University of Washington
Introduction
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Figure 10
Figure 11
Conclusion
ABSTRACT
An automotive propulsion concept is presented which utilizes liquid nitrogen as the working fluid for an open Rankine cycle. Ambient heat exchangers are used to power an engine that is configured to maximize heat transfer during the expansion stroke. If sufficient heat input during the expansion process can be realized then this cryogenic propulsive system would provide greater automotive ranges and lower operating costs than those of electric vehicles currently being considered for mass production. Th e feasibility of meeting this engineering challenge has been evaluated and several means of achieving quasi-isothermal expansion are discussed.
The potential of cryogenic energy storage for automotive propulsion has been under investigation at the University of Washington as an alternative to electrochemical batteries for zero-emission vehicles (ZEV). It is anticipated that the use of an inert c ryogen, such as liquid nitrogen (LN2), as an energy storage medium would not pose any environmental burden, and in particular would avoid the issues of heavy metals pollution associated with lead-acid batteries. Another potential advantage over electro-c hemical batteries is that the installation of a cryogen distribution system could be realized by straight-forward modifications to the existing petroleum retail stations. Several means of utilizing the thermal energy potential of cryogens have been exami ned and their performance capabilities are presented.
The basic idea of the LN2 propulsion system is to utilize the atmosphere as a heat source to vaporize and superheat the cryogenic fluid for use in a thermal power cycle. This is in contrast with typical heat engines which utilize an energy source at temp erature significantly above ambient and use the atmosphere as a heat sink. In both cases the efficiency of conversion of thermal energy of the source to work (W) is limited by the Carnot efficiency, h = W/Qh = 1 - Tl/Th, where Qh is heat input, Tl is the sink temperature, and Th is the temperature of the heat source. The ideal thermal efficiency is impressively high (74%) for a heat engine operating on the temperature difference between ambient (Th = 300 K) and LN2 stored at atmospheric pressure (Tl = 7 7 K). The ideal work recoverable from an expansion engine as LN2 is evaporated and brought up to ambient temperature is given by the difference in thermodynamic availability between liquid and ambient states. This ``reversible work'' is Wr = 769 kJ/kg-L N2 which is significantly higher than the 180-300 kJ/kg achieved with lead-acid batteries, thus only 40% of the reversible work needs to be recovered to provide the LN2-propelled vehicle with a driving range commensurate with that of advanced battery-powe red vehicles of comparable weight. The key issues are the ability to design a practical energy conversion system that can take advantage of this high thermal efficiency and the available energy of the cryogen while still being cost competitive with conve ntional electric vehicles.
Prior work conducted at the University of Washington has indicated that significant gains in the overall energy efficiency of an ambient heated LN2 propulsion system would result if an effective isothermal engine could be developed.1 Figure 1
Fig 1: Specific work output for ideal isothermal and adiabatic expansion process
shows the specific work plotted as a function of peak cycle pressure, with peak temperature as a parameter, for ideal adiabatic and isothermal expanders (LN2 pump efficiency of 80% is assumed). The cut-off point for LN2 injection is adjusted so that the final pressure is always 0.11 MPa. For the range of injection pressures shown the isothermal work increases monotonically with increasing pressure, whereas the adiabatic cycle is only weakly dependent on peak cycle pressure above 4 MPa. The inclusion o f pump work results in a specific work maximum for both expansion processes, even though it is not evident in the isothermal work plotted here. It is apparent that the need to efficiently use LN2 dictates that the expander operate at as high a pressure a s mechanically feasible and that heat transfer be maximized during the expansion process.
LIQUID NITROGEN PROPULSION SYSTEM
A schematic of the proposed LN2 propulsion system is shown in Fig. 2.
