Introduction

This benchmark aims to simulate an oil-cooling jet impinging on a copper surface. The experimental results from Bennion and Gilberto [1] are used to demonstrate the potential to reproduce the experiment using SPH. The aim, like in the paper, is to characterize an impinging oil jet for Electric Motor (E-Motor) cooling applications. The first step is to verify the methodology against existing empirical models for impinging jets. A flat surface is used as the target to achieve this goal. The second step is to use a target surface that mimics the surface of a copper end-winding found inside an E-Motor.

Fig. 1. Setup of the impinging oil jet test bench for the experiment

Flow phenomena

Convective Heat Transfer

Conductive Heat Transfer

3D Impinging Jets

Geometry

The simulation setup is based on the experimental setup described in [1]. Figure 1 above describes the apparatus used. Transmission oil at a controlled temperature is injected at the top of the system. A nozzle plate with a 2mm (d) opening focuses the oil into a jet. The target sample made of copper onto which the jet is impinging is placed at a distance H/d = 5 away from the nozzle plate. The target sample has a diameter of D/d = 6.35. The surface of the test sample can either be flat or textured to mimic the copper windings found in e-Machines (see Figure 2 below).

Fig. 2. Flat target surface (left) and a target surface mimicking the end-winding of an electric motor with a wire of 26AWG (right)

Boundary conditions

The target surface is maintained at a constant temperature. In the experiment, the resistance heater is adjusted until the two embedded thermocouples report the appropriate temperature difference to get the desired temperature on the surface of the test sample (See Figure 1). The inlet temperature is set such to obtain the following temperature differences with the target surface: ΔT = 20, 40, and 60°C. The inlet velocity profile follows a fully developed laminar pipe flow with the following normalized average velocity: uf/d = 250, 1400, 2500, 3750, and 5000 s-1. The developed laminar pipe flow velocity equation reads:

Where uf, r, and R are respectively the average inlet velocity, the distance from the center of the pipe, and the radius of the pipe. For the outlet, particles are removed from the domain once they are sufficiently far away from the impingement point. In this case, the forces from the forced convection are higher than the adhesion forces. The transmission oil used is called Ford Mercon oil [3] and its properties are studied by Kemp and Linden [4]. The inlet temperatures used are: 50, 70, and 90 °C. The corresponding thermal conductivity for each temperature is: 0.1586, 0.1553, and 0.1520 W/m/K [4].

Initial conditions

The domain is empty of fluid at the start of the simulation. Gravity is acting on the fluid. The geometrical initial conditions are described in Figure 1. The Reynolds numbers is defined as

where ρ, d, and μ are respectively the fluid density, the nozzle diameter, and the dynamic viscosity. Its value ranges from 48 to 2730.

Discretization

The benchmark was simulated with PreonLab [2] from Fifty2 Technology which implements the IISPH method. Adaptive particle sizes (s) were used to reduce the computing cost. The particle sizes range is 40 < d/s < 160. At the inlet, 40 particles are found across the diameter.

Results specifications

The Heat Transfer Coefficient (HTC) is computed at every particle of the solid and then averaged. It is defined as:

The temperature difference is fixed (boundary condition) and the heat flux q is measured. From this metric the Nusselt number can then be derived:

Where k is the conductivity of the fluid. The simulation is carried out until the heat transfer on the plate reaches a steady state.

Results format

The resulting heat transfer at the end of the simulation is stored in heat_transfer.csv: column1=target type (-), column2=temperature difference (°C), column3=normalized inlet velocity (m/s), column4=average Nusselt number.

Benchmark results

For a flat target, the jet at the end of the simulation for uf/d=2500 s-1 and ΔT = 60°C is rendered in Figure 3. The heat flux and corresponding heat transfer coefficient are measured once the simulation has reached steady state.

Fig.3. Impinging oil jet on a flat target at the end of the simulation. The normalized jet velocity is uf/d=2500 s-1 and the temperature difference is ΔT = 60°C.

After executing the velocity and inlet temperature sweep, the results are collected and compared with the experimental data as shown in Figure 4. SPH compared favorably with the experimental results from Bennion and Gilberto [1] and the empirical models from Ma [6], Leland [5], and Metzger [7].

Fig. 4. Average Nusselt for various inlet velocities and temperatures for a flat target

Switching to a winding surface, the jet at low and high velocity is rendered in Figures 5 and 6 respectively. Like in the experiment [1], the oil film is deflected off the surface at high velocity.

Fig. 5. Impinging oil jet on a surface with 26AWG winding. The normalized jet velocity is uf/d=2500 s-1 and the temperature difference is ΔT = 60°C. The oil is not deflected.

Fig. 6. Impinging oil jet on a surface with 26AWG winding. The normalized jet velocity is uf/d=5000 s-1 and the temperature difference is ΔT = 60°C. The oil is deflected.

A velocity and temperature sweep are again performed and compared with the experimental data in Figure 7.

Fig. 7. Average Nusselt number for various inlet velocities and temperatures for a 26AWG surface

Download

You can download the full test case below:

References

[1] K. Bennion and G. Moreno. Convective Heat Transfer Coefficients of Automatic Transmission Fluid Jets with Implications for Electric Machine Thermal Management. In International Electronic Packaging Technical Conference and Exhibition, volume 56901, page V003T04A010. American Society of Mechanical Engineers, 2015.

[2] Fifty2 Technology, PreonLab, https://www.fifty2.eu/preonlab/

[3] Ford Motor Company, Product Data Sheet Mercon LV, https://www.motorcraft.com/content/dam/ford-motorcraft/en_us/motorcraft_global/products/lubricants/Product-Data-Sheet-MERCON-V.pdf

[4] S. Kemp, J. Linden. Physical and Chemical Properties of a Typical Automatic Transmission Fluid. No. 902148. SAE Technical paper, 1990.

[5] J.E Leland and M.R. Pais. Free Jet Impingement Heat Transfer of a High Prandtl Number Fluid Under Conditions of Highly Varying Properties. Journal of Heat Transfer, 121(3):592–597, 08 1999.

[6] C.F. Ma, Q. Zheng, and S.Y. Ko. Local Heat Transfer and Recovery Factor with Impinging Free-Surface Circular Jets of Transformer Oil. International Journal of Heat and Mass Transfer, 40(18):4295–4308, 1997.

[7] D.E. Metzger, K.N. Cummings, and W.A. Ruby. Effects of Prandtl Number on Heat Transfer Characteristics of Impinging Liquid Jets. In International Heat Transfer Conference Digital Library, 1974.