Perturbation solution to the nonlinear problem of oblique water exit of an axisymmetric body with a large exit-angle

In this paper,a nonlinear,unsteady3-D free surface problem of the oblique water exitof an axisymmetric body with a large water exit-angle was investigated by means of theperturbation method in which the complementary angle a of the water exit angle waschosen as a small parameter.The original3-D problem was solved by expanding it into apower series of a and reduced to a number of2-D problems.The integral expressions forthe first three order solutions were given in terms of the complete elliptic functions of thefirst and second kinds.The zeroth-order solution didn‘t turn out to be a linear problem asusual but a nonlinear one corresponding to the vertical water exit for the same body.Computational results were presented for the free surface shapes and the forces exerted upto the second order during the oblique water exit of a series of ellipsoids with various ratiosof length to diameter at different Froude numbers.     

Confined creeping flow around an axisymmetric body: increase of the shape effect by a tube wall

Using a specially adapted experimental technique, associated with a visualization method based upon solid tracers, we have obtained the flow pattern induced by the very slow uniform translation of an axisymmetric body along the axis of a vertical tube filled with a viscous liquid, both in a fixed frame (the frame is attached to the tube) and in a “relative” frame (the frame accompanies the body in its translation). The body, whose shape evolves from a sphere to a cylinder frustum, is free from any attachment or interaction with any other body; only the tube wall interaction is relevant. In these conditions, the upstream-downstream symmetry, relative to the creeping regime hypotheses, has been very well verified and quantitative information concerning, in particular, the velocity field has been deduced with sufficient precision (better than 2%) to exercise the control of a numerical process capable of giving all the details of the hydrodynamic field including those not directly available from the experiments. By comparison with the unbounded flows around the same bodies, the strong increase of the shape effect by the presence of the confining tube wall has been pointed out and evaluated, on the drag as well as on the surface vorticity and pressure distributions.     

Profiling of plane and axisymmetric supersonic channels that realize discontinuous parameters at the exit and equalization of the flow

Supersonic channels realizing given nonuniform isentropic parameters at the exit section have been profiled numerically by Kraiko, Kireev, et al. [1–3]. The problem of profiling model channels to ensure a continuous isentropic flow at the exit in the case of a constant entropyS ₁ at the entrance was formulated by Kraiko and Shelomovskii [1]. In the present paper, two classes of supersonic channel are constructed. One of them realizes at the exit given discontinuous distributions of the entropy and the pressure p or the angle of inclination of the velocity vector w to the x axis. The other transforms a flow with discontinuous distributions of the gasdynamic parameters into a flow uniform with respect to p and . Schemes are proposed for the profiling of these classes of channels, and the results are given of calculations made by the classical method of characteristics and its layerwise modifications.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 155–159, May–June, 1984.We are very grateful to A. N. Kraiko for valuable discussions in preparing the material of the paper.     

Exact solution of plane isolated crack normal to a bimaterial interface of infinite extent

This paper presents an exact solution for the transverse interface crack in the plane strain case. The crack is perpendicular to the interface and in one material. The exact complex stress functions are first obtained with some unknown constants. The satisfactions of all boundary conditions are then checked, the condition at infinity is considered and the unknown constants are determined. Further study may focus on the case with different shear moduli and the influence of the large deformation.The English text was polished by Keren Wang.     

Wall-modeling for large-eddy simulation of flows around an axisymmetric body using the diffuse-interface immersed boundary method

A novel method is proposed to combine the wall-modeled large-eddy simulation(LES) with the diffuse-interface direct-forcing immersed boundary(IB) method.The new developments in this method include:(i) the momentum equation is integrated along the wall-normal direction to link the tangential component of the effective body force for the IB method to the wall shear stress predicted by the wall model;(ii) a set of Lagrangian points near the wall are introduced to compute the normal component of the effective body force for the IB method by reconstructing the normal component of the velocity. This novel method will be a classical direct-forcing IB method if the grid is fine enough to resolve the flow near the wall. The method is used to simulate the flows around the DARPA SUBOFF model. The results obtained are well comparable to the measured experimental data and wall-resolved LES results.     

