Notes to go with computer animation of

              Stirling and thermoacoustic-Stirling hybrid engines

                              gws January 1999

                                   tashe



        This seems to run ok on most DOS-style machines.  Old ones might seem 

a little slow;  486/33MHz or faster is really smooth.  This will run on a 

Mac only if it has a dos emulator.  There are sometimes wierd flickers in

a DOS window running out of Windows....sorry I haven't figured this out.



        The first time through, type "m" when prompted at the bottom of the

Los Alamos credits/disclaimer display.  This will ensure that the menu line

is always displayed, so you know what your options are.  When you're really 

familiar with this animation and are using it to explain these ideas to 

others, you may want to suppress the menu line so it doesn't distract 

the others from the meaningful parts of the display.  Initially typing any 

character other than "m" will suppress the menu display.



        Thereafter, typing a letter will access a particular display:



s   Stirling engine

i   isolated Stirling engine

t   thermoacoustic-Stirling hybrid, ie a traveling-wave engine



v   toggles the display of P dV ellipses on and off

d   toggles the display of 4-step words on and off (in Stirling only)



r   regenerator details, magnified

b   thermal buffer tube (like a "pulse tube") details, magnified



F   faster

S   slower



q   quit



        In the discussion here, I'll do them in the order listed above....        

but you can select them in any order.  



        stirling and isolated Stirling show the parts, the helium motion and

pressure, and the mean temperature profile.



        v (short for volume toggle) turns on and off several p dV ellipses.  

It works during stirling, isolated Stirling, and thermoacoustic modes.



        When switching among stirling, isolated Stirling, and thermoacoustic

the change is immediate;  when one of the two magnified views is invoked, a

slow zoom action takes you from one view to another.  (To stay oriented, I

am in the habit of going back to an overall view after each magnified view,

but you can actually zoom directly from one magnified view to the other.)



        You can also change the period of oscillation by hitting "F" for 

faster or "S" for slower.  Each time you hit one of those keys you change 

speed by a factor of 2.



        Quit at any time, and return to the operating system, by hitting "q".





***** stirling *****



        This is a traditional two-piston Stirling engine.  The pistons 

move with different amplitudes and phases, such that the gas is compressed, 

displaced rightward, expanded, and displaced leftward.  The upper trace shows

the pressure as a function of time.  Viscosity in the regenerator causes a

small pressure gradient in the regenerator, in phase with the velocity.

The vertical moving blue lines in the refrigerator are tracer lines 

in the gas---imagine thin wisps of smoke.  They crowd closer together

when the pressure is high, signifying increased density.



        The red arrows show heat rejection and absorption at the heat 

exchangers.



        When "v" is toggled on, ellipses are drawn that trace the

pressure and piston-face position for each piston.  Since the volume in

front of a piston is the product of area and position (with suitable choice 

of the zero of position), the area of each ellipse represents the 

cycle-integral of P dV, i.e. the work.  Think about the signs carefully.  

Both pistons move to the right when pressure is high and move to the left

when pressure is low.  This means that the sense of work flow is from left

to right.  Hence, the left piston does work on the gas, while the right

piston absorbs work from the gas.   Note that the work absorbed by the

right piston is larger than the work delivered by the left piston.  Part

of the work absorbed by the right piston from the gas is usually fed back

to the left piston, thereby "priming the pump".

Sometimes the work is fed back via a crankshaft and other mechanical

linkages;  that is what you should imagine when viewing this animation.

(However, in Stirling machines having a "displacer" piston, the hot gas

does work on the hot end of the displacer piston, and the ambient end of the

displacer piston delivers that same work to the ambient gas space to the left

of the ambient heat exchanger.)



***** isolated *****



        This is a Stirling engine, with a thermal buffer tube to allow the

"hot" piston to be at ambient temperature.  



        From left to right, we have the ambient piston, ambient heat

  exchanger, regenerator, hot heat exchanger, buffer tube, and 

"hot" piston.



        When "v" is toggled on, we can imagine p dV ellipses for imaginary

pistons at various places in the apparatus.  At any location of a blue 

gas-position marker, we could imagine instead a thin piston with the same 

motion.  The work associated with that piston is the cycle integral of 

the pressure at that location d position.  This work is absorbed from the 

gas on the left of the imaginary piston by the left face of the 

imaginary piston and the same work is delivered to the gas on the right of

the imaginary piston by the right face of the imaginary piston.  Note

that the work flow at the left and right ends of the buffer tube are equal

(because there is no dissipation in between) although the details are 

different (tilt of ellipse changes due to compressibility of gas in between).



