Inviscid Incompressible Flow Research Articles

Effect of Hinge Gap on Aerodynamics of Thin Airfoils Having an Oscillating Flap

Nonsteady load distributions on a thin airfoil in inviscid incompressible flow having an oscillating flap with a narrow hinge gap are investigated. The angle of attack is assumed to be zero in front of the hinge gap. The problem is first attacked numerically through Poisson’s integral equation to compare it with analytical methods derived later. The logarithmic singularity in the kernal function is treated with special care. Secondly the method of matched asympototic expansions is used to analyze the problem. It brings forth simple closed-form expressions. Comparisons of results of the two methods show excellent agreement with each other, when gap width-to-chord ratio is less than 0.1. In the Appendix, a simplified method is presented where no inner solution needs to be considered. It is useful for the gap/chord ratio less than 0.01.

Unsteady lifting-line theory as a singular perturbation problem

Unsteady lifting-line theory is developed for a wing of large aspect ratio oscillating at low frequency in inviscid incompressible flow. The wing is assumed to have a rigid chord but a flexible span. Use of the method of matched asymptotic expansions reduces the problem from a singular integral equation to quadrature. The pressure field and airloads, for a prescribed wing shape and motion, are obtained in closed form as expansions in inverse aspect ratio. A rigorous definition of unsteady induced downwash is also obtained. Numerical calculations are presented for an elliptic wing in pitch and heave; compared with numerical lifting-surface theory, computation time is reduced significantly. The present work also identifies and resolves errors in the unsteady lifting-line theory of James (1975), and points out a limitation in that of Van Holten (1975, 1976, 1977).

Computation of inviscid incompressible flow with rotation

The standard hyperbolic methods used to solve the compressible Euler equations are not effective in the limit of incompressible flow. The sound waves dominate the system and it becomes poorly conditioned for numerical solution. For steady flow governed by the incompressible Euler equations, artificial compressibility is a technique that removes the troublesome sound waves. It leads to a hyperbolic system of equations that we solve by finite-volume differences centred in space, and explicit multistage time-stepping. The stability of this novel system is analysed, its allowable discontinuities are described, and appropriate far-field and solid-wall boundary conditions are introduced. Results are presented for both two- and three-dimensional flows, including vorticity shed from a delta wing. Whether vorticity is produced or not depends very strongly on the body geometry, the accuracy of the solution method, and the transient discontinuities that evolve in the flow field. The results are analysed for the total-pressure losses in the flow fields, and for the diffusion of the vortex sheets.

Vortex Induced Lift on a Flat Plate with a Curved Forward‐Facing Flap

Free streamline solutions are obtained for two dimensional inviscid incompressible flow past a flat plate with a forward‐facing curved flap. It is shown that it is possible to shape the curved flap to make the adverse pressure gradient on top of the flap less severe than for a straight flap and thus increase the prospects of making the flow experimentally realizable.

Evaporation from a two-dimensional meniscus

Evaporation from a two-dimensional meniscus, caused by the heating of a flat platinum plate immersed vertically in a pool of water, is modeled and analyzed. Bernoulli's equation for incompressible inviscid fluid flow is applied to the meniscus line, which is approximated to be a streamline of the liquid flow. The effects on evaporation heat transfer of two types of resistance are examined parametrically: 1) that due to the evaporation coefficient at the liquid-vapor interface, and 2) that due to the presence of a nonevaporating thin film at the wall. A logarithmic coordinate transformation is used to stretch the region in the neighborhood of the wall, and the numerical results show that in this region the velocity at, and heat flux through, the meniscus line have maximum magnitudes. Using physically plausible values for resistance of the first type, the numerical results show that both the local and the total Nusselt numbers are insensitive to all physically plausible values for resistance of the second type. If, on the other hand, resistance of the first type is ignored altogether, serious errors can arise in the computed values for the total Nusselt number.

Variational properties of stationary inviscid incompressible flows with possible abrupt inhomogeneity or free surface

The inviscid flows, possibly rotational and nonsmooth, which satisfy the equation of stationary incompressible hydrodynamics, are characterized as giving zero variation rate to some real functional when the corresponding scalar and vector fields are transported by what is called a carrier, i.e. a mobile differential manifold. This transport does not have to preserve volumes; the Bernoulli function figures as the natural unknown scalar field rather than the pressure. Inhomogeneity may be sharp, implying in particular the presence of free surfaces. The key mathematical concept is that of a divergence-free vector measure convected by a carrier. For easier handling of this concept, some versions of the main variational statement are derived, involving vector potentials and stream functions in two or three dimensions; axially symmetric flows are also considered.

