Showing papers in "Fluid Dynamics in 1984"
TL;DR: In this article, a quasi-one-dimensional model of the capillary breakup of thin free jets of dilute polymer solutions is investigated theoretically and the evolution of the jet surface shape in the nonlinear stage of deformation, when elastic effects are important, is described.
Abstract: The capillary breakup of thin free jets of dilute polymer solutions is investigated theoretically. The evolution of the jet surface shape in the nonlinear stage of deformation, when elastic effects are important, is described in the framework of a quasi-one-dimensional description. The initial tension of the jet is shown to have a decisive influence on the breakup dynamics. The delay in breakup due to the orientation and stretching of the polymer coiled macromolecules in the initial section of the jet is determined.
77 citations
TL;DR: In this article, it was shown that integrable and non-integrable singularities of the mixture can exist and that the model of noninteracting particles is valid in a wide range of determining parameters, since the distance between the particles remains much greater than the particle diameter.
Abstract: Some examples of the motion of a disperse mixture in which regions of unbounded growth of the particle concentration arise are considered. It is shown that integrable and nonintegrable singularities of the concentration can exist. The distribution function for the distances between the particles found by Chernyshenko [9] is used to determine the conditions for the absence of interaction of the particles. It is shown that in the case of integrable singularities of the concentration the model of noninteracting particles is valid in a wide range of the determining parameters, since, despite the infinite value of the concentration, the distance between the particles remains much greater than the particle diameter.
43 citations
29 citations
TL;DR: In this article, a study is made of the influence on the thermocapillary convective motions of two different factors, curvature of the interface and gravity, which can lead to significant changes in the flow structure and hysteresis transitions between convection regimes.
Abstract: In an earlier study [1], the present authors used the complete nonlinear hydrodynamic equations to investigate thermocapillary convection in a two-layer system. Oscillatory instability of the equilibrium was established for some ratios of the parameters. In the present paper, a study is made of the influence on the thermocapillary convective motions of two different factors — curvature of the interface and gravity. It is established that curvature of the interface can lead to significant changes in the flow structure and hysteresis transitions between convection regimes. In the case of the joint influence of the thermogravitational and thermocapillary instability mechanisms, many different flow regimes are found: steady motions with different directions of rotation of the vortices and periodic and nonperiodic oscillatory motions with different spatial structures.
27 citations
26 citations
TL;DR: In this article, the appearance of the monochromatic signal is explained by the presence in the near wake of a standing wave of the required frequency, the wave being formed by two scattering points.
Abstract: In experimental investigations of the wake flow behind a plate, a monochromatic (in time) signal is usually observed immediately behind the end of the plate. Downstream, the signal is distorted and then becomes random, i.e., a turbulent flow regime is realized. Theoretically, a branch point is found at the experimentally observed frequency in the spectrum of three-dimensional perturbations of the problem linearized with respect to the steady solution [1]. Mattingly and Criminale [1] attribute all the characteristics of the observed signal to this point. As in other similar investigations, the mechanism of the appearance of the monochromatic signal in the near wake was not elucidated in [1]. In the present paper, the problem of the characteristic oscillations of the flow in the near wake is studied. The appearance of the monochromatic signal is explained by the presence in the near wake of a standing wave of the required frequency, the wave being formed by two scattering points. The first is the end of the plate, and the second the branch point in the spectrum of linear three-dimensional perturbations.
24 citations
TL;DR: In this article, the authors studied the thermocapillary oscillations in a two-layer convective system and established the following forms of transitions between convection regimes: transition from oscillatory to steady motion through an unbounded increase in the period; bifurcation of the period accompanied by rearrangement of the three-dimensional structure of the flow.
Abstract: Finite-amplitude convective motions that arise in a two-layer system under the influence of the thermocapillary mechanism are studied. Numerical calculations have been made by the grid method for different relationships between the parameters of the fluids. A new type of instability of equilibrium is found — thermocapillary oscillations. The evolution of the oscillatory motions as the Marangoni number changes is studied. The following forms of transitions between convection regimes are established: transition from oscillatory to steady motion through an unbounded increase in the period; bifurcation of the period, accompanied by rearrangement of the three-dimensional structure of the flow. It is shown that the thermogravitational instability mechanism leads to suppression of the oscillations.
18 citations
TL;DR: In this paper, a study was made of the problem of finding the optimal shape of the section of an irrigation channel from the point of view of minimizing the seepage loss.
Abstract: A study is made of the problem of finding the optimal shape of the section of an irrigation channel from the point of view of minimizing the seepage loss; the inverse boundary-value problem method [1] is used.
