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Laminar stability analysis of condensate film flow

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Abstract

The linear stability theory is used to study stability characteristics of laminar gravity-induced condensate film flow down an arbitrarily inclined wall. The coupled equations describing the velocity and temperature disturbances are solved numerically. The results show that laminar condensate films are unstable in all practical situations. Several stabilizing effects are acting on the film flow; these are: the angle of inclination, the surface tension at large wave numbers, the condensation rate at small Reynolds numbers, and to a certain extent the Prandtl number. For a vertical plate, the expected wavelengths of the disturbances are presented as functions of the Reynolds numbers of the condensate flow.

Zusammenfassung

Mit Hilfe der linearen StabilitÄtstheorie werden die StabilitÄtseigenschaften laminarer Kondensatfilme an ebenen WÄnden untersucht. Die Gleichungssysteme, die Temperatur- und Geschwindigkeitsstörungen beschreiben, werden numerisch gelöst. Es zeigt sich, da\ Kondensatfilme in jedem praktischen Fall ein unstabiles Verhalten aufweisen. Der stabilisierende Einflu\ von OberflÄchenspannung, Schwerkraft und Stoffübertragung durch Kondensation werden diskutiert. Für eine senkrechte Wand werden die zu erwartenden WellenlÄngen der Störungen als Funktion der Reynoldszahlen des Kondensatfilms angegeben.

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Abbreviations

C*=C *r + iC *i :

dimensional complex wave velocity

C=C*/u0 :

dimensionless wave velocity

cp :

specific heat at constant pressure

g:

gravitational acceleration

hn :

defined by Eq. (16)

hfg :

latent heat

k:

thermal conductivity

Pe=PrRe:

Peclet number

Pr:

Prandtl number

Py :

defined by Eq. (15)

q:

iaPe

Re=u0 δΝ:

Reynolds number

S:

temperature disturbance amplitude

t* :

dimensional time

t=t* u0/δ:

dimensionless time

T:

dimensional temperature

Ts :

saturation temperature

Tw :

wall temperature

δT =Ts−Tw :

temperature drop across liquid film

u*, v* :

dimensional velocity component

v=v*/u0 :

dimensionless velocity components

u0 :

dimensional surface velocity of undisturbed film flow

x*, y* :

dimensional coordinates

x=x*/δ:

dimensionless coordmates

Yn :

functional vector defined by Eq. (20)

α:

dimensionless wave number

Β :

roots of Eq. (20)

γn:

defined by Eq. (21)

δ :

local thickness of undisturbed condensate film

λ * :

wavelength, dimensional

\(\lambda = \frac{{\lambda *}}{\delta }\) :

wavelength, dimensionless

\(\theta = \frac{{T - T_s }}{{T_w - T_s }}\) :

temperature variable

Ν :

kinematic viscosity of liquid

ρ :

liquid density

ρ g :

vapor density

σ :

surface tension

Φ :

stream function disturbance amplitude

ψ :

stream function

Ω :

angle of inclination

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of California, 93106, Santa Barbara, California

    E. Marschall (Associate Professor)

  2. Gulf General Atomic Company, 92112, San Diego, California

    C. Y. Lee

Authors
  1. C. Y. Lee
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  2. E. Marschall
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Lee, C.Y., Marschall, E. Laminar stability analysis of condensate film flow. Wärme- und Stoffübertragung 7, 14–21 (1974). https://doi.org/10.1007/BF01438316

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