In modern electric drive systems, effective thermal management and lubrication are critical for ensuring performance, efficiency, and longevity. The injection pipe, a key component within the electric drive system, plays a vital role in distributing oil to cool and lubricate critical parts such as gears, bearings, and motor windings. Insufficient lubrication can lead to overheating, wear, noise, and even catastrophic failure, directly impacting the overall reliability of the electric drive system. Traditionally, the design of such injection pipes has relied heavily on empirical knowledge and experimental optimization. However, due to the inherent challenges in directly measuring flow rates inside the sealed electric drive system during operation, computational simulations have become an indispensable tool in the design and evaluation phase. This study focuses on employing Computational Fluid Dynamics (CFD) to analyze the internal flow characteristics of an injection pipe within an electric drive system under various operating conditions. The primary objectives are to assess the injection performance, understand the flow distribution, and identify areas for optimization to enhance the cooling and lubrication efficiency of the electric drive system.
The core of this investigation is a specific injection pipe configuration commonly found in electric drive systems. It consists of a main pipe with one inlet and five branch pipes, each terminating in a nozzle aimed at specific components. The internal flow domain of this geometry serves as the basis for our CFD analysis. A detailed numerical model was constructed to simulate the three-dimensional, viscous, turbulent flow of the lubricating oil. The working fluid is a specific oil type, TF7S, whose properties vary significantly with temperature, influencing the flow behavior within the electric drive system. The simulations encompass a range of temperatures (-20°C, 20°C, and 90°C) and inlet pressures to replicate realistic operating scenarios for the electric drive system, from cold starts to normal high-temperature operation.
To accurately capture the complex flow phenomena, the Reynolds-Averaged Navier-Stokes (RANS) approach was adopted. The Shear Stress Transport (SST) k-ω turbulence model was selected for its robust performance in handling flows with adverse pressure gradients and separation, which are anticipated near branch junctions and nozzle exits within the injection pipe of the electric drive system. The governing equations for this model are presented below. The turbulence kinetic energy (k) and specific dissipation rate (ω) are solved using their respective transport equations:
$$ \mu_t = \rho \frac{k}{\omega} $$
$$ \frac{\partial (\rho k)}{\partial t} + \frac{\partial (\rho u_j k)}{\partial x_j} = \frac{\partial}{\partial x_j} \left[ \left( \mu + \frac{\mu_t}{\sigma_k} \right) \frac{\partial k}{\partial x_j} \right] + \tau_{ij} \frac{\partial u_i}{\partial x_j} – \beta^* \rho k \omega $$
$$ \frac{\partial (\rho \omega)}{\partial t} + \frac{\partial (\rho u_j \omega)}{\partial x_j} = \frac{\partial}{\partial x_j} \left[ \left( \mu + \frac{\mu_t}{\sigma_\omega} \right) \frac{\partial \omega}{\partial x_j} \right] + \frac{\omega}{k} \left( \alpha \tau_{ij} \frac{\partial u_i}{\partial x_j} – \beta \rho k \omega \right) + (1 – F_1) 2 \rho \frac{1}{\omega \sigma_{\omega 2}} \frac{\partial k}{\partial x_j} \frac{\partial \omega}{\partial x_j} $$
Here, $\mu_t$ is the turbulent viscosity, $\rho$ is the fluid density, $u_i$ are the velocity components, and $\sigma_k$, $\sigma_\omega$, $\beta^*$, $\beta$, $\alpha$, and $F_1$ are model constants. The fluid properties for the TF7S oil at the analyzed temperatures are crucial inputs and are summarized in Table 1.
| Temperature (°C) | Kinematic Viscosity (mm²/s) | Dynamic Viscosity (mPa·s) | Density (kg/m³) | Thermal Conductivity (W/m·K) | Specific Heat Capacity (kJ/kg·K) |
|---|---|---|---|---|---|
| -20 | 719.28 | 624.00 | 867.53 | 0.1546 | 1.8301 |
| 20 | 51.59 | 43.80 | 844.09 | 0.1474 | 1.9841 |
| 90 | 7.47 | 5.97 | 798.84 | 0.1344 | 2.2535 |
The computational domain representing the internal flow passage of the injection pipe was discretized using a hexahedral-dominant unstructured mesh. Special attention was paid to refining the mesh in regions of expected high flow gradients, such as the junctions between the main pipe and branch pipes, and at the nozzle exits. A grid independence study was conducted to ensure that the solution was not dependent on the mesh size. The final mesh comprised approximately 411,225 cells, providing a balance between computational accuracy and cost. The boundary conditions were set as follows: the inlet was specified as a total pressure boundary, allowing the mass flow rate to be a result of the simulation based on the applied pressure and system resistance; all five branch outlets were set as pressure outlets with atmospheric relative pressure (free outflow); and all pipe walls were treated as no-slip adiabatic walls.
