Transonic Gas Flow Research Articles

Multidomain solution algorithm for potential flow computations around complex configurations

A method is presented for the computation of irrotational transonic flows of perfect gas around a wide class of geometries. It is based on the construction of a multidomain structured grid and then on the solution of the full potential equation discretized with finite elements. The novelty of the paper is the combination of three embedded algorithms: a mixed fixed-point/Newton algorithm to treat the non-linearity, a multidomain conjugate gradient algorithm to handle the grid topology and another conjugate gradient algorithm in each of the structured domains. This method has made possible the calculations of flows around geometries that cannot be treated in a structured approach without the multidomain algorithm; an application of this method to the study of the wing-pylon-nacelle interactions is presented.

Computing nonpotential transonic gas flows in nozzles from stream function and generalized potential equations

Computing nonpotential transonic gas flows in nozzles from stream function and generalized potential equations

Boundary Singularities in Steady Potential Compressible Flow Through Plane Two-Dimensional Channels

Boundary singularity solutions are reviewed, which relate to the steady, transonic potential flow of a perfect gas, through plane, two-dimensional convergent channels. Two singularities occur in the physical plane, one at upstream infinity and the other at the concave corner in channels that have a parallel entry section followed by a convergent section that ends at the throat plane. Solutions of these singularities are obtained from the general solution of Chaplygin's stream function equation in the hodograph system of coordinates. Uniform, uni-directional subsonic entry flow, in a finite-length channel, gives rise to a boundary singularity in the hodograph plane. The stream function is multi-valued at this singularity, where it varies between one and zero, while the flow direction is zero. This condition is removed by introducing circular polar coordinates (r, α) with origin at the singular point. For a sufficiently small value of r, a second-order partial differential equation of the stream function is obtained in the new coordinates. A particular solution of this equation is given, when r is small, rs say, in which the stream function gradient in the radial direction is taken as zero for all values of α at rs. The full series solution of the new equation is given in a paper which is to follow. Finally, consideration is given to the problem of matching the subsonic and supersonic flow regions at the sonic surface. A new system of equations is given, which determine the stream function gradient at sonic points from values of the stream function in the expansion region. Computed results are given that relate to the steady, choked flow of a perfect gas through a 15° convergent channel. The overall solution is shown to converge.

Level of self-excited vibrations of aerodynamic control surfaces during attached flow of a transonic gas flow past them

The model of this phenomenon proposed earlier [2] made it possible to examine one of the possible mechanisms of formation of unsteady aerodynamic exciting forces and hinge moments leading to the occurrence of self-excited vibrations. It follows from an analysis of the model, in particular, that unlike classical flutter, self-excited vibrations of aerodynamic control surfaces exposed to an attached transonic gas flow with shock waves can occur in the presence of just one degree of freedom. In the general case, such self-excited vibrations of the aerodynamic control surface of unit range with one degree of freedom are described by a second-order differential equation with a right-hand side

Conditions for excitation of vibrations of aerodynamic control surfaces in an attached transonic gas flow

This article examines the conditions for excitation of vibrations of aerodynamic control surfaces in a transonic gas flow with shock waves. It is shown that the hinge moments with the largest exciting effect, due to features of the interaction of the vibrating control surfaces with the shock waves, are seen when the Mach numbers M of the undisturbed flow are such that the shocks are located near the trailing edge of the airfoil. Approximate analytic expressions are obtained which make it possible to evaluate the maximum exciting hinge moments for control surfaces. A graphical interpretation of these expressions is also presented.

Nonlinear singular sturm‐liouville problems and an application to transonic flow through a nozzle

AbstractWe consider a class of singular Sturm‐Liouville problems with a nonlinear convection and a strongly coupling source. Our investigation is motivated by, and then applied to, the study of transonic gas flow through a nozzle. We are interested in such solution properties as the exact number of solutions, the location and shape of boundary and interior layers, and nonlinear stability and instability of solutions when regarded as stationary solutions of the corresponding convective reaction‐diffusion equations. Novel elements in our theory include a priori estimate for qualitative behavior of general solutions, a new class of boundary layers for expansion waves, and a local uniqueness analysis for transonic solutions with interior and boundary layers.

An analysis of the impact of T. M. Cherry's work on asymptotic expansions

AbstractDuring the late 1940s, T. M. Cherry published a series of research papers on uniform asymptotic formulae for transition points in ordinary differential equations. This work, together with his research into transonic gas flows, for which it was a necessary precursor, is probably his best known and most widely quoted piece of research. An analysis is made of the impact of Cherry's work on subsequent developments in this field, both in comparison to the work of others and with respect to Cherry's work on other topics.

Calculation of stationary subsonic and transonic non-potential flows of an ideal gas in axially symmetric channels

A generalization of a method of calculating stationary subsonic and transonic non-potential flows of an ideal gas based on the numerical solution of the equation for the stream function, written in an arbitrary system of coordinates, is proposed. In order to find the density during calculations of transonic flows, a marching method is proposed for solving one of the projections of the Euler equation. The results of calculations are presented.

