The 90 cc D-90 engine is fully described in Andy Ross' fascinating book "Making Stirling Engines" (1993). At Ohio University we have a D-90 engine which forms part of the Senior Lab course - a required course for all Mechanical Engineering students. In this section we examine the results of performing an Ideal Adiabatic simulation of the D-90 engine under specific typical operating conditions as follows
In order to simulate the engine by means of the Ideal Adiabatic model equation set given previously, we require the equations for the Yoke-drive volume variations and derivatives Vc, Ve, dVc and dVe (all functions of crank angle q), as well as the void volumes of the heat exchangers Vk, Vr, and Vh.
The cyclic convergence behaviour of the Ideal Adiabatic model is extremely good, and using 360 increments over the cycle, the system effectively converges within 5 cycles. The convergence criterion chosen is that after a complete cycle both variable temperatures Te and Tc must be within one degree Kelvin of their initial values. We now consider the solution of the temperature variables Tc and Te, the heat energy variables Qk, Qr, Qh, and the work energy variables Wc, We, and the net work done W. These results are presented as plots showing the variation of these parameters with the crank angle q.
In the temperature-theta diagram we observe a large cyclic temperature
variation of the gas in the expansion space (> 100 K), its
mean value being less than that of the heater temperature of 923
K. Similarly the mean gas temperature in the compression space
is higher than the coller temperature. This suggests that the
adiabatic working spaces effectively reduce the temperature limits
of operation, thus reducing the thermal efficiency to less than
that of the Carnot efficiency.
The energy-theta diagram shows the accumulated heat transferred
and work done over the cycle. Notice that the work done W starts
with the (positive slope) expansion process then the compression
process, and again returning to the expansion process, Thus the
total work excursion is almost 15 joules, however the net work
done at the end of the cycle is only 3 joules. The most significant
aspect of the energy-theta diagram is the considerable amount
of heat tranferred in the regenerator over the cycle, almost ten
times that of the net work done per cycle. This tends to indicate
that the engine performance depends critically on the regenerator
effectiveness and its ability to accomodate high heat fluxes.
This aspect will be revisited in the section on the "Simple" analysis, when we
examine the effect of imperfect heat exchangers on Stirling engine
performance. Significantly the energy rejected by the gas to the
regenerator matrix in the first half of the cycle is equal to
the energy absorbed by the gas from the matrix in the second half
of the cycle, thus the net heat transfer to the regenerator over
a cycle is zero. It is for this reason that the importance of
the regenerator was not understood for about 100 years after Stirling's
original patent describing the function and importance of the
regenerator. The Lehmann machine on which Schmidt did his analysis
was apparently not fitted with a regenerator, and it is conceivable
that Schmidt did not appreciate its importance, He refers to the
textbook by Zeuner as containing a "complete, simple and
clear theory" of air engines, but in the same textbook Zeuner
decries the use of regenerators for air engines (Finkelstein,
T., 1959, Air Engines in The Engineer part 1, 27
March.)
It is of interest to examine the two components, Wc and We,
which added together gives the net work done W. These are shown
as dashed lines in the following diagram.
Notice in particular that the expansion space work done (We) undergoes
a vastly different process from that of heat transferred to the
heater (Qh), however at the end of the cycle they have equal values
(Qh = We). Similarly for the compression space work done (Wc)
and the heat transferred to the cooler (Qk). In retrospect this
must be so in order to retain an energy balance, however it did
catch us unawares and surprised us when we first noticed this.
The ideal regenerator thus behaves as the perfect isolator, isolating
the energy balance of the heater and expansion space from that
of the cooler and compression space. Thus for the Ideal Adiabatic
model over a complete cycle
Qh = We; (Qe = 0)
Qk = Wc; (Qc = 0)
W = Wc + We
Recall that for the Ideal Isothermal model
Qe = We; (Qh = 0)
Qc = Wc; (Qk = 0)
W = Wc + We
Furthermore the Ideal Adiabatic model in itself does not give results which are significantly different from those of the Ideal Isothermal model. The pressure-volume diagram is of similar form, and the power output and efficiency are quantitatively similar (albeit the efficiency of the Ideal Adiabatic model is about 10% lower for reasons described above). However the the behaviour of the Ideal Adiabatic model is more realistic, in that the various results are consistent with the expected limiting behaviour of real machines. Thus the heat exchangers become necessary components without which the engine will not function. The required differential equation approach to solution reveals the considerable amount of heat transferred in the regenerator, indicating its importance in the cycle, and provides a natural basis for extending the analysis to include non-ideal heat exchangers (Simple analysis). Thus the solution of the Ideal Adiabatic model equations is equivalent to a simulation of the engine behaviour in all respects, from setting up the initial conditions until convergence to cyclic steady state is attained. Throughout this process all the variables of the system are available as by-products of the simulation and can be used for extending the analysis. Thus for example the mass flow rates through all the heat exchangers can be used in order to evaluate the heat transfer and flow friction effects over the cycle.
On to the Simple
Analysis
Back to the computer program function set 'adiab'Back to the Stirling Cycle Machines home page