Thermal choking in two-dimensional expansion flows

Delale, CF; Dongen, M. E. H. van

doi:10.1007/s000000050106

Cited by 6 publications

(6 citation statements)

References 8 publications

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“…The supercritical heat addition will lead to thermal choking of the flow [16]. A dimensionless expression for the critical heat addition Q cr in quasi-one-dimensional nozzle flows with vapor condensation is given by Delale [21,22]:…”

Section: Thermal Choking In the Sonic Nozzle With Condensation Phenomenamentioning

confidence: 99%

Experimental and numerical studies on self-excited periodic oscillation of vapor condensation in a sonic nozzle

Ding

Wang

Chen

2015

Experimental Thermal and Fluid Science

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Section: Thermal Choking In the Sonic Nozzle With Condensation Phenomenamentioning

confidence: 99%

Experimental and numerical studies on self-excited periodic oscillation of vapor condensation in a sonic nozzle

Ding

Wang

Chen

2015

Experimental Thermal and Fluid Science

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“…In cases where the flow Mach number M reaches unity due to considerable latent heat addition from condensation, it can be shown that the amount of heat added to the flow, given by Eq. ͑5͒, becomes equal to the critical value q* defined by ͑for details see Delale et al 12 and Delale and van Dongen 21 …”

Section: A Classification Of Singularities and Flow Patternsmentioning

confidence: 99%

On the stability of stationary shock waves in nozzle flows with homogeneous condensation

2001

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The stability limit of stationary normal shock waves in supercritical nozzle flows with homogeneous condensation is investigated by the singularity theory of the quasi-one-dimensional steady-state differential equations of motion. In this case it is shown that a catastrophic change in the phase portraits of the flow variables, where the spiral point turns into a nodal point, occurs when the initial relative humidity exceeds a critical value, resulting in the alteration of the quasi-one-dimensional steady-state condensation structures. In particular, a criterion for the limit of stability, based on the break-up of structural stability of the steady equations of motion in the quasi-one-dimensional approximation, is established by variational analysis and a correlation for the critical initial relative humidity is derived for fixed nozzle geometry keeping appropriate reservoir conditions fixed in the same approximation. A comparison of the values of the critical initial relative humidity, calculated by this correlation, shows excellent agreement with those of experiments and/or numerical simulations for moist air expansions in various slender nozzles under different reservoir conditions.

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“…Figure 1 shows a typical supercritical flow with an embedded shock front KL due to excessive heat release by condensation. It has been demonstrated by Delale & van Dongen (1998) that such a shock wave shows a supersonic to supersonic transition and can, therefore, be assumed to be weak (strong shock waves with supersonic to subsonic transition occur in supercritical flows in ducts and nozzles, e.g. see Schnerr (1989) and Delale, Schnerr & Zierep (1993a, b)).…”

Section: Equations Of Motion and Asymptotic Solution Of The Condensatmentioning

confidence: 99%

“…Results obtained for Smith's experiments by this asymptotic solution showed intersecting characteristics in the heat addition zones, clearly exhibiting the need to incorporate embedded shock waves due to excessive heat release from condensation (supercritical flows). A qualitative theory recently developed by Delale & van Dongen (1998) show that such shock waves are weak. Supercritical Prandtl-Meyer flows have never been calculated, mainly due to the lack of a shock fitting technique for embedded weak oblique shock waves in non-uniform flows.…”

Section: Introductionmentioning

confidence: 99%

Prandtl–Meyer flows with homogeneous condensation. Part 2. Supercritical flows

Delale

Crighton

2001

J. Fluid Mech.

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Prandtl–Meyer flows with embedded oblique shock waves due to excessive heat release from condensation (supercritical flows) are considered by extending the subcritical asymptotic solution of Delale & Crighton (1998). The embedded shock origin is located by the construction of the envelope of the family of characteristics emanating either from the corner or from the deflected wall in the parabolic approximation. A shock fitting technique for embedded oblique shock waves is introduced in the small deflection angle approximation and the law of deflection of a streamline through an embedded oblique shock wave is established within the same approximation. The network of characteristics downstream of the embedded shock front is constructed and the solution for the flow field therein is evaluated by utilizing the asymptotic solution of the rate equation along streamlines downstream of the shock front together with the equations of motion in characteristic form. Results obtained by employing the classical nucleation equation and the Hertz–Knudsen droplet growth law, compared with the supercritical experiments of Smith (1971) for moist air expansions, show that supercritical Prandtl–Meyer flows can only be realized locally when the embedded shock lies sufficiently far downstream of the throat, where the corner is located.

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Thermal choking in two-dimensional expansion flows

Cited by 6 publications

References 8 publications

Experimental and numerical studies on self-excited periodic oscillation of vapor condensation in a sonic nozzle

Experimental and numerical studies on self-excited periodic oscillation of vapor condensation in a sonic nozzle

On the stability of stationary shock waves in nozzle flows with homogeneous condensation

Prandtl–Meyer flows with homogeneous condensation. Part 2. Supercritical flows

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