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I obtain high flow rate by using the Gradual area contraction block . (Simscape Fluids)

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I'm trying to model a simple hydraulic system with Simscape Fluids, as it can be seen below. However, I'm obtaining very high flow rates (145L/min), compared to some calculations I used to check the results. By using Bernoulli equation, if I calculate the velocity of the flow at the small area in the gradual area change (assuming no height change and initial velocity as 0m/s) and then, apply continuity equation to obtain the volumetric flow rate, the result is 28 L/min. This assumes that after the gradual area change, the fluid is ejected to the surroundings.
Any help/advice of why this is occuring? What is causing this?
nozzle tes.png
oil.png
nozzle.png
Thank you in Advance!!

Answers (1)

Luke Halberstadt
Luke Halberstadt on 7 Jan 2023
Edited: Luke Halberstadt on 7 Jan 2023
I agree that what you are seeing in this model does not make physical sense. With an input pressure of 30 MPa, the Bernoulli equation says that the maximum possible velocity with the pressure dropping down to atmospheric is about 266 m/s. With the friction losses that Simscape is accounting for, the actual maximum would be lower. At 266 m/s through a 1.5 mm pipe, only about 28 Lpm of flow is possible through the gradual area change.
The reason the model reports a flow rate of 144.7 Lpm is that the Gradual Area Change block only accounts for viscous friction losses caused by the change in flow area. It does not consider fluid inertia. You can see this in the assumptions and limitations section of the block's Documentation page.
Well, what can we do about this to get more realistic results? The Hydraulics (Isothermal) domain is intended for fluid power applications where the dynamic pressure is usually unimportant relative to the static pressure. Think of a hydrostatic transmission or the cylinders that actuate an excavator. None of the blocks within the Hydraulics (Isothermal) domain directly capture the flow rate limiting effect based on dynamic pressure.
However, it turns out that the Fixed Orifice block uses equations based on the Bernoulli principle to determine the friction losses (and thus flow rate) through a small opening. When I set the discharge coefficient to 1 and the orifice area to , I get 28.22 Lpm as the measured flow rate in Simscape. This matches our expectation. The discharge coefficient of 1 basically means that the total pressure loss due to friction is equal to the Bernoulli drop in static pressure at the throat.
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Luke Halberstadt
Luke Halberstadt on 7 Jan 2023
You might find an accurate way to capture the flow rate of an output oil stream using a combination of a Gradual Area Change for the geometric pressure drop and then a Fixed Orifice block after that to capture additional pressure drop as a result of high speed flow through the narrow exit.

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