The Theory of Transonic Flow

Guderley, Karl G.; Laitone, E. V.

doi:10.1115/1.3636553

Cited by 109 publications

(94 citation statements)

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“…One would therefore like to establish an appropriate infinitesimal perturbation theory in which the shock is contracted into a sonic point on the profile and the perturbation is appropriately singular there. That such a theory should be possible was first proposed by Guderley [12]. However, this objective is beyond the scope of the present paper but an analogous theory can be made for the Dirichlet problem for the Tricomi equation which presents the same contradictions, see [6], [7] and [8].…”

Section: Introductionmentioning

confidence: 89%

The dirichlet problem for the tricomi equation

Morawetz¹

1970

Comm Pure Appl Math

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Section: Introductionmentioning

confidence: 89%

The dirichlet problem for the tricomi equation

Morawetz¹

1970

Comm Pure Appl Math

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“…Frankl [4], K.G. Guderley [5] and others. For unsteady flow, an approximate transonic equation was developed in the study [6], and the main difficulty of the research is that the problem is non-linear in the approximate formulation.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic research of transonic gas flows

Velmisov¹,

Tamarova²

2017

AIP Conference Proceedings

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Abstract. The article is dedicated to the development asymptotic theory of gas flowing at speed next to sound velocity, particularly of gas transonic flows, i.e. the flows, containing both, subsonic and supersonic areas. The main issue, when styding such flows, are nonlinearity and combined type of equations, describing the transonic flow. Based on asymptotic nonlinear equation obtained in the article, the gas transonic flows is studied, considering transverse disturbance with respect to the main flow. The asymptotic conditions at shock-wave front and conditions on the streamlined surface are found. Moreover, the equation of sound surface and asymptotic formula defining the pressure are recorded. Several exact particular solutions of such equation are given, and their application to solve several tasks of transonic aerodynamics is indicated. Specifically, the polynomial form solution describing gas axisymmetric flows in Laval nozzles with constant acceleration in direction of the nozzle's axis and flow swirling is obtained. The solutions describing the unsteady flow along the channels between spinning surfaces are presented. The asymptotic equation is obtained, describing the flow, appearing during non-separated and separated flow past, closely approximated to cylindrical one. Specific solutions are given, based on which the examples of steady flow are formed.

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“…The hodograph equation, originally introduced by Chaplygin (1904) in his seminal work, has been extensively used for studying plane irrotational motions of ordinary fluids (von Mises 1958;Guderley 1962;Lighthill 1964). Its MHD analogues have been discussed by several investigators (Imai 1960;Sears 1960;Seebass 1961, Webb et al 1994.…”

Section: Intrinsic Descriptions Of Plasma Flowsmentioning

confidence: 99%

“…In thermonuclear fusion (tokamaks) and in many astrophysical situations (solar wind, mass outflows from young stellar objects, compact complete (although quite a number of important issues remain to be addressed, both analytically and numerically) (for an overview of the subject see e.g. Guderley 1962;Cole and Cook 1986). In particular, under certain assumptions, the existence theorem for transonic flows satisfying appropriate boundary conditions has been proved (Morawetz 1985;Kloucek and Necas 1990), and powerful numerical methods for finding these flows numerically have been developed (Jameson 1980(Jameson , 1988Bristeau et al 1989).…”

Section: Introductionmentioning

confidence: 99%

Transonic magnetohydrodynamic flows

Lifschitz

Goedbloed

1997

J. Plasma Phys.

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Stationary flows of an ideal plasma with translational symmetry along the (vertical) z axis are considered, and it is demonstrated how they can be described in the intrinsic (natural) coordinates (ξ, η, ϑ), where ξ is a label of flux and stream surfaces, η is the total pressure and ϑ is the angle between the horizontal magnetic (and velocity) field and the x axis. Three scalar nonlinear equilibrium equations of mixed elliptic-hyperbolic type for ϑ (ξ, η), ξ(η, ϑ) and η(ϑ, ξ) respectively are derived. The equilibrium equation for ϑ(ξ, η) is especially useful, and has considerable advantages compared with the coupled system of algebraic-differential equations that are conventionally used for studying plasma flows. In particular, for this equation the location of the regions of ellipticity and hyperbolicity can be determined a priori. Relations between the equilibrium equation for ϑ(ξ, η) and the nonlinear hodograph equation for ξ(η, ϑ) are elucidated. Symmetry properties of the intrinsic equilibrium equations are discussed in detail and their self-similar solutions are described. In particular, magnetohydrodynamic counterparts of several classical flows of an ideal fluid (the Prandtl-Meyer flows around a corner, the spiral flows and the Ringleb flows around a plate, etc.) are found. Stationary flows described in this paper can be used for studying both astrophysical and thermonuclear plasmas.

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The Theory of Transonic Flow

Cited by 109 publications

References 0 publications

The dirichlet problem for the tricomi equation

The dirichlet problem for the tricomi equation

Asymptotic research of transonic gas flows

Transonic magnetohydrodynamic flows

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