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Momentum and heat transfers from fully developed turbulent flow in an eccentric annulus to inner and outer tube walls

Impuls- und Wärmetransport von einer vollentwickelten turbulenten Strömung in einem exzentrischen Ringspalt an die innere und äußere Rohrwand

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Abstract

An analysis and measurement were made of momentum and heat transfers from fully developed turbulent flow in an eccentric annulus to inner and outer tube walls. The eddy diffusivities of momentum and heat obtained in the turbulent flow in a circular tube were applied to the annular flow in the analysis. The result indicates that the calculated friction factor and average Nusselt numbers on the inner and outer tube walls are in fairly good agreement with the measurements.

Zusammenfassung

Es wurden Messungen und eine Analyse über den Impuls- und Wärmetransport von einer vollentwickelten turbulenten Strömung in einem exzentrischen Ringspalt an die innere und äußere Rohrwand durchgeführt. Die turbulenten Austauschgrößen von Impuls und Wärme, wie sie für die Strömung in einem Zylinder bekannt sind, wurden in der Analyse auf die Ringströmung angewandt. Die Ergebnisse zeigen, daß die berechneten Werte von Reibungsfaktor und mittlerer Nusselt-Zahl auf der inneren und äußeren Wand des Ringspalts in ausreichend guter Übereinstimmung mit den Messungen sind.

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Abbreviations

A :

heat transfer area, [m2]

Cp :

specific heat, [J kg−1 K−1]

D eq = 2 (R2 − R1):

equivalent diameter, [m]

e = s/(R2 − r1):

eccentricity

f :

overall friction factor

h :

heat transfer coefficient, [J m−2 s−1 K−1]

k :

thermal conductivity, [J m−1 s−1 K−1]

L :

tube length, [m]

Nu=h Deq/k:

average Nusselt number

Nu ϕ :

local Nusselt number

p :

pressure, [Pa]

R :

radius, [m]

R+ = R u*/v :

dimensionless distance from the wall

Re = Deq ū/v :

Reynolds number

s :

distance between the centers of two tubes, [m]

T :

temperature, [K]

u :

velocity, [m s−1]

ū :

cross sectional average velocity, [m s−1]

u* :

friction velocity, [m s−1]

um :

maximum velocity at constant ϕ, [m s−1]

W :

flow rate of air, [kg s−1]

x,y, z :

rectangular coordiantes, [m]

y+ = yu*/v :

dimensionless distance from the wall

α :

thermal diffusivity, [m2s−1]

γ = R1/R2 :

radius ratio

ɛm :

eddy diffusivity of momentum, [m2 s−1]

ɛh :

eddy diffusivity of heat, [m2 s−1]

η, ϕ :

bipolar coordinates

λ :

scale factor, [m]

μ :

viscosity, [Pa s]

v :

kinematic viscosity, [m2 s−1 ]

ϱ :

density, [kg m−3]

τ :

local shear stress at the wall, [N m−2]

τ ηz :

shear stress, [N m−2]

1:

inner tube wall

2:

outer tube wall

References

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Authors and Affiliations

  1. Department of Chemical Engineering, Kyoto University, 606, Kyoto, Japan

    F. Ogino Professor, T. Sakano (Graduate Student) & T. Mizushina Professor Emeritus

Authors
  1. F. Ogino Professor
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  2. T. Sakano
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  3. T. Mizushina Professor Emeritus
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Dedicated to Prof. Dr.-Ing. U. Grigull's 75th birthday

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Ogino, F., Sakano, T. & Mizushina, T. Momentum and heat transfers from fully developed turbulent flow in an eccentric annulus to inner and outer tube walls. Wärme- und Stoffübertragung 21, 87–93 (1987). https://doi.org/10.1007/BF01377564

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  • DOI: https://doi.org/10.1007/BF01377564

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