Rotating Tube

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 rotating tube internal forced convection are discussed below.

Internal Tube Forced Convection

(i) Rotating tube heat transfer correlation: Used to model the heat exchange from the fluid flowing axially through the rotating tube to the wall of the tube.

Type: Mixed Laminar-Turbulent Duct Nu
Subtype: Rotating Tube Internal Convection

Table 1. Input List
Index	UI Name (.flo label)	Description	Mandatory/Not Mandatory
1	Flow Element (FLOW_ELM)	The flow element ID, which represents the tube in general. On specifying a valid flow element ID, the Flow Simulator solver can automatically extract the hydraulic diameter, fluid velocity, flow area, entrance length and so on, needed for correlation.	Mandatory In the AUTO mode, solver automatically identifies the element upstream to the chamber that is connected to the convector and retrieves the necessary inputs from there. You can also clear the AUTO mode and pick a specific element to get the inputs from. If you want the Flow Simulator solver to use the user-specified fixed values for the necessary inputs, you can leave this option as 0, and enter the input manually by clearing the respective AUTO options. If you want to use a specific fixed Reynolds number value for the correlation, then you can leave the Flow Element input as 0. Clear the AUTO option to enter a hydraulic diameter and axial and rotational Reynolds numbers. The other input can be left as-is. Note: This functionality may not work with inlet effects and entrance length effects for the tube.
2	Type of Fluid Correlation (FL_CORR)	Type of fluid correlation that is used to calculate the heat transfer coefficient.	Mandatory In AUTO mode, Flow Simulator automatically identifies the type of fluid used in the model and utilizes the corresponding HTC correlation namely, Air, Water, or Oil.
3	Rotor Index (ROTOR_IDX)	The index of the rotor that is rotating the tube. The speed for this rotor is set in Run > Reference Conditions tab.	Mandatory
4	Hydraulic Diameter (HYD_DIA)	The hydraulic diameter of the rotating tube.	Mandatory In AUTO mode, Flow Simulator automatically retrieves this information from the flow element input.
5	Flow Area (FLOW_AREA)	The flow area of the rotating tube.	Mandatory In AUTO mode, Flow Simulator automatically retrieves this information from the flow element input.
6	Inlet Effects (INLET_EFF)	The inlet effects over the flow for the rotating tube.	Mandatory The default is No inlet effects. However, you can choose different methods to apply the inlet effect from the drop-down menu. See Tube Elements for more information on this effect.
7	Entrance Length (ENTR_LEN)	The entrance length of the rotating tube.	Mandatory In AUTO mode, Flow Simulator automatically retrieves this information from the flow element input. However, you can enter a specified entrance length by clearing the AUTO option. See Tube Elementsfor more information on this effect.
8	Rotational Reynolds Number (RE_ROT)	The rotational Reynolds number for the rotating tube.	Mandatory In AUTO mode, Flow Simulator automatically calculates the rotational Reynolds number by using the information from provided flow element input, or based on other inputs. If you want to test the correlation for a fixed rotational Reynolds number, verify that the flow element input is 0, a hydraulic diameter is entered, then clear the AUTO option and manually enter the Reynolds number value.
9	Axial Reynolds Number (RE_AX)	The axial Reynolds number for the rotating tube.	Mandatory In AUTO mode, Flow Simulator automatically calculates the axial Reynolds number by retrieving the information from the flow element specified, or based on other inputs. If you want to test the correlation for a fixed axial Reynolds number, make sure the flow element input is 0, a hydraulic diameter is entered, then clear the AUTO option and manually enter the Reynolds number value.
10	HTC Multiplier (HTC_MULT)	A constant multiplier to scale the value of heat transfer coefficient obtained from the correlation.	Not Mandatory Default value is 1.0.

Formulation

For a tube rotating about its axis and has fluid flowing through it axially, the heat transfer coefficient between the air and the tube wall is given as:

For Air Flow (Pr < 1) (Ref. 1):
In the range
$0 < R e_{a} < 3 \times 10^{4}$
and
$1.6 \times 10^{3} < R e_{r} < 2.77 \times 10^{5}$
$N u = 0.01963 R e_{a}^{0.9285} + 8.5101 \times 10^{- 6} R e_{r}^{1.4513}$
For $R e_{r} > 2.77 \times 10^{5}$
$N u = 0.000285 R e_{r}^{1.19}$
For Water Flow (1 ≤ Pr ≤ 100):
In the range
$3521 < R e_{a} < 10563$
and $0 < R e_{r} < 16890$
$N u = A R e_{a}^{B} P r^{0.4} + C R e_{r}^{D} P r^{0.4}$
Values of A, B, C, and D, as per reference (Ref. 2), are 7.438E-03, 0.09683, 9.183E-05, and 1.358 respectively.
For Oil Flow (Pr > 100):
In the range
$30 < R e_{a} < 80$
and
$2375 < R e_{r} < 1.75 \times 10^{5}$
$N u = A {(\frac{1}{R e_{r} * P r})}^{B}$
Values of A and B, as per reference (Ref. 3), are 3.811E-03 and -0.641, respectively.

Table 2. Output List
Index	.flo label	Description
1	TNET	Thermal network ID, which has the convector where this correlations is used.
2	CONV_ID	Convector ID, which is using this correlation.
3	FLOW_ELM	User-defined flow element ID or retrieved under the AUTO mode.
4	FLOW	User-defined mass flow rate or calculated by the solver under the AUTO mode.
5	HYD_DIA	Hydraulic diameter of the fin channel as calculated by the solver under the AUTO mode.
6	CORR	Type of correlation used, depending upon the fluid type.
7	RE_AX	User-defined axial Reynolds number or calculated by the solver under the AUTO mode.
8	RE_ROT	User-defined rotational Reynolds or calculated by the solver under the AUTO mode.
9	PR	Fluid Prandtl number as calculate in the solver.
10	NU	Nusselt number obtained from the correlations.
11	HTC	Heat transfer coefficient calculated as per the correlation.

Heat Transfer Correlation References

Seghir-Ouali, S., Didier Saury, Souad Harmand, O. Phillipart, and D. Laloy. "Convective heat transfer inside a rotating cylinder with an axial air flow." International Journal of Thermal Sciences 45, no. 12 (2006): 1166-1178.
Gai, Yaohui, Mohammad Kimiabeigi, Yew Chuan Chong, James D. Widmer, James Goss, Unai SanAndres, Andy Steven, and Dave A. Staton. "On the measurement and modeling of the heat transfer coefficient of a hollow-shaft rotary cooling system for a traction motor." IEEE Transactions on Industry Applications 54, no. 6 (2018): 5978-5987.
Gai, Yaohui, James D. Widmer, Andrew Steven, Yew Chuan Chong, Mohammad Kimiabeigi, James Goss, and Mircea Popescu. "Numerical and experimental calculation of CHTC in an oil-based shaft cooling system for a high-speed high-power PMSM." IEEE Transactions on Industrial Electronics 67, no. 6 (2019): 4371-4380.