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The “constant velocity piston” problem (Fig. 1), also known as the “piston problem,” is a standard model for a one dimensional, in our case linear, symmetric shock wave moving through an inviscid, perfect gas. The model can be divided into two regions - a perturbed section on the left and an unperturbed section on the right - by a moving shock wave moving left to right. Both the perturbed and unperturbed sections, i.e. the shocked and unshocked regions, respectively, obey the Eulerian conservation equations; however, at the exact location of the shock, there is a mathematical discontinuity not satisfied by the Euler equations. To ensure continuity and conservation of certain quantities when crossing between the unshocked and shocked regions, we evoke a series of equations derived from the Eulerian conservation equations, called the Rankine-Hugoniot equations, or “jump” equations as it is often referred to in the literature on the topic. The classical constant-velocity piston problem assumes the piston features a constant driving velocity (among many other willing suspensions of belief required in the pursuit of a first principles equation model); consequent to this assumption is a constant-velocity shock and a constant-velocity shocked flow state. However, using Lie Group Theory (LGT), also known as symmetry analysis, we can attempt to reinterpret the model with a shock wave of variable velocity in time and space. An extension of the model in this way opens up the possibility for obtaining new analytical solutions to the piston problem for certain shock velocity models. In this report, we use LGT to derive the symmetry determining equations (SDEs), whose solutions are Lie groups, which permit analytical solutions. In the future, we can then use the SDEs to define constraint equations on the shock velocity model and what the successive solutions to the Euler equations might be based off such constraints. This report is structured as follows: Section 2 provides a brief derivation of the Rankine-Hugoniot (“jump”) equations; Section 3 gives an overview of Lie group theory; Section 4 derives the SDEs of the jump equations; Section 5 derives the Euler conservation equations for fluids; and Section 6 presents concluding remarks and opportunities for future studies.
This study investigated the behavior of gasoline direct injection (GDI) sprays using computational fluid dynamics (CFD). The authors developed an approach to identify optimal spray breakup model parameters by evaluating an error function across numerous simulations, with the goal of minimizing discrepancies from experimental data. Using the optimal setup, the simulated spray matched well with projected liquid volume distributions, liquid penetration, and spray width measured in a constant-pressure continuous-flow chamber. To further validate the approach, the same setup was tested across various fuels, injectors, and operating conditions. Subsequently, the optimal setup, along with a recently developed spray-wall interaction model, were applied to a direct-injection spark-ignited engine under late-injection conditions to predict and evaluate fuel film formation and evolution at varying engine coolant temperatures. Here, with the centrally mounted injector directing the spray toward the piston, simulations indicated that the spray tends to impinge on the piston surface. The proposed simulation framework also accurately captured the aggregate film area on the piston surface, aligning with previously published experimental results. Moreover, simulations showed that increasing the coolant temperature from cold start conditions (333 K) to warm conditions (363 K) reduced the fuel mass deposited on the piston by roughly 50%. Furthermore, for the spray-guided engine configuration studied in this work, the CFD model predicted minimal film deposition on the spark plug electrodes regardless of the coolant temperatures due to a relatively weak in-cylinder flow during the compression phase.
Compressors are the primary components of energy consumption in vapor compression systems, drawing considerable research effort to reduce carbon emissions and improve energy efficiency. This work presents an isothermal compressor that integrates the compression chamber with the gas cooler to achieve near-isothermal compression, resulting in up to 30% energy reduction compared to traditional isentropic compression, according to the experiment results. A detailed dynamic model for the isothermal compression cycle of carbon dioxide (CO 2 ) is first presented, coupled with a liquid-piston model for chamber design. The model is experimentally validated on a 3.5 kW prototype, yielding a 6.2% relative error in chamber pressure and a 0.5 K deviation in chamber temperature. The liquid piston exhibits reduced frictional heating and geometric adaptability relative to the mechanical piston. Leveraging these attributes, the study further evaluates approaches that enhance the heat transfer to achieve isothermal compression by increasing the effective heat transfer area during compression. As a result, simulations demonstrated up to a 5% improvement in the coefficient of performance over the baseline case through chamber design, providing guidelines for design of isothermal compression cycle.
