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Porous Medium Modeling of Air-Cooled Condensers

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Abstract

This article presents a porous media transport approach to model the performance of an air-cooled condenser. The finned tube bundles in the condenser are represented by a porous matrix, which is defined by its porosity, permeability, and the form drag coefficient. The porosity is equal to the tube bundle volumetric void fraction and the permeability is calculated by using the Karman–Cozney correlation. The drag coefficient is found to be a function of the porosity, with little sensitivity to the way this porosity is achieved, i.e., with different fin size or spacing. The functional form was established by analyzing a relatively wide range of tube bundle size and topologies. For each individual tube bundle configuration, the drag coefficient was selected by trial and error so as to make the pressure drop from the porous medium approach match the pressure drop calculated by the heat exchanger design software ASPEN B-JAC. The latter is a well-established commercial heat exchanger design program that calculates the pressure drop by using empirical formulae based on the tube bundle properties. A close correlation is found between the form drag coefficient and the porosity with the drag coefficient decreasing with increasing porosity. A second order polynomial is found to be adequate to represent this relationship. Heat transfer and second law (of thermodynamics) performance of the system has also been investigated. The volume-averaged thermal energy equation is able to accurately predict the hot spots. It has also been observed that the average dimensionless wall temperature is a parabolic function of the form drag coefficient. The results are found to be in good agreement with those available in the open literature.

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Abbreviations

A :

Flow cross-sectional area, m2

C F :

Form drag coefficient

c p :

Specific heat at constant pressure (of fluid), J/Kg K

d :

Diameter, m

e p :

Normalized excess pressure drop because of fins

e q :

Normalized heat transfer enhancement because of fins

k :

Turbulent kinetic energy per unit mass, (m/s)2

K :

Permeability, m2

L :

Tube length, m

\({\dot {m}}\) :

Mass flow rate, Kg/s

N :

Number

p :

Pressure, Pa

P * :

Pressure gradient, Pa/m

Q :

Total heat transfer rate, W

q b :

Volumetric heat generation rate, W/m3

Ns :

Entropy generation number

Pr T :

Turbulent Prandtl number

Re K :

Reynolds number with K 1/2 as the length scale, Re K  = V K 1/2/υ

S :

Tube pitch, m

\({\dot {S}_{\rm gen}}\) :

Entropy generation rate, W/K

\({S_\phi}\) :

Source term for \({\phi}\) equation

t :

Fin thickness, m

T :

Temperature, K

u :

x-Velocity, m/s

v :

y-Velocity, m/s

V :

Face velocity, m/s

x :

Horizontal coordinate, m

y :

Vertical coordinate, m

α :

Effective thermal diffusivity of the fluid/porous medium, m2/s

ε :

Dissipation rate of turbulent kinetic energy, m2/s3

\({\Gamma_\phi}\) :

Diffusion parameter for \({\phi}\) equation, m2/s

θ :

Dimensionless temperature

ρ :

Fluid density, Kg/m3

υ :

Kinematic viscosity, m2/s

\({\phi}\) :

Generic variable

φ :

Porosity

ave:

Average

b:

Bundle

eff:

Effective

f:

Fin

in:

Inlet

m:

Mean

out:

Outlet

ref:

Of reference temperature

t:

Tube

T:

Turbulent

w:

Wall

x, y:

In x, y direction

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Authors and Affiliations

  1. School of Mechanical and Mining Engineering, The University of Queensland, Brisbane, QLD, 4072, Australia

    K. Hooman & H. Gurgenci

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  1. K. Hooman
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  2. H. Gurgenci
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Correspondence to K. Hooman.

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Hooman, K., Gurgenci, H. Porous Medium Modeling of Air-Cooled Condensers. Transp Porous Med 84, 257–273 (2010). https://doi.org/10.1007/s11242-009-9497-8

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