Oscillatory and simple shear flows of a flour-water dough: a constitutive model

We reported some dynamic and viscometric data on an Australia strong flour-water dough. In oscillatory shear flow experiments, we found the linear viscoelastic strain limit is extremely low, of O(10^–3), consistent with other published data on doughs. The relaxation spectrum derived from the dynamic data is broad, indicating the blend nature of dough. In the start-up of a simple shear flow, we found the shear stress increases nonlinearly with time to a peak value and then decreases rapidly, with no steady-state response. The concept of steady-state viscosity is not very meaningful here, unless the strain at which the measurements are taken is also specified. The stress peaks are strain-rate dependent; but they occur at a strain of O(10), for the strong flour/water dough used, over four decades of strain rates. The experimental data were used to construct a phenomenological model for dough, consisting of an hyperelastic term (representing the elastic gluten network of permanent cross-linked long chain polymers), and a viscoelastic contribution (representing the suspension of starch globules and other long-chain components in dough that are not parts of the permanent cross-linked gluten network). The model predictions compared favourably with experimental data in oscillatory and shear flows.     

Design of a two-element airfoil in a range of angles of attack

A numerical-analytical solution of an inverse boundary-value problem of aerohydrodynamics is obtained for a two-element airfoil in the full formulation, based on the velocity distribution defined on the sought airfoil contours in a range of angles of attack. It is demonstrated that flow separation does not occur in the entire range considered for a specified non-separated velocity distribution on the upper surfaces at the maximum angle of attack and on the lower surface at the minimum angle of attack. An example of constructing a sectional airfoil is given; verification of the results obtained is performed with the use of the Fluent software package. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 107–114, November–December, 2008.     

Quasi-Euler-Poinsot motion of a rigid body

The phase-plane method of nonlinear oscillation is used to discuss the influence of the small dissipation upon the Euler-Poinsot motion of a rigid body about a fixed point. The equations of phase coordinates are applied instead of Eulerian equations, and the global characteristics of the motion of rigid body are analysed according to the distribution and the type of the singular points. A Chaplygin's sphere on a rough plane, a rigid body in viscous medium and one with a cavity filled with viscous fluid are discussed as examples. It is shown that the motions of rigid bodies dissipated by various physical factors have a common qualitative character. The rigid body tends to make a permanent rotation about the principal axis of the largest moment of inertia. The transitive process can change from oscillatory to aperiodic with the decrease in dissipation.     

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.     

Mathematical modeling of the motion of a portion of helium under pulsed injection over a fixed bed of cenospheres

A mathematical model is constructed and an analytical solution is obtained for the problem of a one-dimensional steady flow of a mixture of different gases with hollow permeable particles. The case of a one-dimensional unsteady flow of such a mixture is analyzed numerically. The numerical solutions are compared with experimental data on the motion of the peak concentration of helium in a fixed bed filled with cenospheres (solid hollow permeable spherical particles). The permeability of cenosphere walls and the drag coeficient of cenospheres in the gas flow are determined. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 92–102, May–June, 2007.     

The inlet effect on the drag factor of a sphere in a tube

The creeping motion Ground a sphere situated axisymmetrically near the entrance of asemi-infinite circular cylindrical tube is analyzed using infinite series solutions for thevelocity components. pressure and the stream function. Truncating the infinite series. thecorresponding coefficients in the series are determined by a collocation technique. The dragfactor and the stress distribution on the surface of the sphere are calculated for the sphere inmotion in quiescent fluid and for the flow with uniform velocity at the entrance past a rigidlyheld sphere. The results indicate that a sphere near the entrance which has a uniformentrance velocity profile will suffer larger drag than that in infinite tube.Theconvergence of the collocation technique is tested by numerical calculation. It is shown thatthe technique has good convergence properties.     

