Free Rotating Disk

Description

This HTC correlation can be used on an isolated rotating disk. An isolated disk has no through flow, other than the flow induced by the disk rotation, and the far field ambient fluid has no swirl. The correlation is based on several sources and the equation coefficients and exponents can be modified, if needed, to match other situations.

The correlation can be applied to convector resistors.

Type: BI_ROT_CAV_NU
Subtype: FREE_ROTATING_DISK

Table 1. Input List
Index	UI Name (.flo label)	Description
1	Local Disk Radius (DISK_RAD)	The local radius for the HTC calculation. If AUTO, the radius of the flow chamber attached to the convector will be used.
2	Rotor Index (ROTOR_IDX)	The index of the rotor shaft containing the RPM for the disk surface. The speed for this rotor shaft is set in the Run > Reference Conditions tab. If AUTO, the rotation assigned to the thermal node attached to the convector will be used.
3	Laminar Coefficient (LAM_COEF)	Coefficient to be used in the laminar Nu equation. If AUTO, use the value described in the Formulation section.
4	Laminar Exponent (LAM_EXP)	Exponent to be used in the laminar Nu equation. If AUTO, use the value described in the Formulation section.
5	Turbulent Coefficient (TUR_COEF)	Coefficient to be used in the turbulent Nu equation. If AUTO, use the value described in the Formulation section.
6	Turbulent Exponent (TUR_EXP)	Exponent to be used in the turbulent Nu equation. If AUTO, use the value described in the Formulation section.
7	Local or Average HTC (LOC_AVG)	1 = Calculate an HTC at a given radius (DISK_RAD) 2 = Calculate an average HTC from radius=0 up to the given radius (DISK_RAD).
8	Laminar-to-Transition Re (RE_LAM)	Reynolds number where the laminar regime of flow ends and the transitional regime starts. If AUTO, RE_LAM=100,000.
9	Transition-to-Turbulent Re (RE_TURB)	Reynolds number where the transitional regime of flow ends and the fully turbulent regime starts. If AUTO, RE_TURB=280,000.
10	HTC Multiplier (HTC_MULT)	A constant multiplier to scale the value of the heat transfer coefficient obtained from the correlation.
11	Free Convection Nu (FREE_HTC)	The equation to use for the free convection blending. None (do not calculate the free convection HTC). McAdams Vertical Plate. Horizontal Plate. Churchill-Chu Horizontal Cylinder. If AUTO, FREE_HTC=2.
12	Free Mixing Sign (FREE_ASSIST)	The sign of the free and forced HTC blending. Assist (positive). Oppose (negative). If AUTO, FREE_ASSIST=1.
13	Free Length Scale (FREE_LEN)	The length scale for the free convection HTC calculation. If AUTO, FREE_LEN = LENGTH.
14	Horizontal Free Surface Dir (FREE_SURF_DIR)	The direction of the horizontal plate that is used if FREE_HTC=3 Up or radially out. Down or radially in.

Formulation

This correlation uses a simple Nu formulation, with coefficients and exponents used according to geometry and flow conditions.

$N u = c o e f f * R e_{r o t}^{e x p}$

$R e_{r o t} = \frac{ρ * ω * R a d i u s^{2}}{μ}$

The default coefficient and exponent are set if the inputs are set to AUTO. These values can be found in several references, including those shown in the table below. These values are also appropriate for Prandtl numbers near 0.7 (like air).


	Local HTC LOC_AVG=1	Average HTC LOC_AVG=2
LAM_COEF	0.456 (ref 1, eq 32)	0.320 (ref 2, section B)
LAM_EXP	0.478 (ref 1, eq 32)	0.500 (ref 2, section B)
TURB_COEF	0.035 (ref 1, eq 33)	0.0151 (ref 2, eq 36)
TURB_EXP	0.746 (ref 1, eq 33)	0.800 (ref 2, eq 36)

$H T C = \frac{N u * k}{R a d i u s}$

$R e_{r o t} = R o t a t i o n b a s e d R e y n o l d s n u m b e r$

$ρ = f l u i d f i l m d e n s i t y$

$μ = f l u i d f i l m v i s c o s i t y$

$ω = r o t a t i o n i n r a d i a n s / s e c o n d$

Table 2. Output List
Index	.res label	Description
1	TNET	Thermal network ID that has the convector where this correlation is used.
2	CONV_ID	Convector ID that is using this correlation.
3	DISK_RAD	The local radius for the HTC calculation.
4	RPM	Disk rotations per minute.
5	LAM_COEF	Coefficient used in the laminar Nu equation.
6	LAM_EXP	Exponent used in the laminar Nu equation.
7	TUR_COEF	Coefficient used in the turbulent Nu equation.
8	TUR_EXP	Exponent used in the turbulent Nu equation.
9	RE	Rotational Reynolds number.
10	NU	Calculated Nusselt number.
11	HTC	Calculated Heat Transfer Coefficient

Heat Transfer Correlation References

Pelle, J., Harmand S., "Heat transfer measurements in an opened rotor–stator system air-gap", Experimental Thermal and Fluid Science 31 (2007) 165–180.
Howey, D. A., Childs R. N., Holmes A. S., "Air-gap convection in rotating electrical machines", IEEE, 2010.