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2-D transonic flow with energy supply by homogeneous condensation: Onset condition and 2-D structure of steady Laval nozzle flow

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Abstract

A generalized form of the similarity law for the condensation onset Mach number of water vapor in air in the transonic and supersonic range for water vapor flow in moist air is derived from well known basic approaches for supersonic nozzles. These statements are confirmed by extensive experimental investigations in Laval nozzles, as well as by results of other authors and computations on the basis of the Euler equation linked with the classical theory of nucleation and droplet growth. In this experimental research priority is given to the qualitative description of the two-dimensional condensation processes, and their effects in transonic flows in nozzles of different geometrical configuration (e. g. slightly or well curved). A quantitative discussion of 2-D structures in condensation regions requires the introduction of a characteristic angle along streamlines. It is then directly possible to describe the different types of compression disturbances in supersonic flows with heat addition.

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Abbreviations

a :

exponent of the similarity law

g :

condensate mass fraction [gH2O-liquid/kgmoist air]

p :

static pressure

R :

radius of the wall curvature

T :

absolute temperature

x :

cartesian coordinate, mixing ratio [gH2O-vapor/kgdry air]

y :

cartesian coordinate

α:

coefficient of the similarity law, Mach angle

α :

coefficient of the similarity law

\(\bar \alpha \) :

coefficient of the similarity law

α:

coefficient of the similarity law, average value

β:

coefficient of the similarity law

β:

coefficient of the similarity law, average value

δ:

angle between characteristic and iso-Mach line

Δ:

difference

ad :

adiabatic

c :

condensation onset

f :

frozen

n :

neutral point

s :

saturation

0:

stagnation condition

1:

initial state

*:

critical condition

-:

average value

=:

average value

K :

characteristic quantity of geometry

M :

Mach number

γ:

specific heat ratio

Φ:

relative humidity

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  1. Institut für Strömungslehre und Strömungsmaschinen, Universität (TH) Karlsruhe, Kaiserstraße 12, D-7500, Karlsruhe 1, F. R. Germany

    G. Schnerr

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This work is dedicated to my teacher of science, Professor Dr.-Ing. J. Zierep, on the occasion of his 60th birthday.

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Schnerr, G. 2-D transonic flow with energy supply by homogeneous condensation: Onset condition and 2-D structure of steady Laval nozzle flow. Experiments in Fluids 7, 145–156 (1988). https://doi.org/10.1007/BF02332979

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