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A turbulent near-wall model on convective heat transfer from an abrupt expansion tube

Ein Turbulentmodell zur Erfassung des konvektiven Wärmeaustausches in der Nähe einer abrupten Rohrerweiterung

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Abstract

Turbulent heat transfer from a sudden expansion pipe subjected to an externally convective boundary condition is studied numerically using the proposed modified turbulence model. Both HYBRID and QUICK schemes are employed for comparison purposes. The calculated velocity distribution and turbulent kinetic energy show a significant improvement over the existing model solutions. The present results of center-line velocity, temperature distribution and Nusselt number under a limiting condition compare well with the available experimental data.

Zusammenfassung

Mittels des vorgeschlagenen modifizierten Turbulenzmodells wurde die turbulente Wärmeübertragung in der Nähe einer abrupten, extern einer konvektiven Grenzbedingung unterliegenden Rohrerweiterung untersucht. Sowohl HYBRID- als auch QUICK-Verfahren fanden zu Vergleichszwecken Anwendung. Die berechnete Geschwindigkeitsverteilung und die turbulente kinetische Energie zeigen eine signifikante Verbesserung gegenüber den existierenden Modell-Lösungen. Die vorliegenden Ergebnisse für die Geschwindigkeit entlang der Mittellinie, die Temperaturverteilung und die Nusselt-Kennzahl stimmen unter einschränkenden Bedingungen gut mit vorhandenen experimentellen Daten überein.

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Abbreviations

A :

model constant

C f :

friction coefficient

C 1,C 2,C μ :

model constants

C p :

specific heat

d :

diameter of inlet pipe

D :

diameter of outlet pipe

f 1,f 2,f μ,f ε :

model functions

G K :

turbulent energy production

h 0 :

outside wall heat transfer coefficient

h i :

inner wall heat transfer coefficient

H=(D-d)/2 :

step height

k :

thermal conductivity

K :

turbulent kinetic energy

Nu=h i D/k :

Nusselt number

Nu DB :

Nusselt number of fully developed pipe flow based on Dittus-Boelter equation

P :

mean pressure

Pr=μC p /k :

Prandtl number

Pr t :

turbulent Prandtl number

q w :

heat flux through pipe wall

r :

radial coordinate

R=D/2 :

radius of outlet pipe

Re D =UD/v :

Reynolds number based on outlet pipe diameter

Re d =Ud/v :

Reynolds number based on inlet pipe diameter

R t =K 2/(vε) :

turbulent Reynolds number

S Φ :

source term of Φ

S ΦP,S ΦC :

source coefficients of Φ

t :

temperature fluctuation

T :

time mean temperature

T i :

mean temperature at the inlet plane

u i :

velocity fluctuation ini-th direction

U :

axial time mean velocity

U i :

time mean velocity ini-th direction

U c :

center line velocity

U iC :

center line velocity at inlet

U in :

average velocity at the inlet plane

V :

radial time mean velocity

x :

axial coordinate

x i :

spatial coordinate ini-th direction

y :

distance from the wall

y +=C 1/4 K 1/2 y/v :

dimensionless distance from the wall

α t :

turbulent thermal diffusivity

αΦ :

under-relaxation factor for Φ

K=0.41:

model constant

ΓΦ :

diffusivity for Φ

ε:

turbulent energy dissipation rate

∀:

control volume

μ:

dynamic viscosity

v :

kinematic viscosity

v t :

eddy viscosity

V eff=V+V t :

effective viscosity

σ K , σε :

model constants

Φ:

common variable

δ ij :

Kronecker delta

References

  1. Baughn, J. W.;Hoffman, M. A.;Takahasi, R. K.;Launder, B. E.: Local Heat Transfer Downstream of An Abrupt Expansion in A Circular Channel with Constant Wall Heat Flux. J. Heat Transfer 106:789–796 (1984)

    Google Scholar 

  2. Khezzar, L.;Whitelaw, J. H.: Round Sudden-Expansion Flows. Proc. Inst. Mech. Eng. 200:447–455 (1986)

    Google Scholar 

  3. Durrett, P. R.;Stevenson, W. H.;Thompson, H. D.: Radial And Axial Turbulent Flow Measurements with an LDV in an Axisymmetric Expansion Air Flow. J. Fluids Eng. 110:367–372 (1988)

