The Effect of the Walls of an Arbitrary Tank in the Problem of Separation–Free Impact on a Floating Body

An algorithm for constructing an asymptotic power series for large depths is proposed. It allows one to use the well–known solution of the problem of impact on a rigid body floating on the surface of a fluid half–space to obtain an approximate solution of the impact problem for the same body floating on the surface of a fluid in a bounded basin. The case where the domain occupied by the fluid has two perpendicular planes of symmetry is considered. Asymptotic expressions are given for the velocity potential on the wetted part of the body surface and for the added mass. Examples of solutions are considered.     

Controlling the Free‐Surface Profile of Film Flow over Complex Topography

A twodimensional model describing nonisothermal viscous thin film flow over complex topography is considered. The model is based on the Navier–Stokes equations in the Oberbeck–Boussinesq approximation. A numerical analysis of the effect of thermal loading on the location of the film free surface is performed. It is shown that changing the substrate temperature function, it is possible to control the freesurface profile on separate topographical features. The results of solution of model problems are presented).     

Effect of Allowance for Small‐Scale Perturbations of the Carrier Phase on Properties of the System of Equations of a Two‐Fluid Flow with Incompressible Phases

The effect of the fluctuating components of kinetic energy and stress tensor of the carrier phase, which were previously obtained by the cell technique, on the properties of the system of equations of a gas–liquid flow with incompressible phases is considered. It is shown that the characteristic properties of this system and also the possibility of modeling the Zuber–Findlay empirical relation are determined by the tensor of fluctuating stresses of the carrier phase.     

Description of a Flow of a Gas‐Condensate Mixture in an Axisymmetric Capillary Tube by the Density‐Functional Method

An isothermal flow of a twophase multicomponent mixture through a smalldiameter capillary tube is examined by the densityfunctional method. For low ratios of the characteristic radius of the capillary to its length, a general form of the dominating term in the asymptotic solution is found. An improved version of the law of mixture transfer is obtained. The form of possible corrections to the Darcy law for the filtration rates of the phases is discussed.     

Effect of Dynamic Prehistory on Aerodynamics of a Laminar Separated Flow in a Channel Behind a Rectangular Backward‐Facing Step

The effect of dynamic prehistory of the flow and the channelexpansion ratio on aerodynamics of a steady separated laminar flow behind a rectangular backwardfacing step located in a planeparallel channel is numerically studied. It is shown that the boundary layer upstream of the flow separation exerts a strong effect on flow characteristics behind the step. A decrease in the boundarylayer thickness in the cross section of the step leads to a decrease in the separationregion length, and an increase in the channelexpansion ratio with a fixed initial boundarylayer thickness and Reynolds number leads to an increase in the separationregion length.     

Effect of Evaporation of Liquid Droplets on the Distribution of Parameters in a Two–Species Laminar Flow

A calculation model was developed, and the heat– and mass–transfer characteristics in a laminar air—vapor—droplet flow moving in a round tube were studied numerically. The distributions of parameters of the two–phase flow over the tube radius were obtained for varied initial concentrations of the gas phase. The calculated heat and mass transfer is compared to experimental data and calculations of other authors. It is shown that evaporation of droplets in a vapor—gas flow leads to a more intense heat release as compared to a one–species vapor—droplet flow and one–phase vapor flow     

Experimental and Numerical Study of a Hypersonic Separated Flow in the Vicinity of a Cone‐Flare Model

An axisymmetric laminar separated flow in the vicinity of a coneflare model is studied experimentally and numerically for a Mach number M = 6. The distributions of pressure and Stanton numbers along the model surface and velocity profiles in the region of shock wave–boundary layer interaction are measured and compared with the calculated data. The influence of the laminar–turbulent transition on flow parameters is studied numerically.     

On the Propagation of Long‐Wave Perturbations in a Two‐Layer Free‐Boundary Rotational Fluid

A mathematical model for the propagation of longwave perturbations in a freeboundary shear flow of an ideal stratified twolayer fluid is considered. The characteristic equation defining the velocity of perturbation propagation in the fluid is obtained and studied. The necessary hyperbolicity conditions for the equations of motion are formulated for flows with a monotonic velocity profile over depth, and the characteristic form of the system is calculated. It is shown that the problem of deriving the sufficient hyperbolicity conditions is equivalent to solving a system of singular integral equations. The limiting cases of weak and strong stratification are studied. For these models, the necessary and sufficient hyperbolicity conditions are formulated, and the equations of motion are reduced to the Riemann integral invariants conserved along the characteristics.     

Effect of free‐stream turbulence on the boundary‐layer structure with diffusion combustion of ethanol

The effect of turbulization of a subsonic air flow on the boundarylayer structure was experimentally studied during evaporation and combustion of ethanol behind an obstacle 3–6 mm high. It is shown that turbulization increases the thermal boundarylayer thickness by a factor of 2, where as the dynamic boundarylayer thickness changes weakly. For 1–18% turbulence at the entrance, the change in the momentum thickness along the channel is close to the change in the momentum thickness for a laminar isothermal boundary layer without injection. Local regions of elevated turbulence with a high intensity of heat and mass transfer arise in the case of combustion behind the obstacle at a distance of 40–50 obstacle heights.     

Effect of the Conductance and Thickness of a Conducting Plate on the Signal from a Material–Velocity Inductive Transducer

The perturbation problem of the magnetic field of a constant–current turn located above a conducting plate set into motion by a plane shock wave with a rectangular profile is considered. It is shown that not only the velocity of the plate but also its dynamic conductivity can be determined on the basis of the electromotive force of induction recorded by means of the turn. For the case where the conductance of the plate is known for both the conducting half–space and for a plate whose thickness is comparable with the skin–layer thickness, approximatecalculated dependences for the velocity of the plate are obtained. A comparison with experimental data and the clarification of the calculated dependences allows one to conclude that the approaches proposed can be used for determining the conductance of metals in shock–wave processes.     

