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At least 37 records · Page 2

All sources NASA NTRS DOE OSTI

DOE OSTI2019

Gas-Induced Motion of a Piston in a Vibrated Liquid-Filled Housing

We present that models and experiments are developed to investigate how a small amount of gas can cause large rectified motion of a piston in a vibrated liquid-filled housing when piston drag depends on piston position so that damping is nonlinear even for viscous flow. Two bellows serve as surrogates for the upper and lower gas regions maintained by Bjerknes forces. Without the bellows, piston motion is highly damped. With the bellows, the piston, the liquid, and the two bellows move together so that almost no liquid is forced through the gaps between the piston and the housing. This Couette mode has low damping and a strong resonance: the piston and the liquid vibrate against the spring formed by the two bellows (like the pneumatic spring formed by the gas regions). Near this resonance, the piston motion becomes large, and the nonlinear damping produces a large rectified force that pushes the piston downward against its spring suspension. A recently developed model based on quasi-steady Stokes flow is applied to this system. A drift model is developed from the full model and used to determine the equilibrium piston position as a function of vibration amplitude and frequency. Corresponding experiments are performed for two different systems. In the two-spring system, the piston is suspended against gravity between upper and lower springs. Lastly, in the spring-stop system, the piston is pushed up against a stop by a lower spring. Model and experimental results agree closely for both systems and for different bellows properties.

42 ENGINEERING↗

DOE OSTI2022

Effects of a CFD-improved dimple stepped-lip piston on thermal efficiency and emissions in a medium-duty diesel engine

Diesel piston-bowl shape is a key design parameter that affects spray-wall interactions and turbulent flow development, and in turn affects the engine’s thermal efficiency and emissions. It is hypothesized that thermal efficiency can be improved by enhancing squish-region vortices as they are hypothesized to promote fuel-air mixing, leading to faster heat-release rates. However, the strength and longevity of these vortices decrease with advanced injection timings for typical stepped-lip (SL) piston geometries. Dimple stepped-lip (DSL) pistons enhance vortex formation at early injection timings. Previous engine experiments with such a bowl show 1.4% thermal efficiency gains over an SL piston. However, soot was increased dramatically [SAE 2022-01-0400]. In a previous study, a new DSL bowl was designed using non-combusting computational fluid dynamic simulations. This improved DSL bowl is predicted to promote stronger, more rotationally energetic vortices than the baseline DSL piston: it employs shallower, narrower, and steeper-curved dimples that are placed further out into the squish region. In the current experimental study, this improved bowl is tested in a medium-duty diesel engine and compared against the SL piston over an injection timing sweep at low-load and part-load operating conditions. No substantial thermal efficiency gains are achieved at the early injection timing with the improved DSL design, but soot emissions are lowered by 45% relative to the production SL piston, likely due to improved air utilization and soot oxidation. However, these benefits are lost at late injection timings, where the DSL piston renders a lower thermal efficiency than that of the SL piston. Energy balance analyses show higher wall heat transfer with the DSL piston than with the SL piston despite a 1.3% reduction in the piston surface area. Vortex enhancement may not necessarily lead to improved efficiency as more energetic squish-region vortices can lead to higher convective heat transfer losses.

42 ENGINEERING↗

NASA NTRS1990

Sibling cycle piston and valving method

A double-acting, rotating piston reciprocating in a cylinder with the motion of the piston providing the valving action of the Sibling Cycle through the medium of passages between the piston and cylinder wall. The rotating piston contains regenerators ported to the walls of the piston. The piston fits closely in the cylinder at each end of the cylinder except in areas where the wall of the cylinder is relieved to provide passages between the cylinder wall and the piston leading to the expansion and compression spaces, respectively. The piston reciprocates as it rotates. The cylinder and piston together comprise an integral valve that seqentially opens and closes the ports at the ends of the regenerators alternately allowing them to communicate with the expansion space and compression space and blocking that communication. The relieved passages in the cylinder and the ports in the piston are so arranged that each regenerator is sequentially (1) charged with compressed working gas from the compression space; (2) isolated from both expansion and compression spaces; (3) discharged of working gas into the expansion space; and (4) simultaneously charged with working gas from the expansion space while being discharged of working gas into the compression space, in the manner of the Sibling Cycle. In an alterate embodiment, heat exchangers are external to the cylinder and ports in the cylinder wall are alternately closed by the wall of the piston and opened to the expansion and compression spaces through relieved passages in the wall of the reciprocating, rotating piston.

