Mailing List flyrotary@lancaironline.net Message #18382
From: Ernest Christley <echristl@cisco.com>
Subject: Bill Schertz's cooling analysis
Date: Fri, 04 Mar 2005 17:58:06 -0500
To: Rotary motors in aircraft <flyrotary@lancaironline.net>
I've been working through Bill Schertz's example analysis that he did of Todd's system, trying to divine an answer to the question "How much flow is enough?"

Let's simplify everything and just arbitrarily look at 200Hp.  I've followed Bill's example and assumed a 100F day, and a max temp of 180F for the coolant.

The first step is getting a dT for the water going through the engine at a specified flow rate. 20GPM will produce a 37F dT and 30GPM move it down to 27F dT.  From that point on, the curve starts heading to the stratosphere, with ridiculous amounts of flow required to produce any worthwhile reduction in dT.  Going up to 40GPM only reduces the dT to 20F.  You have to boost the flow another 15GPM to 55GPM in order to get another 5F dT.

But lowering the dT gives us more headroom to heat the air.  At 55GPM, the water leaving the radiator is still 165F.  That allows us to heat the air from 100F all the way up to 165F.  Stepping to the second graph, we see that it doesn't continue up to a 65F dT, but the graph has bottomed out, so I'll extrapolate and say that the airflow required is 5000CFM.

If we're only flowing 30GPM, with it's dT of 27F for the water, then we can only heat the air to 153F.  The second chart says that we'll need about 6000CFM.  For the 20GPM and 37F dT, we'll need 8000CFM since there is only 43F of headroom.

For a 50in^2 intake, the 8000CFM results in a 262MPH intake velocity for the air.  30GPM/6000CFM will result in an intake velocity of about 196MPH.  At 55GPM, the air only has to move at 164MPH.

200Hp will push a typical RV size plane at just over 200MPH (using Tracy's performance at Sun'n'Fun as my only point of reference).  From these numbers, however contrived they may be, I would say that somewhere around 30GPM is sufficient unless you're building a drag queen.

Lowering the OAT, or increasing the coolant temp will change the numbers.  An engine exit temp of only 190F would mean that the 20GPM's coolant dT of 37F will tranlate to a air dT that matches the 30GPM at 180.  That is, if you can accept coolant temps of 190F, then you only need a 20GPM pump for sustained max power cruise.  With a 30GPM pump, you could maintain a max power climbout at 165MPH.  However, we're playing on the bottom part of a log curve.  Increasing the dT of the air is having less and less of an effect on the outcome.
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