2.1. Experimental Facilities
Figure 2a depicts the schematics of the rotating test rig that is driven by a 15,000 W DC electric motor (1). The length, width, and height of the rotating rig are 4.4 m, 1.2 m, and 2.3 m, respectively. The radially rotating looped thermosyphons (RLTs) (2) are installed on the two rotor platforms (3) with the eccentricity (R) of 450 mm. With the extended eccentricity from the typical range of an electric motor, the centrifugal acceleration of a cooling component in a rotor of an electric motor can be simulated by the rotating rig at a reduced rotor speed. A 36-channel instrumentation slip ring (4) is installed at the axial end of the shaft (5) to transmit the signals of thermocouples and pressure transducers to the computer via the Fluke NetDAQ data logger. An online condition monitoring program is installed in the computer to scan the measured RLT temperatures and pressures at each rotating test condition. To feed the electrical heating power to the evaporator section of each RLT, the adjustable electric power supply unit is connected with the power slip-ring unit (6), through which the electric cables are connected in series between the heating foils and the adjustable DC power supply. The rotor speed is detected from the optical detector marked on the shaft (7).
In
Figure 2a, the schematic of the instruments measuring the temperatures and pressures of RLTs, as well as the heating powers and rotational speed, is included. The signals of temperatures and pressures of the RLTs are transferred to the data logger via the instrumental slip ring (4). As indicated in the photo of the rotating rig, the instant scans of wall temperature and pressure of the RLTs are permissible using the Fluke data acquisition program. The voltage and current of heater power fed by the electric power regulator, as well as the rotational speed, are manually input for subsequent data processing.
Figure 2b shows the RLTs with and without coil insert. In
Figure 2b(A–F) denote the thermocouple locations for
Tw measurements along the RLT. Such notations are similarly adopted for presenting the
Tw distributions along the RLTs, as later illustrated. Considering the strength requirement for a cooling element in a rotating machine, the RLT is made of a 1 mm thick square-sectioned stainless steel duct with an inner height (width) of 30 mm, which is selected as the characteristic length (d) for defining the non-dimensional parameters. The coil made of a 2 mm diameter (d
c) stainless steel wire with a helical pitch of 10 mm, giving the ratio of d
c/d as 0.07, is fitted in each of the two straight legs of the RLT. The orientation of the helical vector for the coil in each straight leg of the RLT is aligned with the direction of the vapor–liquid circulation in the RLT.
The axial spans of the evaporator and condenser are 410 mm and 203 mm, respectively. As indicated in
Figure 2b, the nominal length (L
RLT) and centerline width of the looped thermosyphon are 583 and 190 mm, respectively. The radii of curvature for each of the two 180° bends at the condenser and evaporator sections are identical, at 80 mm. In
Figure 2b, the origin of the loop-wise S coordinate system is positioned at the interface between evaporator and condenser of the inner leg. On the rotating platform, all the outer surfaces of the condenser are exposed in the airflow induced by rotation at the ambient temperature. The direction of the S coordinate follows the circulation direction of the working fluid in each RLT. On the flat endwall of each RLT, there are six foil-type thermocouples installed at the locations A–F along the S-wise centerline to measure the wall temperatures (
Tw) along the evaporator and condenser, as indicated in
Figure 2b. The distance between the thermocouple and the inner wall of the RLT is 0.5 mm. To emulate the basically uniform flux heating condition, the four evaporator walls are heated by the flexible foil-type electrical heaters with the widths and lengths matching the outer surfaces of the evaporator. The electrical resistance per unit length of each electrical heater is identical. As described previously, these heaters are electrically connected in series to ensure the constant electric current through each heater. The supplied heat flux is determined from the measured heating power and the total heating area of the evaporator. To eliminate air gaps between the evaporator and heater, a thin layer of thermal paste is applied as an interface. As shown by the photos in
Figure 2b, the entire evaporator section with the thermocouples and the heating foils is wrapped by a 30 mm thick thermal insulation fiber to minimize the external heat loss. A 10 mm × 10 mm thermal insulation layer with a thickness of 2 mm covers each foil-type thermocouple on the condenser to minimize the effect of airflow on the
Tw measurement.
