Development of Low-Exergy-Loss, High-Efficiency Chemical Engines

Investigators

Chris F. Edwards, Associate Professor, Mechanical Engineering; Shannon L. Miller,

Matthew N. Svrcek, Sankaran Ramakrishnan, Graduate Researchers, Stanford University.

Abstract

In this report we describe our continuing efforts to develop ultra-high efficiency

chemical engines. This work is divided into two branches, one for batch processes and

one for steady flow. Both are based on what we have termed the ‘extreme-states

principle’—that reducing efficiency losses due to unrestrained combustion requires

performing the reaction at the highest possible internal energy state.

In the exploration of batch processes, we previously completed construction of a free-

piston device capable of hosting combustion at volumetric compression ratios in excess

of 100:1, with the goal of achieving 60% thermal efficiency. Our work for this past year

has focused on three areas. First, we characterized the non-reacting performance of the

device. A quantitative measure of combined heat and mass transfer losses during the

compression-expansion process was obtained. Second, light-load combustion was

introduced (equivalence ratio ~ 0.3), and indicated thermal efficiency was measured for

compression ratios from 30:1 to 100:1. In this first pass, efficiency peaked at 50.5%.

Third, full-bore optical access in the end-wall of the combustor was used to perform

high-speed schlieren and direct photography of the spray and combustion. A study of

non-reacting spray penetration and dispersion was completed, and a study of combusting

spray penetration, dispersion, and ignition delay has begun.

Taken together, these three areas of progress represent a systematic approach to

achieving our goal of 60% efficiency. Comparing the measured thermal efficiency to an

ideal cycle, we identified two main areas of losses. The first is the heat and mass transfer

measured in the non-reacting experiments and associated with the current device

geometry and sealing technique. The second is due to un-optimized combustion. The

optical access work addresses this latter point, as we begin to study the combustion event

in detail.

The extreme-states principle has also been shown to apply to steady-flow engines. A

number of differences from the batch engine, i.e. turbomachinery irreversibility, material

temperature limit, and the availability of kinetic energy as an additional parameter,

impact the feasible optimal possibilities. Our recent work showed that a temperature-

constrained combustion process at feasible extreme states is the optimal choice for

efficiency maximization, as opposed to the conventional choice of a Brayton cycle with

reduced pressure ratios. Further work includes the control of kinetic energy, thus

extending the extreme-states principle to both stationary and aviation steady-flow

engines.

Introduction

A majority of energy uses today involve the transformation of chemical bond energy

to work, including transportation, power generation, and industrial applications.

Improving the efficiency of engines that perform these chemical energy transformations

is likely to be a necessary part of any solution to climate change and energy security. Our

effort focuses on significantly improving the efficiency of chemical engines by taking a

fundamental approach—we start with purely thermodynamic considerations, determine

where efficiency losses occur, and attempt to identify and investigate solutions to these

losses.

In our first GCEP project, taking this approach led to the identification of an extreme-

states principle for combustion engines: The only way to reduce the efficiency loss due

to unrestrained reaction in an internal combustion engine is to conduct the energy

conversion at the highest-possible state of energy density [1]. In this project, we

undertake an implementation of the extreme states principle for batch processes (e.g.

piston-cylinder engines) by investigating the feasibility of operating at compression ratios

of 100:1 or greater. Combustion at such states requires a very different engine design—

most likely free-piston with electromagnetic extraction. As a first step, we identified the

following key research issues: whether combustion could be successfully conducted

(initiated, phased, and completed) under such conditions, and whether the indicated

efficiency after real-world-implementation losses would be sufficient to warrant

development of such a class of engines.

Development of the above work for a batch process followed the logic path of

thermodynamically defining the optimal process, identifying the key parameters for ultra-

high efficiency operation, and then implementing and testing in hardware. We are

following the same path for the other major class of chemical engines: steady-flow, such

as gas turbines. This branch of our work is currently in the phase of thermodynamic

analysis and optimization—developing the analogous extreme states principle for steady-

flow devices. This report details progress made in both of these efforts over the past

year.

