On Flows with Heat Addition in Laval Nozzles

Möhring, W.

doi:10.1007/978-3-642-67220-0_19

Cited by 6 publications

(4 citation statements)

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“…Various investigations, primarily devoted to thermal choking of flows in constant area ducts or in quasi-one-dimensional nozzles, assume given heat addition to achieve a relatively easier analysis (e.g. see Shapiro (1953), Jungclaus and van Raay (1967), Möhring (1979), Zierep (1990); for applications to flows with nonequilibrium condensation see Wegener and Mack (1958), Pouring (1965) and Barschdorff (1967) ). Only recently has it been possible from the work of Delale et al (1993a) that a detailed mathematical description of thermal choking in quasione-dimensional nozzle flows with given heat addition and with nonequilibrium condensation can be given.…”

Section: Introductionmentioning

confidence: 99%

“…The singularities for this case occur at points where Ma = 1 and α(s) = β(s) (e.g. seeMöhring (1979),Zierep (1990),Delale et al (1993a)). Figure 2 (a)shows the case of subcritical heat addition with a saddle point singularity without heat addition at the throat s 1 = 0.Figure 2 (b)shows the case of supercritical heat addition with three singularities: (i) a saddle point without heat addition at s 1 = 0 (the classical throat), (ii) Variation of α(s) and β(s) in quasi-one-dimensional nozzle flows with given heat addition (a) below the critical heat, (b) exceeding the critical heat.…”

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confidence: 99%

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Thermal choking in two-dimensional expansion flows

Delale

Dongen

1998

Z. angew. Math. Phys.

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Two-dimensional supersonic flows with heat addition from given internal sources and/or nonequilibrium condensation are considered. The critical amount of heat necessary to thermally choke the flow is defined at any point in the flow field, and the necessary and sufficient conditions for thermal choking are identified from the singularities of the equations of motion along streamlines. In particular, for any practical purposes, it is shown that the flow Mach number reaches unity at any point where the heat added to the flow along the streamline passing through that point reaches the critical value. Thermally choked flows are then identified as those flows where the critical heat along streamlines is exceeded leading to embedded oblique shock waves with a local subsonic flow field downstream.Mathematics Subject Classification (1991). 35L67, 76J20, 76L05, 76N15.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

Thermal choking in two-dimensional expansion flows

Delale

Dongen

1998

Z. angew. Math. Phys.

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“…Möhring [6] investigated analytically all singularities of equation ( 34) at M ¼ 1 for Laval nozzle flow with specified heat addition by assuming reasonable analytical expressions for A(x) and of q(x) -supersonic heat addition only. After local linearization of equation (34) in the vicinity of the singularities, the discussion of the characteristic homogeneous differential equation yields all possible trajectories emerging from the singular points.…”

Section: Singularities and Thermal Chokingmentioning

confidence: 99%

“…Fig.16Sketch of one-dimensional Laval nozzle flow with heat addition; summary of qualitative solutions consisting of saddle points, nodal points, and with spirals; original picture of Möhring[6] …”

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Unsteadiness in Condensing Flow: Dynamics of Internal Flows with Phase Transition and Application to Turbomachinery

Schnerr

2005

Proceedings of the Institution of Mechanical Engineers, Part C:

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Steady flows of condensable fluids may become unsteady if one component of the fluid starts to condense. In high-speed expansion flows, typical for large-scale steam turbines, the subcooled vapour state collapses after nucleation, typically in flow regimes close to Mach number 1. After the formation of steady shocks, instantaneous thermal choking initiates selfexcited high-frequency oscillations which is the focus of this article. The driving mechanism is the interaction of compressibility and energy supply in flows close to maximum mass flux density and is therefore not controlled by the viscosity of the fluid. Additional viscosity-driven excitation mechanisms exist and superpose the primary diabatic instability, especially in axial cascades. Typical are shedded shear layers from blade trailing edges and the periodic interference of wakes separating from the stator with the rotor blades. This article presents a review of the authors and various co-workers' research, supplemented by important references to complete the subject under consideration. This article starts with an introduction in the most simple flow model of given heat addition in constant area flow and ends with mixed homogeneous/heterogeneous condensation in a transonic axial cascade stage with a high-resolution sliding interface for preservation of submicron condensate convected from the stator into the rotor. Numerical simulations are compared with experiments of flows with and without carrier gas.

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