Rotor Disk Farthing

Description

This HTC correlation can be used on the rotating disk surfaces of a cavity with bore flow that is typically found in gas turbine compressors. The correlation is based on the paper by P.R. Farthing, reference 1.

The correlation can be applied to a convector resistor.

Type: BI_ROT_CAV_NU
Subtype: ROT_DISK_FARTHG

Table 1. Input List
Index	UI Name (.flo label)	Description
1	Local Disk Radius (LOCAL_RAD)	The local radius for the HTC calculation. If AUTO, the radius of the flow chamber attached to the convector will be used.
2	Disk Outer Radius (OUTER_RAD)	The outer radius of the disk. Also called the shroud radius in reference 1.
3	Disk Bore Radius (BORE_RAD)	The inner radius of the disk. Also called the bore radius in reference 1.
4	Bore Temperature Chamber (BORE_T_CHM)	A flow chamber that contains the temperature of the bore flow entering the rotor-rotor disk cavity. If AUTO, the chamber upstream of the Bore Flow Element will be used. If BORE_T_CHM=0, use the temperature of the fluid chamber attached to the convector.
5	Bore Flow Element (BORE_FLOW_ELM)	An element containing the flow rate going through the bore.
6	Tube Rotation 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.
7	HTC Multiplier (HTC_MULT)	A constant multiplier to scale the value of the heat transfer coefficient obtained from the correlation.
8	Free Convection Nu (FREE_HTC)	The equation to use for 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.
9	Free Mixing Sign (FREE_ASSIST)	The sign of the free and forced HTC blending. Assist (positive). Oppose (negative). If AUTO, FREE_ASSIST=1.
10	Free Length Scale (FREE_LEN)	The length scale for the free convection HTC calculation. If AUTO, FREE_LEN = LENGTH.
11	Horizontal Free Surface Dir (FREE_SURF_DIR)	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 Nusselt number found in reference 1. The heat flux uses the fluid temperature from the bore (BORE_T_CHM) and not the fluid temperature of the chamber attached to the convector.

R e_{b o r e} = \frac{{\dot{m}}_{b o r e} * 2 * R a d i u s_{b o r e}}{A r e a_{b o r e} * μ}

Reference Re limits,

20, 000 < R e_{b o r e} < 160, 000

G r = ω^{2} * R a d i u s_{l o c a l}^{4} * {(\frac{ρ}{μ})}^{2} * β * a b s (T_{w a l l} - T_{f l u i d})

Equation 7 from reference 1.

N u = .0054 * R e_{b o r e}^{0.3} * G r^{.25} * {(\frac{R a d i u s_{o u t e r}}{R a d i u s_{l o c a l}} - 1)}^{.25}

HTC and heat flux.

H T C = \frac{N u * k}{R a d i u s_{l o c a l}}

q = H T C * (T_{w a l l} - T_{f l u i d})

T_{w a l l} = d i s k s u r f a c e t e m p e r a t u r e

T_{f l u i d} = f l u i d t e m p e r a t u r e f r o m BORE_T_CHM

R e_{b o r e} = R e y n o l d s n u m b e r f r o m b o r e f l o w

G r = G r a s h o f n u m b e r u s i n g c e n t r i p e t a l a c c e l e r a t i o n

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

P r = f l u i d P r a n d t l N u m b e r

{\dot{m}}_{b o r e} = m a s s f l o w r a t e

β = f l u i d b u l k c o m p r e s s i b i l i t y f a c t o r

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 which is using this correlation.
3	RPM	Disk rotations per minute.
4	BORE_ELM	Bore flow element.
5	FLOW	Flow rate in the bore flow element.
6	BORE_RAD	The inner radius of the disk.
7	LOCAL_RAD	The local radius for the HTC calculation.
8	OUTER_RAD	The outer radius of the disk.
9	RE_AX	Reynolds number for the bore.
10	GR	Grashof number.
11	NU	Calculated Nusselt number.
12	HTC	Calculated Heat Transfer Coefficient.

Heat Transfer Correlation References

Farthing, P. R., Long, C. A., Owen, J. M., and Pincombe, J. R., “Rotating Cavity with Axial Throughflow of Cooling Air: Heat Transfer,” ASME J. Turbomach., 114(1), 1992, pp. 229–236.