On the unsteady inviscid force on cylinders and spheres in subcritical compressible flow

The unsteady inviscid force on cylinders and spheres in subcritical compressible flow is investigated. In the limit of incompressible flow, the unsteady inviscid force on a cylinder or sphere is the so-called added-mass force that is proportional to the product of the mass displaced by the body and the instantaneous acceleration. In compressible flow, the finite acoustic propagation speed means that the unsteady inviscid force arising from an instantaneously applied constant acceleration develops gradually and reaches steady values only for non-dimensional times c(infinity)t/R approximately >10, where c(infinity) is the freestream speed of sound and R is the radius of the cylinder or sphere. In this limit, an effective added-mass coefficient may be defined. The main conclusion of our study is that the freestream Mach number has a pronounced effect on both the peak value of the unsteady force and the effective added-mass coefficient. At a freestream Mach number of 0.5, the effective added-mass coefficient is about twice as large as the incompressible value for the sphere. Coupled with an impulsive acceleration, the unsteady inviscid force in compressible flow can be more than four times larger than that predicted from incompressible theory. Furthermore, the effect of the ratio of specific heats on the unsteady force becomes more pronounced as the Mach number increases.     

Boundary element simulation of inviscid flow around an oscillatory foil with vortex sheet

The dynamic performance of a rigid foil with harmonic vertical and rotational motions in fluid flow has been studied through velocity potential theory. A boundary element based time stepping scheme is introduced to simulate the flow around the foil and the vortex wake. The body surface condition is satisfied on the exact foil surface and the motion and deformation of the wake sheet shed at the trailing edge is tracked. Kelvin condition is satisfied and a Kutta condition for the unsteady motion is proposed to circumvent the singularity at the trailing edge. Point vortex, which is reduced from wake vortex dipole, is introduced to approximate the vorticity. The performance of foil NACA0012 with harmonic vertical and rotational motions are studied extensively; the propulsion/swimming mode, energy harvesting mode and the flying mode are analysed in detail.     

Solution of the two-dimensional unsteady diffusion equation for vortex flow

A numerical method of solution based on the use of probability analogies is presented. An example of a calculation by the scheme developed is given.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 30, No. 6, pp. 1107–1111, June, 1976.     

Numerical analysis of the inviscid incompressible flow in two-dimensional radial-flow pump impellers

The flow through a two-dimensional centrifugal impeller fitted with equiangular blades of arbitrary geometry is investigated using a combination of conformal mapping with a boundary element technique. The blades can be thin or thick of arbitrary cross-section. A theoretical analysis and a numerical procedure are developed to determine the pressure distributions along the blade.     

Explicit solution for the potential flow due to an assembly of stirrers in an inviscid fluid

The motion of an irrotational incompressible fluid driven by an assembly of stirrers, of arbitrary shape, moving at specified velocities in the fluid is considered. The problem is shown to be equivalent to a standard mathematical problem in potential theory known as the modified Schwarz problem. It turns out that the solution to this problem can be written down, in closed form, as an explicit integral depending on the conformal mapping to the fluid region from a canonical pre-image region and a kernel function expressed in terms of a transcendental function called the Schottky–Klein prime function. In this way, an explicit integral solution, up to conformal mapping, for the complex potential of the flow generated by an arbitrary assembly of stirrers can be written down.     

A uniformly valid solution for the three-dimensional inviscid supersonic flow past blunt bodies with strong compression in the shock wave

Summary An analytical uniformly valid approximate solution is developed for the steady threedimensional supersonic flow past blunt bodies. The inverse problem is investigated, i.e. the shock shape is prescribed. Viscosity and heat conduction are neglected. The approximation is based on two main assumptions: i) the density ratio across the shock is very small, ii) the pressure does not change its order of magnitude along a normal to the shock surface. The pattern of the streamlines projected on to the shock surface is calculated from an ordinary differential equation of second order by taking into consideration the pressure gradients. By evaluating two integrals the flow quantities and the streamlines are determined in the shock layer together with the body shape. The solution is also valid for sharp nosed bodies.The method is applied to paraboloidal or hyperboloidal shock shapes of various cross sections. Results are presented for the streamline projections in the entire flow field. The flow quantities and the streamline pattern in the shock layer are calculated in the symmetry plane of the flow field. The streamlines differ from the geodesics, i.e. the solution according to the Newtonian model. The flow quantities on the body and the body shape show good agreement with numerical results of the direct problem by Rusanov.With 10 Figures     