14 citations
TL;DR: In this paper, an experimental and theoretical study has been made of the motion of an air bubble due to the thermocapillary effect in a thin horizontal layer of liquid bounded above and below by solid walls.
Abstract: An experimental and theoretical study has been made of the motion of an air bubble due to the thermocapillary effect in a thin horizontal layer of liquid bounded above and below by solid walls. The dependence of the speed of thermocapillary drift of the bubble on its radius has three characteristic regions, which correspond to different ratios of the bubble diameter to the thickness of the liquid layer. The results of theoretical solution of the problem for each of the three regions are compared with the experimental results.
14 citations
TL;DR: In this article, the Navier-Stokes equations for a compressible viscous perfect heat conducting gas have been used in a numerical investigation of laminar separation in the case of supersymmetric axisymmetric flow past cylinders with a conical nose and a spike at the front of finite thickness.
Abstract: The complete Navier-Stokes equations for a compressible viscous perfect heat conducting gas have been used in a numerical investigation of laminar separation in the case of supersymmetric axisymmetric flow past cylinders with a conical nose and a spike at the front of finite thickness. The flow structure has been studied in its dependence on the length of the spike and the half-angle of the conical tip. For the considered free-stream parameters (2 ⩽ M∞ ⩽ 6, 100 ⩽ Re∞ ⩽ 500) and spike lengths, which do not exceed the diameter of the cylinder, the existence of steady flow regimes has been established and it has been shown that the spike in front of the body reduces its total drag and the heat flux to its surface.
14 citations
TL;DR: In this article, an expression for the effective (reduced to the neutral surface) intensity of Tollmien-Schlichting waves induced by thermal motion in a boundary layer with Blasius velocity profile was obtained.
Abstract: An expression is obtained for the effective (reduced to the neutral surface) intensity of Tollmien-Schlichting waves induced by thermal motion in a boundary layer with Blasius velocity profile. On this basis, an expression is found for the amplitude of a quasisinusoidal wave at Reynolds numbers corresponding to the stabilization of the transition point in Wells's study [7].
TL;DR: In this article, a study of convective flow and heat transfer in a vertical cylindrical vessel with heat supplied to the free surface of the fluid, using the numerical simulation method, was made.
Abstract: A study was made in [4] of convective flow and heat transfer in a vertical cylindrical vessel with heat supplied to the free surface of the fluid, using the numerical simulation method. The results of this study were obtained for a comparatively short heating time for a fixed ratio of heat fluxes to the side and free surfaces. The present study is a continuation of the one in [4]. By using a more precise numerical simulation method, calculations could be made over a fairly wide range of determining parameters, and results were obtained for both short and long heating times.
TL;DR: In this article, the results of an experimental investigation into the kinematics of water flow in a channel rotating with different intensities were given. But the results were restricted to the case of rotating channels with straight and curvilinear axes.
Abstract: Laminar flow in a channel rotating about a transverse axis has been studied numerically [1–3] and analytically [4–7] at small Reynolds numbers. The drag coefficient of rotating channels with straight and curvilinear axes has been measured [4, 8, 9]. The present paper gives the results of an experimental investigation into the kinematics of water flow in a channel rotating with different intensities. The flow was visualized by means of hydrogen bubbles and a dye. A study was made of the process of flow separation in a rapidly rotating channel into a core with homogeneous velocity distribution in the direction parallel to the rotation axis and thin shear layers on the walls normal to this axis. The values of the dimensionless numbers were found that correspond to flow rearrangement accompanied by formation of longitudinally oriented vortex structures in the region of higher pressure, and also the values of the rotation parameter needed for the almost complete suppression of turbulence in the region of lower pressure. A general analysis is made of the forms of instability in the different regions of the flow and of the possible flow regimes in a rotating channel.
TL;DR: In this paper, it was shown that long nonlinear waves on shallow water in the presence of a horizontal magnetic field can also be described by the Benjamin-Ono equation, and not the Korteweg-de Vries equation, as in the case when there is no field.
Abstract: Benjamin [1] and Davis and Acrivos [2] derived an equation for long steady nonlinear internal waves in an infinitely deep stratified fluid when the density varies only in a layer whose thickness is small compared with the characteristic perturbation length. Ono [3] generalized this equation to the unsteady case. The resulting equation was subsequently called the Benjamin—Ono equation. Steady solutions of this equation were found by Benjamin and Ono in the form of solitons and periodic waves. In the present paper it is shown that long nonlinear waves on shallow water in the presence of a horizontal magnetic field can also be described by the Benjamin—Ono equation, and not the Korteweg—de Vries equation [4], as in the case when there is no field. Moreover, in contrast to a soliton in a stratified fluid a soliton on shallow water in a horizontal magnetic field moves with a velocity less than the velocity of infinitely long perturbations of small amplitude. The dependence of the parameters of a soliton and a periodic wave on the intensity and direction of the unperturbed magnetic field is investigated.