Mitchell, Matthew P.↗

DOE OSTI2024

Asynchronicity in opposed-piston RCMs: Does it matter?

Rapid Compression Machines (RCMs) are widely utilized to study combustion phenomena at engine-relevant conditions, and significant efforts are typically made to create a quiescent environment, particularly for investigations of autoignition chemistry. Opposed-piston configurations can be advantageous due to shorter compression times and reduced surface area to volume ratios. Each side must be actuated simultaneously, but this can be challenging in practice. These devices, like most RCMs, utilize hydraulics for actuation, speed control and arrestation of the piston at the end of the stroke; there is no mechanical control or linkage of the two piston trajectories. To quantify the magnitudes and effects of piston asynchronous behavior, this work employs both detailed experimental measurements and, for the first time, high-fidelity, Direct Numerical Simulation (DNS). The boundary conditions are carefully considered applying insight from high-resolution linear variable differential transformer (LVDT) measurements of the piston trajectory and a zero-dimensional kinematics model of the piston-shaft assembly. Sufficient resolution in the piston crevice region is used. The complicated fluid dynamical behavior that can evolve during piston compression and the ensuing delay processes due to offset timings from t offset = 0-10 ms is elucidated. It is found that near t offset = 6 ms and beyond, the boundary layer on the face of the first-seating piston can be sufficiently perturbed, due initially to reemergence of gas from the crevice of the firstseating piston, so that the adiabatic core can become degraded at long ignition delay times. Substantial mixing of colder gas into the interior of the reaction chamber can alter the measurements, similar to effects previously observed for improper piston crevice configuration. In conclusion, experimental techniques to mitigate asynchronous behavior are discussed and demonstrated.

33 ADVANCED PROPULSION SYSTEMS↗

NASA NTRS1944

Researches on the Piston Ring

In internal combustion engines, steam engines, air compressors, and so forth, the piston ring plays an important role. Especially, the recent development of Diesel engines which require a high compression pressure for their working, makes, nowadays, the packing action of the piston ring far more important than ever. Though a number of papers have been published in regard to researches on the problem of the piston ring, none has yet dealt with an exact measurement of pressure exerted on the cylinder wall at any given point of the ring. The only paper that can be traced on this subject so far is Mr. Nakagawa's report on the determination of the relative distribution of pressure on the cylinder wall, but the measuring method adopted therein appears to need further consideration. No exact idea has yet been obtained as to how the obturation of gas between the piston and cylinder, the frictional resistance of the piston, and the wear of the cylinder wall are affected by the intensity and the distribution of the radial pressure of the piston ring. Consequently, the author has endeavored, by employing an apparatus of his own invention, to get an exact determination of the pressure distribution of the piston ring. By means of a newly devised ring tester, to which piezoelectricity of quartz was applied, the distribution of the radial pressure of many sample rings on the market was accurately determined. Since many famous piston rings show very irregular pressure distribution, the author investigated and achieved a manufacturing process of the piston ring which will exert uniform pressure on the cylinder wall. Temperature effects on the configuration and on the mean spring power have also been studied. Further, the tests were performed to ascertain how the gas tightness of the piston ring may be affected by the number or spring power. The researches as to the frictional resistance between the piston ring and the cylinder wall were carried out, too. The procedure of study, and experiments conducted by the author, on this subject will be fully described in the following paragraphs.