A meshless solution of two-dimensional unsteady flow

The boundary element method (BEM) is a very useful numerical method for groundwater flow models. Particularly, this method was used to solve problems in homogeneous domains. However, it presents even greater difficulties than the other numerical methods when coping with non-homogeneities which are so characteristic in the groundwater hydraulics. Recently, meshless method which is based on a local boundary integral approach is introduced. It uses distributed nodal points, covering the domain. These points can be randomly spread over the domain. Every node is surrounded by a simple surface centered at the collocation point and the boundary integral equation is written on this local boundary. The unknown variables, in the local sub-domains, are approximated by some of the interpolation method. In this paper the combination of radial basis functions and the dual reciprocity method is used to solve the time-dependent groundwater flow.     

Semianalytic solution to the problem of scattering from multiple cylinders above a perfectly conductive surface

We present a novel semianalytical method using multipole expansion technique to solve the problem of scattering from multiple perfectly conducting cylinders placed above a perfectly conducting ground plane. The idea behind the formulation is based on the observation that an infinite flat ground plane can be approximated as a cylinder with a radius approaching infinity. Using Green's representation of the electromagnetic fields and using addition theorem of Bessel function, we expand the fields in terms of multipoles. Applying the appropriate boundary condition on the surface of the cylinders and the ground plane based on the field polarization results in a set of linear systems of equations containing the multipole's coefficients. The technique presented here is highly efficient in terms of computing resources, versatile, and accurate. The near fields are generated for single and multiple object examples.     

Numerical solution of a multi-ion one-potential model for electroosmotic flow in two-dimensional rectangular microchannels

A new more general numerical model for the simulation of electrokinetic flow in rectangular microchannels is presented. The model is based on the dilute solution model and the Navier-Stokes equations and has been implemented in a finite-element-based C++ code. The model includes the ion distribution in the Helmholtz double layer and considers only one single electrical' potential field variable throughout the domain. On a charged surface(s) the surface charge density, which is proportional to the local electrical field, is imposed. The zeta potential results, then, from this boundary condition and depends on concentrations, temperature, ion valence, molecular diffusion coefficients, and geometric conditions. Validation cases show that the model predicts accurately known analytical results, also for geometries having dimensions comparable to the Debye length. As a final study, the electro-osmotic flow in a controlled cross channel is investigated.     

Distribution of volume-averaged parameters of vortex flow over the energy separation chamber of a vortex tube with supplemented flow

The profiles of averaged circular and axial velocity components, temperature, and pressure are measured in the axisymmetric channel of the energy separation chamber of a vortex tube with the introduction of additional flow in the near-axis zone on the side cross section where throttle is located.Rybinsk Aviation Engineering Institute. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 62, No. 4, pp. 534–538, April, 1992.     

Complete solution for a two-dimensional tanh-conductivity arc

This paper is a sequel to an earlier work on the dynamics of a two-dimensional tanh-conductivity arc. We present here a complete solution, based on the Galerkin technique, for the characteristic variation of current-voltage through an arc. The present results are qualitatively very similar to those obtained in earlier theoretical and experimental studies. The solutions obtained are the modification of the basic equations, which has led to quantitative investigations of the present problem. The influence of various arc parameters on the arc formation is also discussed.     

Equilibrium vortex density in a rotating two-dimensional superfluid

The equilibrium state of a two-dimensional superfluid in rotation is discussed. It is shown that, in equilibrium, the presence of polarizable vortex-antivortex pairs does not affect the critical angular velocity at which free vortices enter the system, nor does it affect the free vortex density at higher angular velocities.     