The commercial CFD solver ANSYS CFX was utilized for the simulations. The coupled solver algorithm was employed, and the high-resolution advection scheme was used for spatial discretization. Convergence was monitored through the reduction of residuals for mass, momentum, and turbulence equations below a threshold of $10^{-4}$. The simulations provided detailed data on velocity fields, pressure distributions, and, most importantly, the volumetric flow rate through each nozzle of the injection pipe in the electric drive system.
The simulation results first reveal the profound impact of oil temperature on the injection capability of the pipe within the electric drive system. This relationship is quantitatively presented in Table 2, which shows the total combined flow rate from all five nozzles at different inlet pressures and temperatures.
| Inlet Pressure Condition | Flow Rate at -20°C (L/min) | Flow Rate at 20°C (L/min) | Flow Rate at 90°C (L/min) |
|---|---|---|---|
| Low Pressure (e.g., 0.3 bar gauge) | ~0.12 | ~1.65 | ~2.00 |
| High Pressure (e.g., 1.0 bar gauge) | ~0.45 | ~3.25 | ~3.95 |
The data clearly indicates that at low temperatures, the high viscosity of the oil severely restricts flow, leading to very low injection rates. This is a critical consideration for the electric drive system during cold starts. As temperature increases, viscosity drops dramatically, resulting in a significant increase in flow rate for the same pressure differential. At the typical operating temperature of 90°C for an electric drive system, the injection flow rate is sufficient to meet cooling and lubrication demands, even at moderate pressures. A comparison with experimental data collected on a test bench for the 90°C condition showed that the CFD-predicted flow rates were within a 20% margin of error, validating the numerical model’s accuracy for analyzing the electric drive system’s lubrication subsystem.
Beyond overall flow rates, the uniformity of distribution among the five nozzles is paramount for the balanced cooling of the electric drive system components. The CFD results demonstrate excellent flow distribution. Under a given operating condition (e.g., 90°C and 1.0 bar inlet pressure), the individual nozzle flow rates are nearly identical. This uniformity can be expressed through a coefficient of variation (CV). If $Q_i$ represents the flow rate from the i-th nozzle and $\bar{Q}$ is the average flow rate, then:
$$ \text{CV} = \frac{\sqrt{ \frac{1}{N} \sum_{i=1}^{N} (Q_i – \bar{Q})^2 }}{\bar{Q}} \times 100\% $$
For the simulated cases at 90°C, the CV was calculated to be less than 5%, confirming that the design provides even lubrication to all targeted areas within the electric drive system.
The internal flow field analysis offers deeper insights. Velocity streamlines and contour plots were extracted from the simulations. A key observation is the development of a low-velocity or “dead water” zone in the main pipe section furthest from the inlet. This is a region where fluid velocity approaches zero, as shown in the middle cross-section of the main pipe. The existence of this zone has implications for potential sediment accumulation and must be considered during the cleaning and maintenance procedures for the electric drive system’s injection pipe. The mathematical reason can be linked to the pressure recovery and flow division at each branch; the momentum of the fluid is progressively depleted as it feeds the branches.
Another significant finding relates to the velocity acceleration within the branch pipes. The flow from the relatively large-diameter main pipe enters the narrower branch pipes, causing an increase in velocity due to the continuity principle ($A_1 v_1 = A_2 v_2$ for incompressible flow). This acceleration is further amplified as the branch pipe diameter is reduced towards the nozzle exit. The velocity at the nozzle exit ($v_{nozzle}$) is critical for the jet penetration and impingement on the components of the electric drive system. The relationship can be approximated using Bernoulli’s principle and accounting for minor losses:
$$ \frac{P_{in}}{\rho g} + \frac{v_{in}^2}{2g} = \frac{P_{out}}{\rho g} + \frac{v_{nozzle}^2}{2g} + h_{loss} $$
where $P_{in}$ and $v_{in}$ are pressure and velocity at the branch entry, $P_{out}$ is atmospheric pressure at the exit, and $h_{loss}$ represents head losses due to friction and geometric changes. The simulation results confirmed that for a fixed inlet pressure, reducing the nozzle diameter ($D_{nozzle}$) increases the exit velocity substantially, following an inverse square relationship ($v_{nozzle} \propto 1/D_{nozzle}^2$). This is a direct lever for optimizing the cooling effectiveness in the electric drive system.
