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Comment/Rebuttal Response to the Comments: Fuel Efficiency of Internal Combustion Engines R. Tao,* K. Huang, H. Tang, and D. Bell Department of Physics, Temple UniVersity, Philadelphia, PennsylVania 19122 ReceiVed March 5, 2009. ReVised Manuscript ReceiVed May 6, 2009 ¨ mer Gu¨lder recently claims In his comments1 on our paper,2 O that internal combustion engines built in the last 10-20 years already reached the combustion efficiency of 98-99%; therefore, there is no room for us to improve the fuel efficiency more than 2% because “it violates the first law of thermodynamics”. Gu¨lder may not be alone. Because this issue is very important, especially, at the time when cleaner and more efficient combustion of 21st century transportation fuels are critically needed, we are writing this response, showing that his statement has no scientific base. The fuel efficiency of internal combustion engines depends upon the combustion speed and timing. With the same engine, even if 100% of the fuel is burned inside the engine chamber, the fast-combustion process has a much higher fuel efficiency than that of the low-combustion process. Therefore, with the same engine, injection of small fuel droplets leads to much better performance than that with large fuel droplets. Gu¨lder’s “combustion efficiency” is the burning percentage, which equals 100% minus the heat loss through the exhausting system with his eqs 1 and 2. In other words, it only counts the loss through the exhausting system and assumes that the rest of the chemical energy is released inside the engine chamber. This method was originally used to calculate the percentage of fuel burned in a burner or boiler by counting the chemical energy escaped from the chimney as the only loss. For a burner or boiler as a heating device, the released heat is to warm up the substance and not to be converted into work as internal combustion engines. Even so, people are warned that this definition of “combustion efficiency” can be misleading because it only counts the chemical energy escaped from the chimney and tells nothing about any other kinds of heat losses for boilers and burners.3 It is important to understand that, quite different from burners or boilers, the burning fuel in internal combustion engines releases the heat, expanding the gas and pushing the piston to do the work. The combustion speed and timing is very crucial here. If the combustion is slow, some heat released at the time when the piston is near the bottom center (BC) crank position will not do the work for the engine, and then the combustion cannot be efficient. Therefore, even in the case that 100% of the fuel chemical energy is released inside the engine chamber, * To whom correspondence should be addressed. Fax: 215-204-5652. E-mail:
[email protected]. ¨ . L. Energy Fuels 2009, 23, 591–592. (1) Gu¨lder, O (2) Tao, R.; Huang, K.; Tang, H.; Bell, D. Energy Fuels 2008, 22, 3785– 3788. (3) For example, see http://www.habmigern2003.info/3_combustionefficiency.html.
the difference in the combustion speed and timing can lead to a significant difference in the fuel efficiency. To illustrate our point, let us consider a typical four-stroke cycle engine (Figure 1) with two widely used ideal models of engine combustion process: constant-volume combustion process and constant-pressure combustion process.4 The constantvolume combustion process is represented by the pressure-volume (P-V) diagram in Figure 2, where, immediately after the fuel is injected into the chamber, the combustion is infinitely fast as the piston comes at the top center (TC) crank position. The constant-pressure combustion process is a slow combustion, which is represented by the P-V diagram in Figure 3. The fuel efficiency is defined by ηf ) Wc,i/(mfQLHV)
(1)
where Wc,i is the indicated work per cycle, i.e., the sum of the compression stroke work WC and the expansion stroke work WE, Wc,i ) WC + WE, mf is the fuel mass injected into the chamber per cycle, and QLHV is the heating value of the liquid fuel. From the laws of thermodynamics, for the constant-volume combustion process in Figure 2, we have WC ) U1 - U2 ) mcv(T1 - T2) and WE ) U3 - U4 ) mcv(T3 - T4), where m is the gas mass inside the chamber and cv is the specific heat of the gas at constant volume. We use cp as the specific heat at constant pressure. For ideal gas, both cv and cp are constants and their ratio is γ ) cp/cv.5 When the fuel is burned completely inside the chamber, mfQLHV ) mcv(T3 - T2). Then, from eq 1, ηf,v ) 1 - (T4 - T1)/(T3 - T2). We define γc as the ratio of the maximum cylinder volume to the minimum cylinder volume, γc ) V1/V2. For adiabatic and reversible expansion and compression, we have T2/T1 ) T3/T4 ) (γc)γ-1. Therefore, for the constant-volume combustion process, the fuel efficiency is given by ηf,c ) 1 -
1 γcγ-1
(2)
For the constant-pressure combustion process in Figure 3, WC ) U1 - U2 ) mcv(T1 - T2) and WE ) P2(V3 - V2) + U3 - U4 ) m[γcvT3 - cvT4 - (γ - 1)cvT2], while mfQLHV ) mγcv(T3 T2). From eq 1, we have ηf,p ) 1 - (T4 - T1)/[γ(T3 - T2)]. (4) Heywood, J. B. Internal Combustion Engine Fundamentals; McGrawHill Book Company: New York, 1988; pp 161-197. (5) Kittel, C.; Kroemer, H. Thermal Physics; W. H. Freeman and Company: New York, 1980; pp 165-167.
