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Heat transfer calculations in turbulent boundary layers using integral relations

Berechnung des Wärmeüberganges in turbulenten Grenzschichten unter Verwendung von Integralverfahren

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Summary

An integral method for the computation of turbulent thermal boundary layers is presented which is based on two integral relations each for the flow and temperature fields. This required the evaluation of a heat flux integralC T from experimental data. In the incompressible case, an approximation forC T was obtained which permits the fast and reliable computation of turbulent heat transfer problems. Finally, the experimental and numerical requirements for the extension to compressible flows are discussed.

Zusammenfassung

Es wird ein Integralverfahren zur Berechnung von turbulenten Temperaturgrenzschichten vorgestellt, das sich auf je zwei Integralbedingungen für das Geschwindigkeits-und Temperaturfeld stützt. Aus Experimenten bei inkompressiblen Strömungen wurde ein Wärmeaustauschintegral bestimmt. Mit einer Näherungsformel dafür ließ sich der Wärmeübergang in turbulenten inkompressiblen Strömungen schnell und zuverlässig berechnen. Schließlich werden die experimentellen und numerischen Anforderungen für die Erweiterung der Methode auf kompressible Strömungen dargelegt.

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Abbreviations

b :

heat transfer parameter

c 1...c4 :

coefficients in (21)

C f :

friction coefficient

C D :

dissipation integral

C T :

heat flux integral

G :

function, approximating the velocity field (21)

h :

total energy

I 1...I 3 :

higher order integrals (13)

Ma:

Mach number

Pr:

Prandtl number (16)

ρ:

pressure

q :

total heat flux

Re:

Reynolds number (21)

St:

Stanton number (16)

t, ū :

dimensionless temperature and velocity

u, v :

velocity components

x, y :

phys. coordinates

α, β:

coefficients in (24)

δ:

outer edge of boundary layers

\(\left. \begin{gathered} \delta _1 \ldots \delta _1 \hfill \\ \Delta _1 ,\Delta _2 \hfill \\ \vartheta _1 ,\vartheta _2 \hfill \\ \end{gathered} \right\}\) :

characteristic boundary layer thicknesses (6), (15)

η, η* :

dimensionless wall distance

κ:

c p/cv

λ:

thermal conductivity

μ:

dynamic viscosity

ρ:

density

τ:

effective shear stress

ω:

wake function

e :

effective (molecular+by turbulent exchange generated)

F :

of the flow field

T :

of the temperature field

ω:

at the wall

δ:

at outer edge of boundary layer

References

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Authors and Affiliations

  1. DFVLR-Institut für angew. Mathematik und Mechanik, Hebelstraße 27, D 7800, Freiburg i. Br., Federal Republic of Germany

    B. Schulz-Jander

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Schulz-Jander, B. Heat transfer calculations in turbulent boundary layers using integral relations. Acta Mechanica 21, 301–312 (1975). https://doi.org/10.1007/BF01303072

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