Foil loading limit to avoid cavitation?

[S V]

Design subject: ~6m LOA hydrofoil (a bit less than 20 feet) assisted catamaran planning (LDL???) power catamaran. To be exact - submerged tandem foils operating near the surface, at 0.2-0.4 chord depth
Operational speeds - 20-32kts
There is a limit for the foils of around 0.8m of tunnel width, as I want to make that cat less than ~2.25m wide total with all the possible appendages.
I am using at this moment quick and dirty Excell spreadsheet to calculate lifting force, and the bad part is that I have to stick with aspect ratio AR =~3 and pretty high angle of attack of in the range 4.5-5.5 degrees. The foils are fully passive and in the keel depth - similar to HYSUCAT type.
At 30 knots I am getting 5000N loading on 0.2 sq m foil, so it is 25000N (~2500kg) on 1 sq m. which I feel is way too much

The question is: what is the reasonable limits of the foil loading to avoid cavitation at such speeds?
The foil profile is still under question, but would like to stick with flat bottom ones for the simpler manufacturing process.

My calculations are attached

 

[mc_rash]

I guess you really mean cavitation due to low pressure and not ventilation due to too small water immersion?

Cavitation occurs if the absolute pressure at the low pressure side of the foil is lower than the vapor pressure.

Basically one can assume that water starts vaporing at 2 kPa (arround 20° C which might be pretty warm for water, the lower the temperature the lower the vapor pressure), p_vapor = 2 kPa

The absolute static pressure p at a given depth will be (I assume 1 m, pretty much I guess it will be less immersed)
p_atm + p_water = 100 + 9.81 = 109.81 (kPa)

The absolute pressure at the low pressure side of the foil is not known and I assume it won't be 25 kPa since it is a combination of high and low pressure etc, also it will vary very much about the surface of the foil but we can use this value for a first calculation, so p_foil

For no cavitation:
p-p_foil < p-p_vapor
=> p_foil > p_vapor
=> 25 kPa > 2 kPa

There are many values used by me which are assumed/rounded/not accurate but for a first estimation there should not accure cavition. I can't garantuee that my assumptions and conclusions are correct.

 

[mc_rash]

What are your requirements except for breadth max (0.8 m), tandem foil (I guess this means front and aftfoil?)? So weight and resulting needed lift?

If the weight is known you know the total required lift, you can choose preliminary a proven foil section and calculate the required area. Using the breadth max you can calculate the chord length.

For the choosen foilsection there should be some information about pressure coefficients at different angle of attacks, which leds you determine the pressures and thus the low pressure areas where cavitation could occur. Note that the lowest pressure might be near the leading edge, also the chance of cavitation rises with higher AoA.

 

[mc_rash]

You should also note that due to high density of water a relative small hydrofoilarea may be used, different as seen with planes and large wings due to low density of air.

 

[S V]

Dear mc_rash

Thank you very much for prompt reply!

I guess you really mean cavitation due to low pressure and not ventilation due to too small water immersion?

...I leaned back from the first sentence of your reply. Yes, I basically have to worry about both

Basically one can assume that water starts vaporing at 2 kPa (arround 20° C which might be pretty warm for water, the lower the temperature the lower the vapor pressure), p_vapor = 2 kPa

The absolute static pressure p at a given depth will be (I assume 1 m, pretty much I guess it will be less immersed)
p_atm + p_water = 100 + 9.81 = 109.81 (kPa)

The absolute pressure at the low pressure side of the foil is not known and I assume it won't be 25 kPa since it is a combination of high and low pressure etc, also it will vary very much about the surface of the foil but we can use this value for a first calculation, so p_foil

For no cavitation:
p-p_foil < p-p_vapor
=> p_foil > p_vapor
=> 25 kPa > 2 kPa

Yes, in even 30° C water it will be ~4kPa of boiling pressure, so not that much difference.
If I am not right, please correct me: the pressure on the suction side of the foil depends besides other conditions from speed AND attack angle? So, the the foil of the same span but longer chord can be used at smaller attack angles and will generate the same lift but will have smaller pressure difference and thus it will be less prone to cavitation, right?

