could widely spaced in-line props reduce cavitation while

[yipster]

all very interesting and ad my findings with bravoIII drives, ok not widely spaced but on planning hulls they perform well
added weight was the first thing seeing the boat a little lower at the stern again so risers had to be installed
driving out of the box was a mixed pleasure, better grip made the boat go twice as fast stationairy
top speed was a little higher and boat tracked notable better. complexity, cost and what i'm reading above makes sence too
never figererd out why i didnt go for 2 single props counter rotating but the old alfa's allready took out much of the wheel effect
i have had single props tho that diverted so much energy sideway's they didnt steer anymore, seen ships with cr props too, hmm
been imagining that plane's bowprop above on a bulbbow but try to think simple wheels on a cat now..

[daiquiri]

Baeckmo,
Incredibly I have only now come upon and read your reply in this thread!
It is an excellent explanation, crystal clear, and has opened my eyes on few things about prop design I didn't know.
Thank you very much for putting so much effort and time into writing this. It was very useful for me.
Cheers!

Originally Posted by baeckmo

To get a grip on this balance, it is useful to go back to basic momentum theory, regarding the propeller disc a "black box" that imparts a velocity increase to the incoming flow. In a free flow (neglecting hull influence) the propulsion efficiency (etaprop) is the product of the jet (or momentum) efficiency (etajet) and the hydromechanical efficiency (etapump)of the pumping mechanism that creates the velocity increase.

For a given thrust and disc area (Ad) we have a thrust coefficient Ct = Thrust/(density/2*Va^2*Ad). From Ct we get etaj = 2/(1+(Ct+1)^0.5).

Since we also have etaj = 2*Va/(Va+Vj); the required jet velocity (Vj) can be calculated for the given design problem. Regardless of what is inside the black box, the jet efficiency and the velocity increase is fixed from fixing thrust and diameter.

Now to the hydromechanical mechanism inside the black box. This is in fact a pump, that creates a pressure increase equal to (Vj^2-Va^2)*(density/2); in N/m2. In 1756, Leonhard Euler published the theory on pressure difference in pumps and turbines, it is still valid....... It states that, for a pump runner with axial inflow, the head increase dH = U2*dCu/g; where H = (pressure/(2*g)); U2 = runner peripheral speed at discharge; dCu = change in peripheral composant of discharge flow.

This implies that no matter what is inside the black box, it has to deliver the same sum of dCu, provided diameter, thrust and rpm are fixed. If we have one heavily loaded propeller or two in tandem (same rotation) is equal, the swirl rate out of the box is the same, giving the same loss (yeah, I will come back to counterrotation later!). Thus for a fixed diameter propulsor, the jet velocity (thereby the jet efficiency) and the rotation of the outlet flow is fixed.

If we have been forced, by any design constraints, to use a restricted diameter, we also have been forced to increase the pressure increase of the runner. This is where the simple tandem configuration actually gives us possibilities to improve the hydromechanical efficiency ("pump efficiency")! With a single impeller ("propeller, runner, screw,.....) the pump efficiency generally drops with increased pressure load. Cavitation has a similar effect.

If we split the power between two tandem impellers, the detrimental effects of cavitation and pressure loading are reduced, i.e. the hydromechanical efficiency is improved. The positive effect of using the front propeller as an inducer, suppressing cavitation on the second stage is so strong, that the tip speed of the "combo" may be increased, or the pressure loading of stage two can be increased while keeping its hydromechanical efficiency high. We havea situation where 1+1>2.

Now to the counterrotating two stage unit. Keeping the dia fixed (=design constraint), the velocity increase for a given thrust is exactly the same as for a single, or tandem unit, and so is the jet efficiency. Again, the difference lies in the pump efficiency. The dCu from the front impeller is normally ~50 to 60 % of the total increase. But in the CR case, the second stage is adding its share of dCu in the opposite direction, leaving only ~0 to 10 % of residual swirl in the discharge. This is where the CR earns its improved pump efficiency.

But in this case, the preswirl coming into the second rotor is detrimental to its cavitation performance, and the pulsating inflow due to the blade-to-blade velocity profile leaving the first stage is giving a varying incidence angle to the second rotor. All in all, this means that the total benefit of the added mechanical complexity is not as high as expected. In fact, a single prop, selected free from diameter constraint may very well have a better overall efficiency. As I said in my first note here, two-stage impellers are best used in special cases; the tandem on a common shaft is sadly overlooked as a means to solve cavitation problems.

[yipster]

my thanks too, i re-read this thread as well with growing understanding, some considerations on a Ducted-Tip Propeller ?
reading up on propulsion theory instead of propellor handbook graphs but most math is beyond me, fascinating nevertheless