Q volume airflow rate - C _Q airflow rate coefficient (v _g/v ) - C _f skin friction coefficient - v _j/v - C _f0 C _f ifQ=0 andv _j=0 - _f C _f/C _{f 0} - d diameter of an axisymmetric body - L length of body - C _Q 4 · ·Q/d ² v - C _D 4 ·D/1/2v ² ·d ² - C _Q 4 ·Q/d ² v - Q _j volume flow rate of water jet - C 8 ·Q _jv_j/d ² v ² - 1 fluid density of main flow - 2 fluid density of wall jet - B ₁ main stream total pressure - B ₂ wall jet total pressure - v ₁ main stream velocity - Be (B ₂ –B ₁)/1/2₁ v ₁ ² = Bernoulli number - ₂ v ₂/₁ v ₁ - p _st static pressure - p _at atmospheric pressure - p _st/p _at - D hydrodynamic drag of body     

Numerical Analysis of the Influence of Thermal Stresses on the Nonlinear Thermomolecular Pressure Difference Effect

On the basis of a numerical analysis of the non-Navier-Stokes gas-dynamic equations for slow non-isothermal gas flows, the nonlinear thermomolecular pressure difference effect due to a large temperature gradient along the lateral surface of a capillary is investigated. It is shown that the magnitude of the effect is substantially different from the values calculated using the Navier-Stokes equations. For two models of molecular interaction (Maxwell molecules and hard spheres), the possibility of a quasi-one-dimensional interpretation of the effect for experimental estimation purposes is demonstrated. The solutions of the relaxation kinetic equation for flow in a plane capillary at small Knudsen numbers and the gas-dynamic equations for slow non-isothermal flows are compared and the range of their applicability is estimated.     

The influence of the drag force due to the interstitial gas on granular flows down a chute

Fully-developed steady flow of granular material down an inclined chute has been a subject of much research interest, but the effect of the interstitial gas has usually been ignored. In this paper, new expressions for the drag force and energy dissipation caused by the interstitial gas (ignoring the turbulent fluctuations of the gas phase) are derived and used to modify the governing equations derived from the kinetic theory approach for granular–gas mixture flows, where particles are relatively massive so that velocity fluctuations are caused by collisions rather than the gas flow. This new model is applied to fully-developed, steady mixture flows down an inclined chute and the results are compared with other simulations. Our results show that the effect of the interstitial gas plays a significant role in modifying the characteristics of fully developed flow. Although the effect of the interstitial gas is less pronounced for large particles than small ones, the flowfields with large particles are still very different from granular flows which do not incorporate any interactions with the interstitial gas.     

Partially invariant solutions for a submodel of radial motions of a gas

All partially invariant solutions in terms of the group of extensions for a model of radial motions of an ideal gas are found. The solutions are obtained by the method of separation of variables in an equation containing functions of one variable but different functions of different independent variables. The solutions predict different continuous unsteady convergence or expansion of the gas under the action of a piston with a point sink or source. If the sink or source affects all particles simultaneously, a collapse or an explosion occurs. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 26–34, September–October, 2007.     

Influence of curvature on drag reduction by opposition control in turbulent flow along a thin cylinder

Opposition controlled fully developed turbulent flow along a thin cylinder is analyzed by means of direct numerical simulations. The influence of cylinder curvature on the skin-friction drag reduction effect by the classical opposition control (i.e., the radial velocity control) is investigated. The curvature of the cylinder affects the uncontrolled flow statistics; for instance, skin-friction coefficient increases while Reynolds shear stress (RSS) and turbulent intensity decrease. However, the control effect in the case of a small curvature is similar to that in channel flow. When the curvature is large, the maximum drag reduction rate decreased. However, the optimal location of the detection plane is the same as that in a flat plate. Further, the drag reduction effect is achieved even on a high detection plane where the drag increases in the flat plate. Although a difference in the drag reduction effect can be observed with a change in the curvature, its mechanism considered in this analysis based on the transport of the Reynolds stress is similar to that of the flat plate.     

Formation of a gas hydrate due to injection of a cold gas into a porous reservoir partly saturated by water

Specific features of formation of gas hydrates due to injection of a gas into a porous medium initially filled by a gas and water are considered. Self-similar solutions of an axisymmetric problem, which describe the distributions of the basic parameters in the reservoir, are constructed. The existence of solutions is demonstrated, which predict gas hydrate formation both on the frontal surface and in the volume zone. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 137–150, May–June, 2008.     

