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Influence of free convection on the heat transfer from hot-wire probes

Einfluß der freien Konvektion auf den Wärmeübergang bei Hitzdrahtsonden

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Abstract

The present paper is concerned with the experimental determination of the influence of free convection on the heat transfer from horizontal hot-wire probes in cross flow. Free convective flow can be minimized under microgravity conditions and its quantity can be determined by comparisons with terrestrial investigations. Using the developod experimental setups it is possible to investigate all three flow regimes, i.e. pure free, mixed, and pure forced convection (o ≤Re ≤ 0.1). It was found that the influence of free convection is limited to Reynolds numberRe ≤ 0.0045, independent of the overheat ratio. Based on the findings of Collis and Williams [12], the influence of free convection can be neglected forRe > 0.58 ·Gr 1/3. The fluid properties are computed at the film temperature. Two correlations are established for the regime of pure forced convection. End losses to the supports were determined in a vacuum experiment, thus allowing comparison with theoretical investigations. The difference between the analytical computations and the measurement data in the range 0 ≤Re ≤ 0.02 is caused by the three-dimensional heat transfer occuring in the experimental investigation.

Zusammenfassung

Die vorliegende Untersuchung beschäftigt sich mit der experimentellen Bestimmung des Einflusses der freien Konvektion auf den Wärmeübergang bei quergeströmten Hitzdrahtsonden. Die freie Konvektionsströmung kann unter Schwerelosigkeit minimiert und ihre Größe durch den Vergleich mit terrestrischen Untersuchungen ermittelt werden. Mit den erstellten Experimentaufbauten ist es möglich, alle drei Strömungsbereiche von der rein freien über die gemischte bis zur rein erzwungenen Konvektion zu untersuchen (0 <-Re ≤ 0,1). Dabei wurde festgestellt, daß der Einfluß der freien Konvektion sich unabhängig von Überhitzungsverhältnis nur bis zu einer ReynoldszahlRe ≤ 0,0045 erstreckt. Zur Vernachlässigung der freien Konvektion kann in Anlehnung an Collins und Williams folgende Beziehung angegeben werden:Re > 0,58 ·Gr 1/3. Die Stoffwerte werden bei der Filmtemperatur berechnet. Für den Bernich der rein erzwungenen Konvektion wurden zwei Korrelationer aufgestellt. Durch einen Vakuumversuch wurden die Endverluste in die Haltespitzen ermittelt und somit der Vergleich mit theoretischen Arbeiten ermöglicht. Der Unterschied zwischen den analytischen Berechnungen und den Meßdaten im Bereich 0 ≤Re ≤ 0,02 ergibt sich durch den dreidimensionalen Wärmeübergang bei der experimentellen Untersuchung.

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Abbreviations

A, B :

numerical constants

a :

overheat ratio

a :

speed of sound

b :

wall distance

d :

wire diameter

g :

gravitational acceleration

Gr :

Grashof number =g(T w −T ∞)βd 3/υ 2

Kn :

Knudsen number =λ/d

l :

wire length

m :

temperature loading factor

Ma :

Mach number =ν/a

n :

exponent of Reynolds number

Nu :

Nusselt number =αd/λ

Pr :

Prandtl number = υ/α

Q :

heat transfer rate per unit area

R :

resistance

Re :

Reynolds number =ν dρ/η

T :

temperature

U :

voltage

ν :

flow velocity

α :

heat transfer coefficient

β :

coefficient of thermal expansion

η :

dynamic viscosity

λ :

thermal conductivity

λ :

mean free path

υ :

kinematic viscosity

ρ :

density

ψ :

angle of attack

B:

Wheatstone's bridge

c:

continuum

crit:

critical

f:

arithmetric mean of (T w −T ∞)

m:

without end losses

min:

minimum

vac:

vacuum

w:

wire

o:

zero velocity

∞:

ambient conditions

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Authors and Affiliations

  1. Zentrum für angewandte Raumfahrttechnologie und Miktogravitation (ZARM), Universität Bremen, D-28359, Bremen, Germany

    F. R. Stengele & H. J. Rath

Authors
  1. F. R. Stengele
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The authors acknowledge the support of the Deutsche Agentur für Raumfahrtangelegenheiten (DARA) under grant number 50-QV 8898-1.

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Stengele, F.R., Rath, H.J. Influence of free convection on the heat transfer from hot-wire probes. Warme - Und Stoffubertragung 29, 299–307 (1994). https://doi.org/10.1007/BF01578414

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