The average stress tensor in systems with interacting particles

The derivation of an expression of the macroscopic stress tensor in terms of microscopic variables in systems of finite interacting particles is discussed from different points of view. It is shown that in volume averaging the introduction of a fictitious “interaction stress field”T ^I with special boundary conditions on the boundary of the averaging volume is needed. In ensemble averaging similar results are obtained by using a multipole expansion of the local stress and force fields. In the appropriate limiting cases, the obtained results are shown to be consistent with the results of kinetic theories of polymer solutions. Paper, presented at the First Conference of European Rheologists at Graz, April 14 – 16, 1982.     

Hydrodynamic diffusivity of spherical particles in polymer solution

In this research experiments were performed to examine the hydrodynamic diffusion of spherical particles in a highly filled suspension. The suspension consisted of nearly monodisperse polymethylmethacrylate spheres in a density matched polymer solution. The polymer solution was prepared by dissolving 0–700 ppm of polyacrylamide in a mixture of ethyleneglycol and glycerine. The polymer solution did not show appreciable shear thinning. The particle loading was varied from 30 to 55%. The hydrodynamic diffusivity was estimated by measuring the time-dependent viscosity when the suspension was subjected to a circular Couette flow with an air bubble trapped under the rotor of the Couette apparatus. The results show that the dimensionless diffusivity (D/γ˙a ²) of particles in polymer solution is not proportional to shear rate (γ˙), as in the case of a Newtonian fluid, but that it decreases with increasing shear rate. The diffusivity also decreases with increasing polymer concentration. It is suggested that the elongational thickening behaviour and the increased lubrication force due to the first normal stress difference may be responsible for the reduction of diffusivity in the polymer solution. Received: 18 January 2000 Accepted: 6 April 2000     

The propagation mechanism of high speed turbulent deflagrations

The propagation regimes of combustion waves in a 30 cm by 30 cm square cross–sectioned tube with an obstacle array of staggered vertical cylindrical rods (with BR=0.41 and BR=0.19) are investigated. Mixtures of hydrogen, ethylene, propane, and methane with air at ambient conditions over a range of equivalence ratios are used. In contrast to the previous results obtained in circular cross–sectioned tubes, it is found that only the quasi–detonation regime and the slow turbulent deflagration regimes are observed for ethylene–air and for propane–air. The transition from the quasi–detonation regime to the slow turbulent deflagration regime occurs at (where D is the tube “diameter” and is the detonation cell size). When , the quasi–detonation velocities that are observed are similar to those in unobstructed smooth tubes. For hydrogen–air mixtures, it is found that there is a gradual transition from the quasi–detonation regime to the high speed turbulent deflagration regime. The high speed turbulent deflagration regime is also observed for methane–air mixtures near stoichiometric composition. This regime was previously interpreted as the “choking” regime in circular tubes with orifice plate obstacles. Presently, it is proposed that the propagation mechanism of these high speed turbulent deflagrations is similar to that of Chapman–Jouguet detonations and quasi-detonations. As well, it is observed that there exists unstable flame propagation at the lean limit where . The local velocity fluctuates significantly about an averaged velocity for hydrogen–air, ethylene–air, and propane–air mixtures. Unstable flame propagation is also observed for the entire range of high speed turbulent deflagrations in methane–air mixtures. It is proposed that these fluctuations are due to quenching of the combustion front due to turbulent mixing. Quenched pockets of unburned reactants are swept downstream, and the subsequent explosion serves to overdrive the combustion front. The present study indicates that the dependence on the propagation mechanisms on obstacle geometry can be exploited to elucidate the different complex mechanisms of supersonic combustion waves. Received 5 November 2001 / Accepted 12 June 2002 / Published online 4 November 2002 Correspondence to: J. Chao (e-mail: jenny.chao@mail.mcgill.ca) An abridged version of this paper was presented at the 18th Int. Colloquium on the Dynamics of Explosions and Reactive Systems at Seattle, USA, from July 29 to August 3, 2001.     

