Orifice DP radial into high velocity stream

[dbachovchin]

I have a very high velocity gas stream inside a pipe. The pipe has several small holes in it, with a higher pressure gas on the outside. I need to calculate the pressure drop into the pipe. I know the equations for contaction and expansion loss, but how do I assess the loss due to direction change of the inflowing fluid? I thought about using the Crane 410 mitered bend, but I cannot accurately say what f-sub-t should be. Any thoughts?

 

[rbcoulter]

f sub t is the friction factor for complete turbulence, which looks like your case. Determine the relative roughness of the pipe and read it off the table on page A-23, "Relative Roughness of Pipe Materials and Friction Factors For Complete Turbulence".

Don't understand the part about the holes and the high pressure gas on the outside. Could you elaborate?

 

[dbachovchin]

I'm looking for the pressure drop of the gas flowing into the pipefrom the outside via the small drilled holes.

 

[fvincent]

The radial flow through each hole will undergo a pressure drop equal to a coefficient (approx = 1.0) times the dynamic pressure associated to the velocity of the flow (density * velocity ^2 / 2).

The main flow inside the main pipe will be in charge of accelerating the incoming radial flow. This is not properly a pressure drop. It is more adequate to consider it as a momentum transference from radial direction to axial direction. The radial flow cannot accelerate itself to the axial direction (in fact, if there were no flow through the inner pipe and the ends were open, the injected flow would split in two semi-flows with the same moduli of momentum)

Therefore I would consider to calculate the extra pressure "consumption" of the main flow as:

Given:
inlet conditions:
Pressure = p1
Section area = S1
velocity = v1
specific mass = d1

outlet conditions:
Pressure = p2
Section area = S2 = S1 (straight pipe)
velocity = v2
specific mass = d2

So:
p1 - p2 = d2*v2^2 - d1*v1^2 (momentum balance for constant area)

density d2 can be calculated by mixture of radial and inlet mass flows at their respective temperatures and heat capacities

v2 can be obtained after d2, given section area and total mass flow

That is what I would do, but please check it.

regards





fvincent
Figener S/A

 

[poetix99]

I think that "fvincent" is onto something in referring to the axial acceleration of the radial inflow.

The radial component of the inflow fluid acceleration can be approximated by (V-radial*V-axial)/(delta-radius), where "delta-radius" is the approximate radial distance over which the flow is turned to the axial direction - the angular acceleration of the fluid.

This is, in a sense, the dynamic "head" associated with turning the radial inflow. I suggest that you reduce the static pressure drop used to calculate the radial inflow (as, for example, in an orifice equation) with the above dynamic head. Estimating the turning radius is somewhat uncertain; you obviously have some physical limits established by the pipe.

As the net axial mass flow is increasing from the radial "intrusion", conservation of (axial) momentum implies that the axial velocity is decreasing. It cannot be that the pressure of the gas is increasing in the direction of flow, so the density is increasing consistent with conservation of momentum.

Interesting problem. I'll think some more about what I've said; maybe it won't make any sense in the morning.