Fig. 2: Schematic of liquid nitrogen propulsion system
The cryogen ``fuel'' is stored in a vacuum jacketed vessel which would have appropriate relief features to safely accommodate boil off. A cryopump would pressurize the fluid to the supercritical operating pressure of the system and a carefully designed heat exchanger will enable the working fluid to be warmed to near ambient temperature without suffering a detrimental build-up of frost. The gaseous N2 fills a receiver which minimizes pressure surges in the system due to changing power demands. Variab le timed valves provide controllable cut-off to release N2 gas into the expander as needed. More details of these components can be found in the cited references.8,9
A ``warmant'' fluid is circulated through the expander walls to maintain them at near ambient temperature (Fig. 2). The warmant must be pumped through another heat exchanger system (a conventional radiator would suffice) to efficiently conduct ambient he at into the engine. A quasi-isothermal reciprocating expander is proposed for this embodiment and its work output is transmitted to the wheels by means of a conventional transmission. Since the exhaust N2 is near ambient temperature it is prudent to use it to preheat the pressurized LN2 in an economizer to minimize contact of cold cryogen lines with ambient air.
THEORETICAL ANALYSIS OF EXPANDER
The thermodynamic simulation of a reciprocating expander has been developed to examine the impact of various engine design and operational parameters on the LN2 consumption of an ambient powered cryomobile. A theoretical model for heat transfer was used in this analysis to determine the effects of injection pressure and temperature on the work output of the expander as a function of bore, stroke, and engine RPM.10 The simulation procedure was generalized to enable the examination of a wide range of pisto n-cylinder head configurations. The warmant flow rate and ambient heat exchanger size were determined for the most promising configuration studied here. The details of the simulation methodology are discussed in this section.
RECIPROCATING ENGINE MODEL A one-zone, time-dependent analysis is applied on the control volume bounded by the piston and cylinder walls shown in Fig. 3. The cylinder contents are assumed to have uniform properties and be governed by the ideal gas equ ation of state. The heat transfer to the gas is coupled with the expansion process once the cut-off point is reached and ceases when the piston reaches bottom-dead-center (BDC). The surface temperature of all internal surfaces is assumed to be constant. The work output is then determined from the pressure-volume indicator diagram.
Fig. 3 Control volume for expander analysis
The instantaneous state of the N2 gas in the control volume is determined from energy conservation and the ideal gas equation of state. The energy equation for the cylinder contents is expressed as:
dP/dq = (g-1) / V {dQ/dq - g / (g-1) P dV/dq +
dmi/dt hi - dme/dt he} (Eq. 1)
where P is pressure, q is crank angle, g is specific heat ratio, V is volume, Q is heat transfer, dm/dt is mass flow rate, h is enthalpy and the subscripts i and e refer to injection and exhaust gas properties, respectively. The cylinder volume is obtain ed from the standard slider-crank relationship as follows:
V = Vh + Vc + p d2 S / 8 (1 - cosq + R - (R2 - sin2q)1/2) (Eq. 2)
where d is the cylinder diameter, S is the length of stroke, and R is the ratio of connecting rod to crank radius. The clearance volume Vc is a measure of the minimum gap between piston and cylinder head; whereas the head volume Vh accounts for all the v olume inside the expansion chamber that is not occluded by the piston when it is at top-dead-center if Vc = 0. The expression for dV/dq is found by differentiating Eq. 2.
PISTON-CYLINDER HEAT TRANSFER In order to evaluate the trade off between bore, stroke, and revolution rate of a practical reciprocating expander, a means for estimating the heat transfer rate to the N2 during the expansion process is required. Much of the piston-cylinder heat transfer research in the open literature has been directed to examining heat losses in fired engines and the resulting empirical correlations for average heat transfer coefficient are affected by radiative heat transfer. ``Mo toring'' studies which determine the heat losses from an engine without combustion are closer to the desired situation and provide experimental data to validate the proposed heat transfer model. For purposes of this study the heat transfer from the cylin der walls is assumed to be similar to turbulent heating of gas in a tube as follows:
where Nu is the Nusselt number, Re is Reynold's number, and Pr is Prandtl number. The m exponent is typically assumed to be 0.8 for fully developed turbulent flow and n = 0.3 or 0.4 for cooling or heating, respectively. The functional dependences on tem perature for the N2 thermal conductivity k and viscosity m in the temperature range of 200 - 300 K were determined from examination of thermodynamic data tables to be; k ~ T0.85 and m ~ T0.76, respectively.