Wave Propagation Over the Free Surface of a Two‐Phase Medium with a Nonuniform Concentration of the Disperse Phase

The boundaryvalue problem of waves on the surface of a twophase medium with a nonuniform (exponential) distribution of the disperse phase is formulated. An asymptotic solution of the linear problem in the form of damped progressive waves is obtained. The phase velocity, frequency, and damping decrement for the waves are found. The perturbation of the admixture concentration is determined, which, unlike in the case of a uniform distribution, is manifested even in a linear approximation. Numerical calculations were performed for concrete media.     

Existence and Uniqueness of the Flow of Second‐Grade Fluids with Slip Boundary Conditions

. This paper treats the solvability of the equations of motion for an incompressible fluid of grade two subject to nonlinear partial slip boundary conditions in a bounded simply‐connected domain. The existence of a unique classical solution, global in time, is proved under suitable regularity and growth restrictions on the initial data, the slip law and the body and surface forces. The method is based on a fixed-point formulation of the problem. (Accepted October 5, 1998)     

Effect of Small Bluntness on Formation of Görtler Vortices in a Supersonic Compression Corner Flow

The influence of small cylindrical bluntness of the leading edge of a flat plate on formation of spatial structures in a nominally two-dimensional supersonic compression corner flow at the Mach number M∞ ≈ 8 and a laminar state of the undisturbed boundary layer is studied by the method of temperature-sensitive paints. Streamwise vortices are found in the region of reattachment of the separated flow in a wide range of Reynolds numbers (0.15 · 10⁶–2.55 · 10⁶) for various angles of flow deflection and plate lengths. It is demonstrated that the existence of these vortices induces spanwise oscillations of the heat transfer coefficient; the amplitude of these oscillations may reach 30%. The maximum deviations of the Stanton number reaching 80% are observed in the case with significant roughness of the leading edge of the flat plate. Both the maximum Stanton numbers in the reattachment region and the amplitude of spanwise oscillations of the Stanton number induced by streamwise vortices are found to decrease significantly in the case of small bluntness of the leading edge. Solutions of three-dimensional Navier–Stokes equations are obtained for some test conditions. The computed results are in good agreement with experimental data, which points to a significant stabilizing effect of small bluntness on the intensity of streamwise vortices.     

Numerical Study of Hydrodynamics and Heat and Mass Transfer of a Ducted Gas–Vapor‐Droplet Flow

A computational model has been developed to predict heat and mass transfer and hydrodynamic characteristics of a turbulent gas–vapor–droplet flow. Turbulent characteristics of the gas phase are computed using the k– model of turbulence. It is shown that, with increasing inlet droplet diameter, the rate of heat transfer between the duct surface and the vapor–gas mixture decreases appreciably, whereas the wall friction increases only insignificantly. The predicted values agree fairly well with available experimental and numerical data     

Waves on the free surface of a two‐phase medium

A boundaryvalue problem is posed to determine the wave motion caused by propagation of a gravity wave on the free surface of a layer of a twophase medium. The problem is solved analytically in the linear approximation. The shape of the free surface, the phase velocity, and the frequency and damping factor of the wave are determined. An example of the solution of the problem is given.     

Modelling Surface Runoff and Infiltration of Rain by an Elliptic-Parabolic Equation Coupled with a First‐Order Equation on the Boundary

. (Accepted April 9, 1998)     

Estimate of the Latent Free Energy and Damage at the Tip of an Opening–Mode Crack

A method of estimating the latent elastic energy associated with the microinhomogeneity of the stress and plastic–strain fields inside the plastic zone localized near the tip of an opening–mode crack (Dugdale zone) under conditions of plane stresses is proposed. The microinhomogeneity of plastic flow upon small strain hardening is taken into account only in the form of considerable distortion of the geometry of the free surfaces of the plastic zone. The damage that developes because of release of the latent free energy is estimated depending on the magnitude of the crack opening.     

Existence of a Weak Solution to a Nonlinear Fluid–Structure Interaction Problem Modeling the Flow of an Incompressible, Viscous Fluid in a Cylinder with Deformable Walls

We study a nonlinear, unsteady, moving boundary, fluid–structure interaction (FSI) problem arising in modeling blood flow through elastic and viscoelastic arteries. The fluid flow, which is driven by the time-dependent pressure data, is governed by two-dimensional incompressible Navier–Stokes equations, while the elastodynamics of the cylindrical wall is modeled by the one-dimensional cylindrical Koiter shell model. Two cases are considered: the linearly viscoelastic and the linearly elastic Koiter shell. The fluid and structure are fully coupled (two-way coupling) via the kinematic and dynamic lateral boundary conditions describing continuity of velocity (the no-slip condition), and the balance of contact forces at the fluid–structure interface. We prove the existence of weak solutions to the two FSI problems (the viscoelastic and the elastic case) as long as the cylinder radius is greater than zero. The proof is based on a novel semi-discrete, operator splitting numerical scheme, known as the kinematically coupled scheme, introduced in Guidoboni et al. (J Comput Phys 228(18):6916–6937, 2009) to numerically solve the underlying FSI problems. The backbone of the kinematically coupled scheme is the well-known Marchuk–Yanenko scheme, also known as the Lie splitting scheme. We effectively prove convergence of that numerical scheme to a solution of the corresponding FSI problem.