| Nozzle Diameter (mm) | Calculated Average Exit Velocity (m/s) | Estimated Impingement Force Ratio (Relative to Φ1.2mm) |
|---|---|---|
| 1.2 | ~12.9 | 1.00 |
| 1.0 | ~18.6 | ~2.08 |
| 0.8 | ~29.0 | ~5.18 |
The geometry of the junction where a branch pipe is inserted into the main pipe was found to have a considerable influence on the local flow structure and associated pressure losses. The CFD analysis revealed the formation of vortices and flow separation at these junctions. The insertion depth of the branch pipe emerged as a critical parameter. A deeper insertion creates a more pronounced obstruction in the main pipe flow, leading to larger and more energetic vortices. This not only increases the local pressure drop (an undesirable loss in the electric drive system’s lubrication circuit) but can also disrupt the smooth flow entry into the branch, potentially affecting the injection stability. The pressure loss coefficient $K$ for a junction can be analyzed, where:
$$ \Delta P_{junction} = K \cdot \frac{1}{2} \rho v_{main}^2 $$
Simulations comparing different insertion depths showed that $K$ increased by approximately 15-30% for a deeper insertion compared to a shallower one. This parameter requires careful optimization in the design of the injection pipe for the electric drive system to minimize energy waste in the oil pump and ensure consistent branch flow.
The velocity profile within the branch pipes themselves was also examined. The flow becomes fully developed some distance after the junction, exhibiting a parabolic-like profile characteristic of laminar or turbulent flow in a pipe. At the nozzle exit, the profile is crucial for the spray pattern. The simulations showed a axisymmetric profile with maximum velocity at the center, which is ideal for directing a coherent jet towards a specific point in the electric drive system, such as a gear mesh or bearing.
To further generalize the findings for application in electric drive system design, dimensionless analysis can be applied. The flow behavior can be correlated using Reynolds number ($Re$) and Euler number ($Eu$). The Reynolds number for the main pipe indicates the flow regime:
$$ Re_{main} = \frac{\rho v_{main} D_{main}}{\mu} $$
For the typical 90°C condition, $Re_{main}$ was in the order of $10^3$, indicating transitional or turbulent flow. The Euler number, representing the ratio of pressure forces to inertial forces, is useful for scaling:
$$ Eu = \frac{\Delta P}{\rho v^2} $$
By analyzing $Eu$ for the overall pipe and for individual junctions across different temperatures, design charts can be created to predict the performance of geometrically similar injection pipes in other electric drive system configurations.
In conclusion, this comprehensive CFD-based study provides a detailed analysis of the fluid flow within an injection pipe of an electric drive system. The key takeaways are multifaceted. First, the injection performance is highly sensitive to oil temperature due to viscosity changes, which must be accounted for in the thermal management strategy of the electric drive system, especially during cold starts. Second, the examined design offers excellent flow distribution uniformity among its multiple nozzles, ensuring balanced cooling and lubrication. Third, internal flow analysis revealed areas for design attention: the presence of a low-velocity zone in the main pipe’s dead-end section, which has maintenance implications, and the significant impact of branch pipe insertion depth on vortex generation and pressure loss. Fourth, the nozzle exit velocity, critical for effective impingement cooling, can be effectively tuned by modifying the nozzle diameter, following fundamental fluid dynamics principles.
The insights gained from this analysis form a solid foundation for optimizing injection pipe designs in electric drive systems. Future work could involve coupling this CFD analysis with thermal models of the gears and bearings to perform conjugate heat transfer simulations, further refining the cooling strategy. Additionally, multiphase flow simulations could be considered if air entrainment or cavitation is a concern in the high-speed regions of the electric drive system’s lubrication circuit. Ultimately, the integration of advanced simulation tools like CFD is indispensable for developing more efficient, reliable, and compact electric drive systems, pushing the boundaries of electrified mobility.