Progress and Results

Demonstration of Low-Irreversibility Combustion by Extreme Compression

The extreme compression device is shown schematically in Figure 1. A free piston is

accelerated down the cylinder bore, driven by compressed air from a reservoir via a fast-

acting poppet valve. Near the end of its stroke, the piston enters a forged steel combustor

section, that contains ports for multiple diesel fuel injectors and a pressure transducer. A

sapphire window is mounted in the end-wall of the combustor, providing full-bore optical

access. The cylinder stroke is chosen to be around 2.5 meters to reduce surface-to-

volume ratio at the minimum volume (top dead center, or TDC). The combination of

high piston speed and high pressure eliminates the possibility of using traditional

pressure-energized, oil-lubricated piston seals. Our current strategy uses fixed graphite

rings, the diameter of which is within very close tolerance to the cylinder bore—in effect

using clearance control between the ring and wall to provide the pressure drop across the

piston. Piston position during a run is determined by magnetic sensors distributed along

the length of the cylinder. Since the time of the last GCEP report we have added an

optical position sensor, similar to an optical encoder, near the combustor section to

provide high accuracy piston position measurements near TDC. Piston position,

synchronized with pressure data, provides the indicated work output of the device. Fuel

injection is via a high-pressure, common-rail Bosch Diesel pump and injectors, with

custom nozzle tips that allow a variety of injection strategies. Our previous GCEP report

provides further detail about the design of the experiment [2].

Optical sensing section

Ferrous washer

Clearance control ring

Airreservoir,70 bar

Fast-acting poppet valve assembly

2.5 m long cylinder

High-speed camera

Free-piston

Optical access

Highpressurefuelinjectors

VR sensors

Optical insert for position sensing

Pressure transducer

Pressuretransducer

2 channel,high-speeddata acquisition

16 channel,multiplexeddata acquisition

High-strength combustor

Injection System: 1500 bar common rail,fuel pump and injector controller

Figure 1: Schematic of the extreme compression device.

At the time of the previous GCEP report, we had completed a handful of initial

experiments demonstrating that the device was capable of operating in the desired space

of compression ratio and piston speed. This put us in a position to use the device over the

past year to begin exploring operation and combustion at extreme-compression

conditions. Our work has been in three main areas: (1) characterization and analysis of

non-reacting performance of the device, (2) preliminary mapping of combustion

performance over the compression ratio range, and (3) use of the full-bore optical access

to begin detailed exploration of the spray and combustion process. Progress in each of

these areas is described below.

Non-Reacting Performance A necessary step toward understanding operation at extreme compression ratios is to

characterize the compression-expansion process in the free-piston device. The first set of

tests demonstrated the ability to repeatably and predictably target compression ratios

from 30 to 100:1. Unlike a traditional slider-crank engine, the piston motion is not

mechanically constrained, but rather depends on the reservoir pressure, the valve opening

profile, and friction forces during the run. Using the clearance-control sealing strategy

mentioned above, our initial tests showed compression ratio repeatability within 1% for

any given initial conditions.

An unexpected discovery was the generation of significant acoustic waves in the

cylinder during compression at high accelerations. The plots in Fig. 2 both show pressure

traces for a compression ratio of 45:1 but with different piston masses and, therefore,

mean piston speeds (90 and 60 m/s on left and right, respectively). Even though the peak

piston speeds are well below sonic, the acceleration is sufficient to generate finite-

amplitude compression waves with the lighter piston. The origin, frequency, and

amplitude of these waves have been confirmed by calculations using the method of

characteristics. We note their significance both because they can be easily suppressed by

increasing the mass of the piston, and because they may provide an opportunity to

engineer a regenerative heating process during the intake stroke using the heat capacity of

the cylinder wall. Inasmuch as we anticipate using a net-adiabatic cooling strategy for

this type of high-efficiency engine, this example serves to illustrate that new,

unanticipated opportunities are likely to be uncovered as we begin systematic studies at

these operating conditions.

58 59 60 61 62 63

20

40

60

80

100

120

140

160

Time (ms)

Pre

ssu

re (

bar)

350 g piston

78 80 82 84 86

20

40

60

80

100

120

140

160

Time (ms)

Pre

ssu

re (

bar)

800 g piston

Figure 2: Pressure vs. time for 45:1 compression ratio; two different

piston masses.

