Diffusion in a nonuniform velocity field

The effect of a nonuniform velocity field on the diffusion process is examined. When the local passive admixture transport equation is averaged over the channel cross section, the differential equation for the average concentration over the cross section is obtained in the form of an infinite asymptotic series whose terms are linear combinations of the derivatives of the average concentration with respect to the coordinate and time, while the coefficients depend on the degree of transverse nonuniformity of the velocity field and the radial Péclet number. Estimates show that in most of the cases encountered in practice to ensure that the calculations have the necessary accuracy the series must include derivatives up to the third order. An approximate solution of the averaged equation is found by the method of asymptotic expansions and the initial moments of the residence time distribution function are determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 122–128, September–October, 1989.     

Numerical investigation of the process of displacement of oil by steam

A calculation model of the process of displacement of oil by steam, based on the equations of three-phase nonisothermal flow with allowance for phase transitions in the water-steam system, is proposed. This model is used for the numerical investigation of the recovery of oil from wateroil zones by means of steam injection. The extraction of oil from wateroil zones is one of the difficult problems of the theory of exploitation of petroleum deposits. The presence of two zones with sharply different fluid resistances leads to considerable nonuniformity in production rates. It is shown that injecting steam significantly reduces this nonuniformity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 78–84, July–August, 1987.     

Analysis of Displacement Variances in Stochastic Nonuniform Flows by Means of a First Order Analytical Model and Comparison with Monte-Carlo Simulations

Flow, particle displacement and particle arrival time statistics in 2D nonuniform flows, without microdispersion, are studied both theoretically, in the framework of stochastic modelling, and numerically by means of Monte-Carlo simulations.Turning, radial convergent and dipolar flow fields are considered. These three types of flow are numerically investigated in heterogeneous media with different levels of heterogeneity. Monte-Carlo simulations show (1) that the scale separation hypothesis, frequently used in fluid mechanics, is justified for one-point flow statistics; and (2) how displacement variances, and consequently the dispersivities defined as their spatial derivatives, depend on the type and the amplitude of flow nonuniformity: in none of the investigated cases does the assumption of scale separation hold for displacement, except in the turning flow when the spatial scale associated to the nonuniformity is much greater than the correlation scale of transmissivity.The theoretical approach of displacement and arrival time statistics relies on the analysis of particle trajectory. Displacement variances expressions are derived by the perturbation method for each type of flow and for different approximation orders. The proposed expressions of displacement variances are, on the whole, in good agreement with the numerical results. On the other hand, the uniform flow approximation – commonly used for the interpretation of tracer experiments – chosen such as to satisfy the mean arrival time to the pumping well, gives the best prediction of the breakthrough curves.     

Formation and decay of a quasisteady detonation complex in a nonuniformly heated combustible gas

This work is a continuation of the study of explosive reaction regimes associated with an initial nonuniformity of the reaction induction period. Relations determining the time and place of formation and decay of a quasisteady detonation complex are obtained for a linear nonuniformity. These are compared with the results of numerical calculations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 161–168, March–April, 1991.     

Numerical modeling of the process of oil displacement from reservoirs with zonal nonuniformity

In extracting oil from nonuniform reservoirs a considerable fraction remains unrecovered from the zones of lesser permeability. The mechanism of displacement of oil from reservoirs with zonal nonuniformity is investigated within the framework of the two-dimensional Muskat-Meres model of combined oil, water and gas flow [1]. A wholly conservative difference scheme implicit in the saturations and pressure is used for the calculations. Various reservoir exploitation regimes are considered with the object of seeking means of improving the characteristics of the process.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 177–180, September–October, 1987.     

Heat transfer in a turbulent boundary layer with stepped injection

The asymptotic theory of a turbulent boundary layer has been applied to derive relationships for the heat and mass transfer when there is injection and consequent nonuniformity in the gas composition. Experimental studies are reported on heat and mass transfer with stepped injection of homogeneous and inhomogeneous gases; the results confirm the equations for the heat and mass transfer at a permeable surface when a foreign gas is blown in.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 124–129, July–August, 1973.     

Supersonic flow over a cone with heat release in the neighborhood of the apex

Supersonic flow over a cone mounted in the wake of a spherical source of heat release is investigated. The free-stream nonuniformity generated by the source leads to effective drag reduction.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 110–114, March–April, 1993.     

Pressure Waves in a Gas–Liquid Medium with a Stratified Liquid–Bubbly Mixture Structure

Evolution and decay of pressure waves of moderate amplitude in a vertical shock tube filled by a gas–liquid medium with a nonuniform (stepwise) distribution of bubbles over the tube cross section are studied experimentally. The gas–liquid layer has the form of a ring located near the tube wall or the form of a gas–liquid column located in the center of the tube. It is shown that the nonuniformity of bubble distribution over the tube cross section increases the attenuation rate of pressure waves.     

