# 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).

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:

$Nu=G\left[2R{e}^{0.5}{\left(1+0.005R{e}^{0.55}\right)}^{0.5}\right]P{r}^{0.42}$

Where:

${A}_{r}=\frac{{D}_{h}^{2}}{4{r}^{2}}$

Reynolds number:

Reference ranges:

## 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:

$Nu=\left[{C}_{1}R{e}_{Dh}^{m}\frac{l}{{D}_{h}}{A}_{r}+{C}_{2}R{e}_{L}^{n}\frac{l}{L}\left(1-{A}_{r}\right)\right]P{r}^{0.4}$

Where:

$L=\frac{0.5\left(\sqrt{2}l-{D}_{h}\right)+0.5\left(l-{D}_{h}\right)}{2}$
${A}_{r}=\frac{\pi {D}_{h}^{2}}{4{l}^{2}}$

Relate target plate radius to square target edge length:

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

Reynolds number:

Reference ranges:

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.