What are your requirements except for breadth max (0.8 m), tandem foil (I guess this means front and aftfoil?)? So weight and resulting needed lift?

If the weight is known you know the total required lift, you can choose preliminary a proven foil section and calculate the required area. Using the breadth max you can calculate the chord length.

For the choosen foilsection there should be some information about pressure coefficients at different angle of attacks, which leds you determine the pressures and thus the low pressure areas where cavitation could occur. Note that the lowest pressure might be near the leading edge, also the chance of cavitation rises with higher AoA.

Yes, the practical limit is ~0.8m for tunnel width as I want the cat to be no more than 2.2m or even less beam. The total displacement with full fuel, cargo will be 1.4 metric tonns in the worst case, and I would like to get substantial ammount of foil assist on speeds 20+ kts.
Also for the very practical reasons the foils have to be at the keel depth, o even 0.5-1 cm higher , so there is no situation where the full weight of the catamaran is caried be the foils alone. That means in theory whole boat should be self ballacing: foils lift the boat to the limit where due to the surface effect they loose the lift and the boat stays at the fixed height.

I would like to get ~320 kg * 2 of lift at 20knots, and the ~500 kg * 2 at 30 knots with the surface effect, which looks achievable at ~5° AoA. I tailored the calculations in the xls file to get there with aspect ratio AR =3, but I somehow feel that the values are too much optimistic... Pictures attached.

The foil has to have these properties: easy to fabricate, in the best case flat bottom, cavitation free in up to 32-35kts, to have good properties in AR < 4, structurally hold at least 1000kg of weight @ 0.8m beam (500kg + safety factor), so preferably of high thickness, because if in some miraculous way there is a chance to avoid vertical support strut - I would like to pursue it.
And last but not least as dear mc_rash mentions - ability to operate close to surface, up to 10-5cm. Bonus requirement: the first foil has not to leave total foam of air and water for the second one...

Now the question is - which proven foil sections I could start with?

 

[mc_rash]

Actually, you don't need to worry about caviation and ventilation if proper designed

Both, pressure on low pressure side as also the high pressure side, depends on angle of attack. This also effects the lift- and drag coefficient. The speed actually only effects the real forces produced by the foil - For example the lift force
L = 0.5 * rho * A * v^2 * Cl
(rho = density, A = surface area, v = speed, Cl = lift coefficient)
(Please correct me if I'm wrong)
But yes, the speed will have impact on wether cavitation occurs or not.

 

[mc_rash]

For clearance:
Pressure-, lift- and drag coefficients do not change with speed but with angle of attack.
The occuring pressure, lift and drag changes with speed (see example formula above), and the pressure depending on speed defines if cavitation may occure or not.

 

[DCockey]

Foil shape and thickness affects the pressure distribution and thus the onset of cavitation. In general a foil profile with a smaller radius leading edge may have a larger magnitude low pressure peak.

 

[Heimfried]

For clearance:
Pressure-, lift- and drag coefficients do not change with speed but with angle of attack.
[...]

I don't think this claim is correct. Look at any graph of lift or drag coefficients of a foil. There are usually several different curves shown, each belonging to a certain Reynolds number. Because the viscosity (of water or air) and the chord are fix in this regard, the Reynolds number is only depending on speed.

 

[mc_rash]

Thanks @Heimfried for correcting my mistake, I am sorry for the misinformation I spread!
Do you know how it behaves with higher Reynolds number? If comparing the NACA4412 on Airfoiltools.com for different Rn the max visible Rn is = 10^6. For @S V 's issue we need higher Rn for a chordlength = 0.26 m (@20 kn Rn = ~2.6*10^6, @30 kn Rn = ~4*10^6)
with chordlength resulting from the excelsheet's area A = 0.213 m^2 and tunnelwidth = 0.8 m

Also, if the coefficients at low Rn are NOT taken into account, the coefficients get closer together. I wonder if at higher Rn the coefficients tend to converge? Do you know something about that @Heimfried ?

