Who needs a lab?

Actually, we do. That's basically what my dining room has evolved into over the past two years - this is my 'dining' table...

This is an experimental setup to pressure-map small orifices. Air is drawn through a HEPACap filter, down a length of tubing and into a mass flowmeter, on through a 'test choke', then through a plenum where the static pressure is measured, then through a precision metering valve to enable fine adjustment, and then finally into the vacuum pump. There is a desk fan that blows air over the pump to stop it heating up so quickly - and a BBQ thermometer system to monitor the pump temperature and sound an alarm when it goes too high. As we have 43 chokes to test, and they are direction-specific, we have 83 pressure-maps to perform - so that's several day's work. The other essential items are therefore noise-cancelling headphones, to drown out the pump - and coffee!

My wife asked, "Why is there a kettlebell on the table?" (of all the questions...!) - the kettlebell simply holds the metering valve steady so that it can be easily and finely adjusted, with one hand ??

When I get stuck on tricky fluidics problems I usually have a chat with James Tibbatts - he kindly assured me when I called him yesterday that I wasn't making mountains out of molehills, as - during the first preliminary test runs - I was finding some very strange behaviour. Whilst the pressure-flow response of a converging nozzle can be reasonably well described by a simple quadratic, this wasn't at all the case for the same nozzle in a diverging configuration:

This is the pressure-map of a ?0.3 mm diameter orifice, 8 mm in length and with an expansion combined angle of 7 degrees. A quadratic regression, forced through zero, clearly doesn't work well. It's worth noting that the R2 value is actually pretty good - 0.979 - probably sufficient to meet the acceptance criteria of most DoE software (the dangers of black boxes!) Anyway, as far as I was concerned it wasn't good enough, and hence resulted in me disturbing James on his relaxing Saturday afternoon. It turns out that the tricky part is that you don't know at what point - either when or where - the flow will detach from the wall inside the nozzle. So as you increase the flowrate, at some point the flow will detach from the wall and effectively begin to choke, or at least throttle the system - i.e. a large increase in pressure will not increase the mass flowrate substantially through the nozzle. This can occur well before turbulence has kicked in, and well before the nozzle is fully choked (sonic flow with a pressure ratio > 1.89:1).

So what now? For our grand plan to map out the design space of small orifices to work, we need an accurate and robust way to mathematically describe the characteristics of the airflow through them. I'm afraid my skills at curve-fitting in Excel were becoming increasingly challenged, and had to resort to using something way more competent - CurveExpert Professional. This software enabled me to explore the virtues of a large number of different regression models, and whilst our intention is certainly to interpolate the dataset we acquire, it is good to know that a small degree of extrapolation could be possible should we need it. So now here is a plot of the same raw pressure-map data, this time with a Weibull model regression applied:

The datum are the raw data and the line is the Weibull fit - a manually calculated R2 value for this is 0.99987 - so much more closely representative of the real data than the simple quadratic was.

The plan is now to pressure map all the orifices / nozzles, and build a comprehensive mathematical model of the design space that is built upon sound empirical data. This in turn will enable us to develop a fully optimised dry powder inhaler engine from the outset.

So lots more work to do, and perhaps one day we might have a real lab...