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This presentation will give you an overview of the
techniques we use to %uh solve the unsteady flow equations.
These are equations, they're partial differential equations
and they're quite difficult to solve.
But we're going to use, they're several methods here,
the surge program uses the wave plan method which is one that we've developed
%uh that
offers some advantages of being intuitive
and that much easier to
%uh prepare the models.
The models themselves or composed
of line segments,
components such as pumps and valves, junctions which include open
closed ends,
and surge control devices.
These are all shown here there's the pipeline
here's a valve, here's a surge control device.
Now the method that we use, the "Wave Plan"
method, is
it's simply described here
pressure waves to generated at the source of the disturbance
such as this valve closing.
The waves that travel at sonic speed
and at junctions
and at components such as pumps
they're reflected and transmitted. So this wave travels down this line at sonics speed.
It now gets transmitted down the adjacent line reflected back into this line.
These waves then go on
%uh this wave travels to the pump,
affects conditions at the pump and gets reflected off of there. This wave
goes to the valve affects conditions there and gets reflected and so on. So this
is the
process that we use
to solve the equations.
Some of the key
%uh equations that we use, pressure wave of course travels the sonics speed
it changes the pressure by the amount delta P and the
velocity that the amount dealt V.
This very simple equation
that relates to pressure change, and feet head to the flow of change.
The constant is wave speed over GA
and since wave speed be is pretty high this is a fairly large number
and down here this gives you a
an idea
%uh what sort of pressure changes accompanies a flow change.
For in a steel pipe
one foot per second
change in velocity will produce a fifty to sixty PSI wave.
So that's quite a large wave and that's
so significant.
Here we can use this simple approach to %uh
estimate
the effects of a surge.
For example the maximum upsurge
due to the closure of a valve, if you have initial velocity say it's six feet per second
for two meters, we can calculate in this simple equation.
It would be about seven hundred fifty feet or two hundred thirty meters.
The maximum down surge
also is computed based on the velocity change.
That would be minus seven hundred fifty feet or two hundred thirty meters.
So it's very significant and this very simple calculation
can help you estimate that.
The way speed is given by this equation
%uh as the thickness of the pipe but decreases the pipe is more flexible
%uh we get a reduction of wave speed
so %uh there is some help in your
a
Surge two thousand that will help you calculate
the wave speeds.
Now the
program itself consist of a
subroutine to handle components.
%uh were
a wave comes in it changes the conditions at the components they're reflected and transmitted
wave.
This includes the components, includes valves
and on valves we have relationships for the area
going through the valve
that the water see verses the
stem position and these sort
of relationships
%uh are available and are used within the program to model valves.
Pumps, you can model pumps two ways. We can use just a standard
ABC characteristic.
%uh This works only for normal operation.
If we have a pump trip where the pump can turbine
and %uh
the flow could reverse, we have to use these
sutter diagrams which are
dynamic characteristics over the entire range of possible.
%uh For junctions,
if pressure waiver approaches the junction
you'll get a transmitter wave
into the junction in a reflective wave back these are quite simple to calculate.
And here's an example we have a hundred four wave
approaching this junction with these
characteristics
this is the %uh
wave speed over GA.
We would get a wave of a hundred fourteen actually of magnification of the wave
%uh being transmitted down and reflective wave of fourteen going back.
%uh Open and closed-ends are sort of special cases.
A wave at an open end is reflected negatively.
A wave at a closed end is reflected positively.
Both of these have a
profound effect on the transient response.
Closed-ends because of a positive reflection
can increase pressures even
further in a piping system.
%uh We have surge control devices
these are almost always
based on flow entering or leaving the system.
And we set up a subroutine to handle these devices.
These include open and close surge tanks,
feed tanks, blatter tanks,
pressure release valves,
surge anticipation valves,
and air valves,
which have an effective inflow outflow
orifice.