RE: [PSUBS-MAILIST] hydrodynamics question

[Alec Smyth <Asmyth@changepoint.com>]

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