Investigation of the hypersonic viscous shock layer around blunt bodies in a nonuniform flow

Unseparated viscous gas flow past a body is numerically investigated within the framework of the theory of a thin viscous shock layer [13–15]. The equations of the hypersonic viscous shock layer with generalized Rankine-Hugoniot conditions at the shock wave are solved by a finite-difference method [16] over a broad interval of Reynolds numbers and values of the temperature factor and nonuniformity parameters. Calculation results characterizing the effect of free-stream nonuniformity on the velocity and temperature profiles across the shock layer, the friction and heat transfer coefficients and the shock wave standoff distance are presented. The unseparated flow conditions are investigated and the critical values of the nonuniformity parameter a_k [10] at which reverse-circulatory zones develop on the front of the body are obtained as a function of the Reynolds number. The calculations are compared with the asymptotic solutions [10, 12].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 154–159, May–June, 1987.     

Hypersonic three-dimensional viscous shock layer in a nonuniform gas flow in the neighborhood of the stagnation point

Three-dimensional hypersonic viscous gas flow past smooth blunt bodies in the presence of injection or suction is considered. The effect of the nonuniformity of the approach stream on the shock-wave standoff, the flow structure and the friction and heat transfer coefficients is investigated with reference to the examples of flow from a supersonic spherical source and flow of the far wake type. It is shown that this effect depends importantly on the Reynolds number, the nature of the nonuniformity and the shape of the body.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 136–145, November–December, 1987.     

Calculation of interaction of a turbulent near-wake behind a step with a supersonic jet

Existing computational methods [1–5] do not enable one to calculate complex flows behind steps, accounting for nonuniformity of the incident supersonic flow and the effect of compression and expansion waves arriving in the near-wake region. For example, computational methods based on the methods of [1] or [2] are used mainly in uniform supersonic flow ahead of the base edge and, for the most part, cannot be used to calculate flow in annular nozzles with irregular conditions. An exception is reference [6], which investigated flow in an annular nozzle behind a cylindrical center-body. The present paper suggests a method, based on references [7, 8] for calculating the base pressure behind two-dimensional and three-dimensional steps, washed by a supersonic jet.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 43–51, November– December 1977.     

Radial oscillations of vapor bubbles in solutions

The dynamics and heat and mass transfer of vapor bubbles in binary systems are investigated. An anomalous effect of the component composition on the bubble dynamics in boiling nonideal solutions is established. It is shown that in some binary systems the value of the logarithmic decay rate for small free radial oscillations does not lie within the limiting values calculated for the pure components, which is associated with the cardinal importance of the effect of diffusion in the liquid phase on the intensity of the phase transitions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 108–113, May–June, 1989.     

Vibrational-convective instability of a horizontal fluid layer with internal heat sources

The convective motion of a nonisothermal fluid in a gravity field in a vibrating cavity is caused by two mechanisms: the usual static mechanism and a vibrational mechanism. The same mechanisms are also responsible for mechanical equilibrium crisis under the conditions in which such equilibrium is possible. The research on these questions is reviewed in [1]. The problems of vibrational-convective stability examined so far relate to cases in which the nonisothermicity was created by specifying the temperature at the boundaries of the region. The present study is concerned with the vibrational-convective stability of a fluid in which the temperature nonuniformity is created by internal heat generation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 3–7, September–October, 1985.     

Simulation of ratcheting strain to a high number of cycles under biaxial loading

The Ohno–Wang kinematic hardening rule is modified to incorporate the Burlet–Cailletaud radial evanescence term for an improved simulation of the ratcheting behavior. The Delobelle parameter δ^′ is implemented in the modified model to compromise shakedown of the Burlet–Cailletaud hardening rule and over-prediction of the Ohno–Wang model. An evolution equation is proposed for δ^′ to simulate the ratcheting strain over an extended domain of cycles. Ratcheting tests were conducted on S45C steel under four types of nonproportional axial–torsional loading. The new model is found to yield reasonably accurate predictions of ratcheting strain to a much higher number of cycles compared with other studies.     

The flow of a dielectric liquid

The nature of the forces acting on a dielectric liquid in an electric field in the presence of a temperature gradient is investigated. It is shown that the electrical forces produced by nonuniformity in the electrical conductivity of the medium can give rise to a hydrodynamic flow.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 136–137, November–December, 1973.     

Determination of mechanical properties of fiber–matrix interface from pushout test

For ceramic matrix composites, the pushout test is the most widely used test for finding the two mechanical properties of the fiber–matrix interface – (1) the coefficient of friction and (2) the residual radial stress. Experimental measurements from the pushout test do not directly give the values of these two mechanical properties of the fiber–matrix interface, but need to be regressed to theoretical models. Currently, approximate theoretical models based on shear–lag analysis are used for regression. In this paper, the adequacy of the shear–lag analysis model in accurately finding the mechanical properties of the fiber–matrix interface is discussed. An elasticity solution of the pushout test based on boundary element method is developed. Regressing one set of available experimental data from a pushout test to both shear–lag analysis and boundary element method models gives values differing by 15% for the coefficient of friction but similar values for the residual radial stress. Parametric studies were also conducted to show the difference between the shear–lag analysis and boundary element method results for factors such as fiber to matrix elastic moduli ratios, coefficient of friction and fiber volume fractions.     