Assuming that the gas velocity is proportional to the average piston speed Up results in the heat transfer coefficient hx having the following dependence on engine parameters:
hx = (0.1129) d-0.2 P0.8 Up0.8 T-0.594 (Eq. 4)
where the constant was determined for SI units by matching the heat transfer coefficient to an experimental data point found in Ref 11. The effects of piston stroke S and engine revolution rate N are incorporated in the average piston speed. This approa ch is not meant to rigorously quantify the heat transfer but rather to enable a reasonable investigation of the performance capabilities of various engine configurations.
The rate of heat input to the gas is the determined by assuming that hx applies to all surfaces in the expansion chamber and that the wall temperature Tw is uniform and constant throughout the cycle. The corresponding heat transfer is:
dQ/dt = hx Aw (Tw - T) (Eq. 5)
The total surface area exposed to heat transfer, Aw, at any crank angle is determined from:
Aw = Ap + Ah + Ac + p d S / 2 (1 - cosq + R - (R2 - sin2q)1/2)
where Ap is area of piston face, Ah is internal area of head volume, and Ac is surface area of clearance volume that is always exposed.
PISTON RING FRICTION The lost work due to piston ring friction is accounted for since it is expected to be highly dependent on the cylinder aspect ratio. The gas pressure is assumed to expand the rings against the cylinder walls and a constant value for the sliding friction coefficient (mr) corresponding to the ``equivalent coefficient of friction under non-hydrodynamic conditions'' is used.12 Thus the differential element of friction work dWf for the compression ring can be expressed as:
where tr is the ring thickness and dS is fraction of piston stroke through which this force acts. This expression is integrated over a complete engine cycle to account for the work lost to friction, which is then subtracted from the net cycle work. This energy is primarily dissipated into the cylinder walls and piston rings; however, its influence on the heat transfer is ignored at this time.
WARMANT CIRCULATION SYSTEM The warmant fluid is assumed to be a standard antifreeze mixture of water and ethylene-glycol. A conventional automobile radiator and water pump are proposed for this application since they are readily available. The water pump is assumed to have a 90% mechanical efficiency. The ambient heat transfer takes place at a lower temperature difference than in conventional automobiles; however, the amount of heat input required is less than that typically needed to be rejected f rom the fuel-burning engine. Heating of warmant in the ambient heat exchanger is governed by turbulent duct flow (Eq. 3) and the friction factor f is determined from Reynold's analogy as follows:
where St is the Stanton number. The heat transfer coefficients for the warmant flowing around the expansion chamber and through the head based are the heat transfer correlations for cross-flow over cylinder walls and that through a flat plate for the cyl inder head as follows:13
Nuc = (0.35 + 0.56 Red0.52) Pr0.3 (Eq. 9)
Nuh = 0.332 Red1/2 Pr1/3 (Eq. 10)
An energy balance for a given fluid temperature change determines the warmant flow rate needed to provide the desired cylinder heat flux through the expansion chamber walls.
The first set of calculations investigated the effects of bore-to-stroke ratio (d/S) and engine RPM on the isothermicity (I) of the cycle which is defined as the ratio of cycle work wcyc to the isothermal work wi determined for the same pressure and volum e ratios. The isothermicity of a set of engines having a 1 cm bore diameter operating over an injection pressure range of 1 - 30 MPa with an exhaust pressure of 0.11 MPa and injection temperature of 290 K is shown in Fig. 4. Engine RPM and d/S are used as parameters. It can be seen that very long strokes and low RPM encourage heat transfer during the expansion process. The case of a 10 cm piston having a 1 : 4 bore-to-stroke ratio is also shown in Fig. 4. The reduction in work output due to bore size is evident. These calculations indicate that small bore and low RPM are desirable for an efficient quasi-isothermal engine. The corresponding low power density will result in careful design trade-off between high efficiency and the potential mechanica l complexity of multiple-cylinder engines required to generate sufficient power for automotive propulsion.
The temperature and specific work as function of crank angle for an engine having a 1 cm diameter piston and 10 cm stroke operating at 1000 RPM under isothermal and non-adiabatic conditions are shown in Fig. 5. The cut-off point is between 12\xb0 and 13\ xb0 for these conditions. It can be seen that the majority of the lost work in the non-isothermal case arises in the first 60\xb0 of crank angle. During this phase of the expansion process the highest rate of work output is realized, thus creating the greatest demand for heat input to approach isothermal performance.
