Explore the vast range of titles available.

An inviscid vortex shedding model is numerically extended to simulate falling flat plates. The body and vortices separated from the edge of the body are described by vortex sheets. The vortex shedding model has computational limitations when the angle of incidence is small and the free vortex sheet approaches the body closely. These problems are overcome by using numerical procedures such as a method for a near-singular integral and the suppression of vortex shedding at the plate edge. The model is applied to a falling plate of flow regimes of various Froude numbers. For Fr=0.5, the plate develops large-scale side-to-side oscillations. In the case of Fr=1, the plate motion is a combination of side-to-side oscillations and tumbling and is identified as a chaotic type. For Fr=1.5, the plate develops to autorotating motion. Comparisons with previous experimental results show good agreement for the falling pattern. The dependence of change in the vortex structure on the Froude number and its relation with the plate motion is also examined.

A well-posedness theory for the initial-value problem for hydroelastic waves in two spatial dimensions is presented. This problem, which arises in numerous applications, describes the evolution of a thin elastic membrane in a two-dimensional (2D) potential flow. We use a model for the elastic sheet that accounts for bending stresses and membrane tension, but which neglects the mass of the membrane. The analysis is based on a vortex sheet formulation and, following earlier analyses and numerical computations in 2D interfacial flow with surface tension, we use an angle–arclength representation of the problem. We prove short-time well-posedness in Sobolev spaces. The proof is based on energy estimates, and the main challenge is to find a definition of the energy and estimates on high-order non-local terms so that an a priori bound can be obtained.

An inviscid vortex shedding model for separated vortices from a solid body is studied. The model describes the separated vortices by vortex sheets and the attached flow via conformal mapping. We develop a computational model to simulate the vortex shedding of a moving body, with varying angle. An unsteady Kutta condition is imposed on the edges of the plate to determine the edge circulations and velocities. The force on the plate is obtained by integrating the unsteady Blasius equation. We apply the model to two representative cases of an accelerated plate, with impulsive start and uniform acceleration, and investigate the dynamics for large angles of attack. For both cases, the vortex force is dominant in the lift over times. The lift coefficients are initially high and decrease in four chord lengths of displacement, in general. For large angles of attack, the appearance of a peak of lift at an early time depends on the power-law velocity, which differs from the behavior for small angles of attack. The lift and drag from the model are in agreement with the Navier–Stokes simulation and experiment for moderate Reynolds numbers. We also demonstrate the vortex shedding of hovering and flapping plates. In the hovering motion, the large increase in lift at the early backward translation is due to the combined effect of the vortex force and added mass force. In the flapping plate, our model provides an improvement in the prediction for the induced force than other shedding models.

A review of fundamental theoretical studies concerning plane vortex flows in an incompressible fluid is presented. Problems connected with flow in the vicinity of the point of a vortex sheet vanishing from a solid surface, with self-similar flows of an ideal and viscous fluid, with flow in the cores of spiral vortex sheets, with the stability and diffusion of vortex flows, and with the development of a theory of boundary-layer separation from a solid surface are considered.

A review of fundamental theoretical studies concerning the theory and application of the nonsteady-state analogy to an incompressible fluid flowing around slender bodies is presented. Problems related to the application of nonsteady-state analogy to wings, to the wake behind an elliptically loaded wing, as well as methods for numerical calculation of the evolution of vortex sheets and for determining the positions of lines of low separation from solid surfaces are considered taking into account viscous-inviscid interactions. The issues of nonuniqueness and asymmetry of solutions for the problems of a separated flow moving around slender bodies are discussed.