Efficiency loss mechanisms for the device can be divided into two general categories:

those associated with the compression-expansion process, and those associated with the

combustion process. To characterize this first category, a number of experiments were

performed without fuel injection over the operating range of the device. Representative

pressure-volume plots for a few compression ratios are shown in Fig. 3. Also shown is

the pressure-volume path of an isentropic process (the dashed line), on which an ideal

compression and expansion would fall. For the actual device, a combination of heat and

mass transfer cause the experimental pressure-volume trace to fall below this line. The

work integral of the pressure-volume loop provides a quantitative measure of the

combined losses during compression and expansion.

10-2

10-1

0

100

200

300

400

500

Volume (V/V0)

Pre

ssu

re (

bar

)

Isentrope

CR = 30CR = 49.5CR = 71.8CR = 97.1

Figure 3: Non-reacting pressure-volume traces for several

compression ratios.

Figure 4 depicts two ways of thinking about the magnitude of losses—net work

relative to the work invested during the compression stroke, and the fraction of isentropic

peak pressure obtained. Although much work remains to be done on the piston sealing

system, the figure shows that even with the current, passive strategy we are capable of

obtaining a significant fraction of isentropic peak pressure under “motored” (non-

combusting) conditions. For compression ratios below 30:1, more than 95% of isentropic

peak pressure is realized. As compression ratio is increased, this drops off, approaching

85% at 100:1. One should also note that these results are obtained with cold walls, such

that the heat loss from the gas is much more significant than for a conventional engine

with warm walls. So while reducing heat and mass loss are of critical importance for

achieving high efficiency, the current sealing approach is already sufficient to provide

access to the conditions we need to develop the combustion system.

20 40 60 80 100−22

−20

−18

−16

−14

−12

−10

−8

CR

Wnet/W

com

p (

%)

20 40 60 80 10084

86

88

90

92

94

96

CR

Ppeak/P

S (

%)

Figure 4: Compression-expansion net work divided by compression work (left)

and experimental peak pressure as a percentage of isentropic peak pressure (right).

Over this past year we also began analysis work to further understand the

mechanisms of heat and mass loss in the system. While the data shown in the previous

figures provide a reliable, quantitative measure of total loss, there is no way based on our

current measurements to determine experimentally what fraction of the loss is due to

mass transfer or to heat transfer. Computational fluid dynamics modeling of the non-

reacting compression-expansion, in addition to experimental steady-flow testing of piston

blowby are currently underway, and should provide a quantitative assessment of the two

losses.

Initial Combusting Performance During the past year we obtained an initial map of thermal efficiency under relatively

light-load conditions over a range of compression ratios from 30 to 100:1. For this study,

two high-pressure diesel injectors with custom nozzle tips were used with a 1.5 ms

injection time, resulting in an overall equivalence ratio of around 0.3. Injection timing

was triggered by one of the magnetic position sensors to control combustion phasing.

Fuel flow rate was determined by calibration of the injectors as a function of chamber

pressure. Figure 5 below shows typical pressure-volume traces for an air-only run and

for two combusting runs at 60:1 CR. For the combusting case the pressure-volume loop

goes above the isentrope resulting in a positive net-work integral.

10−2

10−1

100

10−1

100

101

102

103

Volume (V/V0)

Pre

ssure

(bar

)

Air

Combustion

Low−Blowby Combustion

Isentrope

Figure 5: Pressure-volume traces for combusting and non-combusting

data at 60:1 CR.

The net work per unit fuel lower heating value gives the indicated first-law efficiency,

which is plotted as the red points in Fig. 6. For this data set, the efficiency peaked at

around 45% before rolling off at higher compression ratios. To put this in context, the

blue line is the ideal reactive Otto cycle efficiency for the same equivalence ratio.

Subtracting the net work loss found on an air-only experiment at a given compression

ratio from the ideal work output results in the black points and fit. By looking at the

efficiency expected just from air losses, one can see that much of the losses, including the

drop in efficiency at high compression ratio, is due to heat and mass transfer for the air

compression-expansion process. The remaining losses we attribute to the un-optimized

combustion system—a combination of phasing, inadequate combustion rate and air

utilization, product gas wall wetting leading to enhanced heat transfer, etc. Stated

another way, the combination of analysis and results indicates that efforts in development

of both the combustion system and the wall interface sealing are warranted, and each is

likely to contribute significantly to realizing our efficiency potential.

