Gnielinski Combo

Description

A duct flow correlation that accounts for laminar and turbulent flow. This correlation is like the Gnielinski combo correlation found in tube elements, but the correlation described in this section can also be applied to convectors that are not associated directly to tube elements.
Type
Mixed Laminar-Turbulent Duct Nu
Subtype
Gnielinski Combo
Table 1. Input List
Index UI Name (.flo label) Description
1 Flow Element

(FLOW_ELM)

 ID for flow element that is used for the mass flow rate and other correlation inputs.

If AUTO, the correlation must be applied to a convector that is connected to a fluid chamber that has only 1 flow element entering this chamber. The ID of this flow element is used. The element can be of almost any type although some types do not have geometric inputs that can be obtained with the AUTO option of the remaining inputs.
2 Hydraulic Diameter

(HYD_DIA)

 Passage hydraulic diameter.

If AUTO, the hydraulic diameter of the flow element from input 1 is used.
3 Flow Area

(FLOW_AREA)

 Passage flow area.

If AUTO, the area of the flow element from input 1 is used. If the area from the flow element is not available, the passage is assumed circular, and the hydraulic diameter is used to calculate the area.
4 Wall Roughness

(WALL_RGH)

 The passage wall roughness (equivalent sand grain).

If AUTO, the wall roughness of the flow element from input 1 is used.
5 Inlet Effects

(INLET_EFF)

 Option for heat transfer inlet effects.

1: No inlet effects.

2: Abrupt local or uniform average inlet effects.

3: Abrupt average inlet effects.

4: Uniform local inlet effects.

5: Between uniform average and local inlet effects.

6: Between abrupt average and local inlet effects.
6 Entrance Length

(ENTR_LEN)

 Distance from the start of the heat transfer area to the boundary layer start. Used in the inlet effects calculation.

If AUTO, the length of the flow element from input 1 is used.
7 Laminar-to-Transition Re

(RE_LAM)

 Reynolds number where the Laminar regime of flow ends and the Transitional regime starts.

If AUTO, the global transition Re is used (default=2185).
8 Transition-to-Turbulent Re

(RE_TURB)

 Reynolds number where the Transitional regime of flow ends and the fully Turbulent regime starts.

If AUTO, the global transition Re is used (default=2415).
9 HTC 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 Hausen (Ref 1 and 2-eq 8.56) for laminar flow and a correlation from Gnielinski (Ref 2-eq 8.62 and 3) for turbulent flow. A linear interpolation is used if the Re is in the transitional regime.

Reynolds number:

R e = m   ˙ D h A r e a   μ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGsbGaamyzaiabg2da9maalaaapaqaamaaxacabaWdbiaad2ga caGGGcaal8aabeqaa8qacaGGzlaaaOGaamira8aadaWgaaWcbaWdbi aadIgaa8aabeaaaOqaa8qacaWGbbGaamOCaiaadwgacaWGHbGaaiiO aiabeY7aTbaaaaa@4582@

For Re <= RE_LAM:

N u l a m =   3.66   +   0.0688 * G z 1 + 0.4 * G z 2 / 3   w h e r e   G z = D h x   R e   P r MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGobGaamyDa8aadaWgaaWcbaWdbiaadYgacaWGHbGaamyBaaWd aeqaaOWdbiabg2da9iaacckacaaIZaGaaiOlaiaaiAdacaaI2aGaai iOaiabgUcaRiaacckadaWcaaWdaeaapeGaaGimaiaac6cacaaIWaGa aGOnaiaaiIdacaaI4aGaaiOkaiaadEeacaWG6baapaqaa8qacaaIXa Gaey4kaSIaaGimaiaac6cacaaI0aGaaiOkaiaadEeacaWG6bWdamaa CaaaleqabaWdbiaaikdacaGGVaGaaG4maaaaaaGccaGGGcGaam4Dai aadIgacaWGLbGaamOCaiaadwgacaGGGcGaam4raiaadQhacqGH9aqp daWcaaWdaeaapeGaamira8aadaWgaaWcbaWdbiaadIgaa8aabeaaaO qaa8qacaWG4baaaiaacckacaWGsbGaamyzaiaacckacaWGqbGaamOC aaaa@664C@

For Re >= RE_TURB:

N u t u r b = R e − 1000 * 0.5 * P r * f 1 + 12.7 * 0.5 * f * P r .6666 − 1   w h e r e   f = f a n n i n g   f r i c t i o n   f a c t o r MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGobGaamyDa8aadaWgaaWcbaWdbiaadshacaWG1bGaamOCaiaa dkgaa8aabeaak8qacqGH9aqpdaWcaaWdaeaapeWaaeWaa8aabaWdbi aadkfacaWGLbGaeyOeI0IaaGymaiaaicdacaaIWaGaaGimaaGaayjk aiaawMcaaiaacQcacaaIWaGaaiOlaiaaiwdacaGGQaGaamiuaiaadk hacaGGQaGaamOzaaWdaeaapeGaaGymaiabgUcaRiaaigdacaaIYaGa aiOlaiaaiEdacaGGQaWaaOaaa8aabaWdbiaaicdacaGGUaGaaGynai aacQcacaWGMbaaleqaaOGaaiOkamaabmaapaqaa8qacaWGqbGaamOC a8aadaahaaWcbeqaa8qacaGGUaGaaGOnaiaaiAdacaaI2aGaaGOnaa aakiabgkHiTiaaigdaaiaawIcacaGLPaaaaaGaaiiOaiaadEhacaWG ObGaamyzaiaadkhacaWGLbGaaiiOaiaadAgacqGH9aqpcaWGMbGaam yyaiaad6gacaWGUbGaamyAaiaad6gacaWGNbGaaiiOaiaadAgacaWG YbGaamyAaiaadogacaWG0bGaamyAaiaad+gacaWGUbGaaiiOaiaadA gacaWGHbGaam4yaiaadshacaWGVbGaamOCaaaa@7D90@
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@

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 FLOW_ELM Flow element from input 1 or automatically selected.
4 FLOW Mass flow rate used in Re calculation.
5 HYD_DIA The hydraulic diameter used in the HTC calculations.
6 RGH_RATIO Roughness Ratio (wall roughness/hydraulic diameter) used to calculate a friction factor.
7 FRIC_FANNING Fanning friction factor.
8 INLET_HMULT HTC multiplier due to inlet effects (boundary layer start).
9 RE Reynolds number.
10 NU Calculated Nusselt number.
11 HTC Calculated heat transfer coefficient.

Heat Transfer Correlation References

  1. Hausen, H., Z. VDI Beih. Verfahrenstech., 4, 91, 1943.
  2. Incropera, F. and Dewitt, D. Fundamentals of Heat and Mass Transfer, 6th Edition, John Wiley & Sons, 2006.
  3. Gnielinski, V., New equations for heat and mass transfer in the turbulent flow in pipes and channels, (Jahrestreffen der Verfahrensingenieure, Berlin, West Germany, Oct. 2-4, 1973.) Forschung im Ingenieurwesen, vol. 41, no. 1, 1975, p. 8-16. In German.