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Improved correlation of film condensation data based on a more rigorous application of similarity parameters

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Abstract

It is shown that a most consistent application of similarity parameters reduces the “random error” of experimental results in film condensation by 90%, in extreme situations even more. On the basis of physical considerations a correlation of data is presented which shows the Nusselt number as a function not only of the Reynolds number but also in certain ranges of the Prandtl and Weber number. Although the latter parameters varied only moderately in the experiments presented here the general idea is supported clearly. Further experiments will have to provide for quantitatively more reliable results.

Zusammenfassung

Es wird gezeigt, wie man bei möglichst konsequenter Anwendung der Ähnlichkeitsmechanik die durch die „Willkür“ gegebene Streuung der Me\ergebnisse auf ein Zehntel — bei besonderen ZustÄnden auch noch viel weniger — derjenigen bei üblicher Darstellung reduzieren kann. Dabei mu\ allerdings neben dem Einflu\ der Reynoldszahl auf den WÄrmeübergang auch gebietsweise der der Prandtlzahl und Weberzahl berücksichtigt werden. Dies ist vorlÄufig in relativ so engen Bereichen der beiden letztgenannten Kennzahlen geschehen, da\ noch keine semiempirische Gebrauchsformeln hergeleitet werden können. Versuche zur Erweiterung der Kennzahlengebiete sind im Gange.

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Abbreviations

g:

acceleration

Hx, H:

variable total height of vertical cooling surface

Ko:

condensation parameter (see Eq. (8b))

m:

condensate mass flow rate per unit width of cooling surface at the lower tube end

Nu, NuB, Nupr :

reduced Nusselt numbers defined by

NuWe, NuWePr :

Eqs. (7, 9, 15, 20 and 21)

Pr:

Prandtl number, using ηm from Eq. (2)

r:

total enthalpy difference between entering vapour and leaving condensate

\(\dot Q, \dot Q_{cr}\) :

total heat flux, partial heat flux transmitted up to Hcr

\(\operatorname{Re} = \frac{{w\delta }}{{v_m }} = \dot m/\eta _m\) :

condensate Reynolds number at lower tube end

TS :

saturation temperature of vapour

TW :

average temperature of cooling surface

TKA :

adiabatic mixing temperature of leaving condensate

TKWE, TKWA :

average temperature of entering, leaving cooling water

δ T=TS− TW :

driving temperature difference for heat transfer

w, w′:

average condensate velocity at the lower tube edge and characteristic velocity from Brauer [9]

\(We_{cr} = \left( {\frac{{\operatorname{Re} _{cr}^5 }}{3}} \right)^{1/3} \left( {\frac{{g\rho ^3 v_m^4 }}{{\sigma ^3 }}} \right)^{1/3}\) :

critical Weber number

We *cr =(Wecr)−1 :

critical Weber number

aKW :

heat transfer coefficient of cooling water based on the inside tube surface

a :

condensation heat transfer coefficient averaged over the entire tube length

λ, ρ, η, Ν :

thermal conductivity, density, dynamic and kinematic viscosity of condensate at (TS + TW)/2

δ, δx :

film thickness at the lower end of tube, local film thickness, all averaged with respect to time and width

σ :

interface tension condensate-vapour at T=TS

cr:

for quantities in laminar flow regime related to the cross-section just before transition from laminar to turbulent flow

m:

average according to Eqs. (2) and (3)

w, S:

for quantities at wall, saturation temperature

x:

variable quantity

1, 2:

with respect to first, second condenser length

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Authors and Affiliations

  1. Institut für Thermodynamik, Technische UniversitÄt Berlin, Stra\e des 17, D-1, Berlin 12, Deutschland

    R. Gregorig

  2. Department of Chemical Engineering, University of the Witwatersrand, Johannesburg, S.A.

    J. Kern (Senior Lecturer)

  3. HAGENUK, Kiel

    K. Turek

Authors
  1. R. Gregorig
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  2. J. Kern
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  3. K. Turek
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Additional information

Reported on April 1973 at the meeting of the „Ausschu\ für WÄrme- und Stoffübertragung“ in Bad Mergentheim, Germany, by Helmer Rasche, Assistant at the Institut für Thermodynamik/WÄrmeübertragung der Technischen UniversitÄt Berlin, Germany

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Gregorig, R., Kern, J. & Turek, K. Improved correlation of film condensation data based on a more rigorous application of similarity parameters. Wärme- und Stoffübertragung 7, 1–13 (1974). https://doi.org/10.1007/BF01438315

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