0 20 40 60 80 10020

30

40

50

60

70

80

Compression Ratio

Eff

icie

ncy

(%)

Ideal 1st law efficiency

70−80% of 1st law efficiency

Experimental efficiency

Ideal minus air−only losses

Reduced blowby experiment

Figure 6: Cycle efficiency versus compression ratio.

As an illustration of the last point, a single experiment using a special, very-low-

blowby sealing technique was conducted at 60:1 compression ratio. Using this seal, and

a slightly improved method of combustion phasing, an indicated efficiency of 50.5% was

achieved. Although we note that this is indicated efficiency, not brake, and therefore

corresponds to a brake efficiency slightly below 50% when probable mechanical losses

are considered, we also point out that this efficiency was achieved using cold (ambient

temperature) walls, such that the effects of heat loss are much more significant than they

would be in an actual engine. In effect, we are already not far from being able to

demonstrate the possibility of realizing a 50% efficient engine and reiterate that our intent

is to demonstrate the potential to achieve 60%.

Optical Study of Spray and Combustion

During the past year we constructed an optical system for studying the combustion in

detail. A schematic of the optical system is shown in Fig. 7. A collimated beam of 488-

nm laser light reflects off a mirror mounted on the piston, is focused through an

achromatic lens to a schlieren stop and recorded by a high-speed camera. This setup

allows simultaneous recording of schlieren effects from gas density variation in the

cylinder, extinction in the liquid portion of the spray, and direct luminosity from

chemical reaction. In addition, a high-sensitivity photodiode with a UV bandpass filter

detects OH chemiluminescence for defining the start of combustion.

Figure 7: Experimental optics setup.

The first study we completed with the optical system was an exploration of fuel spray

penetration and dispersion without chemical reaction. For this study an injector with a

single orifice injected a spray of diesel fuel across the cylinder starting 1ms before TDC.

To prevent combustion, the cylinder was filled with nitrogen rather than air. Schlieren

images of the spray were recorded at 36000 frames per second and post-processed to

define spray penetration (via spray tip location) and dispersion (via spray angle). Figure

8 shows a sample image from the camera and the resulting spray region.

High-speed Camera

Schlieren Stop

Beam Expander and

Spatial Filter

Beamsplitter

Cylinder

Piston with

Mirror

Lens

Sapphire

Window

Fuel Injector

Argon-Ion Laser

Clearance

Volume

Photodiode

θ

L/2

L

Figure 8: Image from camera and resulting processed spray outline. CR

90:1, 0.6 ms after start of injection.

Penetration was measured versus time for compression ratios from 30 to 100:1 and

compared to spray correlations developed by Naber and Siebers [3]. Figure 9 shows the

experimental penetration data along with the correlations for a number of compression

ratios. Unexpectedly, while the penetration rate agreed well with the correlations at

lower compression ratios, above 60:1 the penetration rate remained essentially constant.

This result is explained by the unique free-piston dynamics, in which the compression is

more rapid at high compression ratios. As shown in Fig. 10, the density at start of

injection, around 1 ms before TDC, is approximately the same for 60:1 and 100:1.

During the early part of injection the penetration profile follows the correlation for the

lower density at start of injection, but near the end of injection the penetration profile

follows the slope of the correlation at higher density.

0 0.2 0.4 0.6 0.8 1 1.20

5

10

15

20

25

30

35

40

45

t (ms)

L (

mm

)

30:1

45:1

60:1

70:1

80:1

90:1

100:1

Data CRCorrel.

−1.5 −1 −0.5 0 0.5 1 1.530

40

50

60

70

80

90

100

t (ms)

Gas

Den

sity

(k

g/m

3)

CR = 60:1

CR = 100:1

SOI, EOI

Figure 9: Non-reacting spray penetration Figure 10: In-cylinder density

data and correlations for several CR. vs. time for 60 and 100:1 CR.

Recently we began extending our fundamental, single plume studies to combustion.

