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.	Not Mandatory In Auto mode, Flow Simulator uses the pressure of the fluid chamber attached to the convector. If the convector is not attached to a fluid chamber, the pressure will be 14.7 PSIA.
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.
9	MODE (MODE)	1 = Solid to Solid, convector is connected to two thermal nodes that represent solid surfaces. 2 = Solid to Fluid, convector is connected to one thermal node representing the fluid in the gap or one fluid chamber.	Not Mandatory In Auto mode, Flow Simulator determines the MODE based on the thermal nodes or fluid chamber attached to the convector.

Formulation

Expression for the Taylor number, for the flow between two concentric cylinders, is given by (Ref 1):

T a = \frac{v_{r}}{µ} \sqrt{\frac{l_{a g}^{3}}{r_{o r}}}

Where,

Expression for the Nusselt number, based on the Taylor number, is provided as (Ref. 1):

Table 2.
$Nu = 2$	$Ta < 41,$ laminar…
$Nu = 0.212 {Ta}^{0.63} {Pr}^{0.27}$	$100 \geq Ta \geq 41$ vortex…
$Nu = 0.386 {Ta}^{0.5} {Pr}^{0.27}$	$100 < Ta$ turbulent…

H T C = \frac{N u * k}{2 * l_{a g}} 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

µ

= dynamic viscosity of air

$v_{r}$ = peripheral speed of the rotor

$r_{or}$ = rotor outer radius

$l_{ag}$ = thickness of the air gap

If MODE=2, Solid to Fluid, the Nu is doubled to account for two convectors that are needed to simulate the heat transfer between the two solid surfaces.

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	NU	Calculated Nusselt number.
8	HTC	Heat transfer coefficient calculated as per the Taylor Rotating Gap correlation (Ref.1).

Heat Transfer Correlation References

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.