Hole Array - Florschuetz

Description

This correlation is for jets from a square array of holes impinging on a flat surface. The correlation includes the HTC reduction for a cross flow deflecting the jets.

Type: Impingement Nu
Subtype: Hole Array - Florschuetz

Table 1. Input List
Index	UI Name (.flo label)	Description
1	Hole Pattern (HOLE_PATTERN)	Pattern of the impingement holes. This affects the path available for the cross flow to exit the post impingement gap. Inline or Staggered, No AUTO option.
2	Impingement Flow Element (IMP_ELM)	ID for the flow element that represents the jet flow through the holes. Can represent the entire hole array or just some of the holes in the array. No AUTO option. An element must always be supplied.
3	Cross flow Element (CROSS_ELM)	ID for flow element that represent the cross flow in the post impingement gap. If AUTO, any flow element (other than the IMP_ELM) entering the flow chamber (based on calculated flow direction) is considered a cross flow element.
4	Hole Diameter (HOLE_DIA)	Diameter of the holes forming the impinging jets. If AUTO, the diameter from the IMP_ELM is used. The IMP_ELM must be an element type that has a diameter input (orifice or tube).
5	Streamwise Hole Spacing (X_HOLE_SPAC)	Distance between the impingement holes in the direction parallel to the cross flow. No AUTO option. A hole spacing must always be supplied.
6	Spanwise Hole Spacing (Y_HOLE_SPAC)	Distance between the impingement holes in the direction perpendicular to the cross flow. No AUTO option. A hole spacing must always be supplied.
7	Number of Holes (NUM_HOLES)	Number of holes represented by IMP_ELM. If AUTO, the “number of streams” of IMP_ELM is used.
8	Distance to Target Surface (DIST_TO_TARG)	The distance from the impingement plate containing the holes to the surface the jets impinge. (Z in paper). No AUTO option.
9	Crossflow Area (CROSS_AREA)	The area for the cross flow in the post impingement gap. If AUTO, the area from the CROSS_ELM is used.
10	Impingement Angle (IMP_ANG)	Angle the impinging jets make with the target surface. No AUTO option.
11	Chamber for Tjet (TJET_CH)	The fluid chamber containing the temperature to be used in the heat flux calculation. This impingement correlation was derived using the pre-impingement air temperature. If AUTO, the upstream chamber for IMP_ELM is used.
12	HTC Multiplier (HTC_MULT)	A constant multiplier to scale the value of the heat transfer coefficient obtained from the correlation.

Formulation

This correlation uses a Nusselt number equation by Florschuetz (ref 1).

Eq 10a from ref 1:

N u = A R e^{m} \{1 - B {[(Z / D_{h}) (G c / G j)]}^{n}\} P r^{.333}

Reynolds number:

R e = \frac{{\dot{m}}_{i m p} D_{h}}{A r e a μ}

The coefficient A and B and the exponents m and n are calculated using eq 10b from ref 1:

A, B, m, a n d n = C {(X / D_{h})}^{n_{x}} {(Y / D_{h})}^{n_{y}} {(Z / D_{h})}^{n_{z}}

Table 2 of ref 1 contains C, nx, ny, and nz. The values are different for inline and staggered hole patterns.

H T C = \frac{N u * k}{D_{h}} w h e r e k = f l u i d c o n d u c t i v i t y a t f i l m t e m p e r a t u r e

Reference ranges:

1 \leq \frac{Z}{D} \leq 3.0, 2, 500 \leq R e \leq 70, 000, 5.0 \leq \frac{X}{D} \leq 15.0, 4.0 \leq \frac{Y}{D} \leq 8.0

Table 2. Output List
Index	.flo label	Description
1	TNET	Thermal network ID, which has the convector where this correlation is used.
2	CONV_ID	Convector ID, which is using this correlation.
3	IMP_ELM	Flow element that represents the jet flow through the holes.
4	IMP_FLOW	Impingement mass flow rate.
5	CROSS_FLOW	Cross flow mass flow rate.
6	CROSS_AREA	Cross flow area.
7	HOLE_DIA	Diameter of the holes forming the impinging jets.
8	TJET_CH	The fluid chamber containing the temperature to be used in the heat flux calculation.
9	X/DIA	Stream-wise impingement hole spacing/impingement hole diameter.
10	Y/DIA	Span-wise impingement hole spacing/impingement hole diameter.
11	Z/DIA	Distance to the target surface/impingement hole diameter.
12	RE	Reynolds number.
13	HTC	Calculated heat transfer coefficient.

Heat Transfer Correlation References

Florschuetz, Truman, Metzger, "Streamwise Flow and Heat Transfer Distributions for Jet Array Impingement with Crossflow" ASME Journal of Heat Transfer, May 1981, Vol 103.