Taylor Rotating Gap

Description

Flow Simulator uses a variety of heat transfer correlations to model the heat exchange phenomenon in flow and thermal networks. The correlation types available with Flow Simulator to model heat transfer in thin rotating gaps are discussed below.

Convection through Thin Gaps

(i) Taylor Rotating Gap
Used to model heat exchange through the thin rotating fluid gap between a stationary and a rotating cylinder.
Type
Thin Gap Nu
Subtype
Taylor Rotating Gap
Table 1. Input List
Index UI Name (.flo label) Description Mandatory/Not Mandatory
1 Rotor Conductor (ROT_COND) The conductor ID that represents the rotor.

On specifying a valid rotor ID, Flow Simulator automatically extracts the rotor dimensions and gap thickness.

Mandatory

In case a valid rotor ID is not known, this input can be left as 0, and the rotor dimensions and gap thickness can be entered as other input for this correlation.

2 Stator Conductor (ROT_COND) The conductor ID that represents the stator.

On specifying a valid rotor ID, Flow Simulator automatically extracts the rotor dimensions and gap thickness.

Mandatory

In case a valid stator ID is not known, this input can be left as 0, and the rotor dimensions and gap thickness can be entered as other input for this correlation.

3 Laminar-Transition Taylor No. (TA_LAM) Taylor number where the laminar regime of flow ends, and the transitional regime starts. Not Mandatory

In AUTO mode, Flow Simulator chooses this value directly from the references.

4 Transition-Turbulent Taylor No. (TA_TUR) Taylor number where the transitional regime of flow ends and the turbulent regime starts. Not Mandatory

In AUTO mode, Flow Simulator chooses this value directly from the references.

5 Fluid Total Pressure (TOT_PRESS) Pressure of the fluid in the gap. Mandatory
6 Gap Thickness (GAP_THK) Thickness of the gap between the rotor and stator. Mandatory

If you have provided a valid rotor and stator conductor ID, which can be used to retrieve and calculate the gap thickness, this can be left as AUTO.

If you have left the rotor or stator conductor input as 0, then you must enter a gap thickness.

7 Rotor Radius (ROT_RADIUS) Rotor outer radius. Mandatory

If you have provided a valid rotor conductor ID, which can be used to retrieve the rotor outer radius, this can be left as AUTO.

If you have left the rotor conductor input as 0, then you must enter a rotor outer radius.

8 HTC Multiplier (HTC_MULT) A constant multiplier to scale the value of the heat transfer coefficient obtained from the correlation. Not Mandatory

Default value is 1.0.

Formulation

Expression for the Taylor number, for the flow between two concentric cylinders, is given by (Ref 1):(1)
T a =   v r µ   l a g 3 r o r MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGubGaamyyaiabg2da9iaacckadaWcaaWdaeaapeGaamODa8aa daWgaaWcbaWdbiaadkhaa8aabeaaaOqaa8qacaWG1cGaaiiOaaaada GcaaWdaeaapeWaaSaaa8aabaWdbiaadYgapaWaa0baaSqaa8qacaWG HbGaam4zaaWdaeaapeGaaG4maaaaaOWdaeaapeGaamOCa8aadaWgaa WcbaWdbiaad+gacaWGYbaapaqabaaaaaWdbeqaaaaa@46AE@

Where,

Expression for the Nusselt number, based on the Taylor number, is provided as (Ref. 1):
Table 2.
Nu = 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqGobGaaeyDaiabg2da9iaaikdaaaa@399F@ Ta < 41 , MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqGubGaaeyyaiabgYda8iaaisdacaaIXaGaaiilaaaa@3AFC@ laminar…
Nu = 0.212 Ta 0.63 Pr 0.27 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqGobGaaeyDaiabg2da9iaaicdacaGGUaGaaGOmaiaaigdacaaI YaGaaeivaiaabggapaWaaWbaaSqabeaapeGaaGimaiaac6cacaaI2a GaaG4maaaakiaabcfacaqGYbWdamaaCaaaleqabaWdbiaaicdacaGG UaGaaGOmaiaaiEdaaaaaaa@4679@ 100 Ta 41 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaaIXaGaaGimaiaaicdacqGHLjYScaqGubGaaeyyaiabgwMiZkaa isdacaaIXaaaaa@3F03@ vortex…
Nu = 0.386 Ta 0.5 Pr 0.27 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqGobGaaeyDaiabg2da9iaaicdacaGGUaGaaG4maiaaiIdacaaI 2aGaaeivaiaabggapaWaaWbaaSqabeaapeGaaGimaiaac6cacaaI1a aaaOGaaeiuaiaabkhapaWaaWbaaSqabeaapeGaaGimaiaac6cacaaI YaGaaG4naaaaaaa@45C7@ 100 > Ta MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaaIXaGaaGimaiaaicdacqGH+aGpcaqGubGaaeyyaaaa@3B06@ turbulent…

µ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqG1caaaa@374C@ = dynamic viscosity of air

v r MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqG2bWdamaaBaaaleaapeGaaeOCaaWdaeqaaaaa@385C@ = peripheral speed of the rotor

r or MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqGYbWdamaaBaaaleaapeGaae4Baiaabkhaa8aabeaaaaa@394A@ = rotor outer radius

l ag MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqGSbWdamaaBaaaleaapeGaaeyyaiaabEgaa8aabeaaaaa@392B@ = thickness of the air gap

Table 3. 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 TA_FLOW Solver-calculated Taylor number for the model.
4 PRESSURE User-defined fluid pressure.
5 GAP_THK Solver calculated/auto-retrieved gap thickness for the model.
6 ROT_RADIUS Solver calculated/auto-retrieved rotor radius for the model.
7 HTC Heat transfer coefficient calculated as per the Taylor Rotating Gap correlation (Ref.1).

Heat Transfer Correlation References

  1. Dave Staton, Aldo Boglietti, Andrea Cavagnino, "Solving the More Difficult Aspects of Electric Motor Thermal Analysis", IEEE Transactions on Energy Conversion, vol. 20, no. 3, pp. 620-628, Sept. 2005, doi: 10.1109/TEC.2005.847979. Eqn. 14-17.