10.1021/ef900193z CCC: $40.75 2009 American Chemical Society Published on Web 05/19/2009
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Figure 1. A typical four-stroke cycle engine, (a) compression stroke, (b) power stroke (fuel injection, combustion, and expansion), (c) exhaust stoke, and (d) intake stroke.
After introducing a parameter β ) V3/V2 ) T3/T2, we have T2/ T1 ) (γc)γ-1 and T3/T4 ) (V4/V3)γ-1 ) (γc/β)γ-1 for the adiabatic and reversible expansion and compression. Hence, the fuel efficiency for the constant-pressure combustion process is given by ηf,p ) 1 -
1 γcγ-1
[
βγ - 1 γ(β - 1)
]
(3)
We note that β is related to the specific enthalpy decrease per unit mass of working fluids during the combustion, Q* ) mfQLHV/m ) γcv(β - 1)T2. Because β > 1, a comparison of eqs 2 and 3 indicates that, for the same engine, the fuel efficiency of the fast-combustion process is much higher than that of the slow-combustion process. The above expressions are most useful if we choose the parameters, γ, γc, and Q*/cvT1 to match the real working fluid properties in a real engine. Therefore, we choose γc ) 12, γ ) 1.3, and β ) 4.12. The fuel efficiency for
the constant-pressure combustion process is ηf,p ) 0.380, while for the constant-volume combustion process, the fuel efficiency reaches ηf,v ) 0.525. This indicates that, while the burning percentage (or “combustion efficiency”) remains 100%, the fuel efficiency can be improved by 38% for the same engine when we increase the combustion speed. If such an engine is on a vehicles, then the fuel mileage of the vehicle can be improved by 38% when we increase the combustion speed. Applying the limited pressure combustion model, we can further show that the fuel efficiency in the engine improves as the combustion speed increases.4 The constant-volume combustion process has the combustion infinitely fast. It thus has the highest efficiency for a given engine. The slow combustion occurs when large fuel droplets are injected into the combustion chambers: the combustion takes more time, and some released heat comes too late to do the work. With small fuel droplets, the fuel can mix with air much better, the combustion goes faster and cleaner, and the heat is
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Figure 2. Constant-volume combustion process: 1-2, adiabatic and reversible compression; 2-3, combustion process at constant volume; 3-4, adiabatic and reversible expansion; 4-5-6, exhaust process; 6-1, intake process.
Figure 3. Constant-pressure combustion process: 1-2, adiabatic and reversible compression; 2-3, combustion process at constant pressure; 3-4, adiabatic and reversible expansion; 4-5-6, exhaust process; 6-1, intake process.
