February 2024
Venturi Flowmeter Design, Build, and Test
Background
Generally flowmeters are an important instrument for propulsion testing. For rocket engines, the rate of consumption of propellant needs to be known in order to quantify performance metrics like specific impulse. Flowmeters are also important tools for characterizing the behavior of individual components and fluid systems. Evaluating the power output of pumps, the heat load of regen channels, and the hydraulic resistance of valves, injectors, and other components necessitates flow measurement. For my purposes, flow measurement is needed in order generate the characteristic curve of my centrifugal pump, helping me understand the relationship between motor speed, duty cycle and the pressure rise across the pump for different flow rates. Additionally I will need data on the resistance of my LOX runline and pintle. The data gathered may be used to iterate hardware and will help me choose pump speed/power setpoints for an eventual hotfire test.
There are lots of viable ways to measure liquid flow rates, each with their pros and cons. Without going too deep into the trades, I chose a venturi with pressure transducers for reasons listed below.
A characterized orifice with the pressure drop high enough to get low uncertainty would incur too much loss and waste pump power
Off the shelf cryo turbine flowmeters are prohibitively expensive and I cant realistically make one
Measuring tank level would either be cumbersome or impossible since I intend to run off a rented dewar
I have some prior experience designing/sizing, and manufacturing venturis from scratch and I can get high DP for accurate measurement without much permanent loss.
Design
For more info on generic venturi design feel free to read my other article. The flow rate through a venturi is found by measuring the differential pressure between the inlet and throat. The differential pressure for a given flow rate increases as contraction ratio (throat dia over inlet dia) decreases. The pressure measurement is typically done with a single differential pressure transducer. I am using 2 individual pressure transducers though because I could not easily find an affordable differential pressure transducer. This doubles the uncertainty of my differential pressure measurement compared to if I was using 1 transducer. The error in pressure measurement propagates to the calculation for flow rate. The theoretical uncertainty in flow rate for a given uncertainty in pressure decreases as the differential pressure increases so my contraction ratio parameter was driven by how much flow rate error I was willing to tolerate. I was able to write a script that allowed me to plot the pressure vs flow curve for given inlet and throat diameters while also indicating uncertainty with errorbars. This tool allowed me to select the throat diameter while making sure the flow rate uncertainty wouldn’t be too crazy.
One reason I chose the venturi was that it could be machined relatively easily yet my machining skills and means are pretty limited so I had to compromise a little. I chose brass as the material because it’s oxygen compatible but much easier to machine compared to stainless steel. To make the converging and diverging sections I found a $5 tapered reamer on amazon with about a 3 deg half-angle which was acceptable for typical venturi diverging angles. Normally it is not necessary for the converging section to have such a shallow angle yet for simplicity I chose to make the design symmetrical so I could use the same tapered reamer for both sides. Also I chose to install the inlet PT on a tee fitting upstream of the venturi because the diameter of the stock I recieved was simply too small to tap even the smallest diameter (1/16”) NPT port. I had ordered 1” stock and was sent 3/4” stock for some reason. This diameter debacle also affected the throat port since normally the codes call for a higher L/D pressure tap connecting the port to the throat but there was simply not room.
As I was fleshing out the design and prior to beginning machining I quickly ran 2D axisymmetric CFD on the geometry to see if it agreed with my calculations and to estimate the pressure recovery. The CFD converged and the results agreed with my code. The pressure recovery looked good but in the velocity contour there was clearly some flow separation in the diverging section. I refined the mesh a little along the wall but it did not really change the result or improve the separation. Since I am not very experienced with CFD and the pressure recovery still looked good I decided to proceed with manufacturing.
Testing and Calibration
After finishing manufacturing the venturi I installed the inlet and throat PTs along with a PT measuring the outlet pressure to get a sense of the overall loss. I also installed a cheapo plastic turbine flowmeter with an LCD screen in series with the venturi. Downstream of the venturi I installed a ball valve which fed into a bucket. I aimed to calibrate the venturi against both the totalized bucket mass and the integrated flow of the turbine. I used a bathroom scale to measure the weight of the bucket, making sure to subtract the weight of the bucket itself. Since the resolution of the scale was 0.2 lbs I made sure to flow for as long as possible so the error would be a small percentage of the overall mass. The setup was connected to a hose bib on my house where the no-flow pressure was about 70psia. I tested 3 different flow rates during separate tests, 0.065, 0.149, and 0.208 Kg/s by opening the ball valve different amounts. Data aquisition was run through the normal jbox and software that I use for the main test stand. The restriction of the hose bib ultimately prevented me from testing higher flow rates. The bucket and plastic turbine flowmeter actually agreed very very closely, not more than 0.003 Kg/s apart remarkably. My initial guess for the venturi Cd (inlet to throat) was 0.95. When analyzing the data, the empirical Cd of the venturi was calculated by using the average flow rate between the bucket and turbine and the PTs installed on the venturi. At the low low flow rate of 0.065 Kg/s I calculated the Cd to be around 0.90. At flow rates of 0.149 and 0.208 Kg/s the Cd was nearly equal to 1.00. Pressure recovery was shown to be worse than predicted by CFD. I am curious to see if the pressure recovery improves when I eventually test at higher flow rates due to having a higher Reynolds number. Perhaps the higher Reynolds number will help the flow stay attached in the diverging section. Maybe the higher viscosity of water is also contributing to the discrepancy since the CFD was done with liquid oxygen. The real-life manufactured part is also objectively worse quality than the idealized CFD mesh so defects and surface roughness could play a roll in the worse pressure recovery. Also I just realized I installed the outlet PT on the other side of a 90deg elbow from the actual venturi outlet so that probably skews it slightly lower too.
Overall the Cd variation I calculated was still actually within the error I had originally predicted for these low flow rates. My estimate of my PT uncertainty may have been too conservative. The flow measurement aspect of this venturi pretty much exceeded what I had planned for which is great. The diverging section is only recovering about half the dynamic pressure from the throat though while the CFD precited like 75% but I think I can tolerate that. I am super curious to see how this changes with higher flow rates. The big question is if it is better than an orifice and I think the answer is definitely yes because the Cd evaluated using the inlet and outlet pressures is around 1.4 while it would be 0.6-0.7 for an orifice of the same contraction ratio.
