Otto Cycle Research Articles

Analysis of the Principle and Applications of Four-stroke Engines in Transportation

Abstract. Four-stroke engines a type of internal combustion engine (IC engine) that can turn the heat provided from the fuel to work, and they are mainly classified as two groups, which are gasoline engines and diesel engines. Four-stroke engines can be applied to high power machines because of its high thermal efficiency. In four-stroke engines, the piston reaches the dead center four times in the cylinder to complete a cycle. This cycle includes the taking in of gas, the compression, the ignition, the expansion and the exhaustion of gas. In gasoline engine, this cycle is called the Otto cycle, and in diesel engine, this cycle is called the Diesel cycle. The greatest difference between these two engines is that they burn different types of fuel. In that way, the procedure of converting the heat to work is different. To help this cycle performs better economically and more efficiently, additional attachments such as hybrid engine and computer assistance are used. This research summarizes and analyses the application of four-stroke engines in land transportation, in aviation and in marine transportation, and this article gives a possible prediction to the future trend of the technology advancements of engines in transportation based on the analyses.

Finite-time measurement-driven Otto cycle

Finite-time measurement-driven Otto cycle

Exploring the role of criticality in the quantum Otto cycle fueled by the anisotropic quantum Rabi-Stark model

Exploring the role of criticality in the quantum Otto cycle fueled by the anisotropic quantum Rabi-Stark model

Thermodynamic properties and performance improvements of fractional Otto heat engine with repulsive bosons

This study presents calculations of a multiparticle system within the framework of fractional quantum mechanics. We specifically explore the energy levels of a bosonic system with repulsive interactions confined in a hard-wall box. The impacts of fractional parameters on the system’s thermodynamic properties are meticulously analyzed. Furthermore, utilizing this model, we construct a quantum Otto cycle and discover that the system exhibits Bose–Fermi duality under varying fractional parameters. Intriguingly, the introduction of fractional parameters enables to optimize the performance of the quantum heat engine, edging it closer to the Carnot efficiency.

Otto cycles with a quantum planar rotor.

We present two realizations of an Otto cycle with a quantum planar rotor as the working medium controlled by means of external fields. By comparing the quantum and the classical description of the working medium, we single out genuine quantum effects with regard to the performance and the engine and refrigerator modes of the Otto cycle. The first example is a rotating electric dipole subjected to a controlled electric field, equivalent to a quantum pendulum. Here we find a systematic disadvantage of the quantum rotor compared to its classical counterpart. In contrast, a genuine quantum advantage can be observed with a charged rotor generating a magnetic moment that is subjected to a controlled magnetic field. We prove that the classical rotor is inoperable as a working medium for any choice of parameters, whereas the quantum rotor supports an engine and a refrigerator mode, exploiting the quantum statistics during the cold strokes of the cycle.

Performance analysis of quantum harmonic Otto engine and refrigerator under a trade-off figure of merit

Abstract We investigate the optimal performance of the quantum Otto engine and refrigeration cycles of a time-dependent harmonic oscillator under a trade-off figure of merit for both adiabatic and nonadiabatic (sudden-switch) frequency modulations. For heat engines (refrigerators), the chosen trade-off figure of merit is an objective function defined by the product of efficiency (coefficient of performance) and work output (cooling load), thus representing a compromise between them. We obtain analytical expressions for the efficiency and coefficient of performance of the harmonic Otto cycle for the optimal performance of the thermal machine in various operational regimes. Particularly, in the sudden-switch regime, we discuss the implications of the nonadiabatic driving on the performance of the thermal machine under consideration and obtain analytic expressions for the maximum achievable efficiency and coefficient of performance of the harmonic Otto thermal machine. Particularly, we show that the quantum harmonic Otto cycle driven by sudden-switch protocol cannot work as a heat engine or refrigerator in the low-temperature limit. Finally, we show that in the high-temperature limit, the frictional effects give rise to a richer structure of the phase diagram of the harmonic Otto cycle. We identify the parametric regime for the operation of the Otto cycle as a heat engine, refrigerator, accelerator, and heater.

