Mathematical model of inchworm locomotion

Inchworms are caterpillars. Their locomotion, involving arching of much of the central portion of their body length, has not been studied as extensively as the peristaltic locomotion of worms or the crawling locomotion of many other caterpillars. A mathematical model is developed to describe the shapes and bending strains of typical inchworm motions. The inchworm is assumed to travel in a straight line on a rigid horizontal substrate. Two basic types of cycles are considered. In Case I, the inchworm body arches and then reverses that motion in becoming flat again. In Case II, the body arches, then cantilevers upward, and then falls down to a flat shape. A continuum model based on an elastica is adopted. The results may be useful in the development of soft robots exhibiting an inchworm mode of motion.     

Laminar-turbulent flow over wedges mounted on sharp and blunt plates

The flow pattern and the heat transfer on sharp and blunt flat plates near a wedge in a Mach 6 stream are experimentally investigated for two Reynolds numbers corresponding to the laminar and transitional states of the undisturbed boundary layer ahead of the wedge. It is shown that, as in a two-dimensional flow, plate bluntness leads to the attenuation of the heat transfer in the boundary layer/shock wave interference zone. However, when a certain threshold value of the bluntness is exceeded, a further increase in the bluntness has almost no effect on the heat transfer. For the first time, an experiment conducted in an intermittent (blow-down) wind tunnel has been based on the comprehensive use of panoramic (global) techniques for measuring the heat transfer and pressure coefficients and a method for visualizing the surface friction employing the luminescence effect after UV irradiation.     

The Flow and Heat Transfer at Start-Up of an Arbitrarily Shaped Body in a Viscous Heat-Conducting Gas

The flow corresponding to the start-up of an arbitrarily shaped body in a viscous heat-conducting gas is analyzed. The established fact of fluid incompressibility at short times is used. In the first approximation, in the neighborhood of each point on the body surface the flow and heat transfer are proved to be the same as for an infinite plate coinciding with the tangential plane at this point. The corrections for the curvature of the body surface are found. For determining the flows near a cylinder of arbitrary shape and near a spherical bluntness, the start-up problems for a circular cylinder and a sphere are considered. The possibility of extending the results to the case of reacting gases is discussed.     

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.     

On the penetration of nonaxisymmetric bodies into a deformable solid medium and their shape optimization

We consider the problem of penetration of rigid pyramidal bodies (impactors) into a strained medium in the case of large speeds of penetration and estimate the depth of the impactor penetration. To this end, we use the two-stage penetration model proposed by Forrestall. We state the shape optimization problem for the penetrating body, which is based on the consideration of a set of bodies of pyramidal external shape with given fixed mass. We study both solid and hollow (shell-shaped) bodies. For the optimization functional we take the penetration depth of the penetrating body, and for the projection variable we take the number of faces of the pyramidal body. We present the results of computations of the penetration depth for different shapes of the impactor and show that, both for shells and solid impactors, the bodies of the shape of a circular cone are optimal. The problems of high-speed penetration of rigid bodies into a deformable medium are nowadays very topical problems [1] which have been studied by Russian and foreign authors [2–8].     

Two-dimensional interaction between an incident shock and a turbulent boundary layer in the presence of an entropy layer

The results of an experimental and numerical investigation of flow and heat transfer in the region of the interaction between an incident oblique shock and turbulent boundary layers on sharp and blunt plates are presented for the Mach numbers M_∞ = 5 and 6 and the Reynolds numbers Re_∞L = 27×10⁶ and 14×10⁶. The plate bluntness and the incident shock position were varied. It is shown that the maximum Stanton number St _m in the shock incidence zone decreases with increase in the plate bluntness radius r to a certain value and then varies only slightly with further increase in r. In the case of a turbulent undisturbed boundary layer heat transfer is diminished with increase in r more slowly than in the case of a laminar undisturbed flow. In the presence of an incident shock the bluntness of the leading edge of the flat plate results in a greater decrease in the Stanton number than in the absence of the shock. With increase in the bluntness of the leading edge of the plate the separation zone first sharply lengthens and then decreases in size or remains constant.     

NEGRETTI采样头切割原理的动力学分析

根据两相流体动力学理论对Negretti采样头中颗粒物的运动规律进行了分析,计算了PM10和 PM2．5采样时颗粒物的运动轨迹,通过计算讨论了气流流量、颗粒物粒径等不同情况下各种因素对颗粒物运动轨迹的影响．结果表明两相流动力学是对采样切割器中颗粒物的运动进行数值模拟的有效工具,能对采样头的设计、制造提供有力的帮助．     

Experimental and Numerical Investigation of Heat Exchange between Underexpanded High-Enthalpy Air Jets and Cylindrical Models

Experiments on heat transfer in supersonic underexpanded high-enthalpy air jets are conducted on the VGU-4 induction plasmatron at the pressure in the compression chamber of 8.5 hPa. At the air flow rate of 3.6 g/s and the high-frequency generator powers of 45 kW(regime 1) and 64 kW (regime 2) the heat fluxes to the copper surface at the stagnation point of watercooled cylindrical models along the axes of dissociated air jets are measured. The models, 30 mm in diameter, could have a flat face or a hemispherical nose. In the same regimes, the stagnation pressures are measured using the Pitot tube in the shape of a cylinder, 30 mm in diameter, having either a flat face or a hemispherical bluntness with a receiving hole, 14 mm in diameter. For the experimental conditions calculations of flows in the plasmatron discharge channel and supersonic underexpanded jets issuing from the discharge channel are performed within the framework of the Navier–Stokes and Maxwell equations. The heat fluxes to the experimental models are computed and compared with the experimental data.     