Ehihara, Keikiti↗

NASA NTRS1996

Spherical Joint Piston and Connecting Rod Developed

Under an interagency agreement with the Department of Energy, the NASA Lewis Research Center manages a Heavy-Duty Diesel Engine Technology (HDET) research program. The overall program objectives are to reduce fuel consumption through increased engine efficiency, reduce engine exhaust emissions, and provide options for the use of alternative fuels. The program is administered with a balance of research contracts, university research grants, and focused in-house research. The Cummins Engine Company participates in the HDET program under a cost-sharing research contract. Cummins is researching and developing in-cylinder component technologies for heavy-duty diesel engines. An objective of the Cummins research is to develop technologies for a low-emissions, 55-percent thermal efficiency (LE-55) engine. The best current-production engines in this class achieve about 46-percent thermal efficiency. Federal emissions regulations are driving this technology. Regulations for heavy duty diesel engines were tightened in 1994, more demanding emissions regulations are scheduled for 1998, and another step is planned for 2002. The LE-55 engine emissions goal is set at half of the 1998 regulation level and is consistent with plans for 2002 emissions regulations. LE-55 engine design requirements to meet the efficiency target dictate a need to operate at higher peak cylinder pressures. A key technology being developed and evaluated under the Cummins Engine Company LE-55 engine concept is the spherical joint piston and connecting rod. Unlike conventional piston and connecting rod arrangements which are joined by a pin forming a hinged joint, the spherical joint piston and connecting rod use a ball-and-socket joint. The ball-and-socket arrangement enables the piston to have an axisymmetric design allowing rotation within the cylinder. The potential benefits of piston symmetry and rotation are reduced scuffing, improved piston ring sealing, improved lubrication, mechanical and thermal load symmetry, reduced bearing stresses, reduced running clearances, and reduced oil consumption. The spherical joint piston is a monolithic, squeeze-cast, fiber-reinforced aluminum piston. The connecting rod has a ball end that seats on a spherical saddle within the piston and is retained by a pair of aluminum bronze holder rings. The holder rings are secured by a threaded ring that mates with the piston. As part of the ongoing research and development activity, the Cummins Engine Company successfully completed a 100-hr test of the spherical joint piston and connecting rod at LE- 55 peak steady-state engine conditions. In addition, a 100-hr transient cycle test that varied engine conditions between LE-55 no-load and LE-55 full-load was successfully completed.

Source record↗

NASA NTRS2001

Piston and connecting rod assembly

A piston and connecting rod assembly includes a piston crown, a piston skirt, a connecting rod, and a bearing insert. The piston skirt is a component separate from the piston crown and is connected to the piston crown to provide a piston body. The bearing insert is a component separate from the piston crown and the piston skirt and is fixedly disposed within the piston body. A bearing surface of a connecting rod contacts the bearing insert to thereby movably associate the connecting rod and the piston body.

Brogdon, James William↗

NASA NTRS1988

Composite piston

A composite piston structure is disclosed which provides a simple and reliable means for joining a carbon-carbon or ceramic piston cap with a metallic piston body. Attachment is achieved by means of a special geometry which compensates for differences in thermal expansion without complicated mechanical fastening devices. The shape employs a flange created by opposed frustoconical shapes with coincident vertices intersecting on the radial centerline of the piston in order to retain the piston cap. The use of carbon-carbon for the piston cap material allows a close fit between the piston and a cylinder wall, eliminating the need for piston rings. The elimination of extra mechanical parts of previous composite pistons provides a lightweight composite piston capable of extended high temperature operation.

Taylor, Allan H.↗

NASA NTRS1994

Carbon-carbon piston development

A new piston concept, made of carbon-carbon refractory-composite material, has been developed that overcomes a number of the shortcomings of aluminum pistons. Carbon-carbon material, developed in the early 1960's, is lighter in weight than aluminum, has higher strength and stiffness than aluminum and maintains these properties at temperatures over 2500 F. In addition, carbon-carbon material has a low coefficient of thermal expansion and excellent resistance to thermal shock. An effort, called the Advanced Carbon-Carbon Piston Program was started in 1986 to develop and test carbon-carbon pistons for use in spark ignition engines. The carbon-carbon pistons were designed to be replacements for existing aluminum pistons, using standard piston pin assemblies and using standard rings. Carbon-carbon pistons can potentially enable engines to be more reliable, more efficient and have greater power output. By utilizing the unique characteristics of carbon-carbon material a piston can: (1) have greater resistance to structural damage caused by overheating, lean air-fuel mixture conditions and detonation; (2) be designed to be lighter than an aluminum piston thus, reducing the reciprocating mass of an engine, and (3) be operated in a higher combustion temperature environment without failure.