Nonequilibrium fluctuations of a quantum heat engine

The thermodynamic properties of quantum heat engines are stochastic owing to the presence of thermal and quantum fluctuations. We here experimentally investigate the efficiency and nonequilibrium entropy production statistics of a spin-1/2 quantum Otto cycle in a nuclear magnetic resonance setup. We first study the correlations between work and heat within a cycle by extracting their joint distribution for different driving times. We show that near perfect correlation, corresponding to the tight-coupling condition between work and heat, can be achieved. In this limit, the reconstructed efficiency distribution is peaked at the deterministic thermodynamic efficiency, and fluctuations are strongly suppressed. We further successfully test the second law in the form of a joint fluctuation relation for work and heat in the quantum cycle. Our results characterize the statistical features of a small-scale thermal machine in the quantum domain, and provide means to control them.

Quantum Heat Engines with Spin‐Chain‐Star Systems

AbstractThis study investigates a theoretical model of a Quantum Otto Cycle (QOC) that utilizes a working fluid spin‐chain‐star model. The system consists of a central atom interacting with multiple Heisenberg spin chains. Employing unitary transformations, the spin‐chain‐star system is transformed into a spin‐star model. The work done and heat transferred for three distinct working fluid configurations: the , , and cases are discussed. The efficiency of the heat engine is examined, and a comparative study between the efficiencies of the three configurations is presented. The study assumes two interaction scenarios for the central atom: either with a single chain (resulting in a two‐qubit system after transformation) or with three Heisenberg chains. The results demonstrate that increasing the ratio between the central atom's frequency in the hot bath and the cold bath leads to an enhancement in positive work performed for the and cases. In the case, the magnitude of this enhancement exhibits a dependence on the system's temperature. The QOC employing the configuration working fluid exhibits superior efficiency compared to the other two configurations. Moreover, increasing the central atom's relative frequency improves efficiency for all three cases.

Refrigeration by modified Otto cycles and modified swaps through generalized measurements

We introduce two types of thermodynamic refrigeration cycles obtained through modification of the Otto cycle refrigerator by a generalized measurement channel. These refrigerators are corresponding to the activation of the measurement-based stroke before (first type) and after (second type) the full thermalization of the cooling medium by the cold reservoir in the related familiar Otto cycle. We show that the coefficient of performance for the first type modified refrigerator increases linearly in terms of measurement strength parameter, beyond the classical cooling of the familiar Otto cycle refrigerator. The second type interestingly introduces an autonomous refrigerator whose supplying work is provided by a quantum engine induced by the measurement channel and operates simultaneously inside the modified cycle. By the considered measurement channel, we also establish such modifications on the swap refrigerator. It is observed that the thermodynamic properties of the obtained modified swap refrigerators are the same as of the modified Otto cycle ones respectively.

NO Formation in Combustion Engines Fuelled by Mixtures of Hydrogen and Methane

The present work addresses the production of nitrogen oxides in ICEs burning hydrogen mixed with methane. A mathematical model that allows the calculation of nitrogen oxide emissions from such combustion was built; this model uses the extended chemical kinetic mechanism of Zeldovich. Numerical simulations were carried out on the production of NO, varying the following variables: proportion of H2 to CH4, the equivalence ratio of the reactant mixture, the compression ratio, and the engine speed. The essential purpose was to assess how NO production is affected by the mentioned variables. The main assumptions were (i) Otto cycle; (ii) instantaneous combustion; (iii) chemical equilibrium reached just at the end of combustion; (iv) the formation of NO only during the expansion stroke of pistons. Results were obtained for various proportions of hydrogen and methane, various equivalence ratios, speeds of rotation, and compression ratios of an engine. In short, the results obtained in the current work show that the lowering of the equivalence ratio leads to a lower concentration of NO; that increasing the compression ratio also lowers the concentration of NO; that NO production occurs until shortly after the beginning of the expansion stroke; and finally, that the NO concentration in the engine exhaust is not very sensitive to the H2/CH4 ratio in the fuel mixture.

Optical and thermodynamic investigation of jet-guided spark ignited hydrogen combustion