Figure 11 shows a sample image of a combusting spray, in this case for a 60:1

compression ratio. In the image one can see: (1) direct luminosity from soot combustion,

(2) sharp density gradients via schlieren at the edge of the reaction zone, and (3) gradients

in the background gas due to in-cylinder fluid mechanics. Spray penetration and

dispersion are determined from the camera images, similar to the non-reacting case. In

addition, a UV-sensitive photodiode detects the start of OH chemiluminscence (which is

not visible in the camera images) allowing for a measurement of ignition delay, as shown

in Fig. 12. This study allows us to further understand the spray combustion behaviour in

the previously unexplored extreme states made accessible by this device, and provides

the basis for designing and optimizing the combustion process that is required for

achieving peak efficiency.

112.15 112.2 112.25 112.3 112.35

0

0.5

1

1.5

2

2.5

3

t (ms)

Lu

min

osity (

A.U

.) Start of Injection (from camera)

Ignition delay

~ 100 µs

Figure 11: Image from camera, CR = Figure 12: Photodiode output vs. time

60:1, 0.94 ms after start of injection. for CR = 60:1.

Theoretical Investigation of Low-Irreversibility, High-Efficiency, Steady-Flow Engines

Over the past few years a thermodynamic framework to define and develop high-

efficiency engine architectures has been developed as part of the research efforts in this

GCEP project. While the initial development was done with emphasis on batch-flow

engines [1], the framework was extended to simple-cycle, gas turbine engines and the key

results were discussed in our previous report [2].

Irreversibility minimization in gas turbine engines follows an extreme-state principle

analogous to the extreme-state principle for the piston-engines. However, unlike piston-

engines, irreversibility inherent in energy transfer as work for gas turbine engines led to a

limited extreme-state (i.e. a limiting pressure ratio for maximum efficiency). This

limiting pressure ratio is a result of irreversibility minimization, and not a pressure limit

obtained from purely material considerations. The variation of this pressure limit with

the extent of irreversibility in the work interactions (polytropic efficiency) is shown in

Fig. 13 for a natural gas/air, gas turbine engine. Figure 14 shows the variation of the total

irreversibility with pressure ratio, for a polytropic efficiency of 0.8 for the engine.

Polytropic Efficiency η

Pre

ssure

Lim

it P

* (

bar

)

0.6 0.65 0.7 0.75 0.8 0.8510

0

101

102

103

0.6 0.65 0.7 0.75 0.8 0.851500

1750

2000

2250

2500

2750

3000

3250

Max

imum

Tem

per

ature

Tm

ax (

K)

Figure 13: Variation of optimal pressure-ratio and peak temperature with polytropic

efficiency.

100

101

102

103

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Pressure Ratio

Entr

opy G

ener

atio

n (

kJ/

kg

mix

K)

Combustion

Fluid Friction

Total

P*

Figure 14: Trade-off between combustion and compression/expansion work

irreversibility for a polytropic efficiency of 80%.

The optimal, simple-cycle engine is realized by minimizing total irreversibility using

optimal control of energy transfer as work. The cycle is characterized by switching

points based on device polytropic efficiencies and results in a desirable operating

pressure ratio well over the currently existing pressure ratios in engines.

However, the limitation imposed by the maximum temperature on a practical

implementation of the optimal process was recognized in the previous report. Unlike the

conventional solution to this limitation, i.e., reducing pressure ratios and introducing

blade-cooling, the temperature limit was considered as a constraint to the irreversibility

minimization approach and efforts in the past year were focused on this.

In view of addressing a broader category of simple-cycle, steady-flow engines, i.e. the

inclusion of propulsion engines, it was recognized that management of kinetic energy

was key to irreversibility minimization and was also studied in the past year.

Efforts in the Last Year

Material temperature limits have been a severe constraint on practical implementation

of extreme-states in gas-turbine engines. This constraint was not considered in our

analysis so far. Hence, including this constraint to find the optimal engine cycle and

exploring its implications for engine architecture was the first key aspect addressed in the

past year. This approach led to a temperature-limited optimal cycle involving a part of

the combustion process at constant-temperature conditions. This architecture is

noticeably different from the currently existing blade-cooled Brayton-cycle engines and

can lead to significant increase in efficiency of simple-cycle engines.

