# Thermal-Hydraulic Modeling of Oil-Inmersed Motor Pump
## 3 Experimental Validations
The observed substantial disparities in calculation outcomes at high rotational velocities can be attributed to the inherent variability in oil viscosity resulting from the temperature elevation of the oil due to dynamic alterations in operating conditions. It should be noted that the preceding text solely accounted for a constant oil viscosity in the determination of the calculation results. The viscosity of Newtonian fluids exhibits a temperature-dependent behavior, whereby changes in temperature directly influence viscosity variations. However, due to the unavailability of initial temperature data, which is essential for predicting viscosity alterations, it becomes imperative to establish a correlation between viscosity and different rotational speeds and their corresponding outlet pressures. This empirical fitting process is illustrated in Figure 11.  
Regarding the global fitting surface, the dynamic viscosity coefficient demonstrates a decreasing trend with increasing rotational speed, exhibiting a quadratic relationship. It initially starts at a value of 3.695 and progressively decreases to 0.496. As the pressure increases, the dynamic viscosity coefficient displays an initial ascending trend followed by a descending trend. The maximum value of 4.01 is observed at 12 MPa, while the minimum value of 2.82 is observed at 18 MPa. Equation (15) defines the fitting equation, wherein \(x\) represents the rotational speed in rpm (revolutions per minute), \(y\) represents the outlet pressure in MPa (megapascals), \(z\) symbolizes the dimensionless viscosity coefficient, and \(\mu_{1}\) is the dynamic viscosity after fitting. In Figure 12, the circled temperature is 39.4 \({}^{\circ}\)C, and the viscosity coefficient \(z\) is close to 1. There is a small difference between the corresponding  
Figure 11: Fitted surface of viscosity coefficient for oil fluids. viscosity value at 33.7 \({}^{\circ}\)C and the standard value, which indicates the correctness of the fitting surface. \[ \begin{array}{rcl}z&=&3.95217-0.00157x+1.61409\times 10^{-7}x^{2}-\\ &&5.48032\times 10^{-12}x^{3}+0.37877y-0.0183y^{2}\\ \mu_{1}&=&z\mu\end{array}  \tag{15}\]  
The viscosity values, recalculated by substituting the fitted viscosity coefficients, are employed in subsequent computations. The outcomes of these calculations are illustrated in Figure 12. Within Figure 12a, the leakage port temperature exhibits a relatively stable profile within the pressure range of 3-18 MPa. However, beyond this range, specifically within the 18-34 MPa pressure interval, the temperature demonstrates an exponential increase. Notably, the calculated values exhibit a parallel trend in variation to the measured values, indicating a comparable pattern. At low pressures, the calculated and actual values of the leakage port oil temperature exhibit a remarkable level of agreement, indicating a high degree of fitting. However, at high pressures, there is a comparatively larger deviation between the calculated and actual values. For the purpose of ensuring precise calculations, the subsequent text will exclusively focus on the temperature fluctuations at different nodes associated with outlet pressures ranging from 3 to 18 MPa. As depicted in Figure 12b, the calculated values exhibit a trend of variation similar to that of the measured values. The temperature follows a pattern characterized by an initial increase with rotational speed, followed by a subsequent decrease, and then a subsequent increase. The underlying mechanism can be explained as follows: with an increase in rotational speed, the churning losses intensify, resulting in an escalation of viscous friction losses between the oil molecules, consequently leading to an elevation in temperature. However, as the temperature surpasses a certain threshold, the viscosity of the oil decreases, leading to a reduction in the viscous friction losses between the oil molecules, which in turn causes a decline in temperature. At 6500 rpm, the temperature reaches its minimum value and the maximum error is 14.1%.