This study presents a reduced-order model (ROM) for computational fluid dynamics (CFD) simulations of cryogenic hydrogen isotope extrusions, focusing on protium (H₂) and deuterium (D₂) piston extruders. Using a 2D axisymmetric ROM in ANSYS-Polyflow, significant computational savings were achieved (runtime reduced from 9∼24 h to 3∼5 min), with extrusion force discrepancies between the 2D ROM and 3D models being on the order of 1%. Parametric studies identified optimal cutoff shear rates in the viscosity model (0.01/s for H₂ and 0.001/s for D₂), providing recommendations for future simulations. Finally, a comprehensive comparison of ROM results with experimental data was performed across varying geometries, cryogenic materials, temperatures, extrusion lengths, and piston velocities. Predictions at low extrusion temperatures met the objective of providing quick and efficient solutions with an acceptable extrusion force error of approximately 10% or less, validating the effectiveness of the 2D ROM approach. However, at high temperatures closer to the triple point, extrusion force error grows, which necessitates developing an improved model that accounts for temperature effects, e.g. melting. Nevertheless, the findings still represent a significant improvement in efficiency of CFD modeling of cryogenic hydrogenic extrusion. The ROM framework can also be extended to tritium (T2) and screw extruders, which will ultimately provide a fast and effective tool for optimizing pellet injector design for ITER and future reactor systems.
Hydrogen (H 2 ) is a promising fuel for reducing emissions in heavy-duty internal combustion engines (ICEs), but its low quenching distance increases the risk of flame propagation into narrow crevice regions, such as piston-liner gaps. This work uses detailed CFD simulations with finite-rate chemistry to investigate premixed H 2 –air flame quenching in a two-dimensional (2D) region consistent with the piston-liner gap of a diesel ICE. Model accuracy was assessed by comparison with experimentally measured quenching distances in an annular stepwise diverging tube (ASDT). A parametric study was conducted to assess the influence of crevice width (0.05–1.18 mm), pressure (50–150 bar), unburned gas temperature (431–573 K), and equivalence ratio ( Φ= 0.3–0.6). Results show that the critical Péclet number for flame survival is no greater than 3.25, consistent with prior literature, even under ultra-lean and high-pressure conditions (Φ ≤ 0.3, > 50 bar). Additionally, flames with Péclet numbers exceeding 6.15 exhibited front wrinkling, suggesting the onset of velocity-driven instabilities and enhanced flame robustness. These findings help define thresholds for flame quenching in confined geometries and support the safe design of H 2 fueled ICEs.
Here, this study provides new insights into the role of interfaces on the deformation and failure mechanisms in shock-loaded Cu–Ta–Cu trilayer system. The thickness of the Ta layer, piston velocities, and shock pulse durations were varied to explore the impact of impedance mismatch and loading conditions on spallation behavior and twin formation. It was found that the interfaces play a crucial role in the dynamic response of these multilayered systems since secondary reflection waves generated at the interfaces significantly affected the peak stress and pressure profiles, influencing void nucleation and failure modes. In the trilayer systems, failure predominantly occurred at interfaces and within the Ta layer, with void nucleation sites and twinning behavior being markedly different compared to single-crystal Cu and Ta. Increasing the Ta layer thickness modified the wave interactions, leading to different failure locations. Higher piston velocities were associated with increased spall strength by enhancing wave interactions and void formation, particularly at the interfaces and within the Ta layer, under specific configurations. Additionally, shorter shock pulse durations facilitated earlier initiation of the release fan, reducing twin formation and altering the failure dynamics by accelerating twin annihilation and pressure release.
U.S. buildings account for approximately 40% of total U.S. energy consumption and 75% of electricity use, emphasizing the need for efficient, resilient, and secure energy solutions. Micro-combined heat and power (micro-CHP) systems provide an effective approach by simultaneously generating electricity and recovering waste heat for thermal use. However, current commercial micro-CHPs face challenges in achieving higher efficiency, lower emissions, and reduced cost. To address these limitations, a novel micro-CHP prototype powered by a unique opposed-piston four-stroke (OP4S) engine was developed. The OP4S features a simplified, low-cost design with reduced heat losses and dual-piston operation that enables higher thermal efficiency. Experimental results demonstrated up to 35.2% AC electrical efficiency under lean combustion, surpassing the best-performing ICE-based micro-CHPs reported publicly. In addition, the micro-CHP enables a total CHP efficiency exceeding 93%. The prototype operates reliably for over 600 hours, providing flexible and efficient thermal and electrical outputs. This novel OP4S-based micro-CHP offers a resilient, low-cost, and energy-efficient solution suitable for residential, light commercial, and remote community applications across diverse climate zones.
