General features of laser engines and laser piston engines are discussed in terms of optimization of operation. The efficiency of laser powered turbine and Stirling engines is also considered

Garbuny, M.

Pechersky, M. J.

English

NASA Technical Reports Server

OPTIMIZATION OF ENGINES OPERATED REMOTELY BY LASER POWER*
Max Garbuny and M. J. Pechersky
Westinghouse Research Laboratories
INTRODUCTION '*N76"2l *? 2 3
The concept of converting electromagnetic energy, such as from solar or microwave power,
remotely into work has been considered for several decades. Only recently, however, have such
conjectures approached feasibility due to the availability of laser beams with aperture — limited
directivity and enormous power flux densities. There exist three basic alternatives for the F
conversion of laser energy into mechanical work by an engine. These are, in ascending order of
intricacy, as well in degree of utilization of the coherence properties of the laser, the following: (1)
the boiler approach in which laser power is applied externally to a heat reservoir just as fossil fuel to
a steam engine; (2) internal heating of a working fluid by resonance absorption of laser radiation
admitted through a suitable window; and (3) selective resonance excitation of a single degree of
freedom without increase of the translational temperature.
Clearly, aside from the optical beam tracking problem, the first approach reverts to the case of P
conventional engines. It should be noted that because thermal materials limitations and reradiation
limit the temperature of the heat reservoir, an important advantage of laser radiation is forfeited. As
will be shown, this disadvantage is, at least in principle, avoided in the second method (ref. 1).
Furthermore, although this approach amounts to a mere modification of conventional engines, it
lends itself to types of operation not achievable in ordinary heat-to-work converters. This leads to
new considerations of engineering thermodynamics, and the scope of this paper is in the main
limited to them. The third approach, first suggested in the concept of the photon engine (refs. 2 and
3) is conceptually more profound. However, it is a field by itself. Moreover, the practical realization r
of its various alternatives encounters obstacles which may prove insurmountable. ^
GENERAL FEATURES OF LASER ENGINES
Engines of the second type, that is, those in which laser radiation is absorbed by the molecular
resonances of a gas, converted into translational heat, and thus used to perform mechanical work,
are in the following referred to as laser engines. In principle, any conventional engine which can
admit radiation through a window to a working fluid, can be modified for this purpose. There exist
now several types of lasers that can deliver, or promise to deliver, high powers in pulsed,
continuous, or shaped-pulse operation. Examples are the gas lasers based on C©2 near 10 p., CO near
5 /LI, HC1 near 3.5 n, and HF near 2.8 jz. The wavelengths of these lasers can be matched with the
resonances of many gases, cross sections of absorption varying from 10 to 10~* cm^ or more.
Thus absorption is nearly complete at 1 atm over path lengths that may be as short as 0.1 mm or
less or, admixed at 1 volume percent to a nonabsorbing gas, over 1 cm or less. The working fluid
"This study was supported by Ames Research Center, NASA, Moffett Field, California.
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may therefore be a monoatomic gas with its K= cp/cy = 1.666. In addition, such gases as helium
were found to have a fast quenching effect so that the time in which the vibrational excitation is
dissipated into a thermal equilibrium is negligible compared with that of the pertinent engine cycle.
The maximum achievable temperature in such an engine deserves some discussion. The laser, in
principle, is a source of infinite black body temperature. An absorbing gas, again in principle, could If
also reach an infinite temperature. There are, of course, material restraints, but these will be
considerably less than in the boiler appraoch. A gas mixture, as described in the previous paragraph,
has a negligible coefficient of thermal emission throughout the spectral range of interest, including
the resonance line. Thus the temperature the gas can reach, or is allowed to reach, is determined by
other factors. These are considered in the following:
1. Engine walls will not tolerate temperatures much in excess of about 2,000°K. However,
in certain configurations, such as that of a piston cylinder, the laser radiation may be focused into a F
smaller space well shielded by the surrounding gas from the walls. Thus an effective temperature
may be reached which is much higher than that which the walls can tolerate.