Numerical simulation of a pulsating flow arising over an axisymmetric spiked blunt body at Mach 2.21 and Mach 6.00

The present paper reports a numerical simulation of the supersonic/hypersonic unsteady flow over a spiked blunt body. Axisymmetric compressible Navier-Stokes equations are solved using a high-resolution unfactored implicit upwind Roe's scheme and a time-accurate pseudo-time method is employed for advancing in time. Unsteady flows arising at Mach 2.21 and Mach 6.00 around a spiked cylinder are simulated and the computational results are compared with measurements. The simulated results are used to increase understanding of the mechanisms of the flow. Received 28 September 1999 / Accepted 26 July 2000     

Contact of a plate with an elastic body: an interface model

The authors study the problem of contact between a plate and an elastic body, using the interface model as introduced by Oden and Martins. The problem is formulated as a variational inequality. The authors use the theory of P-coercive variational inequalities, developed by the authors and K. Schmitt, to examine the existence and uniqueness of the solutions.Work completed with financial support from the National Program of Basic Research in the Natural Sciences of VietNam.     

Heating process simulation for a body subjected to an intensive thermal effect on its surface

An approximate method of calculating the nonstationary temperature fields for the case of rapid and intensive heating of bodies is considered. The fast heating of a body is simulated by various boundary conditions at its heated surface. An approximate method is proposed in a one-dimensional formulation to solve the unsteady-state heat conduction equation with these boundary conditions. The applicability of this method in practice is confirmed by comparing the approximate temperature fields with the exact solution. An approximate temperature field is constructed for a particular case with consideration of a temperature dependence of thermal parameters, which allows one to describe the heat localization in a heated zone.     

Active decoupling of the axisymmetric body wake response to a pitching motion

Controlled interactions between fluidic actuators and the cross flow over the aft end of a wire-mounted axisymmetric wind tunnel bluff body model (Re_D=2.3·10⁵) are exploited for modification of the near wake dynamics, and the consequent global aerodynamic loads. Actuation is effected using an array of four aft-facing synthetic jet modules through narrow, azimuthally-segmented slots that are equally distributed around the perimeter of the tail end. The model is supported by eight wires, each including a miniature inline force transducer for measurements of the time-resolved tension. The model’s position is varied in a prescribed trajectory by synchronous activation of shape memory alloy (SMA) segments in each of the mounting wires, and the aerodynamic forces and moments are manipulated over a range of pitch attitude. The effectiveness of the flow control approach is demonstrated by decoupling of the wake response from the body’s pitch motion at a low pitch frequency (k=0.013). It is shown that, under the active control, the wake symmetry can be restored or its asymmetry can be amplified.     

On profiling planar and axisymmetric nozzles and channels to achieve a given supersonic stream at the exit section

Under the assumption of an ideal gas, methods are described for profiling the supersonic parts of planar and axisymmetric nozzles and channels in order to achieve given, in the general case, nonuniform fields of the parameters at the exit section. Besides shockless arrangements, configurations are considered in which the required distributions of the entropy are produced by a shock formed by the flow past a specially profiled wall.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 94–102, July–August, 1981.We are grateful to V. A. Vostretsova for assistance in the work.     

Dynamic interaction between a sub-interface crack and the interface in a bi-material: time-domain BEM analysis

Summary Transient response of a sub-interface crack in a bi-material is studied with emphasis on the dynamic interaction between the crack and the interface, by combining the traditional time-domain displacement boundary element method (BEM) and the non-hypersingular traction BEM. Computations are performed for an unbounded bi-material with a crack subjected to impact tensile loading on its faces or incident impact waves and a bounded rectangular bi-material plate under remote impact tensile loading. Numerical results of the dynamic stress intensity factors (DSIFs) and dynamic interface tractions are presented for various material combinations and crack locations. It is shown that pronounced increases in DSIFs and the interface tractions may be caused in some cases because of the dynamic interaction between the crack and the interface.This work was initialized during the second author's stay at Institute of Mechanics, TU Darmstadt, Germany under the support of the Alexander von Humboldt Foundation. Discussion on the BEM formulation with Dr. Seelig is gratefully acknowledged. The first two authors are also grateful for the partial support by the China National Natural Science Foundation under Grant No. 10025211 and the NJTU Scientific Paper Fund (PD195).     

Bifurcation of the solution to the problem of steady traveling waves in a layer of viscous liquid on an inclined plane

Traveling waves in a viscous liquid flowing down an inclined plane can be described at small and moderate Reynolds numbers by an ordinary differential equation in the thickness of the layer [1, 2]. As the Reynolds number tends to zero, this equation goes over into an equation of third order with quadratic nonlinearity [3]. Periodic solutions of this last equation bifurcating from the plane-parallel solution have been investigated by Nepomnyashchii and Tsvelodub [3–6]. In the present paper, a study is made of the bifurcation of periodic solutions from periodic solutions, namely, an investigation is made of the values of the wave number for which a periodic solution is not unique; a bifurcation equation is derived, the number of bifurcating solutions is found, and their behavior near a bifurcation point is considered; and the bifurcating solutions are continued numerically with respect to a parameter (the wave number) from the neighborhoods of the bifurcation points.     