Experimental study of HE-II boiling on a sphere

Regimes of superfluid-helium boiling on structural-steel spheres 4.8 and 6.0 mm in diameter, with heaters installed inside, are examined. Experimental data on the evolution of vapor films formed on the spherical surfaces are obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 78–84, November–December, 2006.     

Thermodynamic instability of disperse media isolated from external actions

The evolution of the structure of a medium containing disperse elements (the drops in a weakly viscous fluid, rigid spheres in glycerin, and air pores in a gel) is studied experimentally in the case where the gradient temperature and the concentration fields are absent in the system, and the medium is isolated from the influence of an external force field (including gravity forces). It is shown that these systems are nonequilibrium: if the initial distance between disperse particles is of the order of their sizes, the particles approach until they come in contact (coagulation) irrespective of the scale of the system. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 53–58, May–June, 1999.     

Influence of an acoustic wave on a system of two spheres in a viscous fluid

In this article we formulate and solve the problem of the influence of radiation forces (forces created by the radiation pressure) on two spheres in a viscous fluid during the transmission of an acoustic wave. On the basis of these forces we investigate the nature of the interaction between the spheres as determined by the mutual disturbance of the flow fields around them as a result of interference between the primary and secondary waves reflected from the spheres. A previously proposed [2] approach is used in the investigations. The radiation force acting on one of the spheres is filtered by averaging the convolution of the stress tensor in the fluid with the unit normal to the surface of the sphere over a time interval and over the surface of the sphere. The stresses in the fluid are represented, to within second-order quantities in the parameters of the wave field, in terms of the velocity potentials obtained from the solution of the linear problem of the diffraction of the primary wave by the free spheres. The diffraction problem is formulated and solved within the framework of the theory of linear viscoelastic solids [6]. The case of an ideal fluid has been studied previously [3–5, 7]. Radiation forces are one of the causes of the relative drift of solid particles situated in a fluid in an acoustic field.S. P. Timoshenko Institute of Mechanics, Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 2, pp. 33–40, February, 1994.     

On the aerodynamic characteristics of hovering rigid and flexible hawkmoth-like wings

Insect wings are subjected to fluid, inertia and gravitational forces during flapping flight. Owing to their limited rigidity, they bent under the influence of these forces. Numerical study by Hamamoto et al. (Adv Robot 21(1–2):1–21, 2007) showed that a flexible wing is able to generate almost as much lift as a rigid wing during flapping. In this paper, we take a closer look at the relationship between wing flexibility (or stiffness) and aerodynamic force generation in flapping hovering flight. The experimental study was conducted in two stages. The first stage consisted of detailed force measurement and flow visualization of a rigid hawkmoth-like wing undergoing hovering hawkmoth flapping motion and simple harmonic flapping motion, with the aim of establishing a benchmark database for the second stage, which involved hawkmoth-like wing of different flexibility performing the same flapping motions. Hawkmoth motion was conducted at Re = 7,254 and reduced frequency of 0.26, while simple harmonic flapping motion at Re = 7,800 and 11,700, and reduced frequency of 0.25. Results show that aerodynamic force generation on the rigid wing is governed primarily by the combined effect of wing acceleration and leading edge vortex generated on the upper surface of the wing, while the remnants of the wake vortices generated from the previous stroke play only a minor role. Our results from the flexible wing study, while generally supportive of the finding by Hamamoto et al. (Adv Robot 21(1–2):1–21, 2007), also reveal the existence of a critical stiffness constant, below which lift coefficient deteriorates significantly. This finding suggests that although using flexible wing in micro air vehicle application may be beneficial in term of lightweight, too much flexibility can lead to deterioration in flapping performance in terms of aerodynamic force generation. The results further show that wings with stiffness constant above the critical value can deliver mean lift coefficient almost the same as a rigid wing when executing hawkmoth motion, but lower than the rigid wing when performing a simple harmonic motion. In all cases studied (7,800 ≤ Re ≤ 11,700), the Reynolds number does not alter the force generation significantly.     