Interaction of a weak discontinuity wave with a characteristic shock in a dusty gas

In this paper, the evolution of a characteristic shock in a dusty gas is investigated and its interaction with a weak discontinuity wave is studied. The transport equation for the amplitude of the weak discontinuity wave, which is of Bernoulli type, is obtained. The amplitudes of the reflected and transmitted waves after interaction of the weak discontinuity with the characteristic shock are evaluated by using the results of the general theory of wave interaction.      

The stability of a top rotating on a rough horizontal plane

In the present paper the stability of permanent rotation of a symmetric top rotating on a slightly rough horizontal plane about the erect polar or transverse axis is discussed via the perturbation method. As a perturbation factor, the frictional force is an arbitrary nonlinear function of the sliding velocity. The same stability criterion as that in the Contensou-Magnus linear theory is obtained, but the hypothesis of the linearity for friction can be omitted. It shows that the direction of the sliding velocity at the contact point is an important factor, which influences the stability of the top. And then an explicit physical explanation is given.     

Steady-state conditions of a nonisothermal film with a heat-insulated free boundary

The equilibrium shapes of a nonisothermal liquid film with a heat-insulated free surface for large Marangoni numbers are investigated in the long-wave approximation using a combination of analytical and numerical methods. It is proved that the two-dimensional problem of the equilibrium of a strip-shaped film has a steady-state solution for an arbitrary large temperature gradient on the boundaries of the strip. An increase in this gradient leads to an abrupt thinning of the film near the heated boundary, which can result in instability and rupture of the film. In the equilibrium problem for a film fixed on a circular contour, the nonuniform distribution of the heat flux on the contour was found to have a significant influence on the free-surface shape. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 59–73, July–August, 2008.     

Dynamic buckling of a beam with transverse constraints

A nonlinear dynamic system with continuously distributed mass is studied using several approaches: experimentally, numerically as well as analytically. The nonlinearity of the system consists of geometrical constraints imposed on the motion. It is harmonically loaded and it is demonstrated that for certain choices of the loading parameters, periodic, quasi-periodic or chaotic behaviour may occur depending on the initial conditions. An important issue is to investigate the number of degrees of freedom needed in order to analytically model the system accurately enough that the important characteristics of the motion are retained in the solution. It is found that the impact conditions at the constraints are of crucial importance and a new approach is proposed for modelling of the impacts. The method is based on the fact that the free motion can be approximated with quite a few degrees of freedom, while at impact all the infinite number of degrees of freedom are considered.     

NEWTON'S THEOREM WITH RESPECT TO A LOT OFCENTERS AND THEIR APPLICATIONS

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Reduced model of a rotor-shaft system using modified SEREP

A modified System Equivalent Reduction Expansion Process (SEREP) is reported to reduce large linear system-equations of motion, which also include gyroscopic effect, internal and external damping. The process is employed on equations of motion written in state-space and utilizes both right and left eigenvectors of the original system unlike only the former in conventional SEREP approach. Numerical example with a finite element model representing multi-disc rotor-shaft-bearing-dynamics shows effectiveness of the process. Nice agreement of Campbell diagrams, FRF plots and unbalance response amplitude between reduced and original systems show usefulness of the reduction process.     

Viscosity of a Suspension with a Cubic Array of Spheres in a Shear Flow

Viscous fluid flow past an infinite periodic array of rigid spheres of the same radius is considered. A solution of the Stokes equations periodic in three variables is obtained for viscous incompressible flow with a linear velocity profile. The solution takes into account the hydrodynamic interaction of an infinite number of particles in the array. An expression for the effective viscosity of a suspension with a cubic array of particles is obtained.     

Planar oscillations of a dumb-bell of a variable length in a central field of Newtonian attraction. Exact approach

Dynamics of a dumb-bell of a variable length in a central field of Newtonian attraction is considered. It is assumed that the body moves in a plane fixed in the absolute space and passing through an attracting center. The law of length׳s variation providing an existence of stationary configurations is pointed out. For these configurations the dumb-bell forms a constant angle with a local vertical passing through the center of mass of the dumb-bell, which moves in an elliptic orbit similar to the Keplerian. In particular, the mentioned constant angle may be equal to zero. In contrast to previous investigations (Burov and Kosenko, 2011 [8], [10], Burov, 2011 [9]) the problem is solved within the exact formulation, without supplementary simplifying assumptions concerning smallness of the dumb-bell in comparison to its distance from the attracting center.     