Existence of extra vortex and twin vortex of anomalous mode in Taylor vortex flow with a small aspect ratio

Summary This experimental work on Taylor vortex flow in a gap with a small aspect ratio is concerned with two extra vortices and a twin vortex system, each of which depends on an anomalous cell of the anomalous mode. Extra vortices are smaller than other vortices such as defined cells. At any Reynolds number and aspect ratio extra vortices can be found at the corner of the end plate and inner rotating cylinder and at the corner of the end plate and outer stationary cylinder. For a one-cell flow (anomalous one-cell mode) in a symmetric system, an outer extra vortex develops and grows to the same size as the main cell, only in an aspect ratio of less than one. A twin vortex is observed to form when two vortices are aligned in the direction of the radius. There are three flow fields on the end plate; two are extra vortex flows and the other is the main cell flow. The flow direction of the anomalous cell is from the inner cylinder to the outer one, at the end plate opposite of the flow direction of the normal cell.Nomenclature R ₁ Radius of inner cylinder (2R ₁=40.19±0.006 mm) - R ₂ Radius of outer cylinder (2R ₂=60.11±0.024 mm) - R _r Radius ratio (R ₁/R ₂=0.669) - d Clearance between cylinders (R ₂–R ₁=9.96±0.025 mm) - L Height of working fluid - Aspect ratio=L/d - Rotational angular speed - Kinematic viscosity - Re Reynolds number=R ₁ d/ Other nomenclature is defined as it appears     

Intrinsic dynamics of the boundary of a two-dimensional uniform vortex

The link between the shape of a two-dimensional, uniform vortex and self-induced velocities on its boundary is investigated through a contour-dynamics approach. The tangent derivative of the velocity along the boundary is written in a complex form, which depends on the analytic continuation of the tangent unit vector outside the vortex boundary. In this way, a classical analysis in terms of Schwarz's function of the boundary, due to Saffman, is extended to vortices of arbitrary shape. Time evolution of intrinsic quantities (tangent unit vector, curvature and Fourier's coefficients for the vortex shape) is also analyzed, showing that it depends on tangent derivatives of the velocities, only. Furthermore, a spectral method is proposed, aimed at investigating the dynamics of nearly-circular vortices in an inviscid, isochoric fluid. Comparisons with direct numerical simulations are also established.     

On the linear stability of a compressible inviscid parallel shear flow

Summary By applying an approach similar to that used in the Miles-Howard theory [1], [2] we derive simple constraints on the phase speedc _r ^* of the neutral three-dimensional (3-D) monochromatic disturbances in an inviscid compressible parallel two-dimensional (2-D) shear flow. It is shown that for a boundary layer flow [a ₀ ^*(y ^*)]² —[U ₀ ^*(y ^*)—c _r ^*]² must have a zero in [y ₁ ^*,y ₂ ^*) for the neutral 2-D modes whose phase speedc _r ^* does not belong to the range ofU ₀ ^*(y ^*). For the unstable waves the argument of Chimonas [3] applies leading to the Howard semi-circle theorem. HereU ₀ ^*(y ^*) anda ₀ ^*(y ^*) are the dimensional base velocity and local sonic speed respectively. It is suggested that hypersonic flows possess vertically highly undulated unstable normal modes.     

Noncanonical vortex transformation and propagation in a two-dimensional optical system

We produced an axial and canonical optical vortex by using a computer-generated hologram and then converted it to a noncanonical vortex by passing it through a cylindrical lens. We conducted an experimental study of the shape and trajectory of the noncanonical vortex as it propagates in free space and obtained an analytical expression explaining our experimental results. The computed trajectory and shape of the noncanonical vortex agree quite well with our experimental results.     

Theoretical and numerical results of a deterministic two-dimensional vortex method

The first part of the paper reviews results obtained in earlier work: (1) The outline of the derivation of an integral equation of Fredholm type with respect to vorticity from the Navier-Stokes equations, and (2) the analytical results for two deterministic vortex methods which are based on the corespreading model. The aim of the second part is to confirm the results of the previous analysis and to estimate the accuracy of these methods numerically. In the present paper, the model problem of a transient flow past an impulsively started circular cylinder is studied by several numerical methods. The numerical results show that (1) the Gaussian core-spreading methods are comparable with the random walk vortex method, (2) the numerical fluctuation of the deterministic methods is small, and (3) the number of panels is smaller than those in the random walk vortex method to obtain the flow with almost the same accuracy. The theoretical results in § 2–4 of the present paper are summarized from “Core-spreading vortex methods in two-dimensional viscous flows”,Computer methods in applied mechanics and engineering (in press), by Kida and Nakajima, with permission from Elsevier Science, The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK. The experimental picture is transferred from “The early stage of development of the wake behind an impulsively started cylinder for 40<Re<⁴”, by R Bouard and M Coutanceau,J. Fluid Mech. (1980) 101: 583–607.