Simple Wave Flow Research Articles

Analytical solution of supersonic axisymmetric flow around a sharp convex corner

Supersonic axisymmetric expansion flow is a typical and fundamental issue in gas dynamics. It plays a vital role in the high-speed external and internal flow fields regarding the contour design and performance evaluation of supersonic/hypersonic vehicles and their propulsion systems. The supersonic two-dimensional (2D) planar expansion flow is dominated by the well-known Prandtl–Meyer (P–M) theory. However, no similar explicit relation exists for the supersonic axisymmetric expansion flow, and only the computational fluid dynamics results could be employed at present. Therefore, this work focuses on developing the analytical solution of supersonic axisymmetric flow around a sharp convex corner on the basis of the generic gasdynamic functions in a newly established coordinate system for addressing the aforementioned issue. Theoretical derivations and numerical results prove that the flow deflection angle and Mach number in supersonic axisymmetric flow around a sharp convex corner obey the identical law to the 2D planar situation, that is, the P–M theory, while the local axisymmetric expansion fan is not the simple wave flow despite the conical flow. Meanwhile, the method of characteristics is employed to further explicate the intrinsic connection and difference between the 2D and axisymmetric sharp convex corner flow. The equivalence of sharp corner and curved surface flows with the identical deflection angle is discussed, and three limitations of the proposed analytical solution are clarified.

Wave Interactions in Non-ideal Isentropic Magnetogasdynamics

In this paper, we consider the Riemann problem and wave interactions for a quasi-linear hyperbolic system of partial differential equations governing the one dimensional unsteady simple wave flow of an isentropic, non-ideal, inviscid and perfectly conducting compressible fluid, subject to a transverse magnetic field. This class of equations includes, as a special case of ideal isentropic magnetogasdynamics. We study the shock and rarefaction waves and their properties, and show the existence and uniqueness of the solution to the Riemann problem for arbitrary initial data under certain conditions and then we discuss the vacuum state in non-ideal isentropic magnetogasdynamics. We discuss numerical tests and study the solution influenced by the van der Waals excluded volume for different initial data along with all possible interactions of elementary waves.

Simple waves of the two dimensional compressible full euler equations

In this paper, we establish the existence of four families of simple wave solution for two dimensional compressible full Euler system in the self-similar plane. For the 2 × 2 quasilinear non-reducible hyperbolic system, there not necessarily exists any simple wave solution. We prove the result that there are simple wave solutions for this 4 × 4 non-reducible hyperbolic system, its simple wave flow is covered by four straight characteristics λ0=λ1,λ2,λ3 and the solutions keep constants along these lines. We also investigate the existence of simple wave solution for the isentropic relativistic hydrodynamic system in the self-similar plane.

Simple waves for two-dimensional compressible pseudo-steady Euler system

A simple wave is defined as a flow in a region whose image is a curve in the phase space. It is well known that “the theory of simple waves is fundamental in building up the solutions of flow problems out of elementary flow pattern” see Courant and Friedrichs’s chassical book “Supersonic Flow and Shock Waves”. This paper mainly concerned with the geometric construction of simple waves for the 2D pseudo-steady compressible Euler system. Based on the geometric interpretation, the expansion or compression simple wave flow construction around a pseudo-stream line with a bend part are constructed. It is a building block that appears in the global solution to four contact discontinuities Riemann problems.

Riemann problem and elementary wave interactions in isentropic magnetogasdynamics

In this paper, we consider the Riemann problem for a quasilinear hyperbolic system of equations governing the one dimensional unsteady simple wave flow of an isentropic, inviscid and perfectly conducting compressible fluid, subjected to a transverse magnetic field. This class of equations includes, as a special case, the equations of isentropic gasdynamics. We study the shock and rarefaction waves and their properties, and discuss the geometry of shock curves using the Riemann invariant coordinates. Under certain conditions, we show the existence and uniqueness of the solution to the Riemann problem for arbitrary initial data, and then discuss the vacuum state in isentropic magnetogasdynamics. Finally, we discuss numerical results for different initial data, and discuss all possible interactions of elementary waves. It is noticed that although the magnetogasdynamic system is more complex than the corresponding gasdynamic system, all the parallel results remain identical. However, unlike the ordinary gasdynamic case, the solution inside rarefaction waves in magnetogasdynamics cannot be obtained directly and explicitly; indeed, it requires an extra iteration procedure. It is also observed that the presence of a magnetic field makes both the shock and rarefaction stronger compared to what they would have been in the absence of a magnetic field.