The piezo-metric-type pressure transducers with a precision of 10 Pa are, respectively, installed at the radially inward leg of the condenser and the central of evaporator bend to detect the pressures of condenser and evaporator. As shown by the RLT photo in
Figure 2b, the vacuum/filling port and a shut-off valve are connected with the condenser pressure transducer via a T-joint. Prior to installation of each RLT on the rotating rig, the RLT is vacuumed to the absolute pressure of 7.13 Nm
−2, which is followed by charging the degassed and distilled water with the volumetric filling ratio of 0.5 or 0.8. The saturation temperatures corresponding to the measured condenser and evaporator pressures are selected as the referenced fluid temperatures to evaluate the Nusselt numbers in the condenser and evaporator. Without heating, at the filling ratio of 0.8, a 10 mm thick liquid film is attached on the inner sidewall of the RLT, as shown by
Figure 2a. This layer of liquid film ensures the boiling activities with latent heat transmission at a saturated condition along the inner leg of the evaporator, which considerably improves the heat transfer performance of the RLT, as later demonstrated.
2.2. Data Processing and Experimental Program
The geometrical and heating/cooling configurations of the RLTs with distilled water as the working fluid at the filling ratios of 0.5 or 0.8, with and without the coil insert, predefine the boundary conditions (
BC) for each RLT. The effective thermal conductivity (
keff), thermal resistance (
rth), and the average heat transfer rates over the evaporator (
heva) and condenser (
hcon) inside the RLT are governed by heating power, centrifugal acceleration, and the cooling condition over the condenser, which is determined by the forced heat convection of the airflow surrounding the rotating thermosyphon bend and the airflow temperature. With the room temperature of the test rig controlled at 25 °C using the central air conditioning system, the heat transfer rate of the airflow is relevant to the geometric characteristics of the condenser bend, the angular velocity, and the rotating radius of the RLT. Based on the results in [
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24], the functional structures of effective thermal conductivity (
Keff), thermal resistance (
Rth), and averaged Nusselt numbers of the evaporator (
Nueva) and condenser (
Nucon) in each RLT follow the general dimensionless form of Equation (1):
where
Keff,
Rth,
Nueva, and
Nucon are defined as:
In Equations (2)–(5), kw is the thermal conductivity of stainless steel (RLT wall) of 15 Wm−1K−1; Q and q stand for the net convective heat power and heat flux transferred by the RLT. In this respect, the heat fluxes of the evaporator (qeva) and condenser (qcon) are defined by the total heat transfer areas of the evaporator and the condenser. eva and con are the wall temperatures averaged from the corrected thermocouple readings from the measurement spot to the fluid–wall interface using one-dimensional Fourier conduction law at the heat flux q. The thermal resistance of RLT (rth) is evaluated from the temperature difference between Tw,eva and ambient temperature (Tamb). The referenced fluid temperatures for evaluating the Nusselt numbers of the evaporator (Nueva) and the condenser (Nucon) are the saturated temperatures in the evaporator (Tsat,eva) and the condenser (Tsat,con), which are indicated by the table values at the measured evaporator and condenser pressures. The liquid thermal conductivity (kf) in Equation (3) is calculated from the averaged Tsat,eva and Tsat,con.
The dimensionless centrifugal acceleration (
Ca) and heat power (
Q*) are defined by Equations (6) and (7), respectively, as:
In Equation (6), Ω,
R, and g, respectively, stand for the angular velocity of RLT, the eccentricity between the centerlines of RLT, and the rotating shaft and gravitational acceleration. The liquid dynamic viscosity (
μf) and the latent heat (
hfg) are evaluated at the averaged saturated temperature and pressure of the RLT. In a steady-state condition, the heat flux transferred by the working fluid out of the condenser (
qcon) is balanced with the convective heat flux transferred by the airflow at the air temperature of
Tamb. Based on the temperature difference between the external wall of the condenser and the airflow, the average Nusselt number of the airflow over the rotating condenser bend of the RLT (
Nuext,con) is also measured using Equation (8) as:
In Equation (8),
ext,con and
Tamb are the averaged wall temperature measured from the outer surface of the condenser and the ambient temperature of the airflow respectively. The thermal conductivity of air (
kair) is calculated at the measured
Tamb. The governing flow parameter for
Nuext,con is the rotating Reynolds number (
ReΩ) defined by Equation (9).