On the stress state of shells penetrating into a deformable solid

The motion of an axisymmetric shell in a deformable solid medium is considered. It is assumed that the medium resistance is described by a two-term expression containing a constant term (the rigidity characteristic) and an inertial term quadratic with respect to the penetration velocity. A model of the impactor penetration with the normal interactions with the resisting medium taken into account is proposed. The membrane forces and the arising stresses are determined for decelerated motions of the impactor.     

Interaction between an Inclined Shock and Boundary and High-Entropy Layers on a Flat Plate

The flow structure and heat exchange in the zone of interference between an inclined shock and the surface of a flat plate are investigated experimentally and theoretically as functions of many parameters, the interference being studied in both the presence and the absence of bluntness of the leading edge. The experiments were carried out at Mach numbers M = 6, 8, and 10 and the Reynolds numbers Re _L , calculated using the plate length L = 120 mm and the free-stream parameters, varied over the range from 0.24 ? 10⁶ to 1.31 ? 10⁶. The bluntness radius of the leading edge of the plate, the intensity of the impinging shock, and its location with respect to the leading edge were varied. The numerical simulation was carried out by solving the complete two-dimensional Navier-Stokes equations and averaged Reynolds equations using the q-ω turbulence model. The laminar boundary layer became turbulent inside the separation zone induced by the shock. It is shown that the plate bluntness significantly reduces the heat exchange intensity in the interference zone, this effect intensifying with increase in the Mach number.     

A multiparameter family of phase portraits in the dynamics of a rigid body interacting with a medium

The problem of plane-parallel motion of a uniform symmetric rigid body interacting with a medium only through a flat region of its outer surface is studied. The force field is constructed on the basis of information on the properties of jet flow under quasistationarity conditions. The motion of the medium is not studied. The problem of rigid body dynamics is considered for the case when the characteristic time of motion of the body relative to its center of mass is comparable with the characteristic time of motion of this mass center.     

Effect of boundaries of various shapes on vortex dynamics

The motion of a vortex near a boundary of arbitrary shape is considered within the framework of a two-dimensional problem. Integrable differential equations of motion are obtained. Two forms of the algebraic equation of the vortex trajectories are derived. Examples of vortex motion near a straight-line boundary, in a channel, in an angular domain, in the neighborhood of a flat edge, in a round basin, and near a parabolic boundary.     

Initial stage of the inclined impact of a smooth body on a thin fluid layer

The two-dimensional problem of the oblique impact of a free rigid body with a smooth flat bottom on a thin layer of an ideal incompressible fluid is considered. The initial stage of the impact when the body motion is accompanied by the formation of jets on the boundary of the body-fluid contact zone is investigated. The problem is solved jointly, i.e., the fluid flow initiated by the body motion and the motion of the body itself are determined simultaneously. A priori the “body-fluid” contact zone is unknown and determination of its time evolution represents a significant difficulty and the method of asymptotic matched expansions is used to overcome this difficulty. A system of integro-differential equations is obtained and the motion of the body under the action of hydrodynamic loads is investigated numerically on the basis of this system. It is shown that the hydrodynamic force exerted on the body during the impact is maximum precisely in the initial stage; therefore, the motion of the body varies fairly significantly in time considered.     

Three-Dimensional Interaction of a Blunt Cone with a Hot Region in a Supersonic Flow in the Presence of Surface Injection

The problem of the interaction of a blunt cone placed at zero incidence in a supersonic flow with a spherical hot region in the incident flow is considered for the case in which the hot region center is displaced relative to the axis of symmetry of the body. Two cases are studied: (1) the interaction of temperature inhomogeneity with an impermeable conical surface and (2) interaction in the presence of intense surface injection localized on the spherical bluntness of the body. It is shown that strong surface injection considerably improves the flow pattern and the aerodynamic characteristics of the body.     

