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Empirical models for liquid metal heat transfer in the entrance region of tubes and rod bundles

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Abstract

Experiments focusing on liquid metals heat transfer in pipes and rod bundles with thermally and hydraulically developing flow are reviewed. Empirical heat transfer correlations are developed for engineering applications. In the developing regions the heat transfer is in-stationary. The heat transfer at the entrance is around 100 % higher due to the developing process including the lateral exchange of energy and momentum than for developed flow. Developing flow is not physically considered in the framework of system codes, which are used for thermal–hydraulic analysis of power and process plants with a multitude of components like pipes, tanks, valves and heat exchangers. Therefore, the application to liquid metal flows is limited to developed flow, which is independent of the distance from the flow entrance. The heat transfer enhancement in developing flows is important for the optimization of components like heat exchangers and helps to reduce unnecessary conservatism. In this work, empirical models are developed to account for developing flows in pipes and rod bundles. A literature review is performed to collect available experimental data for developing flow in liquid metal heat transfer. The evaluation shows that the length for pure thermally developing pipe flow is much larger (20–30 hydraulic diameters) than for combined thermally and hydraulically developing flow (10–15 hydraulic diameters). In rod bundles, fully combined developed flow is established after 30–40 hydraulic diameters downstream of the entrance. The derived empirical models for the heat transfer enhancement in the developing regions are implemented into a best estimate system code. The validation of these models by means of post-test analyses of 16 experiments shows that they are very well able to represent the heat transfer in developing regions.

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Abbreviations

c :

Wall drag

cp :

Specific heat

d :

Diameter

e :

Internal energy

h :

Heat transfer coefficient

J :

Bessel function

k :

Thermal conductivity

p :

Rod pitch

p :

Pressure

q :

Heat flux

T :

Temperature

v :

Velocity

x :

Distance

Γ :

Mass transfer rate

α :

Void fraction

δ :

Thickness of the boundary layer

η :

Dynamic viscosity

λ :

Root of the Bessel function

ρ :

Density

Gz:

Graetz number (Gz = Pe·d/x)

Nu:

Nusselt number (Nu = f(Re, Pr))

Pe:

Péclet number (Pe = Re·Pr)

Pr:

Prandtl number (Pr = cp·η/k)

Re:

Reynolds number (Re = ρ·v·d/η)

∞:

Developed

d:

Direct

g:

Gas

hyd:

Hydraulic

i:

Interface

l:

Liquid

t:

Thermal

v:

Hydraulic

w:

Wall

x:

Local

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  1. Institute of Fusion and Reactor Technology, Karlsruhe Institute of Technology, Kaiserstrasse 12, 76131, Karlsruhe, Germany

    Wadim Jaeger

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Jaeger, W. Empirical models for liquid metal heat transfer in the entrance region of tubes and rod bundles. Heat Mass Transfer 53, 1667–1684 (2017). https://doi.org/10.1007/s00231-016-1929-8

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