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Finite element analysis of conductive and radiative heating of a thin skin calorimeter

Berechnung der Wärmeübertragung durch Leitung und Strahlung an einem dünnwandigen Kalorimeter mittels Finiter Elemente

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Abstract

The main purpose of the present work is to investigate the influence of normal and lateral conduction on the temperature distribution and heat transfer coefficient on the surface of a typical sounding rocket.

A two-dimensional heat conduction equation with a time dependent aerodynamic heating condition at one surface and a radiation boundary condition at the other end is solved using finite element method.

Zusammenfassung

Das Ziel der vorliegenden Arbeit ist die Erforschung des Einflusses der normalen und seitlichen Wärmeleitung auf die Temperaturverteilung und den Wärmeübergangskoeffizienten auf der Oberfläche einer typischen Überschallrakete. Dazu wird mit der Methode der Finiten Elemente eine zweidimensionale Wärmeleitungsgleichung mit einer zeitabhängigen Zufuhr von Reibungswärme durch die Luftströmung an einer Wand und Stahlungswärmeaustausch an der anderen Seite als Randbedingung gelöst.

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Abbreviations

¯C:

capacitance matrix

¯F:

heat flux vector

h :

heat-transfer coefficient

¯K:

Thermal conductivity matrix

k :

thermal conductivity

l :

wall thickness

q:

heat flux

T :

temperature

t :

time

Δt :

time increment

X, Y :

Cartesian coordinates

σ :

Stefan Boltzmann constant

ɛ :

emissivity

α :

thermal diffusivity

a :

aeordynamic heating rate

ar :

temperature at which no radiation occurs

aw :

adiabatic wall temperature

FE :

finite element

in :

initial temperature

r :

radiation heat-transfer

s:

skin

References

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  2. Rumsey, C. B.; Lee, D. B.: Measurements of aerodynamic heat transfer and boundary-layer transition on a 15° cone in free flight at supersonic Mach number up to 5.2, NASA TND 888, 1961

  3. Rumsey, C. B.; Lee, D. B.: Measurements of aerodynamic heat transfer and boundary-layer transition on a 10° cone in free flight at supersonic Mach numbers up to 5.9, NASA TND 745, 1961

  4. Kidd, C. T.: Thin-skin technique heat-transfer measurement errors due to heat conduction into thermocouple wires. ISA Transaction. (1985) 1–10

  5. Conti, R. J.: Approximate temperature distributions and streamwise heat conduction effects in the transient aerodynamic heating of thin-skinned bodies. NASA TND-895, 1961

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Authors and Affiliations

  1. Vikram Sarabhai Space Centre, Trivandrum, India

    R. C. Mehta (Engineer, Aerodynamics Div.) & T. Jayachandran (Engineer, Solid Motor Proj.)

  2. Dept. of Mechanical Engineering, Indian Institute of Technology, Madras, India

    V. M. K. Sastri (Professor)

Authors
  1. R. C. Mehta
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  2. T. Jayachandran
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  3. V. M. K. Sastri
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Mehta, R.C., Jayachandran, T. & Sastri, V.M.K. Finite element analysis of conductive and radiative heating of a thin skin calorimeter. Wärme- und Stoffübertragung 22, 227–230 (1988). https://doi.org/10.1007/BF01377245

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  • DOI: https://doi.org/10.1007/BF01377245

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