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Flow field predictions in a model heat exchanger

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Abstract

A numerical study of the two-dimensional isothermal steady flow distribution of an incompressible fluid in the shell side of an experimental heat exchanger is described.

Computations are performed with and without tubes present in the model, for Reynolds numbers up to 10,000. Baffles and tube bundles are modelled by incorporating the “porous medium” concept into the governing equations.

The resulting equations described in primitive variables are solved using a semi-implicit predictor-corrector type scheme. A Multi-Grid technique is employed to solve the linearized pressure correction equation which links momentum and continuity equations. Predictions with the proposed scheme indicate good qualitative agreement when compared with experimental measurements.

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Abbreviations

A :

area of a control volume face

A out :

outlet area of heat exchanger model

a p , a E , a W , a N , a s :

coefficients of finite volume equations

b e , b n :

constant part of linerized source term in momentum equations

C μ :

constant in turbulence model (= 0.09)

d t :

tube diameter

d h :

hydraulic diameter

E :

constant factor

F x i (i = 1, 2):

momentum equations source term

fc :

cross flow friction factor

fp :

parallel flow friction factor

K b :

baffle resistance to flow

Ku 1, Ku 2 :

loss coefficients

l :

average length scale (= 1/2 (2p - d t ) for tube filled; = L m for tube free)

L :

characteristic length (= side of square cavity, or, = L in )

L in :

inlet length

p :

tube pitch

P :

pressure

P * :

best estimate of pressure

P′:

pressure correction

Re :

Reynolds number (Re = L × V/v)

S :

linearized source term

t :

time

U 1, U 2 :

velocity components in x 1− and x 2-direction, respectively

U *1 , U *2 :

velocities based on P *

U 2 o :

normal velocity component at outlet

U 2 0–1 :

normal velocity component just before the outlet

U in :

inlet velocity

V :

reference velocity (= velocity of moving lid for cavity flow, or, = U in )

x i (i = 1,2):

cartesian coordinates

X i (i = 1,2):

normalized cartesian coordinates

β:

local volume porosity = fluid volume/total volume)

β t :

porosity within the tube bundle

Δm :

inflow/outflow mass imbalance

Δ:

time step

(Δt) max :

maximum time step for an explicit formulation

ΔV :

volume of control domain

Δx 1, Δx 2 :

dimensions of control domain

v :

laminar kinematic viscosity

v eff :

effective kinematic viscosity

v t :

turbulent kinematic viscosity

ϱ:

density of fluid

Σ:

summation

φ:

general dependent variable

nb :

nodal locations adjacent to e (or n) location

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of New Brunswick, E3B 5A3, Fredericton, N. B., Canada

    V. M. Theodossiou & A. C. M. Sousa

  2. Engineering Research Branch, Atomic Energy of Canada Limited, CRNL, K0J 1J0, Chalk River, Ont., Canada

    L. N. Carlucci

Authors
  1. V. M. Theodossiou
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  2. A. C. M. Sousa
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  3. L. N. Carlucci
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Additional information

Communicated by S. N. Atluri April 22, 1987

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Theodossiou, V.M., Sousa, A.C.M. & Carlucci, L.N. Flow field predictions in a model heat exchanger. Computational Mechanics 3, 419–428 (1988). https://doi.org/10.1007/BF00301142

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  • DOI: https://doi.org/10.1007/BF00301142

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