Propagation of a soliton along a fluid-filled pipe

In [1, 2] a mathematical model of the motion of a fluid in a pipe whose axis is a curve in space was discussed and certain simplifications of the problem were studied. The propagation of linear and nonlinear waves in the framework of the model was studied. In the present paper we consider a simple wave flow in a pipe with elastic walls suing one of the models introduced in [1], which, unlike [2], takes into account axial displacements of the pipe. The basic equations describing the propagation of waves in the pipe are obtained.

Entropy and simple waves in multidimensional gas flow

AbstractIt is shown that the n-dimensional simple wave flow of a perfect gas, that is, flow in which the velocity components, pressure and density depend on only one generating function, must be isentropic. This result is then employed to explain why two independent investigations of apparently different types of simple waves have led to the same results.

Singular Perturbation Methods in Nonlinear Acoustics

The application of singular perturbation techniques to problems in nonlinear acoustics is demonstrated in two examples. In the first, we show that straightforward perturbation methods, using Lighthill's equation for aerodynamic sound, give a secular series when applied to one-dimensional simple wave flow. The nonuniform secular terms are removed by the introduction of expansions in terms of multiple scaled coordinates, and the Earnshaw solution for the shock-free region is recovered. Such an expansion technique is also applied to solve a problem in compound flow. In the second example, the method of matched asymptotic expansions (MAE) is applied to one-dimensional flow governed by Burgers' equation. If the excitation at the origin is time harmonic, Burgers' equation can be solved exactly, and the solution reduced to an intelligible form in the shock-free, saw-tooth, and saturation regions. These simplified approximate solutions are recovered by a direct application of MAE to Burgers' equation, and in work still under completion, it appears that the same process will yield a uniformly valid approximate solution of the analogous problems in two and three dimensions.

Hydromagnetic simple wave flow in nonuniform ducts. II

The equations governing the quasi-one-dimensional unsteady motion of an ideal, inviscid, perfectly conducting compressible fluid, subjected to an oblique magnetic field, are linearized in the neighborhood of a known simple wave flow and weakly nonisentropic perturbations are considered. The perturbations superposed on simple wave flow in non-uniform ducts may then be determined by quadratures. Because of the arbitrary orientation of the magnetic field, both slow and fast simple waves may be considered. The author's previous work on the case of a transverse magnetic field and the nonmagnetic case is contained as a special case of the analysis.

Hydromagnetic simple wave flow in nonuniform ducts

The equations governing the quasi-one-dimensional unsteady motion of an ideal, inviscid, perfectly conducting monatomic compressible fluid, subjected to a transverse magnetic field, are linearized in the neighborhood of a known simple wave flow and weakly nonisentropic perturbations are considered. The perturbations superposed on centered and non-centered simple wave flow in nonuniform ducts may then be determined quadratures.

The nonisentropic perturbation of a centered magnetohydrodynamic simple wave

After linearization of the governing equations of the one-dimensional nonsteady motion of an ideal, inviscid, perfectly conducting monatomic compressible fluid, subjected to a transverse magnetic field, in the neighborhood of a centered simple wave flow, weakly nonisentropic perturbations are considered, and the solution for the first order terms given by quadratures. The results are a generalization of the work of Germain and Gundersen [2].

Simple Wave Flow in Ducts

A centered simple wave is generated by the impulsive retraction of a piston. The sound speed perturbation and particle velocity perturbation are determined when the wave passes into a slowly diverging (or converging) section or a section which presents a throat. When the section of varying area terminates in a channel of constant cross section, the result of passage through the transition section of varying area is the superposition of a perturbation which tends to decrease the flow velocity by a term which varies inversely with the time for a point moving with the wave, but increases linearly with the time at a fixed point in the channel, in agreement with results first presented by Chester with the use of a two-dimensional analysis. The flow of an arbitrary simple wave in the section of varying area is solved.