INVESTIGATION OF HEAT TRANSFER FROM THE FINNED SECTION OF AN ELECTRIC MOTOR HOUSING USING A MODEL

Yu. V. KOPYLOV, D. I. SANNIKOV

(Presented by the scientific seminar of the Departments of Electrical Machines and Apparatus and General Electrical Engineering)

One of the main tasks in the modern design of electrical machines is to increase their power while maintaining the height of the axis of rotation, chiefly by improving the utilization of electrical-engineering materials, which leads to an increase in heating losses per unit volume of the machine and, consequently, to an increase in the temperature of individual parts.

One way to reduce the temperature is to increase the cooling surface by means of fins. To select the most advantageous fin geometry, it is necessary to have the dependence of the heat-transfer coefficient of the finned part of the frame surface $\alpha$ on the ratio of the fin height to the fin pitch. This dependence can be obtained only experimentally.

The aim of the investigation is to determine this dependence for 4A-series motors with an axis height of 132 mm and a frame length of 270 mm. In order to broaden the possibilities for varying the fin parameters, instead of an entire frame, segments of the finned surface were taken with a width equal to $1/6$ of the frame circumference. With such a segment width, the corresponding element can be replaced by a flat working element for ease of manufacture.

The arrangement of the setup for experimentally determining the heat-transfer coefficient $\alpha$ is shown in Fig. 1.

The finned section, or working element 3, is made in the form of a flat plate with longitudinal fins. The length of the element is equal to the length of the machine housing.

To investigate the influence of fin density, the number of fins on the working elements is varied from 2 to 8; i.e., the ratio of fin height to pitch is varied from 0.85 to 3.14.

The working element is installed above the main heater 4, equal in width and length to the working element. To compensate for the downward heat leakage of the main heater, there is a compensating heater 6 installed beneath the main one. A thermal-insulating layer 5 is placed between the main and compensating heaters. The bases of the heaters and the thermal-insulating layer are made of asbestos-cement board 10 mm thick. The heaters are made of nichrome, laid turn to turn over the surface of the asbestos-cement board. The magnitude of the required compensator power is selected in such a way,

so that the temperature difference between the thermocouples arranged symmetrically on both sides of the heat-insulating layer would be equal to zero. The heating unit is installed in a trough-shaped base 8, made of aluminum. The height of the walls is equal to the height of the heating layer. Between the side wall of the base and the heating unit, in order to reduce heat removal from all sides, there is a 50 mm wide layer of glass wool 7.

The temperature of the working element is measured by means of 15 thermocouples arranged uniformly in its flat part, and 15 thermocouples—in the tips of the fins.

Fig. 1. Installation for investigating heat transfer from a finned surface

The flow-rate measuring unit consists of a fan driven in rotation by a direct-current machine, and a diffuser with a damper, making it possible to vary the air flow rate at a constant fan rotational speed. The air flow rate is measured with micromanometer 11. A straightening grid is installed at the outlet of the flow-rate measuring unit.

The flow velocity \(v_p\) is calculated by the formula

\[ v_p=\frac{V}{S}, \]

where

\[ V \]—air flow rate, \(\frac{m^3}{sec}\);

\[ S \]—area of the ventilation opening, \(m^2\).

The heat-transfer coefficient is determined by the formula

\[ \alpha=\frac{P_1}{\theta_p S},\ \frac{w}{m^2 deg}, \]

\[ \theta_p=\theta_{st}-\Delta\theta_b-\theta_b, \]

where

\[ P_1 \]—power transmitted from the main heater to the working element;

\[ \theta_p \]—mean overheating of the working element;

$S$ — cooling surface;
$\Theta_{\mathrm{v}}$ — ambient-air temperature;
$\Delta \Theta_{\mathrm{v}}$ — heating of the air in the fan;
$\Theta_{\mathrm{st}}$ — mean temperature of the working element.

At the first stage of the experimental investigations, the leakage of heat flux through the side surfaces of the heaters was determined. For this purpose, the surface of the working element was practically completely thermally insulated.

The flux directed downward was compensated by the lower heater. The power of the main heater $P_0$ in this case is equal to the leakage power through the side faces of the heating block. From the overheating of the latter, $\Theta_0$, and the power $P_0$, the conductance of the side leakage is determined as

\[ G_{y0}=\frac{P_0}{\theta_0}. \]

Fig. 2. Dependence $\alpha=f(v_p)$ for working elements with different numbers of ribs

\[ n=1500\ \frac{\text{rev}}{\text{min}} \]

Subsequently, the leakage power was taken into account by the formula

\[ P_1=P_0-G_{y0}\cdot \theta_{\mathrm{n}}, \]

where

$P_1$ — power transmitted to the working element;
$P_0$ — heater power;
$\Theta_{\mathrm{n}}$ — overheating of the heating block.

The heat-transfer coefficient was determined at two fan rotational speeds, 1500 and 3000 rev/min. At each speed, 4 regimes with different flow velocities $v_p$ were carried out. For 1500 rev/min the velocity varied from 0 to 10 m/s, and for 3000 rev/min—from 0 to 25 m/s.

The obtained dependences of \(\alpha\) on the air velocity \(v_{\mathrm{p}}\) are presented in Figs. 2 and 3, respectively, for fan rotation speeds of \(1500\) and \(3000\ \mathrm{rpm}\). The results of the investigations showed that, as the flow velocity increases, \(\alpha\) increases strongly up to a certain value. A further increase in the flow velocity at a constant fan rotation speed does not increase the heat-transfer coefficient. An increase in the fan rotation speed at a constant flow velocity leads to an increase in the heat-transfer coefficient.

Fig. 3. Dependence \(\alpha=f(v_{\mathrm{p}})\) for working elements with different numbers of ribs, \(n=3000\ \dfrac{\mathrm{rev}}{\mathrm{min}}\)

On the basis of an analysis of the experimental results, criterion equations for the heat transfer of the finned surface were obtained for the investigated model of a section of the motor frame

\[ Nu = Nu_0 + C_{\mathrm{p}}(Re_{\mathrm{p}}-\Delta Re)^m + C_0 Re_0^n . \]

Here

\[ Nu=\frac{\alpha d_{\mathrm{g}}}{\lambda} \]

is the Nusselt criterion;

\[ d_{\mathrm{g}}=\frac{4S_{\mathrm{k}}}{P_{\mathrm{k}}} \]

is the hydraulic diameter of the channel;

\(S_{\mathrm{k}}\) is the cross-sectional area of the channel;

\(P_{\mathrm{k}}\) is the “wetted” perimeter of the channel;

\(\lambda\) is the thermal-conductivity coefficient of the medium;

\[ Re_{\mathrm{p}}=\frac{v_{\mathrm{p}}d_{\mathrm{g}}}{\nu} \]

is the Reynolds criterion for the flow velocity;

\(\nu\) is the kinematic viscosity of the medium;

\[ Re_0=\frac{v_0d_{\mathrm{g}}}{\nu} \]

is the Reynolds criterion for the circumferential velocity of the fan;

\(v_0\) — circumferential speed of the fan;

\(m = f\left(\dfrac{h}{d_r}\right)\) — exponent;

\(Nu_0\) — heat-transfer criterion under natural convection.

This equation is valid for the initial portions of the dependences \(\alpha = f(v_p)\) up to the beginning of the bend in the curve.

The values of the coefficients of the equation are given in Table 1.

Table 1

Conclusion

The results of the experiments performed make it possible to select the optimum delivery air velocity \(v_p\) and to carry out the thermal calculation of machines with a rotation-axis height of 132 mm and a frame length of 270 mm for different fin densities.