Hello
I'm trying to make a simulink model for Venturi tube, for the purpose of measuring volumetric airflow by making a pressure difference with a fan.
The paper "Model-based analysis and simulation of airflow control systems of ventilation units in building environments" written by "Wu, Zhuang; Melnik, Roderick V.N.; Borup, Finn" shows some relations about this topic, and I have collected these relations (from the original attached PDF paper) in the attached image (equations 1 to 9).
Question1: when we combine equation (9) with (8), we will get an equation with no relation between ΔPfan,rise (Pressure difference made by the fan) and fan tip speed, in other words, I need an equation that links ΔPfan,rise with fan tip speed (or fan RPM).
Question2: equation (20) shows the the dynamic model for the pressure sensor as follows:
ΔPout =1/τ(ΔPin -ΔPout)dt
is there any simple explanation?
Thanks in advance.
Dear Issam,
Regarding your question, first of all, v_tip represent the speed of fan blade tip point, so, it is a function of N(RPM). v_tip=Pi*d_tip*(N/60).
On the other hand, v_avg represents the velocity of air [m/s].
" I need an equation that links ΔPfan,rise with fan tip speed (or fan RPM)."
It is already mentioned!
ΔP_fan,rise=function of v_tip (RPM) & v_avg.
One more thing would like to withdraw your attention to, v_avg in this work would be obtained by 4, 18 MP-AF
"Airflow measurement probe (transmits input signals
to the controller for controlling the speed of the fans
to obtain the preset airflow rate)"
http://www.tasonline.co.za/toolbox/pump/powtip.htm
v_tip is measured in [m/s]
v_tip=π*d_tip*N/60 (4)
ΔP_fan,rise=ΔP_static+(0.5*ρ* v_2^2) (7)
ΔP_fan,rise=(0.5*ρ* v_tip^2)*ψ+(0.5*ρ* v_avg^2)
ΔP_fan,rise=(0.5*ρ* [π*d_tip*N/60]^2)*ψ+(0.5*ρ* [v'/A_fan]^2) (8)
v' is the volumetric flow
ψ=ΔP_static/(0.5*ρ* v_tip^2) (9)
substituting (9) in (8):
ΔP_fan,rise=(0.5*ρ* v_tip^2)*(ΔP_static/(0.5*ρ* v_tip^2))+(0.5*ρ* [v'/A_fan]^2)
------------
ΔP_fan,rise=ΔP_static+(0.5*ρ* [v'/A_fan]^2) (???)
here is the part which I can't understand.
" I need an equation that links ΔP_fan,rise with fan tip speed (or fan RPM)."
used fan is GL12B4 Comair Rotron
Max. Air Flow 150.0 CFM (4.24m³/min)
Static Pressure 0.486 in H2O (121.1 Pa)
Nominal Speed: 3200 RPM
------------
Thank you very much
Attachments of two datasheets for the used fan.
Does the curve in datasheet2.png give the answer?
Dear,
It is mentioned static pressure, and you need units in IS. I suppose that you are going to use this fan!
All the best.
Well if you intent to use simple solution then use actuator disc theory ..lead to very simple approximation of flow rate ,pressure difference and blade speed. Well another approiach is to use the mean diameter values. If however you need better and more accurate answer then you have draw velocity triangles at blade hub and blade tip . athe work your way through to find the effect on pressure difference.
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