Rotating Cylinder

Description

This HTC correlation can be used on the inner or outer surface of a rotating cylinder. The correlation is based on several sources and the equation coefficients and exponents can be modified, if needed, to match other situations. For some situations, the default values use the horizontal flat plate correlation.

The correlation can be applied to a convector resistor and is found in the “Free Convection Nu – Builtin” type.

Type: BI_FREE_CONV_NU
Subtype: ROTATING_CYL

Table 1. Input List
Index	UI Name (.flo label)	Description
1	Cylinder Radius (RADIUS)	The cylinder radius. If AUTO, the radius of the flow chamber attached to the convector will be used.
2	Length (LENGTH)	The cylinder length.
3	Rotor Index (ROTOR_IDX)	The index of the rotor shaft containing the RPM for the cylinder 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.
4	Surface Dir (SURF_DIR)	1= Radially Out, convection applied to the cylinder's outer surface. 1= Radially In, convection applied to the cylinder's inner surface.
5	Laminar Coefficient (LAM_COEF)	Coefficient to be used in the laminar Nu equation. If AUTO, use the value described in the Formulation section.
6	Laminar Exponent (LAM_EXP)	Exponent to be used in the laminar Nu equation. If AUTO, use the value described in the Formulation section.
7	Turbulent Coefficient (TUR_COEF)	Coefficient to be used in the turbulent Nu equation. If AUTO, use the value described in the Formulation section.
8	Turbulent Exponent (TUR_EXP)	Exponent to be used in the turbulent Nu equation. If AUTO, use the value described in the Formulation section.
9	Laminar-to-Transition Ra (RA_LAM)	Rayleigh number where the laminar regime of the flow ends and the transitional regime starts. If AUTO, RA_LAM=9.8*10^11.
10	Transition-to-Turbulent Ra (RA_TURB)	Rayleigh number where the transitional regime of the flow ends and the fully turbulent regime starts. If AUTO, RA_TURB=1.02*10^12.
11	HTC Multiplier (HTC_MULT)	A constant multiplier to scale the value of the heat transfer coefficient obtained from the correlation.

Formulation

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

$N u = c o e f f * R a^{e x p}$

$R a = G r * P r$

$G r = ω^{2} * R a d i u s * {(\frac{L e n g t h}{2})}^{3} * {(\frac{ρ}{μ})}^{2} * β * a b s (T_{w a l l} - T_{f l u i d})$

$H T C = \frac{N u * k}{(\frac{L e n g t h}{2})}$

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. The values from reference 2 are for a flat horizontal plate.


	Stable Configuration	Unstable Configuration
LAM_COEF	0.27 (ref 2, eq 9.32)	0.44 (ref 1, section 3.2)
LAM_EXP	0.25 (ref 2, eq 9.32)	0.25 (ref 1, eq 3.6)
TURB_COEF	0.27 (ref 2, eq 9.32)	0.15 (ref 2, eq 9.31)
TURB_EXP	0.25 (ref 2, eq 9.32)	0.333 (ref 2, eq 9.31)

The stability is determined by the temperatures and the side of the cylinder (inner or outer). The force vector for a rotating cylinder is radially outward, which is the opposite of a gravity force vector for a horizontal plate.


	Stable Configuration	Unstable Configuration
Cylinder Inner Surface	Twall < Tfluid	Twall > Tfluid
Cylinder Outer Surface	Twall > Tfluid	Twall < Tfluid

$R a = R a y l e i g h N u m b e r$

$ρ = f l u i d b u l k d e n s i t y$

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

$k = f l u i d f i l m c o n d u c t i v i t y$

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

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

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

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	RAD	Cylinder radius.
4	RPM	Cylinder 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	RA	Rayleigh number.
10	NU	Calculated Nusselt number.
11	HTC	Calculated Heat Transfer Coefficient.

Heat Transfer Correlation References

Tang, H., Puttock-Brown M., Owen J. M., "Buoyancy-Induced Flow and Heat Transfer in Compressor Rotors", Journal of Engineering for Gas Turbines and Power, July, 2018.
Incropera, F. and Dewitt, D. Fundamentals of Heat and Mass Transfer, 6th Edition, John Wiley & Sons, 2006.