Equivalent Hydraulic Diameter

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Equivalent Hydraulic Diameter The concept of equivalent hydraulic diameter is introduced to obtain a circular-channelhydraulically-equivalent flow condition for flows which have non-circular cross sectional flow area, especially in term of heat transfer and friction effects on the fluids. Consider a rectangular pin array typical of PWR core:

Let us say that the pitch is 3 cm and the rod diameter is 2 cm, therefore:

flow area = A1 = p 2 − π ( d F / 2 ) = 5.85841 cm2 (actual geometry) 2

hydraulic perimeter = P1 = π × d F = 3.14159 cm (actual geometry) The equivalent hydraulic diameter is expressed as:

De ,hyd =

4 × flow area 4 × 5.85841 = = 7.45916 cm hydraulic perimeter 3.14159

By using the equivalent hydraulic diameter, flow area and hydraulic perimeter are calculated as follow:

flow area = A2 = π ( De, hyd / 2 ) = π ( 7.45916 / 2 ) = 43.69882 cm 2 2

2

(using

equivalent

hydraulic

diameter)

hydraulic perimeter = P2 = π × De, hyd = 23.43364 cm (using equivalent hydraulic diameter) Fluid mass flow is calculated as follow:

m&= ρ Av ⇔ v =

m& 1 × ρ A

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http://syeilendrapramuditya.wordpress.com Let us assume that

m&/ ρ = 1 , therefore v = 1/ A :

v1 =

1 1 = cm/s (actual geometry) A1 5.85841

v2 =

1 1 = cm/s (using equivalent hydraulic diameter) A2 43.69882

The very idea of the introduction equivalent hydraulic diameter concept is that for the same fluid mass flow, the actual fluid and the modeled fluid must pass through a same area of rod wall surface per unit time, such that the two fluids will experience the same heat transfer and friction effects, or in other word, they are hydraulically equivalent. And let us now calculate the wall surface which is passed through by the two fluids in 1 second:

wall surface area = v1 × P1 =

3.14159 = 0.53625 cm 2 (actual geometry) 5.85841

wall surface area = v2 × P2 =

23.43364 = 0.53625 cm 2 (using equivalent hydraulic diameter) 43.69882

That’s all about equivalent hydraulic diameter, quite simple huh?

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For Rectangular array geometry (Light Water-cooled Reactor/LWR)

For Triangular array geometry (Liquid Metal-cooled Reactor/LMR)

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