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Developing turbulent flow in concentric annuli: An analytical and experimental study

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Abstract

In this paper, the problem of the developing turbulent flow in concentric annuli is studied from an integral view-point based on a modified model ofReichardt's expression for the eddy diffusivity of momentum. The analytical results are compared with the experimental data based on the measurement of local flow conditions for air flow through four concentric annuli for a Reynolds number range of about 20,000 to 110,000. In the analysis, it was assumed that the flow is turbulent everywhere and in the experimental work, the flow was tripped at the starting position of the boundary layers.

Zusammenfassung

Mit Hilfe einer Integralmethode und unter Benutzung des Ansatzes vonReichardt für die Impulsausbreitung wurde die turbulente Einlaufströmung im konzentrischen Ringspalt untersucht. Diese Rechnungen wurden mit experimentellen Ergebnissen an einer Luftströmung in vier konzentrischen Ringspalten im Bereich der Reynolds-Zahlen von 20 000 bis 110 000 verglichen. Bei den Rechnungen wurde angenommen, daß die Strömung überall turbulent ist, im Experiment wurden Stolperdrähte am Anfang der Grenzschichten vorgesehen.

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Abbreviations

A + :

dimensionless function defined by Eq. (17)

B + :

dimensionless function defined by Eq. (17)

C :

constant

f :

friction factor

k :

mixing length constance

n :

constant

p :

pressure

r :

radial distant

r + :

dimensionless radial distance parameter,r·u */v

r +1 + :

dimensionless radial distance parameter, r1· u *2 /v

R :

radial distance defined by Eq. (3)

R + :

dimensionless radial distance parameter,R· u*/v

s :

dimensionless parameter defined by Eq. (12)

u :

velocity inx direction

ū :

mean velocity inx direction

u′:

fluctuating velocity component inx direction

u + :

dimensionless velocity parameter,u/u *

u * :

friction velocity, (τ0/ϱ)0.5

x :

distance in flow direction from the entrance

y :

distance from wall

y + :

dimensionless distance parameter,y ·u */v

De :

equivalent diameter of annulus, 2 (r 2−r 1)

De+ :

dimensionless equivalent diameter,De·u */v

Re :

Reynolds number

α :

radius ratio, (r 2/r 1)

δ:

thickness of boundary layer

δ *j :

dimensionless parameter,\({{\delta _j^ + } \mathord{\left/ {\vphantom {{\delta _j^ + } {\left| {r_m^ + - r_j^ + } \right|}}} \right. \kern-\nulldelimiterspace} {\left| {r_m^ + - r_j^ + } \right|}}\)

δ *j :

dimensionless boundary layer thickness parameter,δ j·u *j /v

δ 1/++ :

dimensionless boundary layer thickness parameter, δ1·u *2 /v

ε :

eddy diffusivity

η :

dimensionless parameter defined by Eq. (12)

ν :

kinematic viscosity

ϱ :

density

τ :

shear stress

ϕ :

function

1:

inner wall or inner wall region of annulus

2:

outer wall or outer wall region of annulus

b:

bulk

d:

fully developed

e:

entrance

j:

refers region 1 or 2

m:

maximum

M:

momentum

1:

value at the edge of the laminar sublayer

0:

wall

x:

local

δ :

outside boundary-layer

max:

maximum

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Ottawa, Ottawa 2, Canada

    Y. Lee (Associate Professor) &  S. D. Park M. Eng. Ph. D. Candidate

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  1. Y. Lee
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  2. S. D. Park M. Eng. Ph. D. Candidate
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Lee, Y., Park, S.D. Developing turbulent flow in concentric annuli: An analytical and experimental study. Wärme- und Stoffübertragung 4, 156–166 (1971). https://doi.org/10.1007/BF01443674

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