This paper presents a method to evaluate the near-singular line integrals that solve elliptic boundary value problems in planar and axisymmetric geometries. The integrals are near-singular for target points not on, but near the boundary, and standard quadratures lose accuracy as the distance d to the boundary decreases. The method is based on Taylor series approximations of the integrands that capture the near-singular behaviour and can be integrated in closed form. It amounts to applying the trapezoid rule with meshsize h, and adding a correction for each of the basis functions in the Taylor series. The corrections are computed at a cost of O(nw) per target point, where typically, nw=10–40. Any desired order of accuracy can be achieved using the appropriate number of terms in the Taylor series expansions. Two explicit versions of order O(h2) and O(h3) are listed, with errors that decrease as d→0. The method is applied to compute planar potential flow past a plate and past two cylinders, as well as long-time vortex sheet separation in flow past an inclined plate. These flows illustrate the significant difficulties introduced by inaccurate evaluation of the near-singular integrals and their resolution by the proposed method. The corrected results converge at the analytically predicted rates.

A review of fundamental theoretical publications is presented, wherein the flow of an incompressible fluid in the cores of three-dimensional vortex sheets formed in the case of the separated flow of low-aspect-ratio wings are considered. Problems concerning an inviscid-fluid flow in the core of a conical vortex sheet and a vortex sheet vanishing from the edges of a parabolic wing, as well as the problem of a viscous-fluid flow in the core of a conical vortex structure, are considered.

A theoretical model is proposed to describe fully nonlinear dynamics of interfaces in two-dimensional MHD flows based on an idea of non-uniform current-vortex sheet. Application of vortex sheet model to MHD flows has a crucial difficulty because of non-conservative nature of magnetic tension. However, it is shown that when a magnetic field is initially parallel to an interface, the concept of vortex sheet can be extended to MHD flows (current-vortex sheet). Two-dimensional MHD flows are then described only by a one-dimensional Lagrange parameter on the sheet. It is also shown that bulk magnetic field and velocity can be calculated from their values on the sheet. The model is tested by MHD Richtmyer–Meshkov instability with sinusoidal vortex sheet strength. Two-dimensional ideal MHD simulations show that the nonlinear dynamics of a shocked interface with density stratification agrees fairly well with that for its corresponding potential flow. Numerical solutions of the model reproduce properly the results of the ideal MHD simulations, such as the roll-up of spike, exponential growth of magnetic field, and its saturation and oscillation. Nonlinear evolution of the interface is found to be determined by the Alfvén and Atwood numbers. Some of their dependence on the sheet dynamics and magnetic field amplification are discussed. It is shown by the model that the magnetic field amplification occurs locally associated with the nonlinear dynamics of the current-vortex sheet. We expect that our model can be applicable to a wide variety of MHD shear flows.

In this paper, we address the problem of current–vortex sheets in ideal incompressible magnetohydrodynamics. More precisely, we prove a local-in-time existence and uniqueness result for analytic initial data using a Cauchy–Kowalevskaya theorem.

In vortex methods, vorticity is the primary computed variable. The problem of the accuracy improvement of vorticity generation simulation at the airfoil surface line in 2D vortex methods is considered. The generated vorticity is simulated by a thin vortex sheet at the airfoil surface line, and it is necessary to determine the intensity of this sheet at each time step. It can be found from the no-slip boundary condition, which leads to a vector boundary integral equation. There are two approaches to satisfy this equation: the first one leads to a singular integral equation of the 1st kind, while the second one leads to a Fredholm-type integral equation of the 2nd kind with bounded kernel for smooth airfoils. Usually, for numerical solution of the boundary integral equation, the airfoil surface line is replaced by a polygon, which consists of straight segments (panels). A discrete analogue of the integral equation can be obtained using the Galerkin method. Different families of basis and projection functions lead to numerical schemes with different complexity and accuracy. For example, a numerical scheme with piecewise-constant basis functions provides the first order of accuracy for vortex sheet intensity, and a numerical scheme with piecewise-linear functions gives the second order of accuracy. However, the velocity field near the airfoil surface line is also of interest. In the case of rectilinear airfoil surface line discretization, the accuracy of velocity field reconstruction has no more than the first order of accuracy for both, piecewise-constant and piecewise-linear numerical schemes. In order to obtain a higher order of accuracy for velocity field reconstruction, it is necessary to take into account the curvilinearity of the airfoil surface line. In this research, we have developed such an approach, which provides the second order of accuracy both, for vortex sheet intensity computation and velocity field reconstruction.