Re: Area Ruling?

On Feb 7, 8:58 am, "Ken S. Tucker" <dynam...@xxxxxxxxxxxx> wrote:
On Feb 6, 9:56 pm, bbrought <bbrou...@xxxxxxxx> wrote:
Are you claiming your model was flying faster than
about Mach 0.6 to 0.8? If not, area ruling had nothing to do with it.
If anything improved in range it had to do with the reduction of other
forms of drag that have nothing to do with whether or not something is
area ruled.

That's what I now think too, that's why I think sub-sonic
"Viscosity Analysis" and Area Ruling are intimately linked.
It was repeated experimentation that upgraded the theory.

OK, let's step back and look at the two different subjects you are
talking about:
You keep using the term "viscosity analyis" - you are actually trying
to talk about things that have to do with the fact that the fluid (air
in this case) has viscosity - so you are talking about boundary layer
development, laminar to turbulent transition, separation, etc.
Normally that is called "viscous analysis" - to distinguish it from
inviscid analysis which deals with potential flow or inviscid
compressible flow. "Viscosity analysis" is something completely
different - but we already discussed that in the other thread.

The other subject you brought up in this thread is area ruling - a
fairly good summary of that is given in the Wikipedia article that you
quoted in the beginning. This deals with wave drag reduction, which is
a function of the Mach number. The viscous effects and Mach effects
are usually well separated from each other, so much so that initially
during an aircraft or wing design you often look at the wave drag
using a completely inviscid analysis (usually some sort of CFD code
that solves the Euler equations), and you look at the viscous effects
in junctures using a viscous analysis method that may or may not
include compressible effects (incompressible means it won't capture
any Mach related effects) - depending on local flow speeds, etc.

As with anything in flow, you can never completely separate the
effects - but if the aircraft is flying less than about Mach 0.6,
sometimes as high as 0.8, you can completely ignore wave drag since it
is nonexistent. In fact, often you can do all your analysis using an
incompressible solver and then just do a simple correction later on
for compressibility effects that do not involve shock formation.

The same is not true if you had an aircraft that was operating close
to or within the transonic region. In that case, you are pretty much
forced to use a compressible solver, and in many cases you need to
include viscous effects also. The coupling between the viscous effects
and Mach effects usually happen close to the surface, with shock
induced boundary layer separation being one such example.

So to summarise:
Flight speed < M0.6: Wave drag not a factor, viscous effects
important, may require compressibility correction at speeds greater
than about M0.3, but these corrections assume there are no shocks in
the flow.

Flight speed > M0.6 to 0.8 (depending on the particular design) : Wave
drag and shock wave formation important, may require viscous analysis
depending on what you are trying to do.


A bit of detail: the laminar airflow from the forward
part of the fuselage, (nose) goes over the surface,
call that Laminar Fuselage Flow.
It's sticky and produces  a +p (positive pressure).
At the point LFF contacts Laminar Wing Flow we sum
the pressures, LFF(p) + LWF(p) to produce a
Laminar Mixed Flow,  LMF(p) = LFF(p) + LWF(p)

A few comments on what you describe:
The boundary layer flow along a fuselage usually very quickly
transitions to turbulent. On larger aircraft the flow over the wing is
usually also only laminar for a short distance before it transitions
to turbulent. Most of the time, except maybe for the occasional modern
glider, the boundary layer along the fuselage will already be
turbulent when it reaches the wing root. Whether or not you can add or
subtract pressures from each other has little to do with whether the
flow is laminar, turbulent, attached or separated.

With positive "pressure", I assume you mean pressure relative to free-
stream, since all pressures are "positive" (the lowest pressure you
can get is a pure vacuum, which is zero absolute pressure). For that
reason, we usually non-dimensionalise pressure relative to the free-
stream pressure and we call it pressure coefficient. I see there is a
nice Wikipedia article on it:
http://en.wikipedia.org/wiki/Pressure_coefficient

To get back to pressures - usually the pressure around the wing,
especially on the upper surface, is considerably lower than free-
stream, not higher. The same is true for pressures around most of the
fuselage.

My next paragraph refers to flow that is mostly incompressible and
shock-free - I make this distinction because things get very complex
when shocks are present and all generalisations go out the window:

What normally happens at a wing root, is that there is a stagnation
line (flow speed is zero relative to the wing) running along the wing
leading edge. When the wing is producing lift, this stagnation line is
slightly below the leading edge. This implies the Cp is equal to 1
(again, I refer you to the wikipedia article I linked above). As the
air speed now increases over the top of the wing, the pressure
coefficient quickly decreases to zero (where the speed is equal to the
free-stream) and then continues to increase its speed past the free-
stream speed, which implies the Cp becomes negative. The pressure on
the fuselage, at the same place, is actually also low - so what you
get behind the leading edge of the wing, along the fuselage juncture,
is a very large sudden drop in pressure to a very low suction peak.
This is not really a problem up to this point, because for the flow it
is like running downhill and it stays nicely attached for that short
distance from the stagnation point to the suction peak. Where things
go wrong is when the flow now starts slowing down back towards the
free-stream speed as it progresses towards the trailing edge. If you
go back to the pressure coefficient, it means the pressure now starts
to increase, and since the suction peak was so low it means the
pressure has to increase a lot over a fairly short distance. If you
have no fairing in the wing root, this "uphill" battle for the flow
usually causes massive separation locally in the wing root in a way
which develops into a strong horseshoe vortex (one leg over the top of
the wing and the other over the bottom). The separation in this area
causes a lot of drag. The normal solution is to add a fairing in the
wing root, which helps to spread out the pressure recovery and limit
the amount of separation in the root. Sometimes a strake ahead of the
wing also helps. If you look at the fairings on WWII aircraft, you
will see that they are much larger towards the trailing edge than the
leading edge - that is because the big problem lies in the pressure
recovery region (the region where the pressure increases), which is
towards the rear of the wing/fuselage juncture.

An alternative method that designers have tried was to replace the
fairing with a type of excavation around the fuselage - the theory
there is that you can reduce the suction peak (pressure not quite that
low) and that the extent of the vortex and separation can be limited.
You don't see this on aircraft, because of structural (and the
associated weight) issues, but at one time it was quite popular in the
design of junctions between sailing yacht keels and hulls.

I think what you were trying to say in this thread was that the
pinching that you usually get when you area rule an aircraft fuselage
(understanding of cause that the usual reason for area ruling has very
little with this type of drag) also just happens to reduce the
junction drag. In practice, the situation is usually not that simple -
the contracting of the fuselage usually comes too late to really have
much effect on the suction peak in the juncture, but you can probably
design it to help a little with the recovery portion. In almost all
cases, a properly designed fairing is still needed in the wing
fuselage junction. If you look at new Airbus or Boeing aircraft, you
will see they still use a pretty large fairing. What they also do is
to change the aerofoil section in that region to help reduce the
strength of the suction peak and minimise separation in the junction.

In your explanations, I get the impression you are not completely
comfortable with the meaning of terms, which tends to really confuse
your explanations and conclusions. It would be a good idea to look up
the different meanings of laminar flow, turbulent flow, transition,
attached flow, separation, etc., as well as the differences in the
characteristics of subsonic, transonic and supersonic flow.
.

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