 

[mc_rash]

I just made a quick calculation, based on NACA4412 and Rn = 10^6 (Since Airfoiltools.com does not show higher Rn numbers)

First, calculation of foil length based on Rn:
Rn = v*l/kin.visc
=> l = Rn*kni.visc/v
l = 10^6*10^(-6)/(30*1.852/3.6) = 0.065 m

Second, calculation of required lift coefficient:
L = 0.5*rho*A*v^2*Cl
=> Cl = 2*L/(rho*A*v^2)
Cl = 2*500*9.81/[10^3*(0.8*0.065)*(30*(1.852/3.6))^2] = 0.79
with L = 500*9.81 since OP wants 500 kg of lift

According to the attached graph this would give a required angle of attack about ca. 3°

Am I wrong with my way of calculation? For me it seems to be plausible. Yes, OP wants a flatbottom foil which the NACA4412 is not, but is my calculation usefull for a first estimation?

 

[mc_rash]

@20 kn and a chord length = 0.065 reynoldsnumber is Rn = 6,7 *10^5

I assume that the lift coefficient does not change for AoA = 3° (see graph for different Rn, orange = 10^6, blue = 5*10^5, green = 2*10^5) and stays the same Cl = 0.79

For 20kn speed this would give following lift
L = 0.5*1000*(0.8*0.065)*(20*1.852/3.6)^2*0.79 = 2174 N
or, as OP used weight = 2174/9.81 = 221 kg

 

[Heimfried]

[...]
Also, if the coefficients at low Rn are NOT taken into account, the coefficients get closer together. I wonder if at higher Rn the coefficients tend to converge? Do you know something about that @Heimfried ?

Sorry, no. My knowledge of hydrodynamics is poor. I only know some very basic things.

 

[S V]

Foil shape and thickness affects the pressure distribution and thus the onset of cavitation. In general a foil profile with a smaller radius leading edge may have a larger magnitude low pressure peak.

DCockey, sorry for my poor understanding of English engineering terms - does that mean that in my case smaller radius leading (front) edge foil shape is less suitable? Should I go with the foil profile, which is generally thicker or just the very front of it is the part is the cause of it?

 

[Skyak]

Design subject: ~6m LOA hydrofoil (a bit less than 20 feet) assisted catamaran planning (LDL???) power catamaran. To be exact - submerged tandem foils operating near the surface, at 0.2-0.4 chord depth
Operational speeds - 20-32kts
There is a limit for the foils of around 0.8m of tunnel width, as I want to make that cat less than ~2.25m wide total with all the possible appendages.
I am using at this moment quick and dirty Excell spreadsheet to calculate lifting force, and the bad part is that I have to stick with aspect ratio AR =~3 and pretty high angle of attack of in the range 4.5-5.5 degrees. The foils are fully passive and in the keel depth - similar to HYSUCAT type.
At 30 knots I am getting 5000N loading on 0.2 sq m foil, so it is 25000N (~2500kg) on 1 sq m. which I feel is way too much

The question is: what is the reasonable limits of the foil loading to avoid cavitation at such speeds?
The foil profile is still under question, but would like to stick with flat bottom ones for the simpler manufacturing process.

My calculations are attached

Your statement of requirements indicates you need a low peak suction and all the lift you can get -a flat pressure curve. You can create a such a profile in Xfoil software but Tom Speer has already done so with the H105. I direct you to Foil section? For foil board | Boat Design Net - the profile is given in post #5, a graph explaining the performance envelope is given in post #6, and most importantly, the graph is explained in post #10. Read it slowly. Read it again. When you think you understand it try to draw the path of your foil loading through its operating range.

As I understand it, your foil terminates into vertical hull sides and is short in span so you don't have induced drag or structure challenges. You do have depth problems and I suspect challenges getting the right angle of attack at different speeds. I guess there is some good news as the loss of depth creates a loss of lift -contributing to control.
It looks to me like you are in range (absent the depth discount) with the H105 and you will have to move on to CFD to answer the 3D lift and drag questions, because the depth of water, it's speed and direction is heavily influenced/disturbed by the hulls.

What I wonder is with the lift and drag you end up with being limited by the high top speed -how much would you be giving up going to a super-cavitating profile that doesn't have cavitation speed limits?