2. Bleaching, that is, the production of equal populations in the upper and lower levels of
the absorbing transition occurs at sufficiently high radiant flux densities so that radiation is no
longer absorbed. These power levels, however, increase with the rate of quenching and lead to a
temperature limit much higher than that determined by the other factors.
3. Thermal saturation of the upper level leads to an effect similar to bleaching. Specifically, *
in thermal equilibrium, the ratio of upper level populations r\2 an^ lower level populations nj is
given by n2/nj =(g2/gj) exp (-hf/kT). One can thus define a limiting temperature T§ at which
hv = kTs so that appreciable reduction of absorption occurs; (that is, neglecting the ratio of the
statistical weights g. Except for the effect of the statistical weights, TS is characteristic to some
extent of the laser wavelength rather than of the absorbing molecule. Values of TS for the lasers
mentioned before and their wavelengths are listed in table I. As defined, the values of TS provide
only an approximate value for the temperatures at which absorption is significantly reduced. For
 T-
example, for gj=g2, the absorption cross section of an ideal two-level system decreases to 0.46 of its ^
value at low temperatures, but will be lower for a multi-level molecule.
4. Dissociation is a third cause for the reduction of absorption at elevated temperatures. The
last column of table I shows the dissociation energies (ref. 4) of some gases resonant with the
wavelengths of the four lasers cited. These values provide only a guide for the comparison of various
gases. The rate, as well as the equilibrium value, of dissociation as a function of temperature still
depend on other parameters, notably the collision rate and cross section.
Nevertheless, one can conclude on the basis of these considerations that laser engines can
operate with effective temperatures between 2,000° and 3,000°K, if lasers with wavelengths shorter
than about 5 y. are used as radiation sources. There are two additional features that set laser engines
apart from ordinary heat-to-work converters, at least when applied in combination. The first is the
application of an essentially monoatomic gas as working fluid. The second feature is the option of
the pulse shape. In the internal combustion engine, for example, power is applied in pulses; but the
working fluid is, of necessity, a polyatomic gas mixture.
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THE LASER PISTON ENGINE AND THE OPTIMIZATION OF ITS OPERATION
Schematic diagrams of laser piston engines, including one for experimental use in a simplified
version, are shown in figure 1. In addition, figure 2 shows certain optional features such as a change
of absorption cross section, hence of depletion depth, by frequency shift as the laser pulse develops
and also the method of focusing the laser radiation into a smaller space within the cylinder volume.
The P-V diagram of the engine in figure 3 shows four steps of the simplified cycle: (1) isochoric
pressure increase as the laser pulse arrives; (2) adiabatic expansion (2 - 3) performing external work;
(3) isobaric compression which restores the initial temperature Tj ; and (4) isothermal compression
(4-1) which restores the initial volume Vj at the starting point 1 .
The performance of the engine depends, first of all, on its (theoretical) thermal efficiency 17,
defined by
(1)
or, alternatively, by
- 2 W;in (2)
'in
where Qjn represents the heat provided by the laser, Z Qout the heat rejected by the engine, and
06 W represents the sum of the positive and negative work terms.
The actual efficiency depends also on the efficiency of the work terms, that is, the losses
encountered in isobaric and isothermal compression, as well as in the expansion step. A practical
merit factor is given by the work ratio rw, defined as
W
rw
out
Thermal efficiency and work ratio are best expressed in terms of the ratios A = V^/Vj (that is, the
ratio of the volumes after, and before, the expansion step 2-3) and B = T2/Tj (that is, the ratio of
the temperatures after, and before, the heating step 1 - 2). One has then
Q3_4 (AK/B)
in C.U-B-1)
(4)
and
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l I I l I I I I I i l i l E I I f l
Once the maximum permissible temperature ratio B and a monoatomic gas are chosen, the
only adjustable parameter is the compression ratio A. From equation (4) the maximum thermal
efficiency is derived for the condition
AK-1 = B (6)
It is easy to show that this amounts to the condition that Tg = Tj , (that is, that the heat received
by the engine in step 1 - 2 is equal to the work of expansion 2 - 3. By introducing equation (6)
into equation (4), one obtains the maximum thermal efficiency
Conservative choices of Tj and T2 are, respectively, 300° and 2,000°K so that B = 6.67. We obtain
then from equation (7), T?max = 67 percent.
