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:(1)
Nu=A R e m 1B Z/ D h Gc/Gj n P r .333 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGobGaamyDaiabg2da9iaadgeacaGGGcGaamOuaiaadwgapaWa aWbaaSqabeaapeGaamyBaaaakmaacmaapaqaa8qacaaIXaGaeyOeI0 IaamOqamaadmaapaqaa8qadaqadaWdaeaapeGaamOwaiaac+cacaWG ebWdamaaBaaaleaapeGaamiAaaWdaeqaaaGcpeGaayjkaiaawMcaam aabmaapaqaa8qacaWGhbGaam4yaiaac+cacaWGhbGaamOAaaGaayjk aiaawMcaaaGaay5waiaaw2faa8aadaahaaWcbeqaa8qacaWGUbaaaa GccaGL7bGaayzFaaGaamiuaiaadkhapaWaaWbaaSqabeaapeGaaiOl aiaaiodacaaIZaGaaG4maaaaaaa@5622@
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@
The coefficient A and B and the exponents m and n are calculated using eq 10b from ref 1:(3)
A,B,m,and n=C  X/ D h n x   Y/ D h n y   Z/ D h n z MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGbbGaaiilaiaadkeacaGGSaGaamyBaiaacYcacaWGHbGaamOB aiaadsgacaGGGcGaamOBaiabg2da9iaadoeacaGGGcWaaeWaa8aaba WdbiaadIfacaGGVaGaamira8aadaWgaaWcbaWdbiaadIgaa8aabeaa aOWdbiaawIcacaGLPaaapaWaaWbaaSqabeaapeGaamOBa8aadaWgaa adbaWdbiaadIhaa8aabeaaaaGcpeGaaiiOamaabmaapaqaa8qacaWG zbGaai4laiaadseapaWaaSbaaSqaa8qacaWGObaapaqabaaak8qaca GLOaGaayzkaaWdamaaCaaaleqabaWdbiaad6gapaWaaSbaaWqaa8qa caWG5baapaqabaaaaOWdbiaacckadaqadaWdaeaapeGaamOwaiaac+ cacaWGebWdamaaBaaaleaapeGaamiAaaWdaeqaaaGcpeGaayjkaiaa wMcaa8aadaahaaWcbeqaa8qacaWGUbWdamaaBaaameaapeGaamOEaa Wdaeqaaaaaaaa@5CDB@
Table 2 of ref 1 contains C, nx, ny, and nz. The values are different for inline and staggered hole patterns. (4)
HTC= Nu*k D h  where k=fluid conductivity at film temperature 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:(5)
1 Z D 3.0     ,                   2 , 500 R e 70 , 000     ,     5.0 X D 15.0 ,     4.0 Y D 8.0 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaaIXaGaeyizIm6aaSaaa8aabaWdbiaadQfaa8aabaWdbiaadsea aaGaeyizImQaaG4maiaac6cacaaIWaGaaiiOaiaacckacaGGSaGaai iOaiaacckacaGGGcGaaiiOaiaacckacaGGGcGaaiiOaiaacckacaGG GcGaaGOmaiaacYcacaaI1aGaaGimaiaaicdacqGHKjYOcaWGsbGaam yzaiabgsMiJkaaiEdacaaIWaGaaiilaiaaicdacaaIWaGaaGimaiaa cckacaGGGcGaaiilaiaacckacaGGGcGaaGynaiaac6cacaaIWaGaey izIm6aaSaaa8aabaWdbiaadIfaa8aabaWdbiaadseaaaGaeyizImQa aGymaiaaiwdacaGGUaGaaGimaiaacYcacaGGGcGaaiiOaiaaisdaca GGUaGaaGimaiabgsMiJoaalaaapaqaa8qacaWGzbaapaqaa8qacaWG ebaaaiabgsMiJkaaiIdacaGGUaGaaGimaaaa@7515@
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

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