Impingement from a Single Hole

This correlation is for a single jet from one round hole impinging on a flat surface. The correlation has separate equations for gas and liquid jets into a stagnant gas environment.

Type: Impingement Nu
Subtype: Single Jet Impingement

Table 1. Inputs List
Index	UI Name (.flo label)	Description
1	Nozzle Element (NZL_ELM)	ID for the flow element that represents the jet flow through the hole. No AUTO option. An element must always be supplied.
2	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 NZL_ELM is used.
3	Fluid Type (FL_CORR)	The phase of jet’s fluid: liquid or gas. Liquid: Liquid jet into gas environment. Gas: Gas jet into gas environment. If AUTO, the fluid type is automatically found using the fluid in the NZL_ELM.
4	Nozzle Diameter (NZL_DIA)	Diameter of the hole forming the impinging jet. If AUTO, the diameter from the NZL_ELM is used. The NZL _ELM must be an element type that has a diameter input (orifice or tube).
5	Target Plate Radius (PLATE_RAD)	The radius of the impinged surface. If AUTO, the surface area of the convector is used assuming a circular impinged surface.
6	Distance to Plate Surface (DIST_TO_TARG)	The distance from the impingement hole exit to the impinged surface. Not needed for liquid correlation. No AUTO option.
7	HTC Multiplier (HTC_MULT)	A constant multiplier to scale the value of heat transfer coefficient obtained from the correlation.

Formulation for a Gas Jet

The correlation for a gas jet uses a Nusselt number equation by Martin (reference 1) that can also be found in Incropera (reference 2). The HTC is the average over the impinged surface.

Equation 7.75 from Reference 2:

$N u = G [2 R e^{0.5} {(1 + 0.005 R e^{0.55})}^{0.5}] P r^{0.42}$

Where:

$G = 2 * \sqrt{A_{r}} * \frac{1 - 2.2 * \sqrt{A_{r}}}{1 + 0.2 \sqrt{A_{r}} * (\frac{H}{D_{h}} - 6)}$

$A_{r} = \frac{D_{h}^{2}}{4 r^{2}}$

Reynolds number:

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

$D_{h} = n o z z l e d i a m e t e r, r = t a r g e t p l a t e r a d i u s, H = d i s t a n c e t o p l a t e s u r f a c e$

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

Reference ranges:

$2 \leq \frac{H}{D_{h}} \leq 12, 2000 \leq R e \leq 400, 000, 0.004 \leq A_{r} \leq 0.04$

Formulation for a Liquid Jet

The correlation for a liquid jet into a gas environment uses a Nusselt number equation by Womac (reference 3). The correlation was developed for a square target with side length (l). The HTC is the average over the impinged surface.

Equation 15 from reference 3:

$N u = [C_{1} R e_{D h}^{m} \frac{l}{D_{h}} A_{r} + C_{2} R e_{L}^{n} \frac{l}{L} (1 - A_{r})] P r^{0.4}$

Where:

$C_{1} = 0.516, C_{2} = 0.491, m = 0.5, n = .532$

$L = \frac{0.5 (\sqrt{2} l - D_{h}) + 0.5 (l - D_{h})}{2}$

$A_{r} = \frac{π D_{h}^{2}}{4 l^{2}}$

Relate target plate radius to square target edge length:

$l = \frac{4 r}{\sqrt{2} + 1}$

Reynolds number:

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

$D_{h} = n o z z l e d i a m e t e r, r = t a r g e t p l a t e r a d i u s, H = d i s t a n c e t o p l a t e s u r f a c e$

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

Reference ranges:

$.67 \leq \frac{L}{D_{h}} \leq 4.14, 1000 \leq R e_{D h} \leq 51, 000, 670 \leq R e_{L} \leq 128, 000, 0.004 \leq A_{r} \leq 0.04$

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	NZL_ELM	Flow element that represents the jet flow through the hole.
4	FLUID	GAS or LIQUID.
5	JET_VEL	The jet velocity exiting the NZL_ELM.
6	TJET_CH	The fluid chamber containing the temperature to be used in the heat flux calculation.
7	PLATE_RAD/DIA	Target plate radius/nozzle diameter.
8	H/DIA	Distance to plate surface/nozzle diameter.
9	RE	Reynolds number based on the nozzle diameter.
10	HTC	Calculated Heat Transfer Coefficient.

Heat Transfer Correlation References

Martin, H., “Heat and Mass Transfer between Impinging Gas Jets and Solid Surfaces,” in J. P. Hartnett and T. F. Irvine, Jr., Eds., Advances in Heat Transfer, Vol. 13, Academic Press, New York, 1977.
Incropera, F. and Dewitt, D. Fundamentals of Heat and Mass Transfer, 6th Edition, John Wiley & Sons, 2006.
Womac, D. J., S. Ramadhyani, and F. P. Incropera. "Correlating Equations for Impingement Cooling of Small Heat Sources With Single Circular Liquid Jets", ASME Journal of Heat Transfer, 106-115, 1993.