Note that the maximum efficiency depends only on B and not even on the ratio K of specific
heats. Thus this efficiency should be obtainable also for polyatomic gases. However, this can not be
achieved for them because of equation (6). Since A = B*'' ^', they require at least a compression
ratio of 246, whereas monoatomic gases require only that A = 17.2.
The work ratio at maximum thermal efficiency follows from substitution of equation (6) in
equation (5). In combination with equation (7), one obtains then the relationship between work
ratio and maximum thermal efficiency
r w = i * ( 8 )1
 ^max
One can quite generally show that equation (8) is equivalent to the condition Qin = WQut. Since
Wout - 2 Win = Qin - 2 Qout (8>
one obtains then from equation (1):
out w I
which is the statement of equation (8).
If we ask, independent of the thermal efficiency, for maximum work ratio rw, one obtains a
different value for A. Figure 4 shows a graph of rw vs. A obtained with equation (5) for B = 6.666.
One obtains a shallow maximum at A = 7 that is only about 10 percent larger than the value r = 3
at maximum thermal efficiency. Because rw is nearly constant around that point, the optimized
laser energy operates under the condition given by equation (6). The P-V and T-S diagram show
then a particularly simple form, since the isobaric compression step has vanished (see figs. 5 and 6).
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BRAYTON AND STIRLING CYCLES
We have performed a similar analysis for the laser powered turbine and Stirling engine. The
conditions of the Bray ton cycle are summarized in Figure 7. While the efficiency T? is fixed for a
given temperature ratio T2/T|, a maximum work ratio is obtained when (?
r -~
-T? (10)
as before.
The laser powered turbine operates with continuous wave (cw) radiation. The turbine
however, requires a priori larger powers than the piston engine. '
The Stirling engine can be embodied in a variety of designs. One that appears particularly
suitable for modification to laser power is shown in figure 8 and 9 (originally a Phillips, Eindhoven
design). The theoretical thermal efficiency is that of the Carnot engine, and the work ratio is related
to it by equation (10) see (fig. 10).
REFERENCES
1. Garbuny, M.: Laser Engine Operating By Resonance Absorption. NASA Ames Research Center. Laser Energy
Conversion Symposium, NASA TM-X-62269,18-19 Jan. 1973, p. 45-50.
2. Hertzberg, A.: The Photon Engine, ibid. p. 34-44.
3. Christiansen, Walter H.; and Hertzberg, Abraham: Gasdynamic Lasers and Photon Machines. Proc. IEEE, Vol.
61, no. 8, Aug. 1973, p. 1060-1072.
r
4. Gaydon, A. G.: Dissociation Energies and Spectra of Diatomic Molecules. 2nd rev. ed., Chapman and Hall
LTD, London 1953.
TABLE 1. - VALUES OF T0
Laser
C02
CO
HC1
HF
Wavelength, pt
10.6
4.7
3.5
2.8
hi>,eV
0.11
0.26
0.35
0.44
Ts = hiVk, °Kd
1,300
3,000
4,100
5,100
.Absorbing gas
SF6
CO
HC1
HF
Ediss. *V
3.13
11.1
4.4
5.9
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• 1 I 1 1 1 I I I 1 fi I i I 1 I I I I
Telescope
Expansion cyde
Volume -
1. Laser pulse stem
2. Pube ends (max T & P)
3. Power stroke ends
(exhaust valve opens)
4. Back stroke ends
(exh. vatve Cl., intake
opens)
1. Intake valve closed
(cyde completed)
Simplified laser engine
Figure 1.— The laser engine and PV diagram.
Si lent Absorp. config.
(c)
Figure 2.— Alternative details of operation.
Figure 3.— Laser piston engine (not optimized).
4
C
f 3
w
J 2
5 10 15
Compression ratio A ^
Figure 4.— Work ratio vs compression ratio in laser
piston engine.
