# Extrapolating compressor curves for varying pump speeds

I'm currently working on modeling a vacuum system in which a pump is present. the pump is driven at a varying speed $$\omega$$. The manufacturer has only given the characteristic curve at a single speed $$\omega_{ref}$$, which is well-approximated by a 3rd-order polynomial in the mass flow, that is:

$$\Delta p_{\omega=\omega_{ref}}(\dot{m}) = c_3\dot{m}^3 + c_2\dot{m}^2+c_1\dot{m}+c_0.$$

My model however requires this characteristic at arbitrary blower speeds. My current solution is to use the pump affinity laws, i.e.

$$\Delta p(\dot{m}, \omega) = \left(\frac{\omega}{\omega_{ref}}\right)^2 \Delta p_{\omega=\omega_{ref}}(\dot{m}),$$

however this leaves the curve rather "squished", almost like a straight line. Does anyone know of a different way of scaling the characteristic for different speeds?

I also have access to an experimental setup. Here I can impose the pump speed $$\omega$$ and measure back the pressure difference $$\Delta p$$, though the mass flow cannot be measured.

• for low vacuum stuff, you can infer mdot from the dp/dt rate of a big volume. remember to adjust for temperature. Sep 30, 2021 at 12:25