Effect of surface non-flatness on the lubrication characteristics in the valve part of a swash-plate type axial piston pump

The objective of this application study was to investigate the effect of surface non-flatness on the lubrication characteristic of the bearing/sealing part between cylinder barrel and valve plate in a hydrostatic axial piston pump. A developed numerical algorithm facilitated the simultaneous calculation of time-varying cylinder pressure, rotating body motion, and fluid film pressure to observe fluid film geometry and power loss. It was shown that an ideally flat surface might not form full fluid lubrication film properly, and that small-scale machining error, surface waviness, may increase the film thickness to some degree. The shape model of surface waviness considered waviness unit shape as well as its surface lay. However the results demonstrated that surface non-flatness of such small scale did not form the desirable fluid film geometry which minimized the power loss yet. Providing some surface design tips, two particular curved surfaces whose pressure-generating mechanisms differ were selected and analyzed in variation with their shapes and operating conditions. This study asserted that a circumferentially wavy surface would make better performance of motion stability and power efficiency than a radially wedged land surface, and finally that the non-flatness design strategy should be applied with re-considering the clamping ability.     

Stability, Paths, and Dynamic bending of a Blunt Body of Revolution Penetrating into an Elastoplastic Medium

The deep penetration of a thin body with a blunt nose and rear into a lowstrength medium is explored. The motion of the body is described by a system of autonomous integrodifferential equations using the physical model of a separated asymmetric flow over the body and the localinteraction method. An analytical calculation of the Lyapunov stability boundary for straightline motion is performed for bodies with a parabolic meridian. The dependences of the dynamic stability of the body on various parameters are studied numerically. Curved motion paths are constructed in the region of instability, and the classification of paths proposed in previous studies of the motion of pointed bodies is confirmed. It is shown that an reverse ejection is possible when a blunt impactor enters a semiinfinite target. It is established that there is a fundamental possibility of attaining a path close to a specified one and that there is a weak dependence of motion characteristics with a developed separation on the separation angle. Examples are given of calculations of the evolution of the lateral load, the transverse force and moment, and the strength margin of the body using the theory of dynamic bending of a nonuniform rod.     

Shape optimization of impactor penetrating into concrete or limestone targets

The shape of the normally striking impactor that attains the maximum depth of penetration into a concrete or a limestone semi-infinite target for a given impact velocity is found. It is shown that the optimum shape is close to a blunt (in general case) cone and it is independent on the properties of the material of the target in the framework of the employed penetration model. The performance of some other typical shapes of the nose of the impactors (spherical-conic impactors, sharp-conic impactors, truncated-ogive impactors) are analyzed and compared with the optimal impactor.     

Combined method of calculating supersonic ideal-gas flow over a wing with a supersonic blunt leading edge

A combined numerical method, based on the successive calculation of the flow regions near the blunt leading edge and center of a wing, is proposed on the assumption that the angle of attack and the relative thickness and bluntness radius of the leading edge are small. The flow in the neighborhood of the leading edge of the wing is assumed to be identical to that on the windward surface of a slender body coinciding in shape with the surface of the blunt nose of the wing and is numerically determined in accordance with [1]. The flow parameters near the center of the wing are calculated within the framework of the law of plane sections [2]. In both regions the equations of motion of the gas are integrated by the Godunov method. The flow fields around elliptic cones are obtained within the framework of the combined method and the method of [3], A comparative analysis of the results of the calculations makes it possible to estimate the region of applicability of the method proposed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 159–164, January–February, 1989.The authors wish to express their gratitude to A. A. Gladkov for discussing their work, and to G. P. Voskresenskii, O. V. Ivanov, and V. A. Stebunov for making available a program for calculating supersonic flow over a wing with a detached shock.     

An inversion integral for crack-scattering data

The inverse problem of determining the size, shape and orientation of a flat crack from high-frequency far-field elastic waves scattered by the crack is investigated. The results show that desired information on a crack can be obtained from the first arriving scattered longitudinal waves only. It is shown that an approximate high-frequency solution to the direct problem, based on physical elastodynamics, yields an expression for the scattered far-field of longitudinal motion which suggests a solution to the inverse problem by application of Fourier-type inversion integrals to scattering data. Two kinds of inversion integrals are examined. The inversion problem becomes relatively simple if some a-priori information is available, either on the orientation of the plane of the crack or on a plane of symmetry. The method of inversion is verified for a flat crack of elliptical shape. Some computational technicalities are discussed, and the method is also applied to experimental scattering data.     

Investigation of the effect of nozzle shape on supersonic/hypersonic impactors designed for size discrimination of nanoparticles

In this study the flow field and the nanoparticle collection efficiency of supersonic/hypersonic impactors with different nozzle shapes were studied using a computational modeling approach.The aim of this study was to develop a nozzle design for supersonic/hypersonic impactors with the smallest possible cut-off size d_(50) and rather sharp collection efficiency curves.The simulation results show that the changes in the angle and width of a converging nozzle do not alter the cut-off size of the impactor;however,using a conical Laval nozzle with an L/D_n ratio less than or equal to 2 reduced d_(50).The effect of using a cap as a focuser in the nozzle of a supersonic/hypersonic impactor was also investigated.The results show that adding a cap in front of the nozzle had a noticeable effect on decreasing the cut-off size of the impactor.Both flat disks and conical caps were examined,and it was observed that the nozzle with the conical cap had a lower cut-off size.