The compressor holds great promise for enhanced energy efficiency over a wide range of vapor compression systems (VCS). However, the majority of them focused on liquid refrigerant injection or inter-stage cooling technologies to improve heat transfer. Increasing the heat transfer area provides another perspective to promote heat dissipation, which commonly involves shape optimization whilst bringing some limitations, mainly from the manufacturing side. To fill the research gap, this paper compares the performance of isothermal compressors under different compression chamber shapes and chamber connection configurations. Additionally, the fluid control of the liquid piston was combined with shape optimization to explore the potential for further heat transfer enhancement. The simulation results have demonstrated that the COP improvements can reach up to 9% compared with the baseline case by optimizing the chamber shape and properly controlling the liquid piston speed, which provides a guideline for designing and customizing the isothermal compression chamber.
Cooled Spray (CS) and Ducted Fuel Injection (DFI) are in-cylinder technologies for diesel engines that can reduce particulate matter and soot emissions and data has been published showing that these technologies can reduce soot emissions by 75-100% for some engines at some operating conditions. However, little is known about scaling the devices for engine size. Additionally, the performance of either technology over the engine duty cycle has not been explored. This project addresses both of these points through single-cylinder engine investigations. The objectives of this project are to provide details about dimensional scaling of these devices and to demonstrate 75% PM reduction over a range of operating conditions on a single-cylinder engine. Two engines were used for this project: a 125mm bore optically accessible engine at Sandia National Laboratories and a 168mm bore metal engine at Southwest Research Institute. The optical engine was used to study the performance of DFI and CS inserts for a large injector orifice diameter injector that is characteristic of a locomotive engine and to perform scaling studies for DFI. The metal engine was used to perform scaling and alignment studies for CS and to evaluate the technology for both EGR and non-EGR engines over the engine operating map. Modifications were required for both engines to accept the prototype inserts being tested. The optical engine required a new fuel injector, cylinder head and piston so that tests could be run at the pressures and engine speeds required. Additionally, a novel rotating stage was designed for the optical engine to simplify alignment of the modules. The metal engine required a modified cylinder head to accept CS inserts and a modified piston to provide additional space around the fuel injector for the CS inserts. Tests on the optical engine showed that DFI reduces PM emissions for both small injector orifices (0.170mm diameter) and large injector orifices (0.290mm). For high load testing, the DFI modules were not as effective as at low load testing, but it was acknowledged that minimal geometric optimization was performed and more improvements may be possible. Comparing DFI to CS and conventional diesel combustion (CDC), DFI performed better than CS or CDC. The CS geometries used in these studies may not be ideal for that engine and additional modifications likely would improve performance. Tests on the metal engine showed PM reductions as high has 80% at some operating conditions with duty-cycle PM reductions of ~50% for EGR and non-EGR configurations. The CS testing on the metal engine showed that chamfering of the fuel passage inlet either through hydro-erosion or mechanical grinding provided significant improvements in the PM reduction capabilities of the insert. Additionally, alignment sensitivities were explored and the data show that the tolerance to misalignment is approximately 0.05 to 0.1mm for the inserts that were studied here. Air-fuel ratio was shown to be important in the effectiveness of the CS inserts. In several tests, it was shown that the CS inserts are more effective at reducing the PM for high-AFR operating conditions compared to low AFR conditions. In summary, multiple designs were evaluated on both engines. It was found that for the conditions and configurations studied here, a fuel passage diameter of ~2.5mm performed best overall. Significant duty-cycle PM reductions are possible using these technologies and sensitivities to AFR, alignment fuel passage diameter and inlet fuel passage shaping were explored and are reported here. More PM reduction may be possible with improved geometric design and attention to alignment practices.
