Fall 2012 ME 395 - GSI Josh Lacey

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 Suggestions for lab 7 reports

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GSI Overlord
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PostSubject: Suggestions for lab 7 reports   Sun Nov 18, 2012 2:02 am

I think a number of students have been quite anxious about the analysis for this lab so I want to try and help out a bit, especially for those of you with limited or no fluids background.

The whole idea (and power) behind the dimensional analysis is that you can conduct one set of experiments to find a 'characteristic response' of a smaller model and use that analysis to scale the results up for a much larger system. In this particular case, you are finding the characteristic response of a generic turbomachine using the small compressor setup from the lab in order to assess the performance of a larger compressor that was a part of the AC carts that will run a different fluid (water). In simple terms, you are taking the measured quantities from the lab (which have dimensions), performing the non-dimensional model analysis of a generic turbomachine (which has no dimensions), and then backing out calculated values for the performance of the scaled up AC compressor (which now gets you back to dimensional quantities).

One of the major objectives in the report is to prove that the non-dimensional efficiency, a function of L/D, flow coefficient, Re and Fr, can be boiled down to a function of only the non-dimensional flow coefficient. Your method to get to this point could potentially be on two different fronts; first, you can actually determine graphically how the efficiency depends on flow coefficient, Reynolds number and Froude number. Conceptually, and I realize this is hard part for people without adequate fluids background, you can reason if we are even in a flow regime where Re and Fr are important to consider. The first thing I will say to that point is to really study the empirical data to get a sense of how Re and Fr change with volumetric flow for a given blower speed. Remember that Re is a ratio of inertial to viscous (frictional) forces. In our system, the flow is assumed to be well-developed steady-state steady flow with a blower always run at relatively high speed...do you think the viscous forces are important? Are we always in the same flow regime based on Re, which would decrease its relative importance? If you are not sure look at the magnitude of the Reynolds number...

As for the Froude number, there a couple ways to conceptualize this number...the number represents the ratio of fluid flow to the effect of gravitational waves, or how a flow reacts when faced with an obstacle (think of water flowing around a large rock in the middle of a river). Again, based on the differences in height in our system or obstacles in the path of the flow, would this quantity be important? Fr<1, Fr=1 and Fr>1 all represent different flow regimes, and it's possible that every operating point you took was in one of those regimes, which would decrease the relative importance of Fr for the scaling analysis...

The first term, L/D can be neglected because you are assuming the two compressors you are comparing (the one in the lab and the AC compressor) are geometrically self-similar, thus this ratio won't change.

Hopefully this gives everyone at least a start, as well as a good chunk of the conceptual fluids theory you'll want to consider when writing your report.
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PostSubject: Re: Suggestions for lab 7 reports   Sun Nov 18, 2012 1:32 pm

You'll also need to calculate the head coefficient (ψ) and power coefficient (τ) that are in the lab handout to address some of the tasks in the scenario letter, however you probably won't need to repeat all the same conceptual analysis for each one of those metrics. You could just show these on your figure against flow coefficient if you want to, or put them in different figures (just to show how the curves collapse) or maybe even just throw all that data in a table. There aren't too many 'critical' figures in this lab so I think there will be room especially if you put figures side by side. The good news is once you've calculated the efficiency, you've already got all the pieces to do the calculations of the head and power coefficients, so this really a trivial amount of additional work. If you are confused about this, see figure 1b in the lab handout...this is what I'm talking about.
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