A Numerical Study Promoting Algebraic Models for the Lewis Number Effect in Atmospheric Turbulent Premixed Bunsen Flames

This numerical investigation carried out on turbulent lean premixed flames accounts for two algebraic – the Lindstedt–Vaos (LV) and the classic Bray–Moss–Libby (BML) – reaction rate models. Computed data from these two models is compared with the experimental data of Kobayashi et al. on 40 different methane, ethylene and propane Bunsen flames at 1 bar, where the mean flame cone angle is used for comparison. Both models gave reasonable qualitative trend for the whole set of data, in overall. In order to characterize quantitatively, firstly, corrections are made by tuning the model parameters fitting to the experimental methane–air (of Le = 1.0) flame data. In case of the LV model, results obtained by adjusting the pre-constant, i.e., reaction rate parameter, C_R, from its original value 2.6 to 4.0, has proven to be in good agreement with the experiments. Similarly, for the BML model, with the tuning of the exponent n, in the wrinkling length scale, L_y = C_l⋅ l_x(s_L/u′)ⁿ from value unity to 1.2, the outcome is in accordance with the measured data. The deviation between the measured and calculated data sharply rises from methane to propane, i.e., with increasing Lewis number. It is deduced from the trends that the effect of Lewis number (for ethylene–air mixtures of Le = 1.2 and propane–air mixtures of Le = 1.62) is missing in both the models. The Lewis number of the fuel–air mixture is related to the laminar flame instabilities. Second, in order to quantify for its influence, the Lewis number effect is induced into both the models. It is found that by setting global reaction rate inversely proportional to the Lewis number in both the cases leads to a much better numerical prediction to this set of experimental flame data. Thus, by imparting an important phenomenon (the Lewis number effect) into the reaction rates, the generality of the two models is enhanced. However, functionality of the two models differs in predicting flame brush thickness, giving scope for further analysis.     

On the Passage from Atomic to Continuum Theory for Thin Films

We give a rigorous derivation of a continuum theory from atomic models for thin films. This scheme has been proposed by Friesecke and James in [J. Mech. Phys. Solids 48, 1519–1540 (2000)]. The resulting continuum energy expression is obtained by integrating a stored energy density which not only depends on the deformation gradient, but also on ν-1 director fields when ν is the (fixed) number of atomic film layers.     

Near-field instability of variable property jet in normal gravity and microgravity fields

The near-field instability of variable property jets of air, CO₂, and He, issued into the ambient air, has been investigated experimentally within normal gravity and microgravity fields. The density ratio to the ambient air is unity for air jets, more than unity (1.53) for CO₂ jets, and less than unity (0.14) for He jets, respectively. The ratio of kinematic viscosity to the ambient air is unity for air jets, less than unity for CO₂ jets (0.53), and more than unity for He jets (7.75), respectively. The jet velocity is varied from 0.4 to 1.8 m/s and then the jet Reynolds number varies from 60 for Helium jet to 2,000 for CO₂ jet, while the Richardson number varies from negative to positive values. The motion of the jet is visualized using a laser tomographic method and recorded by a high-speed digital video camera with 250 frames/s. The result shows that the instability of the jet is intensified when Re > 800 while it is weakened at Re < 800 at the microgravity field, indicating that the viscosity plays an important role in weakening the instability. Under a normal gravity field, the buoyancy also becomes important. In order to quantify the instability criteria, the quantity of the instability is introduced, which consists of the Kelvin–Helmholtz instability, buoyancy effect and viscous effect. When the ratio of the sum of Kelvin–Helmholtz and buoyancy forces to viscous force exceeds a certain value, around 12 in the present study, the jet becomes unstable even when Re < 800. These results reveal that the instability of variable property jets is influenced by the Kelvin–Helmholtz instability, the viscous effect and the buoyancy effect.     