Gorton, Mark P.↗

NASA NTRS2018

New Runtime Record Set for Free-Piston Stirling Machine

This article describes the recent progress GRC has made in the arena of long-life heat engines for power conversion. NASA has been interested in Stirling-cycle machines for power conversion since the 1970s. At that time, it was recognized that such a device could be designed to achieve long-life continuous operation with high reliability, by leveraging the free-piston configuration in favor of a kinematic engine. The free-piston variant eliminates the wear mechanisms associated with rolling-element bearings, piston rings, and connecting rods, typically found in kinematic Stirling engine designs. By restricting the moving components to linear motion only, there is no need to convert linear piston movement to rotating motion. With this, the moving components can be suspended within their cylinders by non-contacting bearings and seals can be effected with close clearances, also non-contacting. The use of a linear alternator attached directly to the piston enables direct conversion of heat, to mechanical, then to electrical energy, all in one hermetically sealed vessel, The electrical output only requires simple feedthroughs, and the complexity of sealed a rotating crankshaft is eliminated. In the free-piston variant, the displacer-to-piston phase is not implemented by a connection to a common rotating shaft. Instead, the pressure wave itself is used to drive the displacer. The displacer is designed to have a higher natural frequency of motion than the piston, which achieves a leading phase angle required for power production. The free-piston Stirling behaves like a spring-mass-damper system, with a forcing function created by the alternate heater and cooling of the working gas, and damping provided by the current flowing through the linear alternator. Two types of non-contacting bearings are available to designers: flexure and gas bearings. Flexure bearings consist of a spiral-cut disc of metal that has high radial stiffness but a deliberately engineering stiffness in the axial direction, to permit piston and displacer resonant motion. Gas bearings utilize a pressure source and precisely machined flow channels to provide a radial stiffness around the moving component. The pressure source can be supplied by the engine's pressure wave itself.

Oriti, Salvatore M.↗

DOE OSTI2020

Electrically heated balance piston seal

A balance piston seal assembly for a balance piston of a compressor is provided. The balance piston seal assembly may include a balance piston seal configured to be disposed about the balance piston such that an inner radial surface of the balance piston seal and an outer radial surface of the balance piston define a radial clearance therebetween. The balance piston seal assembly may also include a plurality of heaters in thermal communication with the balance piston seal and configured to heat and thermally expand the balance piston seal and thereby increase a radial length of the radial clearance.

42 ENGINEERING↗

DOE OSTI2015

Gas-enabled resonance and rectified motion of a piston in a vibrated housing filled with a viscous liquid

Herein, we show how introducing a small amount of gas can completely change the motion of a solid object in a viscous liquid during vibration. We analyze an idealized system exhibiting this behavior: a piston moving in a liquid-filled housing, where the gaps between the piston and the housing are narrow and depend on the piston position. Recent experiments have shown that vibration causes some gas to move below the piston and the piston to subsequently move downward and compress its supporting spring. Herein, we analyze the analogous but simpler situation in which the gas regions are replaced by bellows with similar pressure-volume relationships. We show that these bellows form a spring (analogous to the pneumatic spring formed by the gas regions) which enables the piston and the liquid to oscillate in a mode that does not exist without this spring. This mode is referred to here as the Couette mode because the liquid in the gaps moves essentially in Couette flow (i.e., with almost no component of Poiseuille flow). Since Couette flow by itself produces extremely low damping, the Couette mode has a strong resonance. We show that, near this resonance, the dependence of the gap geometry on the piston position produces a large rectified (net) force on the piston during vibration. As a result, this force can be much larger than the piston weight and the strength of its supporting spring and is in the direction that decreases the flow resistance of the gap geometry.

42 ENGINEERING↗

DOE OSTI2025

Rotary Inertia Friction Welding of Dissimilar High-Strength 422 Martensitic Stainless Steel and 4140 Low Alloy Steel for Heavy-Duty Engine Piston Fabrication