The temperature difference between wall and gas is initially zero during the injection phase of the cycle; however, it quickly increases as the system does work on the piston, as shown in Fig. 6. The heat transfer coefficient rapidly decreases as the pre ssure drops, even though the increase in piston speed and decrease in gas temperature mitigate this effect. Since a well designed quasi-isothermal expander would have minimal temperature difference between wall and gas, the primary means of enhancing hea t transfer are to increase both the heat transfer coefficient and total wetted area within the expansion chamber.
Fig. 4: Effect of geometry on engine RPM on the isothermicity of an ideal expander with finite heat transfer rates
determine the possible benefits of an enhanced heat transfer coefficient, the simulation for the non-isothermal expander was conducted again assuming that hx did not decrease during expansion. The specific work output and temperature during the first half of the expansion stroke for the same operating conditions, when hx is assumed to maintain its initial value, are shown in Fig. 7 along with the isothermal results. The work and temperature profiles are much closer to the ideal in this case. These results correspond to increasing hx by a factor of 10 during the expansion over the first 60o of crank angle. The ratio of cycle work to isothermal is 0.85 under these conditions as compared to 0 .65 for the variable hx case, which is a significant increase in isothermicity. Increases in the heat transfer coefficient can be realized by inducing turbulence and swirl during the injection process, however, this approach has not yet been pursued suff iciently to evaluate the its feasibility of achieving the needed magnitude of hx enhancement.
Fig. 5 Instantaneous work output and gas temperature as function of crank angle for ideal expander. (Piston diameter = 1 cm),
Since the baseline piston-cylinder configuration used for the prior simulations has a low isothermicity even though it has a very high surface-to-volume ratio (1 cm bore x 10 cm stroke) as compared to conventional expanders, something much different is re quired to achieve significant quasi-isothermal operation. One possibility is a novel piston-head configuration that has the promise of greatly enhancing the heat transfer rate during the first part of the expansion process. This concept consists of a pi ston with multiple conical fins that fit into a heater core, which is imbedded in the top of the expansion cylinder, when the piston is at TDC, as shown in
Fig. 6: Heat transfer coefficient and temperature difference between gas and wall as function of crank angle
Fig. 7: Instantaneous work output and gas temperature for ideal expander when hx is assumed constant. (Piston diameter = 1 cm, stroke = 10 cm)
Fig. 8. The baseline configuration for this analysis consists of a 10-cm diameter piston fitted with 19 truncated conical fins having root and tip diameters of 1.45 and 0.725 cm, respectively. The fin height is 2.9 cm and the wall thickness of the core passages is 2 mm. Two plates of 0.5 cm thickness hold the core tubes and create a means for warmant to be routed over the tube bundle.
Fig. 8: Piston having conical fins and heater core inside expansion cylinder
A head space over the heater core is used for minimizing the pressure drop associated with distributing the N2 through the passages. The pressure drop through the heater core is assumed to be negligible for this analysis. When the injection valve is ope ned at TDC, the gas experiences more surface area as the conical fins are withdrawn from the heater core. No seal is required between the fins and passages; the rings on the cylindrical portion of the piston fulfill this function. Thus a high surface-to -volume ratio is attained at the top of the cylinder where the demand for heat input is the greatest.
Fig. 9: Work output from an ideal expander using conical-finned piston and heater core without any clearance volume or head space.
output for this piston-cylinder combination without any clearance volume or head space is shown in Fig. 9 along with that of a similar piston without fins. The heat transfer is significantly enhanced beyond that of the fin-less configuration as evident in the difference in specific work curves. Without fins, a piston-cylinder configuration of these dimensions would be nearly adiabatic. The improvement in specific work is encouraging because the dimensions of this system are comparable to those of conv entional expanders.
The work output of the finned-piston when there is finite clearance volume and head space is shown in Fig. 10.
Fig. 10: Work output from ideal expander using conical-finned piston and heater core with finite clearance and head volume.