Concrete-surface destruction by powerful microwave-radiation pulses

The destruction of the surface layer of concrete by a powerful microwave-radiation pulse is studied. The conditions for the occurrence of shear and spall fractures in concrete at a given depth are found. The range of electrodynamic parameters within which microwave radiation is the most effective for disintegration of concrete is found. The requirements for a microwave generator that permit one to study experimentally the force action of electromagnetic radiation on concrete are formulated. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 26–33, May–June, 2000.     

Experimental investigation of liquid jet injection into Mach 6 hypersonic crossflow

The injection of a liquid jet into a crossing Mach 6 air flow is investigated. Experiments were conducted on a sharp leading edge flat plate with flush mounted injectors. Water jets were introduced through different nozzle shapes at relevant jet-to-air momentum–flux ratios. Sufficient temporal resolution to capture small scale effects was obtained by high-speed recording, while directional illumination allowed variation in field of view. Shock pattern and flow topology were visualized by Schlieren-technique. Correlations are proposed on relating water jet penetration height and lateral extension with the injection ratio and orifice diameter for circular injector jets. Penetration height and lateral extension are compared for different injector shapes at relevant jet-to-air momentum–flux ratios showing that penetration height and lateral extension decrease and increase, respectively, with injector’s aspect ratio. Probability density function analysis has shown that the mixing of the jet with the crossflow is completed at a distance of x/d _j  ~ 40, independent of the momentum–flux ratio. Mean velocity profiles related with the liquid jet have been extracted by means of an ensemble correlation PIV algorithm. Finally, frequency analyses of the jet breakup and fluctuating shock pattern are performed using a Fast Fourier algorithm and characteristic Strouhal numbers of St = 0.18 for the liquid jet breakup and of St = 0.011 for the separation shock fluctuation are obtained.     

On the modeling of intestinal segment motion

The derivation and justification of model equations simulating the function of a natural or artificially formed (during a surgical operation) intestine segment are given. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 36–42, January–February, 1994.     

Interaction of turbulent natural convection and surface thermal radiation in inclined square enclosures

Two-dimensional numerical studies of flow and temperature fields for turbulent natural convection and surface radiation in inclined differentially heated enclosures are performed. Investigations are carried out over a wide range of Rayleigh numbers from 10⁸ to 10¹², with the angle of inclination varying between 0° and 90°. Turbulence is modeled with a novel variant of the k–ε closure model. The predicted results are validated against experimental and numerical results reported in literature. The effect of the inclination of the enclosure on pure turbulent natural convection and the latter’s interaction with surface radiation are brought out. Profiles of turbulent kinetic energy and effective viscosity are studied to observe the net effect on the intensity of turbulence caused by the interaction of natural convection and surface radiation. The variations of local Nusselt number and average Nusselt number are presented for various inclination angles. Marked change in the convective Nusselt number is found with the orientation of enclosure. Also analyzed is the influence of change in emissivity on the flow and heat transfer. A correlation relevant to practical applications in the form of average Nusselt number, as a function of Rayleigh number, Ra, radiation convection parameter, N _RC and inclination angle of the enclosure, φ is proposed.     

Mathematical simulation of ignition of a coal-dust suspension in air by a low-temperature plasma jet

The process of aerosuspension ignition of a suspension in air in a pulverized-coal burner with a preswitched muffle by a central axisymmetric air stream heated in an electric-arc plasmatron to a temperature of about ≈5000K is numerically simulated. This process is the basis of a new fuel-oil-free method of ignition of the boilers of thermal power stations. The method is rather promising from the viewpoint of both economy and ecology. The goal of numerical simulation is to study the process of ignition of coal particles in the flow and to identify the conditions necessary for the transition to self-sustained burning of a coal-dust mixture. The results obtained revealed the significant role of radiative heat transfer in initializing the burning process of solid fuel particles. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 134–140, May–June, 1998.     

