Theoretical and Experimental Investigation of 2-D Diabatic Transonic and Supersonic Flow Fields

Schnerr, Günter; Dohrmann, Ulrich

doi:10.1007/978-3-642-83584-1_11

Cited by 13 publications

(7 citation statements)

References 7 publications

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“…see Schnerr and Dohrmann (1989)] also support the same hypothesis. Thus we can without hesitation take R(g',x)=Rs(x ) in the interval x~, < x < Xk.…”

Section: Cpo To E'po T'osupporting

confidence: 64%

“…An estimate of 6 requires the solution of the condensation rate equation. For example experiments and numerical computations by and Schnerr and Dohrmann (1989) show that 6 ranges between 0.2 and 0.6 numerically for different nozzle geometries (for estimates of 6 in asymptotic theories see Blythe and Shih and Clarke and Delale). Thus 6 is small compared to unity, but not too small to be ignored.…”

Section: Q*(g' X) _ Q(g' X)mentioning

confidence: 99%

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The mathematical theory of thermal choking in nozzle flows

Delale

Schnerr

Zierep

1993

Z. angew. Math. Phys.

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“…see Schnerr and Dohrmann (1989)] also support the same hypothesis. Thus we can without hesitation take R(g',x)=Rs(x ) in the interval x~, < x < Xk.…”

Section: Cpo To E'po T'osupporting

confidence: 64%

Section: Q*(g' X) _ Q(g' X)mentioning

confidence: 99%

The mathematical theory of thermal choking in nozzle flows

Delale

Schnerr

Zierep

1993

Z. angew. Math. Phys.

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“…By correlating the results of all of these experiments for the nozzles S2 and G1 by Eq. ͑56͒ and by utilizing the shock Mach number-initial relative humidity correlation of Schnerr 9 together with the condensation model of Schnerr and Dohrmann, 13 we find, to a good approximation, the result cϭ6.0ϫ10 3…”

Section: Resultsmentioning

confidence: 97%

“…8 Two-dimensional numerical simulations of such flows were given by Schnerr 9 and Schnerr and Dohrmann. 13 If the heat addition to the flow is further increased ͑e.g., by increasing the initial relative humidity keeping appropriate reservoir conditions fixed͒, the flow becomes unsteady and different patterns of periodic flow structures with moving shock waves occur ͑e.g., see Adam and Schnerr 14 ͒. Unsteady flow phenomena with moving shocks were first discovered by Schmidt 15 in moist air expansions.…”

Section: Introductionmentioning

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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“…for x > xk where xk denotes the onset of condensation (this point can be located either empirically [12], semi-empirically by similarity analysis [13], numerically [14] or by the asymptotic solution of the condensation rate equation [ 11,15]). We herein assume that heat addition to the flow from condensation occurs in the supersonic region of the nozzle so that xk > 0.…”

Section: Thermal Choking Of Real Gas Flows In Nozzlesmentioning

confidence: 99%