The second key aspect studied in the past year is the effect of manipulating kinetic

energy in a simple-cycle, steady-flow engine. It was concluded that optimal control of

kinetic energy complements the extreme-state principle. The control of kinetic energy is

such that combustion occurs at extreme, sensible-energy states. This extends our

thermodynamic framework to propulsion engines. In the following two sections, details

of the temperature-limited, optimal cycle will be explained and key aspects of kinetic

energy management will summarized.

Temperature-Limited Optimal Cycle

The flow of the fuel-air resource through a generic steady-flow engine is modeled as

a Lagrangian control mass and mapped onto a thermodynamic state-space. The

thermodynamic state-space is defined by the entropic representation of state in

enthalpy ( )h , pressure ( )P and species mass-fraction ( )jY coordinates. Transfer of energy

using work interactions is considered as a control and entropy generation is minimized.

For details of this model the reader is referred to the report of the previous year.

The optimal cycle for the non-temperature-limited model advises combustion at the

highest-permissible enthalpy state to minimize entropy generation. It has been shown

that the attractor-state entropy is reduced for combustion at extreme states. However, if

during combustion the temperature exceeds the temperature limit, we can execute

expansion to reduce and maintain the enthalpy at the highest level permitted by the

temperature-limit, i.e., holding the system at the temperature limit and executing

isothermal combustion. The motivation here is to complete combustion at the highest

enthalpy state permitted by the temperature limit. This is different from the conventional

approach of not taking the system to extreme states in order to prevent the temperature

from attaining its limiting value during combustion.

Since we expand before the optimal-expansion switching point for the unconstrained

(by temperature) cycle is achieved, a temperature-limited, combustion cycle is less

efficient. The attractor-state entropy for this cycle increases due to the early expansion

during combustion. However, the cycle still performs better than a reduced pressure ratio

Brayton cycle if the attractor states of the temperature-limited cycle are lower in entropy

than that of the Brayton cycle. To ascertain the behavior of the attractor state trajectory a

thermodynamic simulation is performed.

Figure 15 shows a comparison of two natural-gas/air cycles with maximum pressure

of ratios of 40:1 and 160:1 respectively, executing the temperature-limited cycle, at 1650

K. The figure also shows a traditional 18.5:1 Brayton cycle with a turbine inlet

temperature of 1650 K.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8−1.5

−1

−0.5

0

0.5

1

1.5

s−si (kJ/kg

mixK)

h−

hi (

MJ/

kg

mix

)

Brayton (18.5:1)

CT (40:1)

CT(160:1)

Attractor (160:1)

Attractor (40:1)

fIncreasingwork−output

DecreasingS

genTemperature Limit : 1650K

i

c

Figure 15: Comparison of the optimal temperature-limited cycle with a Brayton cycle at

the same limit.

These curves confirm that the entropy of the equilibrium attractor state is significantly

lowered in comparison with that of the reduced pressure-ratio Brayton cycle. The choice

of the pressure ratios (160:1 and 40:1) is arbitrary. However, the existence of an optimal,

maximum pressure ratio due to irreversibility in turbomachinery is confirmed by the

efficiency roll-off shown in Fig 16. The plot also shows the efficiencies that can be

obtained using this optimal constant temperature (CT) cycle, in comparison with the

highest efficiency Brayton counterparts for three temperature limits.

101

102

103

0.35

0.4

0.45

0.5

0.55

0.6

Pressure Ratio

Exer

gy E

ffic

iency

1650K CT Cycle

1800K CT Cycle

2000K CT Cycle

Max Eff. Braytonwith the TIT above

data5

data6Polytropic Eff 0.9

Figure 16: Variation in efficiency of peak-temperature-limited, optimal cycles with

pressure ratio.

Finally, an observation related to the simulations and any conceivable implementation

of the optimal cycle is in order. The expansion rates required to maintain constant

temperature during premixed combustion are beyond feasible. Any practical

implementation can only be envisioned as a multi-stage injection/combustion process

alternating with expansion stages. The thermodynamic simulation shown takes this

approach.

Kinetic Energy Control

Kinetic energy in a steady-flow engine is an entropy-free form of energy.

