Pressure loss Velocity coupling
 

Hey Guys,

again its me, again there is a problem.

Imagine the following Situation:

There is inlet Pipe of Diameter D,
after 10*D the pipe is interupted with an thin orifice of Diameter d.
(no standard orifice, chamfer at the inlet side)
After the orifice, there is a outlet pipe with length 10*D.


Settings:

Inlet = total pressure (4bar) , Total Temp. 333 K
Outlet = prescribed massflow

Medium:: CH4RK (Methan described with Redlich Kwong) , viskosity with implemented kinetic theory model
turbulence: SST
Energie: Total Pressure
Steady State Analysis
Conergence: no problems

What i want to know is the pressure loss coeficient of the orifice, due to the orifice Diameter d.


What i did:

1. I set up diferent Meshes with different Orifice Diameters

2. I set up a prescribed massflow and pulled it through the different orifice arrangments (inlet Total Pressure always at 4bar)

3. i ended up with different presure losses (dependent on orifice Diameter).

4. I have build a pressure loss koefficient zeta, for the different orifice Diameters with the Inlet conditions.
zeta = 2*(massFlowave(Total Pressure)@Inlet - massFlowave(Total Pressure)@Outlet) /
(massFlowave(Density)@Inlet * massFlowave(Velocity)@Inlet)

5. I changed the massflow to bigger and smaller values

6. I changed the inlet pressure and massflow to find similiar Flow Conditions (RE)


What i expect:

When i look at pressure loss coefficients in the literature, there are always more or less constant, no matter if RE risis by 5000 or not.
Therefore, the loss coefficient is just a function of the Geometry and it is rising with smaller orifice Diameters.

what i see:

smaller Orifice diameter leads to larger pressure loss coeficients (thats OK)
for the same orifice size, the pressure loss coeficient is rising with the massflow , therefore its rising with the Inlet velocity since the
inlet density is equal for all massflows.

I thought i can describe this raising pressure loss coeficient due to rising RE-Numbers at Inlet.
RE = massFlowave(Velocity)@Inlet * D /massFlowave(Viskosity/Density)@Inlet

It works fine for the the first moment.

BUT .....

Then I changed the Inlet pressure (Therefore Density, too) and set up the massflow in a way, that i got the same RE number as in the case before.

just for better understanding a list, for a fix orifice diameter:

pin = 4bar
RE = 50 000 , 100 000, 180 000
zeta= 23 , 25, 29,

pin = 2bar
RE = 50 000
zeta= 25

Therefore its not fitting with the Inlet RE.
I tried to find a way to describe the changing pressure loss.
The only thing what i found, was the Inlet Velocity (massFlowave(Velocity)@Inlet)


pin = 4bar
v = 13 m/s , 25,67 , 45,23
zeta= 23 , 25, 29,

pin = 2bar
v = 25,34 25,77 26,44
zeta= 24,89, 25,23 26,58


Here you see its fitting... raising inlet velocity, leads to raising pressure loss coeficient, regardless of the pressure level.

But somehow i have a bad feeling about the result....
The pressure loss coefficient as a function of orifice diameter (thats OK) but flow velocity ?


For my understanding i should get it as function of orifice diameter and RE , regardless of flow velocity.

What do you think?

thx alot

This is a very specialised case and there is no way I can suggest what the problem could be. All I can suggest is where I would look to see if I could work it out for myself.

Is RK an appropriate constitutive model for this case?

It sounds like some basic benchmarking work is called for here. I would get some simple flows using CH4 where you have high quality experimental results to compare to. You may be able to figure out if you model is missing some important physics. For instance, can you get a boundary layer over a flat plate or along a straight pipe right? Or over a bluff body?