Re: [PSUBS-MAILIST] hydrodynamics question

["Cliff Redus" <dr_redus@devtex.net>]

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