Measuring Free-Fall Mass Flow Rate
Posted on April 26, 2022 Instrumentation & Equipment Design
Real-time flow measurement from falling flows, such as from hoppers or crucibles, is challenging.
Load cells and standard electronics can log the net weight. Numerical differentiation gives mass flow, but the approach has hard limits. A system that can log 8000 flow data points continuously at 12-bit precision requires an unrealistic 25-bit weight measurement. Performing the differentiation with analog electronics up front reduces the digitization requirements to 12 bits.
Impulse from impact must also be addressed. Consider dropping a shovel full of wet sand into a process vessel. As the sand impacts, it will briefly generate a force many times its own weight. Differentiating the force will give a wrong answer: a huge but brief positive flow rate, followed by an almost-as-large negative flow rate. A bit of math reveals that the Green’s function required to exactly remove the effect of the impulse is the response function of an RC filter, with a time constant equal to the time it takes for the sand to fall.
The analog front-end sounds straightforward but has a tight error-budget and requires chopper-stabilization to cancel out component drift. That’s what we’re here for.