Hydrogen as an alternative fuel for engines is gaining interest to decarbonize the heavy-duty sector. Hydrogen combustion in engines conventionally relies on the Otto cycle and either port fuel or direct injection. This combustion concept usually results in poor power density and non-ideal efficiencies due to the lean premixed operation and low compression ratio required to avoid preignition and knocking. In this study, hydrogen is directly injected at high pressures into the combustion chamber and spark-ignited with two different ignition systems (inductive and nanosecond repetitively pulsed discharge) at the periphery of the jet, with fuel conversion taking place predominantly in jet-guided (diffusion) mode while injection remains active.A rapid compression expansion machine (RCEM) is used to investigate the jet-guided hydrogen combustion thermodynamically and optically by combining high-speed Schlieren and OH* chemiluminescence imaging, and spark-induced breakdown spectroscopy (SIBS).SIBS reveals low air to fuel ratios at ignition time and location, ranging from 2.8 up to pure air depending on the condition and significant variation among repetitions. Both OH* chemiluminescence and Schlieren images illustrate how air entrainment pushes the flame-plasma kernel from the ignition location at the periphery of the jet towards the fuel-richer core, resulting in fast combustion of the already premixed fuel. Subsequently, the combustion process becomes dominated by the mixing dynamics. Under conditions of low in-cylinder pressures, the Heat Release Rate (HRR) closely follows the injected mass flow rate multiplied by the lower heating value of hydrogen, i.e., the combustion is mixing controlled. However, as the cylinder pressure increases, the mixing and combustion rates fall below the injected mass flow until lower densities are reached again.The delay between the start of injection and ignition primarily impacts the premixed peak, but the in-cylinder pressure and ignition source also play significant roles. This distinctive combustion process shows essential similarities to compression ignition Diesel combustion. The process holds the potential to achieve high efficiency, as hydrogen can be burned using process parameters typical of Diesel combustion without facing the constraints of knock or preignition and a complete absence of soot.

Work and efficiency fluctuations in a quantum Otto cycle with idle levels.

We study the performance of a quantum Otto heat engine with two spins coupled by a Heisenberg interaction, taking into account not only the mean values of work and efficiency but also their fluctuations. We first show that, for this system, the output work and its fluctuations are directly related to the magnetization and magnetic susceptibility of the system at equilibrium with either heat bath. We analyze the regions where the work extraction can be done with low relative fluctuation for a given range of temperatures, while still achieving an efficiency higher than that of a single spin system heat engine. In particular, we find that, due to the presence of "idle" levels, an increase in the interspin coupling can either increase or decrease fluctuations, depending on the other parameters. In all cases, however, we find that the relative fluctuations in work or efficiency remain large, implying that this microscopic engine is not very reliable as a source of work.

A finite-time quantum Otto engine with tunnel coupled one-dimensional Bose gases

We undertake a theoretical study of a finite-time quantum Otto engine cycle driven by inter-particle interactions in a weakly interacting one-dimensional (1D) Bose gas in the quasicondensate regime. Utilizing a c-field approach, we simulate the entire Otto cycle, i.e. the two work strokes and the two equilibration strokes. More specifically, the interaction-induced work strokes are modelled by treating the working fluid as an isolated quantum many-body system undergoing unitary evolution. The equilibration strokes, on the other hand, are modelled by treating the working fluid as an open quantum system tunnel-coupled to another quasicondensate which acts as either the hot or cold reservoir, albeit of finite size. We find that, unlike a uniform 1D Bose gas, a harmonically trapped quasicondensate cannot operate purely as a heat engine; instead, the engine operation is enabled by additional chemical work performed on the working fluid, facilitated by the inflow of particles from the hot reservoir. The microscopic treatment of dynamics during equilibration strokes enables us to evaluate the characteristic operational time scales of this Otto thermochemical engine, crucial for characterizing its power output, without any ad hoc assumptions about typical thermalization timescales. We analyse the performance and quantify the figures of merit of the proposed Otto thermochemical engine, finding that it offers a favourable trade-off between efficiency and power output, particularly when the interaction-induced work strokes are implemented via a sudden quench. We further demonstrate that in the sudden quench regime, the engine operates with an efficiency close to the near-adiabatic (near maximum efficiency) limit, while concurrently achieving maximum power output.

Implementation of thorium-based fuel for Indonesia Micro Reactor (IMR)

