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Re: [PSUBS-MAILIST] hydrodynamics question
Alec,
1) Fix A2 and assume A1
2) Fix V1 as sub speed
3) Calculate V2 from conservation of mass, A1V1 = A2 V2
4) Fix upstream pressure entering the scoop P1 as the ambient water pressure
at current depth
5) Calculate from Bernoulli equation the pressure upstream of the prop P2
6) Go to step 1 and try another A1 if you are not happy with pressure
profile or velocity profile
7)After happy with P2 which will be lower than ambient pressure due to
kinetic energy gain), use a ducted propeller equation or an axial-flow
turbine equation to relate the pressure upstream of the prop (P2 you just
calculated) and the pressure downstream of the prop, P3 (ambient water
pressure), break horsepower, flowrate, efficiency and slippage. The prop
manufacturer should have a curve that shows the prop head (DP/specific
weight) and efficiency as a function of specific speed.
Good luck
----- Original Message -----
From: "Alec Smyth" <Asmyth@changepoint.com>
To: <personal_submersibles@psubs.org>
Sent: Friday, May 17, 2002 10:23 PM
Subject: RE: [PSUBS-MAILIST] hydrodynamics question
> Cliff,
>
> What a great response! I looked it up on Google and found Bernoulli's
> equation first try. What kills me is that 15 years ago I knew this stuff
> cold. But back to the problem at hand...
>
> Bernoulli adds an equation, yet also adds two new variables; namely the
> pressures at stations 1 and 2. So in a strictly mathematical sense it
leaves
> me further from my objective than if I only considered A1V1 = A2 V2. I
have
> 2 equations, but 5 unknowns:
>
> - A1 (A2 is known, its my prop diameter)
> - V1
> - V2
> - P1
> - P2
>
> This leaves me at a bit of a loss. I can plug in arbitrary values of A1,
> but that still doesn't get me to calculated values of everything else.
>
> However, the formulas have provoked two entirely different thought
patterns:
>
> 1) There is a certain slippage between the speed of the prop wash (V2) and
> the speed of the vessel itself, to which I would ideally match V1. I don't
> know what that ratio might be for a reasonably streamlined body, but
chances
> are there might be typical values out there used as a rule of thumb by
naval
> architects (Carsten?)
>
> If I had that ratio, in conjunction with A1V1 = A2V2 it would have all I
> needed to calculate A1.
>
>
> 2) On the other hand, the whole concept of scoops might be flawed because
> they increase the frontal area when some plain louvers in the "fuselage"
> would provide ample intake in a less invasive way. I can't help note that
> Deep Flight, with similar ducted and tucked-in props, has only louvers.
And
> by the same token the only sub I know with fighter-plane style scoops is
the
> infamous "Alien sub" - not one I want to emulate.
>
> I just emailed a photo of the fairing plug to John's moki page, but I
> haven't seen it appear yet. I hope I did that correctly.
>
> D'you vote for scoops or louvers?
>
>
> thanks,
>
> Alec
>
> -----Original Message-----
> From: Cliff Redus
> To: personal_submersibles@psubs.org
> Sent: 5/17/2002 5:48 PM
> Subject: Re: [PSUBS-MAILIST] hydrodynamics question
>
> Alex, assuming that the water is essentially incompressible, and that
> the
> flow is turbulent (Reynolds Number based on duct diameter >2300) then
> there
> are two equations that define the flow through the duct. The first is
> conservation of mass and the second conservation of momentum. For this
> case (assuming incompressible flow i.e., density is constant),
> conservation
> of mass simplifies to Q1 = Q2 or the volumetric flowrate at station 1 in
> the
> duct equals the volumetric flow rate at station 2. Since Q1=A1 V1 and
> Q2=A2
> V2, this says that he areas at the two stations are related as
> A2/A2=V2/V1.
> In other words if your inlet scoop area (Station 1) is twice as large as
> the
> prop area (Station 2) then, the velocity of the water at Station 1 would
> be
> half that at stations 2 just from the change in cross sectional area and
> not
> the prop. If the areas at stations 1 and 2 are the same, then the
> average
> velocities are the same. The second equation that governs in this
> situation
> is conservation of momentum which simplifies to the famous Bernoulli
> Equation. Look in any undergraduate fluids book for this simple equation
> or
> do a Google search on web. By solving these two equations the velocity
> and
> pressure distributions in the duct can be calculated. These equations
> are a
> bit of a oversimplification for your case in that the prop will
> introduce a
> swirl in the flow field. To rigorously solve for all components of
> velocity
> (axial, radial and circumferential) and pressure, you would need to use
> a
> CFD (Computational Fluid Dynamics) program like Fluent or CFX. Using
> good
> old Bernoulli's equation and Q1=Q2 will, however, get you 95% of the
> answer
> you want. One other point, in general, ducted flows will be less
> efficient
> that than a prop in an open flow field but in some situations, there may
> be
> good reasons for using a ducted prop such as for example safety. The
> last
> bit of guidance is to use graceful streamlined surfaces in the scoop to
> prevent flow separation which is a bad thing in hydrodynamics. Sharp
> angles
> are areas that can cause vortices which waste energy. So the short
> answer
> to your question is give the inlet scoops a greater area than the prop
> area
> and then gradually reduce the area through the duct reaching a minimum
> at
> the prop. The pressure then will drop as you gain higher and higher
> velocity
> until just upstream of the prop the velocity will be at a maximum and
> the
> pressure will be at a minimum. Avoid any sharp bends in the inlet duct.
> See
> discussion in Busby on Propulsion Pgs 371-372 for an overview on free
> versus
> ducted propellers.
>
> Cliff
>
>
>
> ----- Original Message -----
> From: "Alec Smyth" <Asmyth@changepoint.com>
> To: "PSUBS (E-mail)" <personal_submersibles@psubs.org>
> Sent: Friday, May 17, 2002 7:51 AM
> Subject: [PSUBS-MAILIST] hydrodynamics question
>
>
> > My design has twin props astern, in tunnels fed by side-scoops (a la
> fighter
> > jet). I'm currently making the mold for the stern fairing, and I'm
> > contemplating the best size and shape for the scoops. Given that water
> is
> > essentially incompressible, am I correct to assume the frontal area of
> the
> > scoops should be the same as the area of the prop tunnels? Another
> > possibility would be to eliminate the scoops altogether and go with
> NACA
> > intakes or such. But the scoops are definitely sexier.
> >
> > Anyway, since my above assumption is based on intuition instead of
> > knowledge, any educated speculation would be much appreciated!
> >
> > thanks,
> >
> >
> > Alec