# Modeling and Simulation of Multiphase Flow between Rotating and Stationary Disks

#### Abstract

The Clutch in an automotive vehicle transfers power from the engine to the wheels with the speed and torque controlled by a gearbox. To accommodate different speeds and loads, different gear ratios are needed, and the clutch disengages and engages every time those ratios are changed. Since heat is generated when disengaged and when suddenly engaging, lubricating oil is pumped throughout the clutch to cool and to reduce friction. When the clutch is disengaged, drag torque is generated. Drag torque is due to the viscous force from the relative motion between the friction (rotating) disk and the separator (stationary) disk. This drag torque can account for up to 10% of the engine's specific fuel consumption. Thus, it is important to understand how design and operating parameters affect drag torque. A number of investigators have studied drag torque by examining two parallel disks with one or both rotating about a common axis and with lubricating oil forced to flow through the gap between the disks by using experimental, computational, and analytical methods. Experimental studies have shown that when air starts to enter the gap between the disks (referred to as aeration), drag torque is greatly reduced because the viscosity of air is much less than the viscosity of oil. Computational studies have been unable to reliably predict experimentally measured drag torque as a function of the disk's rotational speed and the onset of aeration, and the reasons why are unclear. Analytical models developed to predict drag torque and aeration have required inputs from experiments and have invoked assumptions that are questionable. In this research, a reduced-order model was developed that can predict aeration as a function of the disk's rotational speed, the gap between the disks, and the oil's flow rate. This model was developed by recognizing and demonstrating that the extent of aeration (i.e., how far radially inwards the air has penetrated), denote as Rcr, can be expressed as a ratio of the oil's mean radial velocity at Rcr and its mean radial velocity at the inner radius of the clutch, Rin, and that ratio has three regimes. The three regimes corresponds to the three states of aeration: (1) no aeration, (2) onset of aeration until aeration reaches its maximum extent, and (3) maximum aeration is sustained. This research also showed why past CFD analyses were unable to predict aeration reliably. It was found that both adhesion and cohesion in the surface tension must be included when the Weber number << 1. To enable CFD analysis that can predict aeration as a function of rotational speed of the rotating disk, a surface-tension model was developed such that as the rotational speed increases, adhesion increases over cohesion. Thus, as the rotational speed increases, contact angle of the oil-air interface with the stationary disk reduces.

#### Degree

Ph.D.

#### Advisors

Shih, Purdue University.

#### Subject Area

Aerospace engineering

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