# Thermal-Hydraulic Modeling of Oil-Inmersed Motor Pump
## 3 Experimental Validations  
Figure 8 shows the experimental picture of measuring the temperature of the motor pump. Port A and B are oil inlet and outlet, respectively. As shown in Figure 9, the experimental and calculated values of the inlet temperature remained consistent at approximately 22 \({}^{\circ}\)C and exhibited no changes throughout the operation of the motor pump. Conversely, the test temperature at the outlet experienced a surge of 4.86 \({}^{\circ}\)C, while the calculated temperature value displayed a minimal increment, albeit with an increasing trend. This phenomenon can be attributed to the escalating temperature rise of the overall system during the motor pump's operation. Notably, the calculated value deviates significantly from the experimental value under low pressure, with a maximum error of 22.79%. Nevertheless, as the pressure increases, the calculated value converges more closely to the experimental value. Table 2 presents the maximum error values of the temperature at both the leakage port and outlet. The values listed in the upper section correspond to the case where the temperature at the leakage port is 6 MPa, while those in the lower section correspond to the case where the temperature at the outlet is 34 MPa. In this context, a represents the actual measured value, b denotes the corresponding calculated value, and c denotes the resulting error value. \[c=\frac{|a-b|}{a} \tag{14}\]  
Figure 10 illustrates the temperature curve of each node under distinct rotation speeds, with an outlet pressure of 6 MPa. The temperature of the inlet displays minor fluctuations, which can be attributed to variations in the ambient temperature. However, the temperature of the leakage port experiences an upsurge, primarily due to the increase in churning loss and motor power. The observed escalation in the leakage temperature, as determined through calculations, can be attributed to an exponential growth pattern. This phenomenon is predominantly a consequence of amplified heat generation resulting from heightened churning losses and motor power losses. Consequently, the system experiences a substantial temperature elevation of precisely 59.68 \({}^{\circ}\)C. The temperature measur \begin{table}
\begin{tabular}{c c c} \hline \hline
**Measurement a** & **Calculation b** & **Error c** \\ \hline
33.26 \({}^{\circ}\)C & 25.68 \({}^{\circ}\)C & 22.79\% \\
27.52 \({}^{\circ}\)C & 22.67 \({}^{\circ}\)C & 17.7\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Value of the maximum temperature error of the leakage port and outlet. Figure 10: Comparison of measured and calculated temperature changes at each node with rotational speed under outlet pressure of 6 MPa. a distinctive pattern characterized by an initial ascent, followed by a subsequent descent, and then another subsequent ascent. This observed behavior can be plausibly attributed to the impact of temperature variations on the rheological properties, specifically the viscosity, of the oil fluid. At lower rotation speeds, the higher viscosity of the oil fluid, attributed to lower temperatures, gives rise to pronounced friction losses, leading to relatively elevated temperatures. Nevertheless, as the rotational speed progressively increases, the viscosity of the oil fluid decreases, resulting in a subsequent temperature decline. However, as the rotational speed reaches a critical threshold, the impact of the viscosity changes becomes insufficient to counteract the fluctuations caused by interfacial viscous friction losses. Consequently, this leads to a subsequent temperature rise in the oil fluid. Under high-speed conditions, a substantial disparity is observed between the two measurements, with a maximum deviation of 109.7%. Nonetheless, both measurements demonstrate a convergent growth trend under these high-speed conditions.