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Effect of cavity aspect ratio on flow and heat transfer characteristics in pipes: a numerical study

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Abstract

Using the standard k–ε turbulence model, a two-dimensional turbulent pipe flow was simulated with and without square cavities. Effect of cavity aspect ratio on flow and heat transfer characteristics was investigated. Uncertainty was approximated through experimental validation and grid independence. The simulation revealed circulation inside the cavities. Cavity boundaries were shown to contribute significantly toward turbulence production. Cavity presence was shown to enhance overall heat transfer through the wall, while increasing pressure drop significantly across the pipe. It was predicted that cavities with higher aspect ratio enhance heat transfer more while increasing pressure drop.

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Abbreviations

A R :

cavity aspect ratio=C W/C D

C W :

cavity width, m

C D :

cavity depth, m

C p :

specific heat at constant pressure, kJ/(kg K)

C 1ε :

empirical constant=1.44

C 2ε :

empirical constant=1.92

C μ :

empirical constant=0.09

D :

pipe diameter, m

E :

empirical constant=9.8

E :

total energy, J

f :

friction factor=ΔP/(2(L/D)ρU 2in )

h :

heat transfer coefficient=q/(T w-T bulk), W/(m2 K)

k :

turbulence kinetic energy, m2/s2

k :

fluid thermal conductivity, W/(m K)

L :

pipe length, m

Nu x :

local Nusselt number=hD/k

Nu :

area-averaged Nusselt number

Nu DB :

Nusselt number obtained by the Dittus–Boelter correlation

p :

mean pressure of the fluid, Pa

Pr t :

turbulent Prandtl number

q :

heat flux through the wall, W/m2

Re :

Reynolds number=ρU in D/μ

T w :

wall temperature, K

T in :

inlet temperature, K

U :

mean velocity of the fluid, m/s

Uin :

inlet velocity, m/s

x i :

Cartesian coordinates

δij :

Kronecker delta

δ k :

empirical constant=1.0

δ ε :

empirical constant=1.3

Δρ :

pressure drop through the pipe, Pa

ε:

turbulence dissipation rate, m2/s3

κ:

von Karman constant=0.42

μ:

dynamic viscosity of the fluid, kg/(m s)

μ t :

eddy viscosity, kg/(m s)

ρ:

mean density of the fluid, kg/m3

\( \rho \overline{{U_{i} U_{j} }} \) :

Reynolds stresses, Pa

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Authors and Affiliations

  1. Department of Mechanical Engineering, King Saud University, 800, 11421, Riyadh, Saudi Arabia

    Khalid N. Alammar

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  1. Khalid N. Alammar
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Correspondence to Khalid N. Alammar.

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Alammar, K.N. Effect of cavity aspect ratio on flow and heat transfer characteristics in pipes: a numerical study. Heat Mass Transfer 42, 861–866 (2006). https://doi.org/10.1007/s00231-005-0054-x

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  • DOI: https://doi.org/10.1007/s00231-005-0054-x

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