Hole Array - Kercher

Description

This correlation is for jets from a square array of holes impinging on a flat surface. The correlation includes the HTC reduction for cross flow deflecting the jets.
Type
Impingement Nu
Subtype
Hole Array - Kercher
Table 1. Input List
Index UI Name (.flo label) Description
1 Impingement Flow Element

(IMP_ELM)

ID for 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.

2 Crossflow 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.

3 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).

4 Hole Spacing

(HOLE_SPAC)

Distance between impingement holes (Xn in paper).

No AUTO option. A hole spacing must always be supplied.

5 Number of Holes

(NUM_HOLES)

Number of holes represented by IMP_ELM.

If AUTO, The “number of streams” of IMP_ELM is used.

6 Distance to Target Surface

(DIST_TO_TARG)

The distance from the impingement plate containing the holes to the surface the jets impinge. (Zn in paper).

No AUTO option.

7 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.

8 Impingement Angle

(IMP_ANG)

Angle the impinging jets make with the target surface.

No AUTO option.

9 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.

10 TC Multiplier

(HTC_MULT)

A constant multiplier to scale the value of heat transfer coefficient obtained from the correlation.

Formulation

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

Eq 25 from ref 1:(1)
Nu= ϕ 1 ϕ 2 R e m P r .333 Z D .091 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGobGaamyDaiabg2da9iabew9aM9aadaWgaaWcbaWdbiaaigda a8aabeaak8qacqaHvpGzpaWaaSbaaSqaa8qacaaIYaaapaqabaGcpe GaamOuaiaadwgapaWaaWbaaSqabeaapeGaamyBaaaakiaadcfacaWG YbWdamaaCaaaleqabaWdbiaac6cacaaIZaGaaG4maiaaiodaaaGcda qadaWdaeaapeWaaSaaa8aabaWdbiaadQfaa8aabaWdbiaadseaaaaa caGLOaGaayzkaaWdamaaCaaaleqabaWdbiaac6cacaaIWaGaaGyoai aaigdaaaaaaa@4DBE@
Reynolds number:(2)
R e = m   ˙ i m p D h A r e a   μ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGsbGaamyzaiabg2da9maalaaapaqaamaaxacabaWdbiaad2ga caGGGcaal8aabeqaa8qacaGGzlaaaOWdamaaBaaaleaapeGaamyAai aad2gacaWGWbaapaqabaGcpeGaamira8aadaWgaaWcbaWdbiaadIga a8aabeaaaOqaa8qacaWGbbGaamOCaiaadwgacaWGHbGaaiiOaiabeY 7aTbaaaaa@48CB@

ϕ 1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacqaHvpGzpaWaaSbaaSqaa8qacaaIXaaapaqabaaaaa@38F1@ is based on Fig 16 from ref 1.

ϕ 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacqaHvpGzpaWaaSbaaSqaa8qacaaIYaaapaqabaaaaa@38F2@ accounts for the cross flow effect and is based on figure 17 from ref 1.

m MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGTbaaaa@3706@ is based on Fig. 14 from ref 1.(3)
H T C = 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 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGibGaamivaiaadoeacqGH9aqpdaWcaaWdaeaapeGaamOtaiaa dwhacaGGQaGaam4AaaWdaeaapeGaamira8aadaWgaaWcbaWdbiaadI gaa8aabeaaaaGcpeGaaiiOaiaadEhacaWGObGaamyzaiaadkhacaWG LbGaaiiOaiaadUgacqGH9aqpcaWGMbGaamiBaiaadwhacaWGPbGaam izaiaacckacaWGJbGaam4Baiaad6gacaWGKbGaamyDaiaadogacaWG 0bGaamyAaiaadAhacaWGPbGaamiDaiaadMhacaGGGcGaamyyaiaads hacaGGGcGaamOzaiaadMgacaWGSbGaamyBaiaacckacaWG0bGaamyz aiaad2gacaWGWbGaamyzaiaadkhacaWGHbGaamiDaiaadwhacaWGYb Gaamyzaaaa@6CFB@
Reference ranges:(4)
1 Z D 4.8     ,                   300 R e 30 , 000     ,     3.1 X D 12.5 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaaIXaGaeyizIm6aaSaaa8aabaWdbiaadQfaa8aabaWdbiaadsea aaGaeyizImQaaGinaiaac6cacaaI4aGaaiiOaiaacckacaGGSaGaai iOaiaacckacaGGGcGaaiiOaiaacckacaGGGcGaaiiOaiaacckacaGG GcGaaG4maiaaicdacaaIWaGaeyizImQaamOuaiaadwgacqGHKjYOca aIZaGaaGimaiaacYcacaaIWaGaaGimaiaaicdacaGGGcGaaiiOaiaa cYcacaGGGcGaaiiOaiaaiodacaGGUaGaaGymaiabgsMiJoaalaaapa qaa8qacaWGybaapaqaa8qacaWGebaaaiabgsMiJkaaigdacaaIYaGa aiOlaiaaiwdaaaa@66FE@
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 Impingement hole spacing/impingement hole diameter.
10 Z/DIA Distance to target surface/impingement hole diameter.
11 RE Reynolds number.
12 HTC Calculated heat transfer coefficient.

Heat Transfer Correlation References

  1. Kercher, D.M. and Tabakoff, W., "Heat Transfer by a Square Array of Round Air Jets Impinging Perpendicular to a Flat Surface Including the Effect of Spent Air”, ASME Journal of Engineering for Power, Vol. 92, No. 1, January 1970, pp. 73-82.