Rolling/sliding of a particle on a flat wall in a linear shear flow at finite Re

Recently Lee and Balachandar proposed analytically-based expressions for drag and lift coefficients for a spherical particle moving on a flat wall in a linear shear flow at finite Reynolds number. In order to evaluate the accuracy of these expressions, we have conducted direct numerical simulations of a rolling particle for shear Reynolds number up to 100. We assume that the particle rolls on a horizontal flat wall with a small gap separating the particle from the wall (L = 0.505) and thus avoiding the logarithmic singularity. The influence of the shear Reynolds number and the translational velocity of the particle on the hydrodynamic forces of the particle was investigated under both transient and the final drag-free and torque-free steady state. It is observed that the quasi-steady drag and lift expressions of Lee and Balachandar provide good approximation for the terminal state of the particle motion ranging from perfect sliding to perfect rolling. With regards to transient particle motion in a wall-bounded shear flow it is observed that the above validated quasi-steady drag and lift forces must be supplemented with appropriate wall-corrected added-mass and history forces in order to accurately predict the time-dependent approach to the terminal steady state. Quantitative comparison with the actual particle motion computed in the numerical simulations shows that the theoretical models quite effective in predicting rolling/sliding motion of a particle in a wall-bounded shear flow at moderate Re.     

Horizontal boundary-layer natural convection in a porous medium saturated with a gas

Boundary-layer analysis is performed for free convection flow over a hot horizontal surface embedded in a porous medium saturated with a gas of variable properties. The variable gas properties are accounted for via the assumption that thermal conductivity and dynamic viscosity are proportional to temperature. A similarity solution is shown to exist for the case of constant surface temperature. Numerical results for the stream function, horizontal velocity, and temperature profiles within the boundary layer as well as for the mass of entrained gas, surface slip velocity, and heat transfer rate at different values of the wall-temperature parameter are presented. Asymptotic solutions for large heating are also available to support the numerical work.     

Equations of the shallow water model on a rotating attracting sphere. 1. Derivation and general properties

A shallow water model on a rotating attracting sphere is proposed to describe large-scale motions of the gas in planetary atmospheres and of the liquid in the world ocean. The equations of the model coincide with the equations of gas-dynamic of a polytropic gas in the case of spherical gas motions on the surface of a rotating sphere. The range of applicability of the model is discussed, and the conservation of potential vorticity along the trajectories is proved. The equations of stationary shallow water motions are presented in the form of Bernoulli and potential vorticity integrals, which relate the liquid depth to the stream function. The simplest stationary solutions that describe the equilibrium state differing from the spherically symmetric state and the zonal flows along the parallels are found. It is demonstrated that the stationary equations of the model admit the infinitely dimensional Lie group of equivalence. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 24–36, March–April, 2009.     

Similarity in stationary motions of gas and two-phase medium with incompressible component

In this paper we suggest the transformation between the equations for a perfect gas and the equations describing in one-velocity approach the two-phase medium with any volume occupied by the incompressible phase. It is proved that the motion of a two-phase medium in the transformed coordinate system is similar with certain accuracy to that of a perfect gas. It means that the solutions obtained for perfect gas can be used to solve wave problems for media with incompressible component. There is no necessity directly to solve the problem for medium with incompressible component, and it is only sufficient to transform the known solution of the similar problem for a homogeneous medium. Thus, the solutions of many hydrodynamic problems for multi-component media with incompressible phase can be obtained without solving the original set of equations. The scope for the suggested transformation is demonstrated by reference to the strong explosion in a two-phase medium.     