released on time to push the piston to do work. It is clear that, with the same engine, injection of small fuel droplets can reach much higher fuel efficiency than that with large fuel droplets. In last the 10-20 years, vehicles with internal combustion engines have improved their fuel mileage more than 30%. Most of them come from improving the combustion with increasing fuel pressure or new fuel injectors. The higher fuel pressure produces smaller fuel droplets. This simple fact corroborates our point of view. Misusing the quantity “combustion efficiency” for internal combustion engines is very harmful. This quantity is only estimating the percentage of fuel burned inside the engine chambers and has little to do with the fuel efficiency or engine efficiency. Moreover, to meet the emission standards, currently almost all vehicles have a catalytic converter to absorb CO, HC, unburned fuel, and particulate matter. The emission out from the exhausting lines is just a small portion of the exhausts from the engine chambers. In addition, if the fuel droplets injected into the engine chambers are too big, some fuel may pass the engine in the liquid state and be burned inside the catalytic converter, a well-known fact from the repair of catalytic converters. As mentioned before, industries use the same method to calculate the percentage of fuel burned inside burners or boilers. Because oil burners have no device similar to a catalytic converter to absorb the emission, most burners have this percentage of 73-85%. The “high efficient” burners have this percentage of 85-93%.3 If we include all CO, HC, and other materials collected by the catalytic converter and the fuel burned inside the catalytic converter, the percentage of fuel burned inside the engine cylinders may be away from being complete. In his comments, Gu¨lder states that gasoline engines mix fuel and air at the molecular level and therefore no further atomization is possible. This claim has no scientific base. Almost all current gasoline vehicles use port-injected engines. Gasoline is first injected into cylinders as droplets. Before the ignition, the
gasoline evaporates. Most port-injected gasoline engines have the fuel pressure around 30-70 psi. In our experiment, we used 100 psi for the gasoline injection and found some droplets had a diameter as large as 0.7 mm. Therefore, with fuel pressure of 30 psi, we can expect many droplets with diameters exceeding 1 mm. Because evaporation starts from the droplet surfaces, such large droplets are difficult to be completely evaporated before the ignition comes. In such a case, the combustion starts from gasoline vapor and droplet surfaces. Some heat released from droplet burning may come too late to do the work for the engine. In the worst case, some fuel may pass the engine in the liquid state and is burned at catalytic converter. Therefore, injection of finer gasoline droplets into the port-injected engine will increase the fuel efficiency. The following fact further illustrates the above point. During a cold winter, some gasoline vehicles have difficulties to start or feel powerless at the start just because the gasoline droplets take too long to evaporate at low temperature. The well-known recipe for this problem is to inject much smaller droplets into the engine cylinder. Then, the evaporation is much faster, and the engine is easier to start and feels more powerful at the start. After the engine is started, the metal surfaces are warmed enough to help evaporate the gasoline and the engine may operate fairly well without hesitation. However, in the case of large fuel droplets, the ignition comes when some droplets are still evaporating, the combustion process is not fast enough, and the fuel efficiency cannot be high. To provide the scientific foundation to enable technology breakthroughs in transportation fuel use, the Office of Basic Energy Sciences in the U.S. Department of Energy (DOE) convened at a Workshop on Basic Research Needs for Clean and Efficient Combustion of 21st Century Transportation Fuels from October 30 to November 1, 2006. The report from the workshop claims that the combustion in internal combustion engines is well below the optimal efficiency, gasoline engines can be 50% more efficient, and diesel engines can be 25% more efficient.6,7 Gu¨lder himself also noticed that, in last 40 years, diesel engines have had the fuel pressure continuously increased from 200 to 2000 bar. The direct result of higher fuel pressure is to reduce the injected fuel droplet sizes and have a finer atomization. The achievements of the higher fuel pressure are remarkable: the diesel engines have had the fuel efficiency improved more than 30% in the last 20 years. The DOE workshop also pointed out that one direction to improve the engine efficiency and emission is to have combustion with ultra-dilute mixtures at extremely high pressure, which will be much higher than the current fuel pressure on diesel vehicles to produce finer fuel mist.8-10 Gu¨lder voices his objection to these suggestions, by claiming that the current existing technology already has the fuel pressure high enough. He further tries to convince us that all internal combustion engines built 10-20 years ago already reached efficiency 98-99% and there is no room to improve. We strongly disagree with him. The influence of the viscosity of the fuel on the atomization can be further illustrated by the Ohnesorge number,11 which is defined as (6) http://www.sc.doe.gov/bes/reports/abstracts.html. (7) Manley, D. K.; Mcilroy, A.; Taatjes, C. A. Phys. Today 2008, NoVember, 47–52. (8) Aoyagi, Y.; et al. Advanced diesel combustion using of wide range, high boosted and cooled EGR system by single cylinder engine. 905 SAE Tech. Pap. 2006-01-0077, 2006.
