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Thermal stratification studies in a side heated water pool for advanced heavy water reactor applications

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Abstract

Strong heat source at the isolation condenser wall of an Advanced Heavy Water Reactor, results in natural convection in gravity driven water pool, which leads to a thermally stratified pool. Governing equations simulating fluid flow and heat distribution are solved numerically by a general purpose Computational Fluid Dynamics solver developed at Indian Institute of Technology, Kanpur. Incompressible finite volume method with non-staggered grid arrangement is used in this exercise. This algorithm is fully implicit and semi-coupled. Turbulent natural convection in a boundary layer for high Rayleigh numbers is analyzed by the Lam–Bremhorst k − ε turbulence model. Analysis of unsteady laminar natural convection in a side-heated water cavity is also done for different values of Rayleigh number. Results show a warm fluid layer floating on the top of gradually colder layer (along the vertical direction) that indicates the presence of thermal stratification phenomenon. This fact necessitates additional safety features in such a system so that the detrimental effect such as stratification is minimized.

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Abbreviations

C p :

specific heat (J/kg K)

C1, C2:

constant in ε equation

f 1, f 2 :

damping function in ε equation

g:

gravitational acceleration (m/s2)

h:

heat transfer coefficient (W/m2 K)

k :

thermal conductivity, (W/m K)

n :

surface normal direction

p :

pressure (N/m2)

Pr :

Prandlt number (ν/α)

Q :

heat flux (W/m2)

Ra :

Rayleigh number (gβ∆TL3/να)

Ra * :

modified Rayleigh number (gβqL4/kνα)

σ k , σ ε :

constant in ε equation

S :

volumetric source term

T :

temperature (K)

t:

time (s)

u :

velocity in x direction, (m/s)

v :

velocity in y direction (m/s)

w :

velocity in z direction (m/s)

x, y, z :

coordinates in the physical domain (m)

α:

thermal diffusivity (m2/s)

β:

coefficient of volumetric expansion (1/K)

ε :

dissipation rate of turbulent kinetic energy (J/s)

k :

turbulent kinetic energy (J)

μ:

dynamic viscosity (kg/m s)

μt :

turbulent viscosity (kg/m s)

ν:

kinematic viscosity (m2/s)

νt :

turbulent kinematic viscosity (m2/s)

ρ:

density (kg/s3)

τ:

Reynolds stress tensor

Г:

the thermal conductivity for turbulent equation (W/m K)

θ:

non-dimensional temperature

* :

modified

—:

average

′:

prime

°:

degree

t:

turbulent terms

p:

constant pressure

i, j, k :

index

∞:

air

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Acknowledgments

This work was supported by Board for Research in Nuclear Sciences, Department of Atomic Energy, Government of India.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology, Kanpur, India

    Akhilesh Gupta, V. Eswaran & Prabhat Munshi

  2. Reactor Engineering Division, Bhabha Atomic Research Centre, Mumbai, India

    N. K. Maheshwari & P. K. Vijayan

Authors
  1. Akhilesh Gupta
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  2. V. Eswaran
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  3. Prabhat Munshi
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  4. N. K. Maheshwari
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  5. P. K. Vijayan
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Corresponding author

Correspondence to Prabhat Munshi.

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Gupta, A., Eswaran, V., Munshi, P. et al. Thermal stratification studies in a side heated water pool for advanced heavy water reactor applications. Heat Mass Transfer 45, 275–285 (2009). https://doi.org/10.1007/s00231-008-0429-x

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  • DOI: https://doi.org/10.1007/s00231-008-0429-x

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