AISI 422 martensitic stainless steel with superior high temperature performance (oxidation resistance and strength) is under evaluation for replacing current heavy-duty piston crown materials, AISI 4140 martensitic steel and micro alloyed steel (MAS) 38MnSiVS5, to fabricate a multimaterial piston. This multimaterial piston concept further improved power density and fuel economy by allowing heavyduty diesel engines to operate at higher temperatures and pressures. Joining AISI 422 steel piston crowns with AISI 4140 steel piston skirts is a key manufacturing step for this multimaterial piston. However, the significant differences in strength, elevated temperature flow stress, alloy chemistry, and temper resistance between these two martensitic steels cause some weldability issues (cracking) and metallurgical challenges (alloying element migration/segregation) when using conventional fusion-based welding processes. Rotary inertia friction welding (RIFW), a solid-state welding process, has been the preferred method to join 4140 crowns to 4140 skirts (and MAS crowns to MAS skirts) in high-volume production of current heavy-duty diesel engine pistons. It has been used to join these two materials with relatively comparable alloy chemistry to fabricate pistons with MAS skirts and 4140 crowns. Meanwhile, RIFW has also been a preferred method of dissimilar metal welding. However, RIFW of dissimilar high-strength martensitic steels has yet to be widely pursued. The interfacial microstructure complexities created by the thermomechanical process and highly nonequilibrium phase transformations during RIFW are a significant challenge for understanding and predicting their joining behavior and have not been reported in detail. Here, in this work, defect-free AISI 422 steel-AISI 4140 multimaterial pistons were successfully fabricated using the RIFW process. The interfacial microstructure and mechanical properties of dissimilar 422/4140 steel RIFW in the as-welded condition were experimentally studied in detail. The results provide critical baseline information for understanding RIFW mechanisms and guiding subsequent postweld heat treatment (PWHT) practice.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Evaluation of High-Temperature Martensitic Steels for Heavy-Duty Diesel Piston Applications

Five different commercially available high-temperature martensitic steels were evaluated for use in a heavy-duty diesel engine piston application and compared to existing piston alloys 4140 and microalloyed steel 38MnSiVS5 (MAS). Finite element analyses (FEA) were performed to predict the temperature and stress distributions for severe engine operating conditions of interest, and thus aid in the selection of the candidate steels. Complementary material testing was conducted to evaluate the properties relevant to the material performance in a piston. The elevated temperature strength, strength evolution during thermal aging, and thermal property data were used as inputs into the FEA piston models. Additionally, the long-term oxidation performance was assessed relative to the predicted maximum operating temperature for each material using coupon samples in a controlled-atmosphere cyclic-oxidation test rig. A current commercial steel piston alloy, quenched and tempered martensitic steel 4140, was tested in a single-cylinder research engine for a baseline oxidation and mechanical performance assessment using an abbreviated (50h) durability test plan. The predicted suitability of a candidate piston material in an engine is primarily based on its elevated temperature strength, oxidation resistance, and the complex influence of thermal conductivity, the latter of which is substantially lower for the candidate materials considered in this research relative to the traditional alloys. Although the lower thermal conductivity causes the candidate alloys to operate in higher temperature ranges under identical engine operating conditions and piston geometries, increasing the likelihood of partially or completely negating their strength and oxidation resistance advantages relative to 4140 and MAS steels, this evaluation indicates that several of the candidate piston alloys are predicted to enable improved oxidation resistance under more severe engine operating conditions relative to the current piston materials. However, further evaluation is required to determine if the elevated temperature fatigue strength and durability of these alloys are suitable for more severe engine conditions.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Optical Imaging for Understanding of Thermal Barrier Coated Piston Engine Performance

Thermal barrier coatings (TBC) applied to pistons have been a recently renewed research topic in the field of internal combustion engines. Single cylinder testing of a conventional C15™ Tier 4 final pro-duction steel piston and a TBC coated piston showed that the Yttrium stabilized Zirconia (YSZ) TBC did not significantly alter engine performance, with the TBC piston having slower combustion rates and higher criteria emissions. For deeper understanding, research continued by studying 3D-piston sections optically in a constant pressure vessel using photodiodes, four high-speed cameras (natural luminosity, CH*, and OH*), and visualization of the flame from two orthogonal directions. Particle Im-aging Velocimetry (PIV) algorithms were adapted to perform Combustion Imaging Velocimetry (CIV) to aid in quantification of the observed visual combustion flow field differences. The optical work showed that the TBC piston flame development is slower, spatially different, with lower mixing energy for the TBC variant. Geometric profiles of engine pistons and optical vessel 3D-piston sections were measured using a Coordinate Measurement Machine (CMM), and surface roughness was measured with a stylus surface profilometer. CMM results showed that the TBC piston bowl had reasonable macroscopic accuracy, but the rim had a larger radius with less reentrancy. A discussion of the results and analyses in relation to future TBC effort and direction concludes the work.