***** thermoacoustic-Stirling hybrid engine *****



        The thermoacoustic-Stirling hybrid engine feeds some of the pV

power from the right end of the engine back into the left end of the

engine.  In this feedback, it is similar to the Stirling

engine, whose crankshaft and other mechanisms feed some of the hot power

to the ambient piston.



        The components in the upper half of the display are the same as

those of the stirling and buffered displays.  In fact, the pressure and gas

displacement as functions of time and position are identical to those

of the stirling and isolated displays.



        The new components in the thermoacoustic display are a compliance

(the 180 degree bend at the left), an inertance (the narrow neck at

bottom-center), and the union at the right.  We will see later how these

new components conspire to maintain the desired magnitudes and phases of

pressure and gas displacement in the upper half of the display.

        

        The acoustic oscillations arise spontaneously when sufficient heat

is supplied to the hot heat exchanger.  The heat exchangers and

regenerators can be thought of as amplifiers of the acoustic power flowing

through them.



        Next consider the pressure difference between the left and right

halves of the screen.  The pressure plots are identical at their left

and right extremes, as they must be because the corresponding hardware

components are "connected" via the compliance at the left and the union

at the right, neither of which can sustain a pressure difference.  The

left-to-right pressure difference occurs across the inertance in the

lower part of the display and across the regenerator and heat exchangers

in the upper part of the display.  Note how the pressure difference peaks

in time at the temporal extremes of the pressure oscillation.  The

regenerator is necessarily a resistive component, because it must have

tiny passages to ensure the good thermal contact necessary for efficient

Stirling cycle operation.  Hence the pressure difference across the

regenerator is in phase with the velocity through it;  the pressure

difference is largest when the gas motion is fastest.  In contrast, we

want the inertance to experience as little dissipation as possible, and

hence to have as little resistance as possible.  If it is a pure inertance,

the pressure difference across it is largest when the gas acceleration is

largest, i.e. when the gas velocity is zero.  So the gas motion

in the lower part of the figure leads the gas motion in the upper half

by about 90 degrees.



When "v" is enabled, the areas of the pV loops show the acoustic power

flowing past each point.  Note that the loops in the lower half circulate

counterclockwise, signifying power flow from right to left, while those

in the upper half circulate clockwise, signifying power flow from left to

right.  The left-upper, left-lower, and center-lower ellipses have equal

areas, signifying equal powers, because there is no dissipation between

them in this idealized animation.  Their area is the difference between

the areas of the two ellipses representing the powers flowing into the union

(the power flowing out of the right end of the buffer tube) and the power

flowing out of the right side of the figure to an external load.



***** regenerator *****



        In the regenerator, gaps between solid parts are small, much smaller

than a thermal penetration depth.  Hence the gas blob is always in excellent

thermal contact with the adjacent solid parts, so the temperatures of gas 

and adjacent solid always match.  To accomplish this, heat must flow 

between gas and solid as shown by the red arrows.  This process 

produces work, so the loop in the pressure-volume diagram circulates 

clockwise.  Note that this pressure-volume diagram refers to a 

particular mass element of gas;  this is a different concept than the 

pressure-volume diagrams toggled on and off with the "v" command, which

are associated with pistons or imaginary pistons.



        The transport of entropy from right to left by the gas can also be

seen in this view.  The gas absorbs heat from the solid at the rightmost

extreme of its travel, and rejects heat to the solid at the leftmost extreme

of its travel.  Hence, it has more entropy while it is moving left than

while it is moving right.





***** buffer tube *****



        This region acts like an adiabatic thermal buffer.  The gas

is not in good thermal contact with any solid.  Hence the temperature

of a given blob of gas just goes up and down with the pressure, 

adiabatically.  Nearby blobs are at slightly different temperatures, and 

they also experience adiabatic temperature oscillations.  The overall

picture is of a smooth temperature gradient that moves with the gas and

rises and falls a little with the pressure oscillations.  No work is 

absorbed by this isolated, adiabatic blob, so its pV diagram is simply

a reciprocating adiabat with zero area.  Note the distinction between this

pV diagram for a given mass element of gas vs the pV power transmitted 

along the buffer tube which is visible in the overall view when "v"olume

is toggled on.