Reynolds number scaling limits for Wageningen B-series

[Will Fraser]

For my calculation purposes, I would like to evaluate performance at Rn of 200k-500k.
I realise that at low Rn values there is an increase in minimum section drag and likely a decrease in maximum lift. It is the impact of these on efficiency that I am interested in examining.

In an article "Further computer-analyzed data of the Wageningen B-screw series" by Oosterveld and Van Oossanen, the performance equations are based on a Reynolds number of 2m.

A formula is provided to adjust for scaling up to higher Rn. Examples of the change in performance is given for Rn as high as 2x10^9.
I would like to know what the lowest Rn value is for which the formula still applies.

The article states that the same formula should be used to adjust for changes in blade thickness. The change in thickness is simply expressed as a change in Rn, with thicker blades having a lower equivalent Rn.

The fact that thicker than standard blades are also provided for leads me to believe that there is at least some margin for using Rn values lower than 2m. No maximum limit for thickness is indicated though, so there is no way of telling what the lower limit is for Rn.

Just for reference, the thickness at 75% radius of the standard B-series is a simple function of Ae/A0 (0.3 - 1.05) and number of blades (2 - 7).
The thickest blade section is 11% (Ae/A0 = 0.3, z = 7)
The thinnest blade is 1.5% thick (Ae/A0 = 1.05, z = 2).

 

[jehardiman]

I'm not sure anyone has done B series that low (I assume the Rn is for the blade, not the vessel). In model tests the propeller is over spun to get required similitude thrust. I have designed HPV props at blade Rn's that low but I used blade element theory to calculate T and Q directly. FWIW, full size propellers operating at 1 or 2 rpm do produce thrust...not sure it has ever been studied.

 

[Will Fraser]

I'm not sure anyone has done B series that low (I assume the Rn is for the blade, not the vessel). In model tests the propeller is over spun to get required similitude thrust. I have designed HPV props at blade Rn's that low but I used blade element theory to calculate T and Q directly. FWIW, full size propellers operating at 1 or 2 rpm do produce thrust...not sure it has ever been studied.

Did you use blade foil sections designed specifically for low Rn?

I have been using rc aircraft props for my solar kayak. I found a very useful database of actual windtunnel tests performed by Michael Selig that is published on the UIUC website.
The props were tested up to a max Rn of about 80k. The prop was operating at an Rn of 250k underwater so performance calcs based on the test data is conservative.
What surprised me was how much variation in efficiency there was between some geometrically similar props, even within a specific model range.

 

[jehardiman]

Did you use blade foil sections designed specifically for low Rn?

No, because the cord to thickness was so large, and the blades so thin, they were designed for ease of fabrication. Realistically, in my experience, Rn is so variable in the real world that any controlled test data is worse than useless because it has no real world relevance. Aircraft props are not what you want for water, the area distribution is all wrong. As I said, start with blade element theory, start playing with radial area distribution, and see what falls out.

 

[Will Fraser]

No, because the cord to thickness was so large, and the blades so thin, they were designed for ease of fabrication. Realistically, in my experience, Rn is so variable in the real world that any controlled test data is worse than useless because it has no real world relevance. Aircraft props are not what you want for water, the area distribution is all wrong. As I said, start with blade element theory, start playing with radial area distribution, and see what falls out.

Can you elaborate on the area distribution? Aside from designing to avoid cavitation, how does a change in fluid properties change the optimum blade distribution?

I have done some comparisons with blade element theory in the past but cannot remember any significant changes in efficiency. Obviously the blades with wider tips could absorb more power at a given rpm if diameter was limited.

The data for the rc props also show negligible difference at maximum efficiency despite vastly different chord distributions.

 

[jehardiman]

Can you elaborate on the area distribution?

Air props are designed to operate in static air ahead of the body where increased body drag due to wash is small compared to lift drag. Water propellers are designed to operate in the bodies wake and recover energy from that wake. Additionally, notice the root area of the example air screw; what is it doing for you? That root zone is close to 20% of your disk area. A well designed water prop of the same aspect ratios will have a large hub with the inner part of the blade working for you to push open water efficiency to 75-85%. This is how a well designed prop operating in the vessels wake can achieve 90-100% efficiency.