CFD Simulation of a Pitot Tube and Manometer
Pitot tubes are critical devices used to determine the airspeed of an aircraft. In aerodynamics it is important to know the speed of an aircraft relative to the surrounding air to alert pilots to stall conditions. Pitot tubes are also used in wind tunnels to determine airspeed, sometimes using a manometer to measure the pressure difference between static pressure and total pressure to determine the dynamic pressure. I thought it would be interesting to see if we could simulate a pitot tube connected to a manometer (two-phase flow, air + water) using Computational Fluid Dynamics (CFD) and to share my findings with you.
Blue is water and red is air
Pitot Tube Design
The total pressure opening has to align perpendicular to the onset flow and the static pressure openings need to be positioned tangential to the onset flow. The openings are connected with a tube partly filled with water which indicates the dynamic pressure by the height difference between the 2 water free-surfaces.
I constructed the pitot tube as a multi-volume flow domain to make it easier to initialize the water region separately from the air. The entire pitot tube was embedded within a larger volume so that the onset flow could be imposed.
Given an onset velocity of 50 m/s we should expect to see a height difference in the manometer of 154 mm, based on rhowater * g * h = 1/2 * rhoair * V2, where rhowater = 998.2 kg/m3, g = 9.81 m/s2, rhoair = 1.205 kg/m3, and V = 50 m/s.
Simulation and Results
Initially I tried running a steady state simulation but I found unsteady behavior for the water free-surfaces and poor convergence. Then I tried a transient (unsteady or time dependent) simulation which produced well defined water free-surfaces that shifted location over time. The average location of the free-surfaces varied with a damped harmonic-like motion. The trend of reducing amplitude with increasing time is evident, but having run the simulation for more than 160,000 iterations nonstop over the course of a week I decided to call it a day.
Averaging the height difference of the water surfaces over the last complete motion cycle gives a height difference of 158 mm. This value is in good agreement (within a 2.8% margin) with the predicted height difference of 154 mm.
In the CFD virtual world there is actually no need to simulate a manometer to determine the dynamic pressure to give the airspeed. Instead you can just insert a probe at the location of interest and extract the airspeed directly. If you wanted to determine the dynamic pressure then you could reassign the total pressure and static pressure openings to be walls, extract average pressures on those surfaces and compute the difference.
The multi-volume pitot tube geometry was created in Caedium Professional. The CFD simulations were performed using the incompressible, steady-state, and transient RANS solvers, with VOF free-surface multiphase, and the k-omega SST turbulence model.