Interaction of evaporation fronts with a formation interface in a porous medium

The evolutionarity and structure of water-vapor phase discontinuities formed in a geothermal reservoir on the interface between permeable formations with different properties are considered. In the short-wave approximation a graphic method is proposed for solving the problem of breakdown of an arbitrary discontinuity in a geothermal reservoir consisting of two formations with different properties.     

Conservation of mass for a particle moving with high velocity

I.IntroductionItiswell-knownthatthe"lassofaparticleoranoh.jectisstrictlytoobservethelawofcollservatiollof1llasswbedmovewitlllowvelocity.Butathighvelocity,particularlynearthevelocityoflight,themass(restmass)oftheparticle,accordingtothetheoryofspecialrelativity,increasesrapidlywithitsincrementofthevelocity.Inotherwords,themassisnotinconservatioll\vitllitsvelocity.However.withtheoriesandresearchmethodsbringingforthflewideasandcomplement,andthehumanthoughtdevelopingconstantlywhatthemassisnotconse…     

Development of a heavy demining machine

Heavy demining machines are intended for humanitarian demining of larger mine-suspected areas. Two combinations of tools were considered herein: a working tool with two-flails, and a design with one flail and one tiller, and analyze the function of these variants. Some time ago, it was unimaginable to combine a flail and tiller, mostly because power demands were too high. Nonetheless, by suitably allocating the power to the working tools a realistic option was designed, which should be feasible even for smaller sized machines. In order to destroy AP and AT mines, the primary role is given to a flail of high diameter, and a backup function to the tiller whose diameter is two times lower. The depth and rpm of the tiller may be controlled independently of the flail, which ensures that digging depth is good enough. With two independent and different tools the density of hammer strikes is immediately adaptable to the conditions of mine density at different depths. The required force of the hammer impulse is determined in order to be able to overcome the resistance from digging the soil resistance. Furthermore, the independence of tool adaptation together with remote control improves the speed of mine clearing. A high reliability of mine destruction is thereby ensured. The results of machine testing show high graded performance regarding mine-clearance quality.     

Stability of a spinning liquid-filled spacecraft

Summary The stability of a spinning liquid-filled spacecraft has been investigated in the present paper. Using Galerkin's method, the attitude dynamic equations have been given. The Liapunov direct method was employed to obtain a sufficient condition for stability. Three kinds of characteristic modals were investigated: free motion of inviscid fluid, slosh motion and non-slosh motion. All characteristic problems can be solved numerically by the Finite Element Method or the Boundary Element Method. It has been demonstrated that the viscosity of the fluid has a dissipative effect at large Reynolds number, while the slosh motion plays a destabilizing role. The non-slosh model of fluid does not affect the stability criterion. Accepted for publication 19 October 1996     

PLASTIC POST－BUCKLING OF A SIMPLY SUPPORTED COLUMN WITH A SOLID RECTANGULAR CROSS－SECTION

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Mixing dynamics of a vapor-condensate cloud with the ambient air

The mixing of a wet vapor with a gas is studied using analytical and numerical models. The one-dimensional problem of diffusion mixing accompanied by phase transitions is solved in a self-similar formulation. The versions of mixing of the vapor with a cold and warm gas and with a superheated vapor are analyzed. The atmospheric diffusion of immediate emissions containing water vapor and condensate is modeled numerically in a three-dimensional formulation. A study is made of the evolution of hydrodynamic, concentration, and temperature fields as a function of the initial emission parameters (temperature and humidity) and ambient air parameters. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 114–127, May–June, 2008.