Irreversibility occurs only when this energy is transferred in/out as work or transformed

into enthalpy. It is therefore desirable to know the optimal sequence of kinetic energy

transfers and transformation to be performed in the engine.

The effect of kinetic energy as an independent control on the entropy of the chemical

equilibrium attractor states is given by the following dependence:

( )( . .) 1( )

eq

eq

eq eq

d k edP v vds

T T

βα −−= +

,α β are the irreversibility factors associated enthalpy and kinetic energy transfers and

mutual transformation. These factors can be related to the polytropic efficiencies of the

transfer and transformation devices, i.e. compressors, fans, diffusers etc. A bang-bang

control of kinetic energy with device-based switching points is suggested by the

thermodynamic attractor and was explained in our previous report.

However, a stagnation temperature material limit imposes limitations on both kinetic

energy transfers and its transformation into enthalpy. Also, a desired exit kinetic energy

for propulsion engines must be considered for optimization. These considerations

demand a closer look at the management of kinetic energy in the engine.

Thus an extension of a rigorous optimal-control approach based on intuition provided

by the analysis of the chemical equilibrium attractor has been undertaken in the past year.

Work on the mathematical proofs for the approach is still in progress. However,

preliminary observations from the work suggest that, kinetic energy must be transformed

into enthalpy to achieve extreme states during and before combustion, if the temperature

in the engine is below the temperature limit. This complements the extreme states

principle.

The nature of the cycle changes when stagnation temperatures reach that of the

temperature limit. Kinetic energy control becomes coupled to pressure control. The

control of kinetic energy and pressure should be such that combustion proceeds at

constant stagnation temperature, analogous to the temperature limited optimal cycle

obtained in the previous section.

Exit kinetic energy requirements for propulsion engines, and irreversibility associated

with acceleration of flow in a nozzle, impose a limit on kinetic energy transformation into

enthalpy during combustion. This is analogous to the pressure limit introduced by the

polytropic work in gas-turbine engines.

Future Work

The completion of a temperature-constrained, kinetic energy and pressure controlled

simple-cycle engine would achieve the objective of a systematic extension of the

thermodynamic framework of irreversibility minimization to steady-flow engines with

only work regeneration. The extension of this framework to the class of engines with

regenerative transfers of matter and heat will be the key aspect of future work in this task.

Publications 1. Teh, K.-Y., Miller, S.L., and Edwards, C. F., Thermodynamic Requirements for Maximum IC

Engine Cycle Efficiency (I): Optimal Combustion Strategy. International Journal of Engine

Research 9:449-466 (2008). 2. Teh, K.-Y., Miller, S.L., and Edwards, C. F., Thermodynamic Requirements for Maximum IC

Engine Cycle Efficiency (II): Work Extraction and Reactant Preparation Strategies. International

Journal of Engine Research 9:467-481 (2008). 3. Svrcek, M.N., Miller, S.L., and Edwards, C. F., Effect of Extreme Compression on Diesel Spray

Penetration and Dispersion. Accepted for the International Conference on Liquid Atomization and

Spray Systems (2009).

4. Miller, S.L., Svrcek, M.N., LaCroix, O., Wilson, J., Edwards, C.F., Reducing Combustion

Irreversibility through Extreme Compression: Analyzing Device Performance. Submitted to ASME

International Mechanical Engineering Congress and Exposition (Nov. 2009).

References 1. Teh, K.-Y., Thermodynamics of Efficient, Simple-Cycle Combustion Engines. Ph.D. dissertation,

Dept. of Mech. Eng., Stanford Univ., Stanford, CA, 2007.

2. C. F. Edwards, S. L. Miller, M. N. Svrcek, and S. Ramakrishnan, Development of Low Exergy

Loss, High Efficiency Chemical Engines, GCEP Annual Technical Report, June, 2008

3. Naber, J. D., and Siebers, D. L., Effects of Gas Density and Vaporization on Penetration and

Dispersion of Diesel Sprays. SAE Paper 960034, 1996.

Contacts

Christopher F. Edwards: cfe@stanford.edu

Shannon Miller: slmiller@stanford.edu

Matthew Svrcek: msvrcek@stanford.edu

Sankaran Ramakrishnan: rsankar@stanford.edu