Nonstationary indentation of a blunt rigid body into an elastic layer: An axisymmetric problem

The nonstationary indentation of a blunt rigid body into an elastic layer is studied. The general formulation of the problem includes different boundary conditions in the contact area and on the free surface of the layer. The simplified nonmixed problem that arises at the early stage of interaction and allows obtaining approximate results for later times is solved exactly. The solution obtained is compared with that for the plane case __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 7, pp. 35–46, July 2008.     

Measurements in the flow around a marine propeller at the stern of an axisymmetric body

Experiments were performed in a wind tunnel to study the flow around an axisymmetric body driven by a marine propeller. Measurements were made in the boundary layer and wake of the bare body, on the body with only a dummy hub rotating, and finally, with the propeller in operation. Part 1 of this paper described the experimental arrangement and instrumentation. Also, circumferentially-averaged results were presented to clarify certain aspects of the overall flow. In the present part, measurements made with a triplesensor hotwire are analyzed using phase-averaging techniques to reconstruct the instantaneous velocity and Reynolds-stress fields downstream of the propeller and show the evolution of the wakes of individual blades, blade-tip vortices, and the complex flow associated with vortices generated at hub-blade junctions. It is found that the blade wakes and features of the tip and hub flow are evident up to about two propeller diameters, beyond which the wake of the body-propeller combination can be regarded as a rotationally-symmetric flow.     

Measurements in the flow around a marine propeller at the stern of an axisymmetric body

An experimental study of the flow around and behind an axisymmetric body driven by a marine propeller is reported. Experiments were performed in a wind tunnel to document this complex, unsteady, three-dimensional, turbulent shear flow. Measurements were made in the boundary layer and wake of the bare body with a fixed dummy hub for the propeller, with the dummy hub rotating, and finally, with the propeller in operation. A five-hole yaw probe was employed for the mean-flow measurements, and two- and threesensor hotwires were used to obtained the mean and turbulent velocity fields. Part 1 of this two-part paper describes the experimental arrangement and circumferentially-averaged results which clarify certain overall aspects of the flow when it is viewed as a rotationally-symmetric flow. These are of special interest in marine hydrodynamics. In Part 2, the triple-sensor hotwire data are analyzed using phase-averaging techniques to reconstruct the instantaneous velocity and Reynolds-stress fields downstream of the propeller to show the evolution of the wakes of individual blades, blade-tip vortices, and the complex flow associated with vortices generated at hub-blade junctions.     

Set of steady-state traveling waves on the surface of a liquid film flowing down an inclined plane

The nonlinear evolution equation often encountered in modeling the behavior of perturbations in various nonconservative media, for example, in problems of the hydrodynamics of film flow, is examined. Steady-state traveling periodic solutions of this equation are found numerically. The stability of the solutions is investigated and a bifurcation analysis is carried out. It is shown how as the wave number decreases ever new families of steady-state traveling solutions are generated. In the limit as the wave number tends to zero a denumerable set of these solutions is formed. It is noted that solutions which also oscillate in time may be generated from the steadystate solutions as a result of a bifurcation of the Landau-Hopf type.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 120–125, November–December, 1989.     

Analysis of plane and axisymmetric flows of incompressible fluids with the stream tube method: Numerical simulation by trust-region optimization algorithm

New concepts for the study of incompressible plane or axisymmetric flows are analysed by the stream tube method. Flows without eddies and pure vortex flows are considered in a transformed domain where the mapped streamlines are rectilinear or circular. The transformation between the physical domain and the computational domain is an unknown of the problem. In order to solve the non-linear set of relevant equations, we present a new algorithm based on a trust region technique which is effective for non-convex optimization problems. Experimental results show that the new algorithm is more robust compared to the Newton-Raphson method.     

Use of the plane of the hodograph with the shaping of an axisymmetric laval nozzle by a numerical method

In the development of [1] a method is proposed for solving the problem of the shaping of the subsonic part of an axisymmetric Laval nozzle with a straignt sonic line: the Dirichlet problem with a piecewise-continuous boundary function is stated and solved by a numerical method for a nonlinear equation of the second order in the plane of the hodograph.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 164–168, January–February, 1977.