Evidence for a Second Transport Porosity for the Diffusion of Tritiated Water (HTO) in a Sedimentary Rock (Opalinus Clay - OPA): Application of Through- and Out-Diffusion Techniques

The diffusion of tritiated water (HTO) in Opalinus clay (OPA) samples from bore cores from the Benken area (Northern Switzerland) was studied using the radial through- and out-diffusion technique. Results from inverse modelling of out-diffusion data for HTO indicated the presence of two preferential diffusion pathways: a fast and a slow one. Analysing through-diffusion data, however, provides hardly any information concerning a second transport-relevant porosity. Only by also analysing the out-diffusion phase can finer details of the diffusion process and information on sample heterogeneity be recognised. The extracted values for the effective diffusion coefficient are in the order of 3 × 10^–11 m² s^–1 for the faster transport porosity and roughly an order of magnitude smaller for the slower type of porosity. We had to account for tritium sorption on the clay minerals by a small but non-zero K_d-value in the order of 10^–5 m³ kg^–1 in order to reproduce the data with acceptable precision. In the model applied both porosities are considered as being independent from each other. Roughly 30% of the tracer diffused through the second, slower porosity; such a fact might be interesting for future performance assessments for radioactive waste repositories hosted by clay formations. Based on our present picture from water-saturated OPA, on a microscopic scale three different kind of waters can be discriminated: free water, double layer water and interlayer water. However, using HTO as tracer only, it could not be deduced which type of water-filled pores finally account for the transport-relevant porosity.Author for correspondence: Tel.: +41-56-3102257; Fax: +41-56-3104438; E-mail: luc.vanloon@psi.ch     

Unsteady three-dimensional viscous shock layer in nonuniform gas flow in the neighborhood of a stagnation point

The combined influence of unsteady effects and free-stream nonuniformity on the variation of the flow structure near the stagnation line and the mechanical and thermal surface loads is investigated within the framework of the thin viscous shock layer model with reference to the example of the motion of blunt bodies at constant velocity through a plane temperature inhomogeneity. The dependence of the friction and heat transfer coefficients on the Reynolds number, the shape of the body and the parameters of the temperature inhomogeneity is analyzed. A number of properties of the flow are established on the basis of numerical solutions obtained over a broad range of variation of the governing parameters. By comparing the solutions obtained in the exact formulation with the calculations made in the quasisteady approximation the region of applicability of the latter is determined. In a number of cases of the motion of a body at supersonic speed in nonuniform media it is necessary to take into account the effect of the nonstationarity of the problem on the flow parameters. In particular, as the results of experiments [1] show, at Strouhal numbers of the order of unity the unsteady effects are important in the problem of the motion of a body through a temperature inhomogeneity. In a number of studies the nonstationary effect associated with supersonic motion in nonuniform media has already been investigated theoretically. In [2] the Euler equations were used, while in [3–5] the equations of a viscous shock layer were used; moreover, whereas in [3–4] the solution was limited to the neighborhood of the stagnation line, in [5] it was obtained for the entire forward surface of a sphere. The effect of free-stream nonuniformity on the structure of the viscous shock layer in steady flow past axisymmetric bodies was studied in [6, 7] and for certain particular cases of three-dimensional flow in [8–11].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 175–180, May–June, 1990.     

Circulation flow at the front surface of a sphere in a supersonic wake

Several theoretical and experimental studies of supersonic flow past a blunt body located in the wake behind another body have been made [1–7]. It has been shown that a reverse-circulation flow can occur in the shock layer at the front surface. The possibility of such a flow forming depends on the nonuniformity of the freestream flow and the Reynolds number. This paper presents new results of the theoretical study of the structure of the shock wave at the front surface of such a sphere, obtained on the basis of numerical solution of Navier-Stokes equations. It is shown that for a fixed nonuniformity of the freestream flow, an increase in the Reynolds number and cooling of the surface of the body lead to the formation of a secondary vortex in the region where the contour of the body intersects the axis of symmetry. A study is made of the variations of the drag and heat transfer parameters over the front surface of a cooled and thermally insulated sphere. The possibility of numerical simulation of the flow on the basis of the Euler equations is discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 143–148, May–June, 1985.     

Asymptotic method for solving problems with radial laminar jets of immiscible liquids

Two problems involving radial laminar jets of immiscible liquids are considered: a free radial slit jet and a jet on a rotating disk. An asymptotic method of solution is proposed that makes it possible to determine the flow parameters far from the source. The difference between these flows and those of homogeneous liquids is demonstrated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 192–28, May–June, 1980.