Nonlocal-in-time kinetic energy in nonconservative fractional systems,disordered dynamics,jerk and snap and oscillatory motions in the rotating fluid tube

In this article we generalize the basic theoretical properties of nonlocal-in-time kinetic energy approach introduced in the framework of nonlocal classical Newtonian mechanics for the case of fractional dynamical systems explored in the context of the fractional actionlike variational approach. Two independent fractionally Lagrangians weights are considered independently: the Riemann-Liouville fractional weight and the extended exponentially fractional weight. For each weight, the corresponding nonlocal fractional Newton's law of motion is derived. Three main physical applications were discussed in details: free particles, oscillators and dynamics of particles in a rotating tube with earth frame. A number of differential equations depending on fractional and nonlocal-in-time parameters were obtained and their solutions are discussed accordingly. For specific parameters and particular initial conditions, it was observed that the dynamics exhibit a kind of strange phase plot trajectories that indicate the presence of disordered motions. However one of the main results concerns the physics of particles in the rotating tube which display, for specific values of fractional and nonlocal-in-time parameters, oscillatory motions controlled by the nonlocal-in-time parameter.     

Numerical investigation of the decomposition of gas hydrates coexisting with gas in natural reservoirs

The problem of methane hydrate decomposition in a reservoir saturated with a gas and hydrate mixture is investigated numerically. The results of the numerical simulation and an analytic solution obtained in the linear approximation are compared. It is shown that for high-permeability rocks the convective heat transfer in the near-well space of the reservoir predominates over the conductive transfer. This makes the use of intra-well heaters ineffective. It is found that an increase in the reservoir and well pressures and a decrease in the permeability suppress the formation of an extended hydrate dissociation region. Critical diagrams of existence of the frontal decomposition regime are constructed.     

大瓣片高强钢球壳板冲压成形应力测试与分析

为对大瓣片高强钢球罐壳板成形过程进行应力测试与分析,在分析壳板成形工艺特点和力学特征的基础上,提出了在板材上附加随动测试架的测试方法,该测试架可随板材运动,实现对传感元件的保护,保证测试信号的输出,同时不干扰壳板的工艺条件,实现了准确测定冲压加工过程中特定状态下板壳内的应力分布及变化规律的目的。测试表明,压力加工过程中,当模具完全冲压到位时,在模具中心区域出现最大拉伸应变,应力值也最大,而卸载后该区反而出现了很小的压应力,这对容器的安全是有利的。因此在压制过程中只要控制冲压变形量,使得中间部位应力值小于材料的强度极限,就可保证板材不发生工艺性破裂,而且成形完成后该区也无不利的力学因素。     

Numerical modeling of a turbulent flow behind a heated grid

A numerical model of the dynamics of turbulence and temperature fluctuations behind a heated grid located in a wind tunnel is constructed on the basis of closed Kármán-Howarth and Corrsin equations. Results calculated by this model are in reasonable agreement with available experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 118–126, May–June, 2009.     

Effects of atmospheric pressure and air concentration in the fluid on the motion of a rigid sphere along a wall (experiment)

The effects of the dissolved air concentration and atmospheric pressure on the motion of a rigid sphere along a wall in a fluid are studied experimentally. These effects are the result of the occurrence of a gas bubble in the lubrication layer between the moving sphere’s and the wall. It is found that, depending on the air concentration in the fluid and the atmospheric pressure, during the sphere motion the bubble volume may either increase or remain constant. From the observations, it is clear that the variation of the bubble volume is associated with the unsteady motion of the sphere.     

VIV suppression of a two-degree-of-freedom circular cylinder and drag reduction of a fixed circular cylinder by the use of helical grooves

Experimental investigations have been carried out to examine the effects of triple-starting helical grooves on the drag of fixed circular cylinders and the vortex-induced vibration of elastically supported cylinders. For the elastically supported cylinder, the Reynolds number varied from 1.3×10⁴ to 4.6×10⁴, whilst for the fixed cylinder from 3.1×10⁴ to 3.75×10⁵. A comparative approach which allows direct comparisons of the results was adopted where two cylinders of identical dimensions and physical properties with or without helical surface grooves were tested in exactly same experimental set-ups. In the elastically supported cylinder tests, the cylinders were attached to a vertically cantilevered supporting rod and towed in a towing tank. Both the in-line and cross-flow vibrations were permitted. In the fixed cylinder tests, the cylinders were supported on rigid vertical struts and towed horizontally in the same towing tank. It is found that for the case investigated the helical grooves were effective in suppressing the vortex-induced cross-flow vibration amplitudes with the peak amplitude reduced by 64%. Drag reductions of up to 25% were also achieved in the sub-critical Reynolds number range tested in the study for the fixed cylinders.