Pulsatile waveform of flow rate

amsys · March 2, 2020, 08:23

Hi All,

I am running a transient simulation of flow through a pipe where there is an inlet and two outlets. I am using a fourier series to define the shape of the pulsatile flow.

Currently I am defining my flow using velocity by implementing the following expressions:

v0 = 0.2 [m/s]

vinlet = v0*(a0 +a1*cos(-2*pi*1*f0*t) +b1*sin(-2*pi*1*f0*t) +a2*cos(-2*pi*2*f0*t) +b2*sin(-2*pi*2*f0*t) +a3*cos(-2*pi*3*f0*t) +b3*sin(-2*pi*3*f0*t) +a4*cos(-2*pi*4*f0*t) +b4*sin(-2*pi*4*f0*t) +a5*cos(-2*pi*5*f0*t) +b5*sin(-2*pi*5*f0*t) +a6*cos(-2*pi*6*f0*t) +b6*sin(-2*pi*6*f0*t) +a7*cos(-2*pi*7*f0*t) +b7*sin(-2*pi*7*f0*t) +a8*cos(-2*pi*8*f0*t) +b8*sin(-2*pi*8*f0*t) +a9*cos(-2*pi*9*f0*t) +b9*sin(-2*pi*9*f0*t) +a10*cos(-2*pi*10*f0*t) +b10*sin(-2*pi*10*f0*t) +a11*cos(-2*pi*11*f0*t) +b11*sin(-2*pi*11*f0*t) +a12*cos(-2*pi*12*f0*t) +b12*sin(-2*pi*12*f0*t) +a13*cos(-2*pi*13*f0*t) +b13*sin(-2*pi*13*f0*t) +a14*cos(-2*pi*14*f0*t) +b14*sin(-2*pi*14*f0*t) +a15*cos(-2*pi*15*f0*t) +b15*sin(-2*pi*15*f0*t) +a16*cos(-2*pi*16*f0*t) +b16*sin(-2*pi*16*f0*t) +a17*cos(-2*pi*17*f0*t) +b17*sin(-2*pi*17*f0*t) +a18*cos(-2*pi*18*f0*t) +b18*sin(-2*pi*18*f0*t) +a19*cos(-2*pi*19*f0*t) +b19*sin(-2*pi*19*f0*t) +a20*cos(-2*pi*20*f0*t) +b20*cos(-2*pi*20*f0*t))

And then setting Normal Speed at the inlet boundary and using vinlet as the input.

I now want to define the pulsatile flow by setting a fixed flow rate of 1.0 [ml/s] at the inlet.

Any suggestions on how I can modify the above expressions to do this?

Gert-Jan · March 2, 2020, 11:06

How can it be pulsating if you have a fixed flow rate? This is only possible if you have a gas with a pulsating density. Is this what you are looking for?

Unfortunatley, you can not vary the density on the inlet directly. You can vary pressure on the inlet, but then the inlet massflow will also change. This is simply the outcome of the simulation.

However, if you set a massflow on the outlet then the software will try to keep everything in balance as fast as possible, i.e. speed of sound. So the massflow on the inlet will lag a bit behind on your outlet massflow. The way it will keep up depends on the length and size of your volume. If this is large, then this will damp out the pressure fluctuation.

Not sure if this is a valid and stable combination of boundary conditions. I would give it a try. I think at least you need small time steps in your transient simulation.......

March 2, 2020, 08:23	Pulsatile waveform of flow rate	#1
amsys Member HS Join Date: Sep 2015 Posts: 30 Rep Power: 11	Hi All, I am running a transient simulation of flow through a pipe where there is an inlet and two outlets. I am using a fourier series to define the shape of the pulsatile flow. Currently I am defining my flow using velocity by implementing the following expressions: v0 = 0.2 [m/s] vinlet = v0(a0 +a1cos(-2pi1f0t) +b1sin(-2pi1f0t) +a2cos(-2pi2f0t) +b2sin(-2pi2f0t) +a3cos(-2pi3f0t) +b3sin(-2pi3f0t) +a4cos(-2pi4f0t) +b4sin(-2pi4f0t) +a5cos(-2pi5f0t) +b5sin(-2pi5f0t) +a6cos(-2pi6f0t) +b6sin(-2pi6f0t) +a7cos(-2pi7f0t) +b7sin(-2pi7f0t) +a8cos(-2pi8f0t) +b8sin(-2pi8f0t) +a9cos(-2pi9f0t) +b9sin(-2pi9f0t) +a10cos(-2pi10f0t) +b10sin(-2pi10f0t) +a11cos(-2pi11f0t) +b11sin(-2pi11f0t) +a12cos(-2pi12f0t) +b12sin(-2pi12f0t) +a13cos(-2pi13f0t) +b13sin(-2pi13f0t) +a14cos(-2pi14f0t) +b14sin(-2pi14f0t) +a15cos(-2pi15f0t) +b15sin(-2pi15f0t) +a16cos(-2pi16f0t) +b16sin(-2pi16f0t) +a17cos(-2pi17f0t) +b17sin(-2pi17f0t) +a18cos(-2pi18f0t) +b18sin(-2pi18f0t) +a19cos(-2pi19f0t) +b19sin(-2pi19f0t) +a20cos(-2pi20f0t) +b20cos(-2pi20f0*t)) And then setting Normal Speed at the inlet boundary and using vinlet as the input. I now want to define the pulsatile flow by setting a fixed flow rate of 1.0 [ml/s] at the inlet. Any suggestions on how I can modify the above expressions to do this?

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March 2, 2020, 11:06		#2
Gert-Jan Senior Member Gert-Jan Join Date: Oct 2012 Location: Europe Posts: 1,928 Rep Power: 28	How can it be pulsating if you have a fixed flow rate? This is only possible if you have a gas with a pulsating density. Is this what you are looking for? Unfortunatley, you can not vary the density on the inlet directly. You can vary pressure on the inlet, but then the inlet massflow will also change. This is simply the outcome of the simulation. However, if you set a massflow on the outlet then the software will try to keep everything in balance as fast as possible, i.e. speed of sound. So the massflow on the inlet will lag a bit behind on your outlet massflow. The way it will keep up depends on the length and size of your volume. If this is large, then this will damp out the pressure fluctuation. Not sure if this is a valid and stable combination of boundary conditions. I would give it a try. I think at least you need small time steps in your transient simulation.......