On the design of three-dimensional wind tunnel contractions

A method is given for the calculation of incompressible inviscid flow through non-axisymmetric contracting ducts with rectangular cross-sections. The method is based on a finite difference approximation to Laplace's equation and solved by the method of successive over relaxation. In an attempt to provide practical criteria for the design of such contractions, the flows through a series of contraction shapes were calculated, each shape being based on a pair of matched elliptic arcs. This permitted choice of such parameters as length, local (ie two-dimensional) contraction ratio, position and magnitude of the maximum slope. It was found that reducing the length of the contraction also reduced its effective length, although increasing the effects of overshoot and undershoot. This could be compensated for by designing a contraction with a steep maximum slope which with associated low curvatures at entrance and exit reduced the values of overshoot and undershoot. The axial positions of maximum slope on wall and roof should be the same.The predictions of the numerical method were tested against experiment and, in general, satisfactory comparisons were obtained.

Vortex Induced Lift on Two Dimensional Low Speed Wings

Exact free streamline solutions are found for two dimensional inviscid incompressible flow past a single and a multiple flap wing using a hodograph method. It is shown that solutions do not exist for arbitrary shapes, but that a geometrical constraint must be satisfied between the shape of the wing and the angle of attack. High lift coefficients are obtained for both cases. These solutions model the flow situation for a wing claimed in the past to give high lift at low speed.

Prediction of vortex lift on interacting delta wings in incompressible flow

Vortex flow modeling is used to calculate the steady inviscid incompressible flow past one, two and three delta wing configurations. The wings are modeled with vortex lattices and the leading and trailing-edge sheets are modeled by segmented straight vortex filaments. Aerodynamic characteristics are obtained for a range of geometry and angle of attack.

Hydroelastic Instability of Infinite Strips Under Shearing Load on an Elastic Foundation

The paper examines the hydroelastic instability of an infinitely long plate subjected to shearing load with two different boundary conditions, one side of which is exposed to an incompressible inviscid flow, and the other side supported on an elastic foundation. The analysis is based on the small deflection plate theory and the classical linearized potential flow theory. The Galerkin method and Fourier transforms are used. It is found that the effects of the shearing load and the elastic foundation on the divergence velocity can be illustrated by a single curve for both clamped and simply supported cases.

Hydroelastic instability of orthotropic panels with infinite width under shearing load

An analysis is presented of the hydroelastic instability of an orthotropic plate with finite length and infinite width exposed to an incompressible inviscid flow over its upper surface and subjected to shearing loads along both its edges. On the basis of the small deflection plate theory and the classical linearized potential flow theory, the problem is solved for two different boundary conditions by means of the Galerkin method and Fourier transforms. It is found that an increase of the shearing load larger than about one half of the buckling load reduces rapidly the divergence velocity and increases discontinuously the divergence wavelength.

Regularization of contour dynamical algorithms. I. tangential regularization

Contour dynamical methods are being applied to a variety of inviscid incompressible flows in two dimensions. These generalizations of the “waterbag” method provide simplified models for following the evolution of contours x (J) that separate regions of constant density which are the sources of the flow. The inviscid evolution of contour j, x̂ t (j) is usually an area-preserving map. For physically unstable problems, a piecewise-constant initial condition may result in an ill-posed problem. That is, contours may rapidly grow in perimeter and/or develop singularities and numerically induced small-scale structures in a finite time. To avoid such problems and model realistic weakly dissipative or weakly dispersive flows, contour regularization procedures are required. Dissipative and dispersive tangential regularization procedures for one contour are introduced. A special case of the former, namely ẋ t = μx ss , corresponds in lowest order to a linear diffusion operator in two dimensions. The contour is parameterized with arc length using cubic splines and an adaptive curvature controlled node adjustment algorithm is used. A modified Crank-Nicolson method is used to solve the discrete representation of the full system, x t = x̂ t +μx ss . Numerical results are given for the evolution of initially elliptical shapes according to prescribed area-preserving maps. The numerical results for area evolution agree with analytical results.

Domain decomposition methods for nonlinear problems in fluid dynamics

The numerical solution of finite element approximations of complicated two- and three-dimensional nonlinear problems can be a most formidable task. In order to overcome this difficulty related to dimensionality, domain-splitting methods can be very effective, particularly in view of obtaining a fast and economical conjugate gradient solver, which can be used to precondition the solution of nonlinear problems by optimization methods via nonlinear least squares or weighted residual formulations. A new technique of this type will be introduced and analysed and its efficiency will be discussed from numerical experiments concerning the numerical simulation of transonic flows for compressible inviscid fluids and incompressible viscous flows modelled by the Navier-Stokes equations.