F
B •= Tj/T, - 6.66
A " V3/V, = 17.2 (optimizedl
• 67%
I
Figure 5.— PV diagram for the pulsed piston laser
engine.
Figure 6.— Temperature-entropy diagram for the
pulsed piston laser engine.
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1 1 I 1 I 1 I I I 1 I 1 K I I I I I
Diagram of the Stirling cycle. For clarity, the pitton and displacer
are assumed to move ditcontinuously.
Heater & regenerator
I. Power piston at bottom dead centre.
Displacer piston at top dead centre.
All gat in cold space.
Displacer piston
II. Displacer remaining at top dead
center. Power piston has compressed
gas at lower temperature.
III. Power piston remaining at top dead
centre. Disptacer has shifted gas
through cooler, regenerator and heater
into hot space.
IV. Hot gai expanded. Displacer and
power piston have reached bottom
dead centre together. With power
piston stationary, displacer now forces
gas through heater, regenerator and
cooler into cold space, thus re-attaining
situation I.
Entropy, S
1 — 2 lien tropic compression T
2 — 3 Isobaric heat addition Efficiency; i?*-!---"!- ™-J—
3-4 Isentropic expansion 2 /^2\k-1i sn
4-1 Isobaric heat rejection
. The p-V diagram
| of the Stirling cycle
The discontinuous movement of piston and displacer as a function
of time. B end E indicates the chances in volume of the hot space
(VE), band C those of the cold space (Vc I. The changes in volume
are plotted separately below.
Figure 1- The Bray ton Cycle. Figure 8.- The Stirling engine.
Regenerator
Connecting ducts
.Piston rod rolling seal
Direction
of ro'
of laser beam
Swash plate
Cnmhead 1 -. 2 Isothermal heat rejection
2 -» 3 Regeneration process
3 -» 4 Isothermal expansion
4 -* 1 Storage process
Figure 9.— Laser-driven Stirling engine. Figure 10.— Thermodynamic cycles for the Stirling
engine.
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DISCUSSION
Ken Billman, NASA Ames Research Center - Max, it was not apparent to me why you have concentrated on the
piston engine. In other words, why is the turbine not a viable alternative?
t
Answer: Well, actually it is. In a long term approach, however, we are restricted with maximum turbine blade
temperatures of 2000°K. In the near term approach, we looked into various turbines and found that they require
much higher power than those around the laboratory, that is, 20 to 30 kW. But the real reason is, of course, that
although they run CW, we will have to get around the turbine blade problem.
Ned Rasor, Rasor Associates — I think you showed a 67 percent thermodynamic efficiency. How does that
translate into overall efficiency, or is that the overall efficiency?
Answer: No, we don't claim that we have achieved it — it will be the case when it is built. This is our hope and aim, F
if we can work at this temperature.
Dick Pantell, Stanford University - You described that the third approach, direct use of vibrational energy,
suffered from the engineering problem of separating the upper and lower energy states?
Answer: Well, actually I must confess that I haven't considered using inhomogeneous fields for separation.
Dick Pantell, Stanford University - Yes, that is what I was going to suggest - to use inhomogeneous electrostatic
fields. £
Answer: Yes, it may work, but it seems to be beset with great complexity. I believe a wise man would not
undertake such a scheme easily.
Abe Hertzberg, University of Washington — Let me comment! Piston engines actually scale down better than gas
turbines. There are good large piston engines, however, such as a good diesel engine which could have a thermal
efficiency of 60 percent and maybe you have been working on something closer to the Sargent cycle which will be a
little higher. But the real efficiencies tend to be closer to 37 percent. This is due to the pumping work, friction, and
so on.
Answer: Yes, but it's a "bird in the hand".
Abe Hertzberg, University of Washington — Oh yes, I agree.
Max Garbuny: Incidently, I might mention here something that I glossed over — the window problem. As was
mentioned at the last meeting, it must handle these temperatures with good transmission and strength. Well if we go
to CO wavelengths, we can solve this with the marvelous material: sapphire which can handle something like
170,000 lbs/in^ pressure. So this problem can be solved. £
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Optimization of engines operated remotely by laser power

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