Indonesia has committed to reducing greenhouse gas emissions in the framework of net zero emissions, and nuclear energy will be a part of the energy mix. Indonesia has been developing a 10 MWt micro reactor of high temperature gas-cooled reactor (HTGR) with pebble fuel containing 17 % enriched UO2 kernel with OTTO cycle scheme. For the government’s interest to use thorium, this paper assesses the possibility of replacing uranium with thorium. The assessment is performed by calculating the effective neutron multiplication factor (keff). Neutrons captured by 232Th lead to the formation of two intermediate isotopes, namely 233Th and 233Pa, the latter being a significant neutron absorption cross-section. Neutronics analysis is performed using parameters of thorium mass fraction, core temperature, and active core height. The thorium mass fractions varies from 0 % to 90 % Th. The core temperatures are in the range of the normal operating temperature at 900 K, assumed superheat temperature at 1200 K, and shutdown temperature at 300 K. The active core height varies at 197, 180, 150, 130, and 125 cm. This paper aims to determine the keff of the IMR at maximum thorium/uranium mass fraction composition, maximum active core height, core temperature, and fuel burn-up. The MCNP code is used for analysis. The results show that keff decreases with increasing thorium mass fraction and core temperature, and decreasing active core height. Calculations with thorium mass fraction of 15 %, core active height of 197 cm in 20 steps show that the reactor may be continuously operated for more than 920 days without refueling. The analysis results show that IMR design has negative temperature reactivity, inherent safety characteristics, and the ability to use thorium-based fuels.

Theoretical thermal efficiencies of ideal, supercharged and gasoline engine cycles

This paper updated the perception of theoretical thermal efficiencies of reciprocating engine cycles by the analysis of six ideal cycles (Diesel, Joule-Brayton, Otto, Atkinson, Sabathe and Song). It was theoretically elucidated that more available energy remains in exhaust gas at higher load than at lower one, testifying that the exhaust waster energy recovery is more important at higher load than at lower one. A supercharged cycle was theoretically demonstrated to have lower thermal efficiency than its counterpart naturally-aspirated one, while supercharged engines had been always considered to have higher thermal efficiency. The thermal efficiencies of gasoline engines were first derived, testifying that a homogeneous spark-ignition gasoline engine at part-load has less thermal efficiency than its corresponding Otto cycle and can achieve a higher thermal efficiency by retarding (or advancing) inlet valve closing than by throttling intake flow.

Autonomous quantum heat engine based on non-Markovian dynamics of an optomechanical Hamiltonian

We propose a recipe for demonstrating an autonomous quantum heat engine where the working fluid consists of a harmonic oscillator, the frequency of which is tuned by a driving mode. The working fluid is coupled two heat reservoirs each exhibiting a peaked power spectrum, a hot reservoir peaked at a higher frequency than the cold reservoir. Provided that the driving mode is initialized in a coherent state with a high enough amplitude and the parameters of the utilized optomechanical Hamiltonian and the reservoirs are appropriate, the driving mode induces an approximate Otto cycle for the working fluid and consequently its oscillation amplitude begins to increase in time. We build both an analytical and a non-Markovian quasiclassical model for this quantum heat engine and show that reasonably powerful coherent fields can be generated as the output of the quantum heat engine. This general theoretical proposal heralds the in-depth studies of quantum heat engines in the non-Markovian regime. Further, it paves the way for specific physical realizations, such as those in optomechanical systems, and for the subsequent experimental realization of an autonomous quantum heat engine.

A theoretical framework for the analysis of an opposed piston linear engine design

Traditional crank-based engines face limitations due to mechanical, thermal, and combustion inefficiencies. In contrast, the opposed piston design of a linear engine generator mitigates frictional losses by eliminating rotational motion and crankshaft linkages. Instead, electrical power is generated through the oscillation of a translator within a linear stator. However, the lack of geometric constraints in the free piston design leads to uncertainties regarding dead center positions, resulting in challenges such as misfire, stall, over-fueling, and rapid load changes.This study aims to fill this gap by reviewing existing modeling literature and advancing the fundamental understanding of opposed piston linear engines (OPLE) with springs through the development of an idealized, nondimensional model. A combination of analytical and numerical models was developed to better understand the behavior of the OPLE. The model introduces a streamlined symmetric analytical solution, succeeded by a broader general analytical resolution, with careful attention to the significant influence of thermodynamic effects at each phase, offering insights into the engine's dynamic performance. Limitations inherent to the analytical solutions are addressed by a numerical scheme utilizing the Runge-Kutta technique. This approach guarantees swift and dependable computational outcomes, which captures cyclic variation. The alternator model amalgamates both linear and sinusoidal work profiles, adjusting the magnetic work output in response to fluctuations in the compression ratio relative to the Top Dead Center (TDC) clearance distance. This adjustment dictates the generator load for each translator.The proposed model integrates the dynamics of a damped spring-mass system with thermodynamic expressions representing in-cylinder processes. Simplifications are made assuming perfect springs, ideal gases, instantaneous heat transfer, and an average friction force dependent on stroke length for work output. Selected cases are analyzed to elucidate the system's fundamental behavior, both within and outside the context of the Otto cycle, showcasing natural and forced stability over multiple operation cycles. Notably, enhancing the baseline cylinder pressure, or input heat relative to spring stiffness can elevate the work-to-heat ratio values. The attained work-to-heat ratio within compression ratio window of 16 is approximately 28 %. While this percentage may fluctuate in the context of general FPLE designs, the model developed for OPLE in this work plays a crucial role in maintaining the engine within this narrowly defined efficiency range, without compromising the potential performance demonstrated in this study. Differences in compression ratios provided intriguing insights into the dynamics of the translator and the in-cylinder thermodynamics of the interconnected system. Lower TDC clearance resulted in high translator displacement, velocity, and enhanced thermal efficiency.