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Oh ) η/√FDσ
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(4)
where D is the diameter of the droplet and η, F, and σ are the viscosity, density, and surface tension of the fuel, respectively. As the viscosity η is reduced, the droplet diameter D is also reduced. For diesel fuel, this conclusion was experimentally verified somewhere else.12 In our atomization experiment, we found that, in addition to reducing the average droplet size, as the viscosity of the fuel was reduced, many small droplets with a diameter of several micrometers were produced with our device. While the exact reason has yet to be determined, we believe that it comes from the electrostatic effect when some electrons are attached to the fuel through the device. Because diesel has a higher viscosity than that of gasoline, at the same fuel pressure, diesel has a much larger droplet size than that of gasoline in the atomization. However, Gu¨lder fails to understand that, the higher the fuel pressure, the smaller the droplet size. Therefore, with a pressure of 200 psi, the size of diesel droplets is compatible with the gasoline droplet size at 100 psi but not 10 times smaller. In our paper, three tests were presented, two lab tests and one road test. Our first lab test was carried out at Carnaglia Iveco by its engineers. The power output was improved by 5.5%, exceeding the 1-2% limit set by Gu¨lder. As stated in the paper, from the test at Carnaglia Iveco, we realized that, selecting electric field and time duration for the fuel inside the electric field, we can further improve the performance of our device. The 6 month road test with Mercedes-Benz 300D was actually before the second lab test. From the picture provided in our paper, some readers already identified that the vehicle is a 1993 Mercedes-Benz 300D. The road tests were very controlled. In (9) Hiroshi, M.; et al. The potential of lean boost combustion. 905 2004 FISTA World Automotive Congress, Barcelona, Spain, May 23-27, 2004. (10) Pirault, J. A.; Klippenstein, S. J. J. Phys. Chem. A 2006, 110, 10528–10544. (11) Lefebvre, A. H. Atomization and Sprays; Taylor and Francis: Oxford, U.K., 1989; pp 27-73. (12) Jankowski, A.; Sandel, A. J. KONES Intern. Combust. Engines 2003, 10, 3–4.
fact, the road tests only involved the turn off of the device and turn on of the device, and therefore, the condition was easy to control. We disagree with Gu¨lder, who claims that “road tests are not reliable and do not constitute scientific evidence”. When we purchase a new vehicle, the fuel mileage from the lab tests displayed for the new vehicles is usually higher than that from our road tests. From our own experience, we know that road tests are important, reflecting what we actually acquire. Under the controlled condition, the road tests are very reliable. Because our road tests reported significant fuel mileage improvement, we brought the vehicle for lab tests, which confirmed the road tests and, in fact, had a better result than that of the road tests. We did tests at high fuel consumption (high power outputs about 40-50 hp), low fuel consumption (low power outputs about 0.4 hp), and at acceleration. The improvements were all significant. At high fuel consumption and acceleration, the situation was even better than that at low fuel consumption. However, in our opinion, the low fuel consumption is more representative because the fuel mixes with air better and the different results should be the representative indication between combustion with large fuel droplets and the combustion with small droplets. Therefore, we used the low fuel consumption data in our paper and called it as the “typical lab test result”. After our paper was submitted for publication, our devices were tested on several diesel trucks, which also show significant fuel mileage improvement and reduction of emission. While the details will be published elsewhere, we just want to mention that the fuel mileage improvement well exceeds Gulder’s limit of 1-2%. In summary, the statement made by Gu¨lder that combustion engines built in the last 10-20 years already reached the combustion efficiency of 98-99% and there is no room for us to improve the fuel efficiency more than 1-2% is wrong and misleading. The internal combustion engines are still away from being efficient and clean. EF900193Z