    Google Scholar 

  4. Baughn, J. W.;Hoffman, M. A.;Launder, B. E.;Lee, D.;Yap, C.: Heat Transfer, Temperature and Velocity Measurements Downstream of An Abrupt Expansion in a Circular Tube at A Uniform Wall Temperature. J. Heat Transfer 111:870–876 (1989)

    Article  Google Scholar 

  5. Lee, D.: Turbulent Heat Transfer Downstream of an Asymmetric Abrupt Expansion in a Tube. Proceedings of 32nd Heat Transfer and Fluid Mech. Inst. (1991) 157–170

  6. Prud’homme, M.;Elghobashi, S.: Turbulent Heat Transfer near the Reattachment of Flow Downstream of A Sudden Expansion. Num. Heat Transfer 10:349–368 (1986)

    Google Scholar 

  7. Sparrow, E. M.;Kang, S. S.;Chuck, W.: Relation between the Points of Flow Reattachment And Maximum Heat Transfer for Regions of Flow Separation. Int. J. Heat Mass Transfer 30:1237–1246 (1987)

    Article  Google Scholar 

  8. Yap, C.: Ph.D. Thesis. University of Manchester Inst. of Sci. & Tech. Manchester, UK, 1987

  9. Spalding, D. B.: A Novel Finite-Difference Formulation for Differential Expressions Involving Both First And Second Derivatives. Int. J. Num. Methods Eng. 4:551–559 (1972)

    Article  Google Scholar 

  10. Leonard, B. P.: A Stable and Accurate Convective Modeling Procedure Based on Quadratic Upstream Interpolation. Compute. Meth. Appl. Mech. Eng. 19:59–98 (1979)

    Article  MATH  Google Scholar 

  11. Pollard, A.;Siu, A. L. W.: The Calculation of Some Laminar Flows Using Various Discretization Schemes. Comp. Meth. Appl. Mech. Eng. 35:293–313 (1982)

    Article  MATH  Google Scholar 

  12. Jones, W. P.;Launder, B. E.: The Prediction of Laminarization with A Two-Equation Model of Turbulence. Int. J. Heat Mass Transfer 15:301–314 (1972)

    Article  Google Scholar 

  13. Reynolds, A. J.: Turbulent Flows in Engineering. London, John Wiley & Sons Ltd., 1974

    Google Scholar 

  14. Nagano, Y.;Tagawa, M.: An ImprovedK-ε Model for Boundary Layer Flows. J. Fluids Eng. 112:33–39 (1990)

    Article  Google Scholar 

  15. Kim, S. W.: Near-Wall Turbulence Model and Its Application to Fully Developed Turbulent Channel And Pipe Flows. Num. Heat Transfer (Pt. B) 17:101–122 (1990)

    Google Scholar 

  16. Wassel, A. T.;Catton, I.: Calculation of Turbulent Boundary Layers over Flat Plates with Different Phenomenological Theories of Turbulence and Variable Turbulent Prandtl Number. Int. J. Heat Mass Transfer 16:1547–1563 (1973)

    Article  Google Scholar 

  17. Reynolds, A. J.: The Prediction of Turbulent Prandtl and Schmidt Numbers. Int. J. Heat Mass Transfer 18:1055–1069 (1975)

    Article  Google Scholar 

  18. Patankar, S. V.: Numerical Heat Transfer and Fluid Flow. Washington, D.C., Hemisphere Publishing Co., 1980

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, The University of Akron, 44325-3903, Akron, Ohio, USA

    B. T. F. Chung (F. Theodore Harrington Professor of Mechanical Engineering) & S. Jia (Research Assistant)

Authors
  1. B. T. F. Chung
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  2. S. Jia
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Additional information

This work was supported by a Research Challenge Grant sponsored by the Ohio Board of Regents.

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Chung, B.T.F., Jia, S. A turbulent near-wall model on convective heat transfer from an abrupt expansion tube. Heat and Mass Transfer 31, 33–40 (1995). https://doi.org/10.1007/BF02537419

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