The Elliptic Solution of the Secondary Flow Problem

This paper presents the elliptic solution of the inviscid incompressible secondary flow in curved passages. The three-dimensional flow field is synthesized between 3 sets of orthogonal nonstream surfaces. The two-dimensional flow field on each set of surfaces is considered to be resulting from a source/sink distribution. The distribution and strength of these sources are dependent on the variation in the flow properties normal to the surfaces. The dependent variables in this formulation are the velocity components, the total pressure, and the main flow vorticity component. The governing equations in terms of these dependent variables are solved on each family of surfaces using the streamlike function formulation. A new mechanism is implemented to exchange information between the solutions on the three family surfaces, resulting into a unique solution. In addition, the boundary conditions for the resulting systems of equations are carefully chosen to insure the existence and uniqueness of the solution. The numerical results obtained for the rotational inviscid flow in a curved duct are discussed and compared with the available experimental data.

The use of an error index to improve numerical solutions for unsteady lifting airfoils

The numerical methods of the aerodynamic finite element method are investigated for airfoils in incompressible inviscid flow, using an index parameter. This method can compare large amounts of data in an efficient and precise manner. The first problem is a concentration of error at the airfoil edges, which occurs in all of the cases investigated. This difficulty can be solved by using the semicircular method of computation. The second problem results from the logarithmic singularity of the unsteady kernel function; the difficulty dramatically reduced through a special method for treating the logarithmic singularity. It is found that using the error index parameter has advantages for several schemes of quantizing lift distribution.

Finite‐element method for time‐dependent euler equation

AbstractThis paper presents finite element methods to approximate inviscid incompressible flow problems.First we emphasize the conservation properties of these problems, and we show that finite element methods appear as a very natural way to find conservative schemes such as Arakawa's scheme. We give convergence theorems and an error analysis of finite element discretization schemes. We turn then to the time differencing problem. We derive stability and convergence results for a second‐order semi‐implicit scheme and for the leap‐frog scheme.

A nonlinear Hamiltonian structure for the Euler equations

The Euler equations for inviscid incompressible fluid flow have a Hamiltonian structure in Eulerian coordinates, the Hamiltonian operator, though, depending on the vorticity. Conservation laws arise from two sources. One parameter symmetry groups, which are completely classified, yield the invariance of energy and linear and angular momenta. Degeneracies of the Hamiltonian operator lead in three dimensions to the total helicity invariant and in two dimensions to the area integrals reflecting the point-wise conservation of vorticity. It is conjectured that no further conservation laws exist, indicating that the Euler equations are not completely integrable, in particular, do not have soliton-like solutions.

Unsteady incompressible inviscid aerodynamics of a thin airfoil withnarrow gaps

Nonsteady load distributions are investigated on a two-dimensional thin airfoil having narrow gaps in an inviscid incompressible flow. First, the problem is solved numerically through the Possio's integral equation to yield a basis of comparison with the analytical method. The logarithmic singularity in the kernel function requires a special treatment for highly accurate results when the reduced frequency is large (say, more than 2). Second, under the restriction of very narrow gaps the problem is attacked analytically through the method of matched asymptotic expansion (MAE), which results in simple closed-form expressions. Comparisons of some results obtained from these two methods show excellent agreement with each other.

地面効果を受けた２次元翼の空力特性 前後縁部に重点をおいた簡易計算法

A method on aerodynamic theory of two-dimensional intake in an incompressible inviscid flow is developed. Conformal mapping and modified THEODORSEN-GARRICK transformation are used. Then the method is extended easily to two-dimensional airfoils in ground effect. This method is essentially accurate especially near the leading and trailing edges without special considerations needed often by other methods. Stream line patterns are easily calculated as well as velocity distribution on the wing surface. Computation time required by this method may be substantially less than other methods.

Rotational compressible inviscid flow with rolled vortex sheets. An analytical algorithm for the computation of the core

Previous work on irrotational incompressible inviscid flow (Guiraud & Zeytounian 1977) is extended to rotational and compressible flow. A formal proof is given that, within the core, one may avoid computing with the sheet by defining an equivalent continuous flow. One shows how the vorticity and the entropy gradient between the turns of the sheet are transported along trajectories of the equivalent continuous flow.