TL;DR: In this paper, a method for calculating the three-dimensional boundary layer on a delta wing in a regime of strong viscous interaction with the exterior hypersonic flow is proposed, and the results of numerical solution of a boundary-value problem are given.
Abstract: A method is proposed for calculating the three-dimensional boundary layer on a delta wing in a regime of strong viscous interaction with the exterior hypersonic flow. The results of numerical solution of a boundary-value problem are given.
TL;DR: In this article, a self-consistent integrodifferential equation for weakly nonlinear perturbations of the surface of a spontaneously radiating shock wave is derived, which can have solutions that increase unboundedly with the time.
Abstract: A self-consistent integrodifferential equation is derived for weakly nonlinear perturbations of the surface of a spontaneously radiating shock wave. This equation can have solutions that increase unboundedly with the time.
TL;DR: In this article, the authors derived equations that can be used either to make the boundary-layer solution more accurate or estimate its applicability, and two numerical algorithms were proposed for solving the problem; one of them is for equations in von Mises variables.
Abstract: Periodic wave solutions in a film of viscous liquid near optimal regimes have been investigated in the boundary layer approximation by Shkadov et al. [1]. Urintsev [2] has found nonlinear steady solutions near the upper neutral stability curve on the basis of the Navier-Stokes equations. In the present paper, equations are derived that can be used either to make the boundary-layer solution more accurate or estimate its applicability. Soliton type solutions are considered for parameter of the problem in the range δ e (0, ∞). Asymptotic expansions are considered in the limits δ → 0 and δ → ∞. For finite δ, two numerical algorithms are proposed for solving the problem; one of them is for equations in von Mises variables. The numerical solutions revealed the existence of “singular” sections, at which the velocity profile differs strongly from parabolic. The integral characteristics of the soliton — the phase velocity, amplitude, etc. — are found to be close to the corresponding characteristics obtained earlier by the present author [3] by assuming that the velocity profile is parabolic. The first determination is made of the critical value δ = δ** of the onset of boundary layer separation in the vertically flowing viscous film. It is interesting that the separation does not occur on the rigid wall but at an interface near the crest of the soliton.
TL;DR: In this article, a study of the asymptotic behavior of the Green's function of the Cauchy-Poisson problem in the far zone near the wave front is made.
Abstract: A study is made of the asymptotic behavior of the Green's function of the Cauchy—Poisson problem in the far zone near the wave front, i.e., for r ≈ c0t, where\(c_0 = \sqrt {gH} \) is the maximal group velocity of a surface wave. It is shown that the solution to this problem given in the book by LeBlond and Mysak [1] is incorrect, and the correct asymptotic behavior, expressed in terms of the square of an Airy function, is given.
TL;DR: In this paper, an asymptotic theory of Tollmien-Schlichting waves is constructed under the assumption that the Reynolds number tends to infinity, where the departure from parallel flow in a boundary layer is small at large Reynolds numbers.
Abstract: The nonlinear evolution of a Tollmien-Schlichting wave is analyzed with allowance for the flow being nonparallel in a boundary layer. In contrast to the early work of Zel'man [19], strict allowance is made for the fact that the extent to which the flow is nonparallel is not independent of the Reynolds number — the departure from parallel flow in a boundary layer is small only at large Reynolds numbers. Therefore, an asymptotic theory of Tollmien-Schlichting waves is constructed under the assumption that the Reynolds number tends to infinity.
TL;DR: In this article, the boundary-value problem for submerged electroconvective jets with ionic conductivity was formulated and analyzed under two principal assumptions: nonlinear ohmic conductivity and point EHD interaction.
Abstract: The principal feature of electroconvective jets in liquid dielectrics developing under the influence of a high-voltage external field is the large value of the EHD interaction parameter. This leads to the coupling of the hydrodynamic and electric problems. As formulated in [1, 2] the situation is reversed: the EHD interaction parameter is small. In these problems the interest is usually confined to finding the electric characteristics of the jet for a given velocity field. In [3] flows from sharp electrodes in liquid dielectrics were analyzed under two principal assumptions: nonlinear ohmic conductivity and point EHD interaction. This paper deals with the calculation of submerged electroconvective jets with ionic conductivity on the basis of the boundary-value problem formulated in [4]. In this case point EHD interaction is not assumed. It should be noted that in this formulation the problem is of practical as well as theoretical interest, for example, in connection with the problem of designing throttle EHD converters [5].