Calculation of transonic flow past the after-part of a plane or axisymmetric body

On the basis of a modified Godunov finite-difference scheme, a method is given for calculating the transonic flow of an ideal gas past the after-part of a plane or axisymmetric elongated body with large angles of inclination and breaks in the generators. Difference schemes adapted to the flow singularities are used, and a new version of the scheme is realized. Relations for the transonic flow remote from the body are obtained in the linear approximation.

One-dimensional transonic gas flow in a wind tunnel with perforated walls

Near-sonic inviscid gas flow in the working section of a wind tunnel with perforated walls is investigated in the context of the one-dimensional theory with Darcy's boundary condition.

Numerical solution of the problem of the supersonic flow of a gas from a plane slit in hodograph variables

A modification is proposed of a method for calculating steady sub- and transonic flows of an ideal gas in the hodograph plane, when the flow takes place in converging planes and axially symmetric nozzles with rectilinear generator. The modification is more accurate than the original method and yields numerical solutions of second-order of accuracy. Its advantages are illustrated by consideration of the supersonic flow of a gas emerging from a plane slit.

Nonlinear resonance for quasilinear hyperbolic equation

The purpose of this paper is to study the wave behavior of hyperbolic conservation laws with a moving source. Resonance occurs when the speed of the source is too close to one of the characteristic speeds of the system. For the nonlinear system characteristic speeds depend on the basic dependence variables and resonance gives rise to nonlinear interactions which lead to rich wave phenomena. Motivated by physical examples a scalar model is proposed and analyzed to describe the qualitative behavior of waves for a general system in resonance with the source. Analytical understanding is used to design a numerical scheme based on the random choice method. An important physical example is transonic gas flow through a nozzle. This analysis provides a transparent and revealing qualitative understanding of wave behavior of gas flow, including such phenomena as nonlinear stability, instability, and changing types of waves.

Transonic gas flow over a flat plate

The solution of the two-sided Tricomi problem in the hodograph plane is constructed with satisfaction of the entire set of boundary conditions, which ensures its correct asymptotic behavior with respect to vanishing angle of attack. As a result, it is found that the deviation from the Guderley solution begins with the singular terms.

The dynamics of an elastic cylindrical panel during interaction with a transonic gas flow

The dynamics of an elastic cylindrical panel during interaction with a transonic gas flow

Investigation of effectiveness of gas flow action on arc discharge initiated in contact breaking

Heavy-current arc discharges initiated in breaking tubular electrodes were studied. The action of transonic gas flow on discharge electrical characteristics in the case of interelectrode gap monotonic increase was investigated. The electrode mean velocity amounted to 10–40 m/s. All the experiments were carried out on a model of a single-shot circuit breaker with an explosive actuator for breaking a current-carrying element.

Transonic flow past a convex corner with free streamline

An asymptotic analysis in the limit of large Reynolds numbers Re → ∞ is made of the system of Navier—Stokes equations in the neighborhood of a corner in a profile past which there is a transonic gas flow. The flow with free streamline from the corner point at which the velocity of sound is reached is taken as a limiting case. In the first approximation, it is described by a self-similar solution to the Karman—Fal'kovich equation with self-similarity exponent n = 6/5 [1]. In such a flow, the favorable pressure gradient becomes infinite as the corner is approached from the side of the oncoming flow.

Unsteady quasi-one-dimensional transonic gas flows

Unsteady quasi-one-dimensional transonic gas flows

Asymptotic states for hyperbolic conservation laws with a moving source

We construct noninteracting wave patterns (i.e., asymptotic states) for a conservation law with a general moving source term. When nonlinear resonance occurs, which is the case when the characteristic speed is near the speed of the source, instability may result. We identify a stability criterion which is independent of the flux function. This is so, even if composite wave patterns exist, as may be the case for nonconvex flux functions. We study the general scalar model as well as transonic gas flows through a duct with varying cross section. For the latter case, noninteracting wave patterns for such a flow are constructed for arbitrary equations of state. It is shown that the stability of a wave pattern depends on the geometry of the duct, and not on the equation of the state. In particular, transonic steady shock waves along a converging duct are unstable, and flow along a diverging duct is always stable.

Flow in the neighborhood of the trailing edge of a plate in a transonic flow of viscous gas

An investigation is made into the influence of the Mach number and the viscosity on the flow in the neighborhood of the trailing edge of a plate. The Mach number is assumed to satisfy m∞ 2 − 1 = 0(R−l/5), which corresponds to the regime of transonic interaction. It is shown that if the Mach number is such that ¦M∞ 2 − 1¦ > O(R−1/5) the problem in the region of free interaction can be reduced by an appropriate transformation to the already known solutions for an incompressible fluid [5] and supersonic flow [7].

Calculation of space transonic flow past oblong bodies

Using a finite-difference scheme, based on the relaxation method, the problem of constructing the flow field is solved for the noncirculation transonic flow of a nonviscous gas past three-dimensional objects. The calculation results are given for transonic gas flow past a triaxial ellipsoid when the gas flows along the semimajor axis and also over a surface, defined by a table, at a small angle of attack.