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Large eddy simulation of turbulent heat transfer in pipe flows with respect to Reynolds and Prandtl number effects

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Abstract

Heat transfer in a fully developed turbulent pipe flow is investigated by the use of the large eddy simulation technique. Isoflux condition is imposed at the wall. Four Prandtl numbers are considered (0.71, 3, 5, and 7) and three Reynolds numbers (5,500, 10,000, and 20,000). The effects of Reynolds and Prandtl numbers on turbulent heat transfer in pipe flow are investigated in order to obtain a more detailed knowledge of the thermal field in circular pipe flow. The objective of this study is also to examine the effectiveness of the large eddy simulation approach for predicting the turbulent heat transfer at different Prandtl numbers larger than 0.71, for various Reynolds numbers up to 20,000. Validation is achieved by comparing the present predictions to the available results of the literature. The effects of Prandtl and Reynolds numbers on many statistical quantities, such as mean temperature profiles, RMS of fluctuating temperature, turbulent heat fluxes, higher-order statistics, and heat transfer coefficient, are examined. Visualizations of instantaneous filtered temperature fields are analyzed.

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Abbreviations

C d :

Coefficient of the dynamic model

C p :

Specific heat at constant pressure

D :

Pipe diameter (m)

D m :

Molecular diffusivity

F(Θ′):

Flatness factor

h :

Heat transfer coefficient, \({h = -\frac{k}{T_{\rm w}-T_{\rm b}} \frac{\partial T}{\partial r} ({W}/{m}^{2}{K}})\)

k :

Thermal conductivity (W/m K)

L :

Length of the computational domain (m)

Nu :

Nusselt number, Nu =  h D/k

Pe :

Peclet number, Pe =  Re Pr

Pr :

Prandtl number, Pr =  ν/α

q w :

Uniform heat flux at the wall (W/m2)

Re :

Reynolds number Re =  U b D/ν

r :

Dimensionless coordinate in radial direction scaled by the pipe radius

R :

Pipe radius (m)

S(Θ′):

Skewness factor

Sc :

Schmidt number, Sc =  ν/D m

T :

Temperature (K)

T b :

Bulk temperature

T r :

Reference temperature, T r = q w/ρ C p U b

T w :

Wall temperature (K)

T τ :

Friction temperature, T τ = q w/sρ C p u τ

u τ :

Friction velocity (m/s)

U b :

Bulk velocity (m/s)

v r, v z, v θ :

Dimensionless wall-normal, axial, and azimuthal velocity components

y + :

Distance from the wall in wall units, y + = (1−r)u τ/ν

z :

Dimensionless coordinate in axial direction

α :

Thermal diffusivity

θ :

Dimensionless coordinate in circumferential direction

Θ :

Dimensionless temperature, Θ = 〈T w〉−T/T r

ν :

Kinematic viscosity (m2/s)

ρ :

Density (kg/m3)

〈(.)〉:

Statistically averaged

(.)+ :

Normalized by u τ, ν and T τ

(.)′:

Fluctuation component

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Authors and Affiliations

  1. Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME, UMR 8208 CNRS, 5 bd Descartes, 77454, Marne-la-Vallée, France

    M. Ould-Rouiss, M. Bousbai & A. Mazouz

  2. TAFML, Faculty of Physics, USTHB, 16111, Algiers, Algeria

    M. Bousbai

  3. TEMPO-DF2T, Université de Valenciennes, Le Mont Houy, 59313, Valenciennes Cedex 9, France

    A. Mazouz

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  1. M. Ould-Rouiss
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Correspondence to M. Ould-Rouiss.

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Ould-Rouiss, M., Bousbai, M. & Mazouz, A. Large eddy simulation of turbulent heat transfer in pipe flows with respect to Reynolds and Prandtl number effects. Acta Mech 224, 1133–1155 (2013). https://doi.org/10.1007/s00707-012-0796-8

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  • DOI: https://doi.org/10.1007/s00707-012-0796-8

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