Heat transfer from a surface fitted with rectangular blocks at different orientation angle

 An experimental investigation was carried out to study the enhancement of the heat transfer from a heated flat plate fitted with rectangular blocks of 1 × 2 × 2 cm³ dimensions in a channel flow as a function of Reynolds number (Re_h), spacing (S _y ) of blocks in the flow direction, and the block orientation angle (α) with respect to the main flow direction. The experiments were performed in a channel of 18 cm width and 10 cm height, with air as the working fluid. For fixed S _x =3.81 cm, which is the space between the blocks in transverse to the flow direction, the experimental ranges of the parameters were S _y =3.33–4.33 cm, α=0–45°, Re_h=7625–31550 based on the hydraulic diameter and the average velocity at the beginning of the test section in the channel. Correlations for Nusselt number were developed, and the ratios of heat transfer with blocks to those with no blocks were given. The results indicated that the heat transfer could be enhanced or reduced depending on the spacing between blocks, and the block orientation angle. The maximum heat transfer rate was obtained at the orientation angle of 45°. Received on 13 December 2000 / Published online: 29 November 2001     

Prediction of separation flows around a 6：1 prolate spheroid using RANS/LES hybrid approaches

This paper presents hybrid Reynolds-averaged Navier–Stokes (RANS) and large-eddy-simulation (LES) methods for the separated flows at high angles of attack around a 6:1 prolate spheroid. The RANS/LES hybrid methods studied in this work include the detached eddy simulation (DES) based on Spalart–Allmaras (S–A), Menter’s k–ω shear-stress-transport (SST) and k–ω with weakly nonlinear eddy viscosity formulation (Wilcox–Durbin+, WD+) models and the zonal-RANS/LES methods based on the SST and WD+ models. The switch from RANS near the wall to LES in the core flow region is smooth through the implementation of a flow-dependent blending function for the zonal hybrid method. All the hybrid methods are designed to have a RANS mode for the attached flows and have a LES behavior for the separated flows. The main objective of this paper is to apply the hybrid methods for the high Reynolds number separated flows around prolate spheroid at high-incidences. A fourth-order central scheme with fourth-order artificial viscosity is applied for spatial differencing. The fully implicit lower–upper symmetric-Gauss–Seidel with pseudo time sub-iteration is taken as the temporal differentiation. Comparisons with available measurements are carried out for pressure distribution, skin friction, and profiles of velocity, etc. Reasonable agreement with the experiments, accounting for the effect on grids and fundamental turbulence models, is obtained for the separation flows. The project supported by the National Natural Science Foundation of China (10502030 and 90505005).     

Modeling of the unsteady force for shock–particle interaction

The interaction between a particle and a shock wave leads to unsteady forces that can be an order of magnitude larger than the quasi-steady force in the flow field behind the shock wave. Simple models for the unsteady force have so far not been proposed because of the complicated flow field during the interaction. Here, a simple model is presented based on the work of Parmar et al. (Phil Trans R Soc A 366:2161–2175, 2008). Comparisons with experimental and computational data for both stationary spheres and spheres set in motion by shock waves show good agreement in terms of the magnitude of the peak and the duration of the unsteady force.      

On the orders of the best approximations of integrals of functions by integrals of rank σ

We study the values e _σ(f) of the best approximation of integrals of functions from the spaces L _p (A, dμ) by integrals of rank σ. We determine the orders of the least upper bounds of these values as σ → ∞ in the case where the function ƒ is the product of two nonnegative functions one of which is fixed and the other varies on the unit ball U _p (A) of the space L _p (A, dμ). We consider applications of the obtained results to approximation problems in the spaces S _p ^ϕ. __________ Translated from Neliniini Kolyvannya, Vol. 10, No. 4, pp. 528–559, October–December, 2007.