Anisotropy-assisted thermodynamic advantage of a local-spin quantum thermal machine.

We study quantum Otto thermal machines with a two-spin working system coupled by anisotropic interaction. Depending on the choice of different parameters, the quantum Otto cycle can function as different thermal machines, including a heat engine, refrigerator, accelerator, and heater. We aim to investigate how the anisotropy plays a fundamental role in the performance of the quantum Otto engine (QOE) operating in different timescales. We find that while the engine's efficiency increases with the increase in anisotropy for the quasistatic operation, quantum internal friction and incomplete thermalization degrade the performance in a finite-time cycle. Further, we study the quantum heat engine (QHE) with one of the spins (local spin) as the working system. We show that the efficiency of such an engine can surpass the standard quantum Otto limit, along with maximum power, thanks to the anisotropy. This can be attributed to quantum interference effects. We demonstrate that the enhanced performance of a local-spin QHE originates from the same interference effects, as in a measurement-based QOE for their finite-time operation.

Improving performance of quantum heat engines using modified Otto cycle

The efficiency of a quantum heat engine is maximum when the unitary strokes of the quantum Otto cycle are adiabatic. On the other hand, this may not be always possible due to small energy gaps in the system, especially at the critical point (CP) where the gap between the ground state and the first excited state vanishes and the system gets excited. With the aim to regain this lost adiabaticity, we modify one of the unitary strokes of the Otto cycle by allowing the system to first evolve with a time dependent Hamiltonian as in the case of a usual Otto cycle, followed by an additional evolution with a different time independent Hamiltonian so that the system reaches a less excited state. This will help in increasing the magnitude of the heat absorbed from the hot bath so that the work output and efficiency of the engine can be increased. We demonstrate this method using an integrable model and a non-integrable model as the working medium and discuss the generality and limitations of this method. In the case of a two spin system, the optimal value for the time till which the system needs to be freely evolved is calculated analytically in the adiabatic limit. The results show that implementing this modified unitary stroke significantly improves the work output and efficiency of the engine, especially when it crosses the CP.

A numerical procedure to obtain ideal piston trajectories and key design parameters for a hydrogen-fuelled resonating free piston generator

A new numerical procedure is presented to enable a hydrogen-fuelled two-stroke resonating free-piston generator target ideal Otto cycles to provide tracking paths for feedback control to maximise efficiency. Piston trajectories and design parameters are obtained for specified power, compression-ratio, and air-fuel-ratio. These parameters include scavenge port locations, heat release position, equivalent bottom-dead-centre position, and an electrical machine constant which is generally power-switched to take two values within a cycle. The main objectives of the paper are to develop the numerical procedure, and to demonstrate its use in finding a generator with maximum efficiency, and a generator with a single electrical machine constant, avoiding in-cycle power switching. To develop the procedure, a multi-physics generator model provides kinematics to an energy equation, culminating in a novel two-stage procedure. Stage-1 involves iteration and minimisation; Stage-2 just involves minimisation. Testing by simulation involves a 14-kW generator case study with compression ratio of 9, lean air-fuel equivalence ratio of 0.4, plus friction and electrical machine losses. An overall maximum generator efficiency of 54.9% is obtained using the procedure, compared to 51.3% without power switching. Computationally, the two-stage procedure proves highly efficient, typically taking around 11 min in total to complete on a desktop computer. The novelty of the procedure is its ability to optimally design and operate a hydrogen-fuelled resonating free-piston generator to meet a target specification, thereby offering a potentially inexpensive way to decarbonize transport, particularly in heavy duty applications.