ewillia13
Mechanical
- May 14, 2010
- 6
I was recently given the task of calculating the required drain size needed to drain an annulus fed by oil being ejected from a hydrodynamic bearing. This would be a gravity drain that is self venting. It is required that there will not be a fluid level build up in the annulus.
Details: An oil fed bearing is housed in a gear housing, supporting a rotating shaft. To one side of the bearing is the main gear housing enclosure, on the other side is an annulus of diameter 'X1' and width 'W'. At the bottom of this annulus is a vertical drain w/ a rectangular cross section of 'X2' and similar 'W'. Oil of flow rate 'Q' is expelled/sprayed from the bearing all along the perimeter of the shaft. All of the flow is collected in the annulus and drains down to the drain orifice, and through a length ‘L’ of the drain until it drains into the main gear housing. Assume that the rectangular drain intersects the annulus with a sharp edge (for entrance effects). The flow ‘Q’ and properties of the oil are known as well as the surface roughness of the annulus and drain. Assume that the gear case housing and the annulus are at atm. pressure.
I have looked over many examples of tank drainage but all of these assume the area of the tank is much larger than the drain and the relative velocity of the fluid in the tank is zero compared to the velocity at the exit, which is not the case here. I have also considered the case where fluid flows into an initially empty tank, builds up a certain fluid level until the pressure hear is large enough to force the flow out of the drain to equal the in-flow. But in this case the drain is not fully engulfed with fluid. I would guess the fluid exiting the bearing and flowing down the drain are turbulent (the shaft is spinning extremely fast with a large amount of flow) so that should have an effect. The flow through the length of the drain ‘L’ is not fully engulfing the drain so would you even consider the effects of that length?
I believe there has to be some relation between the size of the annulus and the drain but I’m 100% sure.
I’ve been kicking around ideas with formulas and theories such as Manning, Chezy, Froude number, Bernoulli , open channel flow, specific energy, wall shear, and gradually varied flow but either can’t develop the equations or not confident in the validity.
Please take a look at the diagrams I’ve attached and see if you can make any sense of this problem. I’m hoping there is a way to simplify the equations.
Details: An oil fed bearing is housed in a gear housing, supporting a rotating shaft. To one side of the bearing is the main gear housing enclosure, on the other side is an annulus of diameter 'X1' and width 'W'. At the bottom of this annulus is a vertical drain w/ a rectangular cross section of 'X2' and similar 'W'. Oil of flow rate 'Q' is expelled/sprayed from the bearing all along the perimeter of the shaft. All of the flow is collected in the annulus and drains down to the drain orifice, and through a length ‘L’ of the drain until it drains into the main gear housing. Assume that the rectangular drain intersects the annulus with a sharp edge (for entrance effects). The flow ‘Q’ and properties of the oil are known as well as the surface roughness of the annulus and drain. Assume that the gear case housing and the annulus are at atm. pressure.
I have looked over many examples of tank drainage but all of these assume the area of the tank is much larger than the drain and the relative velocity of the fluid in the tank is zero compared to the velocity at the exit, which is not the case here. I have also considered the case where fluid flows into an initially empty tank, builds up a certain fluid level until the pressure hear is large enough to force the flow out of the drain to equal the in-flow. But in this case the drain is not fully engulfed with fluid. I would guess the fluid exiting the bearing and flowing down the drain are turbulent (the shaft is spinning extremely fast with a large amount of flow) so that should have an effect. The flow through the length of the drain ‘L’ is not fully engulfing the drain so would you even consider the effects of that length?
I believe there has to be some relation between the size of the annulus and the drain but I’m 100% sure.
I’ve been kicking around ideas with formulas and theories such as Manning, Chezy, Froude number, Bernoulli , open channel flow, specific energy, wall shear, and gradually varied flow but either can’t develop the equations or not confident in the validity.
Please take a look at the diagrams I’ve attached and see if you can make any sense of this problem. I’m hoping there is a way to simplify the equations.