33 ADVANCED PROPULSION SYSTEMS↗

NASA NTRS1999

Durability, Performance, and Emission of Diesel Engines Using Carbon Fiber Piston and Liner

This report summarizes the research conducted by NC State University in investigating the durability, performance and emission of a carbon fiber piston and liner in our single cylinder research Diesel engine. Both the piston and liner were supplied to NC State University by NASA LaRC and manufactured by C-CAT under a separate contract to NASA LaRC. The carbon-carbon material used to manufacture the piston and liner has significantly lower thermal conductivity, coefficient of thermal expansion, and superior strength characteristics at elevated temperatures when compared to conventional piston materials such as aluminum. The results of the carbon-carbon fiber piston testing were compared to a baseline configuration, which used a conventional aluminum piston in a steel liner. The parameters measured were the brake specific fuel consumption, ignition delay, frictional horsepower, volumetric efficiency, and durability characteristics of the two pistons. Testing was performed using a naturally aspirated Labeco Direct Injection single cylinder diesel engine. Two test cases were performed over a range of loads and speeds. The fixed test condition between the aluminum and carbon-carbon piston configurations was the brake mean effective pressure. The measured data was the fuel consumption rate, volumetric efficiency, load, speed, cylinder pressure, needle lift, and exhaust gas temperature. The cylinder pressure, and fuel consumption, exhaust gas temperature, and needle lift were recorded using a National Instruments DAQ board and a PC. All test cases used Diesel no. 2 for fuel.

Afify, E. M.↗

NASA NTRS1981

Reciprocating piston pump system with screw drive

A pump system of the reciprocating piston type is described, which facilitates direct motor drive and cylinder sealing. A threaded middle potion of the piston is engaged by a nut connected to rotate with the rotor of an electric motor, in a manner that minimizes loading on the rotor by the use of a coupling that transmits torque to the nut but permits it to shift axially and radially with respect to the rotor. The nut has a threaded hydrostatic bearing for engaging the threaded piston portion, with an oil-carrying groove in the nut being interrupted. A fluid emitting seal located at the entrance to each cylinder, can serve to center the piston within the cylinder, wash the piston, and to aid in sealing. The piston can have a long stroke to diameter ratio to minimize reciprocations and wear on valves at high pressures. The voltage applied to the motor can be reversed prior to the piston reaching the end of its stroke, to permit pressure on the piston to aid in reversing the motor.

Perkins, Gerald S.↗

DOE OSTI2022

Extensions of a classical mechanics “piston-model” for understanding the impact of asymmetry on ICF implosions: The cases of mode 2, mode 2/1 coupling, time-dependent asymmetry, and the relationship to coast-time

As long suspected, low mode asymmetry in inertially confined fusion (ICF) implosions has been implicated as a performance limiting factor [Casey et al., “Evidence of three-dimensional asymmetries seeded by high-density carbon-ablator nonuniformity in experiments at the national ignition facility,” Phys. Rev. Lett. 126, 025002 (2021)]. Recently a non-linear, but solvable, theory [Hurricane et al., “An analytic asymmetric-piston model for the impact of mode-1 shell asymmetry on ICF implosions,” Phys. Plasmas 27, 062704 (2020)] based upon the simple picture of a pair of asymmetric pistons has generated new insights and provided some practical formulas for estimating the degradation of an implosion due to mode-1 asymmetry and demonstrated a previously unrecognized connection between measured hot-spot drift velocity, nuclear down-scatter ratio asymmetry, and the concept of residual kinetic energy (RKE). Asymmetry of the implosion “shell,” as opposed to asymmetry of the hot-spot, was key to the classical mechanics model because the majority of the kinetic energy in an implosion is carried by the shell. Herein, the two-piston model is extended to a six-piston model in order to capture mode-2 asymmetry and coupling between mode-1 and mode-2. A key result of this new six-piston model is that the weighted harmonic mean of shell areal density is the fundamental quantity that determines the RKE and performance degradations for a three-dimensional implosion. Agreement is found between the scalings coming from the theory and ICF implosion data from the National Ignition Facility and to large ensembles of detailed simulations. The connection between the piston model's dependence upon the radius of peak velocity and coast-time is also highlighted in this paper. Finally, by extending the two-piston model to include time-dependent “swing,” it is shown in the Appendix that the shell asymmetry at the time of stagnation dominates the solution for RKE.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