It can be seen that a significant penalty is incurred when these volumes are included. Adding in the pump work shows that the maximum specific work occurs in the 6 - 8 MPa range, which is well within the capabilities of current expander technology. Th e kink in the adiabatic specific work curve indicates the point where the high pressure N2 could not be expanded to ambient (0.11 MPa) with the available expansion ratio, thus the exhaust pressure steadily increases with injection pressure and the pressur e ratio remains constant. Even if the pressurization of the system is achieved without a pump, there is not any efficiency to gain by going to pressures higher than 10 MPa for any of these expansion processes.
The degree of isothermicity achieved with the finned-piston, with and without head space and clearance volume, is shown in Fig. 11
Fig. 11 Isothermicity of conical-finned piston with and without clearance and head volume compared with standard piston.
along with the isothermicity of a finless piston for comparison purposes. These calculations indicate that over 80% of the isothermal work available can be generated by the proposed expansion engine. This degree of isothermicity is nearly that which was previously found if hx could be maintained constant during the expansion process. It can be seen that the presence of dead volume not only reduces the available work, it also reduces the isothermicity of the expansion process at higher pressure. Th is effect is also evident in the isothermicity curve for a standard piston. Thus careful piston-head design is essential to realize the full potential of using cryogens as energy storage media. Even with the specific work degradation due to finite head space, the performance of this engine is still good enough to be effectively used in a liquid nitrogen vehicle.
The warmant circulation system is sized such that it can deliver the total heat input required to maintain the wall temperature of a 2-cylinder expander at 10 K below ambient when it is generating twice the power required for level cruising at 97 km/hr. This insures that there will be sufficient heat input during nominal cruising conditions to quickly overcome transient temperature fluctuations arising from acceleration and variations in road inclination. The power required to maintain cruising speed fo r a Honda CRX has been estimated at 7.8 kW.14 This can be generated by a single cylinder of the finned-piston engine when it is operating at 850 RPM with an injection pressure and temperature of 6.0 Mpa and 290 K, respectively, in an 300 K environment. The heat input to the cylinder is ~11 kW under these conditions. Thus the maximum warmant heat transmission requirement is 22 kW which dictates a mass flow rate of 1.1 kg/sec (water/ethylene-glycol mixture) for a 5 K temperature drop. Under cruising ope rating conditions the propulsion system would realize an energy density of 245 kJ/kg-LN2 which makes it competitive with the best of lead-acid batteries being used today.
Time to recharge (refuel), infrastructure investment, and environmental impact are among the issues to consider, in addition to range and performance, when comparing the relative merits of different ZEV technologies. The convenience of pumping a fluid in to the storage tank is very attractive when compared with the typical recharge times associated with lead-acid batteries. Manufacturing LN2 from ambient air inherently removes small quantities of atmospheric pollutants and the installation of large-scale liquefaction equipment at existing fossil-fuel power stations could make flue gas condensation processes economical and even eliminate the emissions of CO2.15 Conversely, liquefaction of air at the local gas station or even at personal residences could provide significant load-leveling to facilitate the efficient generation of electricity. More detailed studies of the consequences of these infrastructure investments would be justified if an effective means of converting the thermal energy potential of LN2 and liquid air can be developed.
The potential for utilizing the available energy of liquid nitrogen for automotive propulsion looks very promising. Heat transfer calculations of a quasi-isothermal reciprocating engine that has a heater core imbedded within its expansion chamber indicat e that nearly 85% of the performance of an ideal isothermal power cycle can be attained. A representative case indicates that a 2-cylinder engine operating with an injection pressure of 6 MPa at 850 RPM would produce 15 kW and 190 N-m torque. This power plant would enable a zero emission vehicle to have a range of 140 km from 200 liters of LN2. Thus even though this expander concept is far from being optimized, it still can provide an effective power plant for a zero emission vehicle.
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Quasi-Isothermal Expansion Engines for Liquid Nitrogen Automotive Propulsion
C. Knowlen, J. Williams, A.T. Mattick, H. Deparis, and A. Hertzberg
Aerospace and Energetics Research Program
Fig. 1 Specific work output for ideal isothermal and adiabatic expansion processes.