A legacy FORTRAN 77 implementation of the Baer–Nunziato two-phase mixture theory for deflagration-to-detonation transition (DDT) in reactive granular materials—hereafter the XDDT (eXplosive DDT) code—has been modularized to Fortran 90 with modular structure, external input files, and adaptive mesh capability. During validation, two code defects were identified and corrected: an inconsistency in the nodal solid pressure evaluation and a nonphysical burn-front tracking criterion. The ignition criterion was also corrected to use the granular surface temperature from the interface heat transfer model, matching the original Baer implementation. An initial attempt to validate against Figure 3 of the original Baer and Nunziato (1986) paper revealed that the code’s detonation velocity on a 201-node mesh (5.5 km/s) was approximately 21% below the expected Chapman–Jouguet value for 70% TMD HMX (∼7 km/s). Validation was redirected to the piston-driven DDT experiments of McAfee et al. (1989), Shot B-9036, for which well-characterized ionization-pin data are available. With the compaction-burn coefficient calibrated to 𝐶 𝛼 = 75, the XDDT code reproduces the DDT transition time to within 0.4% and produces a steady-state detonation velocity within 4% of the McAfee experimental value of 6.36 km/s. The burn model was generalized to support pressure-dependent exponents, enabling application to nitrocellulose-based ball propellants (TS3659) with a cube-root pressure dependence. Validation against the Sandusky/Baer PDC82 piston-impact experiment yielded a reactive wave velocity of 2.3–2.8 km/s, in good agreement with the experimental value of ∼2.2 km/s, and wave coalescence within 5% of the experimental timing. The mathematical model, input parameter requirements, and a roadmap for extending XDDT to PETN with an autocatalytic burn model are presented.
Compressors are the major energy consumption components in vapor compression systems, drawing much research effort in reducing carbon emissions. The isothermal compressor integrates the compressor chamber and gas cooler to achieve near isothermal compression, reaching up to 30% energy reduction compared to the traditional isentropic compression work. This paper presents a detailed isothermal compressor model combined with a generalized liquid piston model to account for the carbon dioxide (CO2) isothermal compression process. The model is established based on MATLAB environment. The model uses the real experimental data as boundary conditions and initial settings, which also considers the CO2 solubility in liquid piston (mineral oil) for designing, optimizing and customizing the compression chambers. The validation was carried out with experimental data using a prototype with 3.5 kW capacity. The results have demonstrated the accuracy of the dynamic model (6.2% relative error for chamber pressure and 0.5 K deviation for chamber temperature), which provide a guideline for designing and customizing the isothermal compression cycle.
Embodiments disclosed may serve the function of a pump, a generator, or a propulsion system. Two flexible fins are coupled via their longitudinal inner edges to fin coupling modules. An external fluid flow causes traveling fin undulations. The angle of the fins relative to each other changes as undulations travel along the fins which can be translated through the fin coupling modules into mechanical work, powered by the external fluid flow. The mechanical work of the fin coupling modules may be the cyclical extension and contraction of pistons or bellows incorporated into the fin coupling modules, which may draw ambient fluid during their extension cycles and compress fluid during their contraction cycles to create a pump. The pistons or bellows may also be sealed from ambient fluid but connected through conduits through which contained fluid is exchanged in a continuous circulation of fluid to power a pump or a turbine.
Here, studies have shown that fuel properties can impact an engine’s operation in several ways, including ignition delay, sooting tendency, mixture formation, and combustion temperature. In mixing-controlled compression ignition (MCCI) engines, the fuel system design and piston bowl geometry significantly affect combustion performance and emissions. Based on current information, it is difficult to draw conclusions about fuel property effects and sensitivities. The central fuel hypothesis approach used in the US Department of Energy Co-Optima program has worked well for spark ignition fuels: identifying critical fuel property ranges is sufficient to screen fuel blends that are expected to maximize efficiency and reduce pollutant emissions. However, for MCCI-relevant fuels, the information gained from past studies is not sufficient to build such a merit function or to allow for performing a similar screening of fuel blends. It is hypothesized that a co-optimization of a fuel’s physical and chemical properties, combustion system geometry, and injection strategy could leverage synergies between the effects of the fuel properties and geometries, resulting in improved performance over state-of-the-art. A machine learning–assisted unconstrained global optimization algorithm was used to explore a design space comprising 23 independent variables. The results show that physical property effects were minimal even for large variations in fuel properties, and the only interaction effect that was observed was the effect of varied fuel density parameters on fuel/air mixture formation. Nevertheless, these interactions were not sufficient in magnitude to significantly affect optimization results. Therefore, analysis of the results suggests that fuel physical properties cannot be leveraged in a co-optimization context to increase engine efficiency.