TL;DR: In this paper, the authors clarified the nature and conditions of occurrence of hysteresis of supersonic flows with separation and proposed a method to clarify the conditions of such a phenomenon.
Abstract: The paper aims to clarify the nature and conditions of occurrence of hysteresis of supersonic flows with separation.
TL;DR: In this paper, two main qualitatively different regimes of the transition from laminar to turbulent flow and an intermediate regime which possesses the characteristic features of both regimes are investigated. But the authors focus on the transition mechanism.
Abstract: Experiments have established that there are two main qualitatively different regimes of the transition from laminar to turbulent flow and an intermediate regime which possesses the characteristic features of both. These regimes reflect the different ways in which a two-dimensional wave pattern can be transformed into a three-dimensional one; they must be a consequence of the initial conditions. The aim of the investigation reported in the present work was to analyze these regimes by systematically varying the initial data, to demonstrate the possibility of controlling the nature of the transition, to obtain some data to test theoretical models of the development of three-dimensional wave patterns on transition, and to make further experimental investigations of the transition mechanisms.
TL;DR: In this paper, the conditions of applicability and examples of the application of Batchelor's model are analyzed and the application examples are presented, along with conditions for applicability.
Abstract: The paper analyzes the conditions of applicability and examples of the application of Batchelor's model.
TL;DR: In this article, the authors considered stationary thermocapillary convection in a thin horizontal layer of fluid with Prandtl number Pr < 1 when it is being locally heated from above in conditions in which the curvature of the free surface is small.
Abstract: The article considers stationary thermocapillary convection in a thin horizontal layer of fluid with Prandtl number Pr < 1 when it is being locally heated from above in conditions in which the curvature of the free surface is small. It is shown that the motion has a cellular structure. The size of the convective cell is determined from the solution to the spectral problem to which the integration of the free convection system of equations reduces. If the Maragoni (Peclet) number is sufficiently high, the length of the convective cell turns out to be large in comparison with the thickness of the layer. The convection picture is considered and an expression obtained for the velocity of the developing flow.
TL;DR: In this paper, the influence of the field on the velocity and shape of a hydrodynamic soliton is considered and the bifurcation of the equilibrium shapes of a charged liquid is solved in the nonlinear formulation of the dynamics of nonlinear solitary forms (lunes, trenches).
Abstract: Plane nonlinear waves in shallow water are described by the Kortewegde Vries equation [1–3]. The present paper contains theoretical investigations of nonlinear waves and nonlinear equilibrium shapes on the surface of a charged liquid. The influence of the field on the velocity and shape of a hydrodynamic soliton is considered. The bifurcation of the equilibrium shapes is investigated. Problems of the equilibrium shapes of a charged liquid are solved in the nonlinear formulation of the dynamics of nonlinear solitary forms (lunes, trenches) on the surface.
TL;DR: In this paper, the authors studied the influence of the angle of slip on the profiles of the temperature and the velocity across the shock layer and made a study of the dependence of the distributions of the pressure, the heat flux and the friction coefficients along the surface of the body on the blowing-suction parameter and the angles of attack and slip.
Abstract: In the framework of the theory of a hypersonic viscous shock layer [1] with modified Rankine-Hugoniot relations [2] at the shock wave a study is made of flow past wings of infinite span with a rounded leading edge. A numerical solution to the problem has been obtained in a wide range of variation of the Reynolds number (5–106), the blowing-suction parameter, the angle of attack (0–45 °), and the angle of slip (0–70 °). Data are given on the influence of the angle of slip on the profiles of the temperature and the velocity across the shock layer. A study is made of the dependence of the distributions of the pressure, the heat flux, and the friction coefficients along the surface of the body on the blowing-suction parameter and the angles of attack and slip.
TL;DR: In this paper, the influence of the determining parameters on the size of the separation region formed when a normal shock wave impinges on a turbulent boundary layer in conical flows is analyzed.
Abstract: Published experimental data [1–5] are used to analyze the influence of the determining parameters on the size of the separation region formed when a normal shock wave impinges on a turbulent boundary layer in conical flows. Empirical dependences are proposed that make it possible to calculate the size of the region and its position relative to the incident shock wave or the direction of the undisturbed flow.