In Equation (8), the kinematic viscosity of the airflow (ν) is evaluated at the ambient temperature (Tamb).
The thermal performance measurements of the two RLTs installed on the two rotor arms of the rotating rig were carried out at the rotating speeds of 100, 200, 300, and 400 rev/min with the corresponding centrifugal accelerations at 4.53, 17.89, 39.63, and 66.62 g. At the rotating speeds tested, five heater powers (Q) in the ranges of 44.42–167.18 W and 152.81–729.47 W for the RLTs with the filling ratios of 0.5 and 0.8 were supplied to alter Q* at a fixed Ca. The maximum wall temperature in the Q* range tested was less than 373 K. After regulating Q* and/or Ca, it generally took 45 min to reach a steady state at which the temperature variations between the several successive Tw scans were less than ±0.3 K.
The net heat transfer power (
Q) for calculating the net convective heat flux (
q) in
Nueva,
Nucon, or
Nuext,con equation is identical. However, the areas selected to define the net convective heat flux (
q) for calculating
Nueva,
Nucon, and
Nuext,con are the inner surface areas of the evaporator and condenser, and the external area of the condenser bend exposed to the ambience, respectively. The net heat transfer power (
Q) for calculating
q is determined by subtracting the external heat loss power (
Qloss) from the supplied electric heating power. To acquire the heat loss correlation for calculating
Qloss, a series of heat loss calibration tests is carried out with the interior of the RLT filled with sand and the exterior of the condenser bend wrapped by the thermal insulation fiber. At each rotating speed of 100, 200, 300, or 400 rev/min, five heating powers are applied to raise the steady-state wall temperatures. It generally takes about 4–8 h to satisfy a steady-state condition during each heat loss test. At each rotating speed,
Qloss is proportional to the wall-to-ambient temperature difference with the proportionality increased along with the rotational speed. The
Qloss correlation is incorporated with the data processing program for subsequent data reduction. To simulate the temperature field of a rotating machine such as an electric motor, the effective thermal conductivity of the RLT (
keff) is an important “property” that permits the definition of a conduction model for a rotating hot component cooled by the present RLT. The
keff measured follows Equation (10) as:
In Equation (10), L
RLT is the aforementioned nominal length of the RLT, shown in in
Figure 2b as 583 mm.
eva and
con are the averaged wall temperatures of the evaporator and the condenser.
The experimental uncertainties of
Ca,
Q*,
ReΩ,
Keff,
Rth,
Nueva,
Nucon, and
Nuext,con are estimated following the statistical inference of Kline and McClintock [
31]. With the fluid properties indicated by the table values, the main sources attributed to the experimental uncertainties are the measurements of temperature, pressure, rotating speed, and heat power. The fluid properties and latent heat involved in the non-dimensional groups are evaluated from the correlations using
Tsat or
Tamb as the determining variable. As the saturation temperatures are correlated into the function of evaporator or condenser pressure in the RLT, the error percentages of
Tsat and its relevant fluid properties are propagated from the pressure measurements. The precision values, data ranges and the maximum error percentages of the various instruments are summarized in
Table 1.
As stated in
Table 1, with the precision value of 10 Pa for the pressure gauge, the maximum uncertainty of pressure measurements was 0.13% in the data range of 0.0767–0.7381 bar. For the temperature measurements, the experimental uncertainty was 0.3 K, giving the maximum error percentages of
Tamb,
Tw,con,
Tw,eva, and
Tw ext,con as 1.2%, 0.75%, 0.75%, and 0.77%. The percentage errors for the hydraulic diameter (d) of the RLT duct and the RLT length (L
RLT) caused by the manufacturing tolerance of ±0.1 mm were 0.3% and 0.02%, respectively. With the maximum error percentages for heat power and rotating speed of 1.5% and 1%, the root-mean-square experimental uncertainties at 95% confidence interval for
Ca,
Q*,
ReΩ,
Keff,
Rth,
Nueva,
Nucon, and
Nuext,con were estimated as 1%, 7.42%, 1.56%, 8.9%, 2.58%, 2.92%, 2.01%, and 1.57% respectively.