Rotating Cavity Duct Flow

Description

This HTC correlation can be used in a location where there is rotational and axial (or radial) velocity. The correlation calculates an HTC for the rotational direction and the axial (or radial) direction and blends them using the third power. The correlation uses the Dittus-Boelter Nu equation for duct flow. Therefore, the rotational direction is treated like a duct and the axial (or radial) direction is also treated like a duct.

The correlation can be applied to a convector, cavity surface, or lab seal element. The convector is the only application where the inputs listed below are used. The cavity surface and the lab seal element applications automatically determine the inputs from the cavity or the lab seal geometry and flow conditions.

Type: BI_ROT_CAV_NU
Subtype: ROT_CAV_DUCT_FLOW

Table 1. Input List
Index	UI Name (.flo label)	Description
1	Velocity Method (VEL_TYPE)	Method to get a velocity for the Reynolds Number. All from the Swirl Chamber. Swirl Chamber and Flow Element. A thru flow element must be defined to use option 2.
2	Swirl Chamber (SWRL_CHM)	ID for the flow chamber that will be used for the velocity. If AUTO, the flow chamber ID that is attached to the convector will be used.
3	Swirl Hydraulic Diameter (SWRL_HYD_DIA)	The hydraulic diameter used for the rotational direction. If AUTO, the SWRL_CHM must be associated with a cavity. The hydraulic diameter of the cavity will be automatically calculated using the cavity surface definition.
4	Thru Flow Element (THRU_FLOW_ELM)	An element used for the axial (or radial) velocity and geometry calculation. If AUTO, the element upstream of the SWRL_CHM will be used.
5	Thru Hydraulic Diameter (THRU_HYD_DIA)	The hydraulic diameter used for the axial (or radial) direction. If AUTO, the diameter of the THRU_FLOW_ELM is used.
7	Laminar-to-Transition Re (RE_LAM)	Reynolds number where the laminar regime of the flow ends and the transitional regime starts. If AUTO, the global transition Re is used (default=2185).
8	Transition-to-Turbulent Re (RE_TURB)	Reynolds number where the transitional regime of flow ends and the fully turbulent regime starts. If AUTO, the global transition Re is used (default=2415).
9	HTC Multiplier (HTC_MULT)	A constant multiplier to scale the value of the heat transfer coefficient obtained from the correlation.
10	Free Convection Nu (FREE_HTC)	The equation to use for the free convection blending. None (do not calculate free convection HTC). McAdams Vertical Plate. Horizontal Plate. Churchill-Chu Horizontal Cylinder If AUTO, FREE_HTC=2
11	Free Mixing Sign (FREE_ASSIST)	The sign of the free and forced HTC blending. Assist (positive). Oppose (negative). If AUTO, FREE_ASSIST=1.
12	Free Length Scale (FREE_LEN)	The length scale for the free convection HTC calculation. If AUTO, FREE_LEN = LENGTH.
13	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 for duct flow that can be found in section 8.5 of reference 1 and other textbooks.

For the rotational (or swirl) direction:

R e_{r o t} = \frac{ρ * V_{r e l_r o t} * D h_{r o t}}{μ}

For the thru flow (axial or radial) direction:

For VEL_TYPE=1,

R e_{t h r u} = \frac{ρ * V_{t h r u} * D h_{t h r u}}{μ}

For VEL_TYPE=2,

R e_{t h r u} = \frac{\dot{m} * D h_{t h r u}}{A r e a * μ}

Calculate a Nusselt number, Nu, for the rotational and thru flow directions using these equations.

For Re > RE_LAM

Use Dittus Boelter equations for the HTC
To heat fluid:
$N u_{t u r b u l e n t} = .024 * R e^{.8} * P r^{.4}$
To cool fluid:
$N u_{t u r b u l e n t} = .026 * R e^{.8} * P r^{.4}$

For Re < RE_TURB

N u_{l a m i n a r} = 3.66

Use a liner blend between laminar and turbulent Nu if Re is in the transition range.

Calculate a Heat Transfer Coefficient, HTC, for the rotational and thru flow directions using these equations.

H T C_{r o t} = \frac{N u_{r o t} * k}{D h_{r o t}} H T C_{t h r u} = \frac{N u_{t h r u} * k}{D h_{t h r u}}

Final HTC

H T C = {(H T C_{r o t}^{3} + H T C_{t h r u}^{3})}^{.3333}

D h = h y d r a u l i c d i a m e t e r

V = f l u i d v e l o c i t y r e l a t i v e t o t h e s u r f a c e

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} = m a s s f l o w r a t e

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	SWIRL	Fluid swirl velocity/solid surface rotational velocity.
4	SWRL_VEL	Fluid swirl velocity relative to the surface.
5	SWRL_DH	The hydraulic diameter used for the rotational direction.
6	SWRL_RE	Reynolds number for the rotational (swirl) direction.
7	SWRL_HTC	Heat Transfer Coefficient for the rotational (swirl) direction.
8	THRU_VEL	Fluid axial (or radial) velocity.
9	THRU_DH	The hydraulic diameter for the axial (or radial) direction.
10	THRU_RE	Reynolds number for the axial (or radial) direction.
11	THRU_HTC	Heat Transfer Coefficient for the axial (or radial) direction.
12	TOTAL_HTC	Final Heat Transfer Coefficient,

Heat Transfer Correlation References

Incropera, F. and Dewitt, D. Fundamentals of Heat and Mass Transfer, 6th Edition, John Wiley & Sons, 2006.