Search Results (16)

Leakage-induced transients in natural gas transmission pipelines can significantly affect operational safety and emergency response. This study develops a physics-based analytical framework for predicting transient pressure evolution, leakage dynamics, and emergency valve response in high-pressure gas pipelines while deriving a closed-form criterion for optimal valve spacing. The governing equations of compressible gas flow are reduced to a diffusion-type model incorporating acoustic wave propagation and frictional attenuation. A dynamic Robin-type boundary condition is introduced to describe valve–pipeline interactions, and closed-form analytical solutions are obtained using the Laplace transform method. An analytical leakage function and an explicit valve spacing criterion are derived directly from the governing equations and boundary conditions. Parametric investigations under representative transmission pipeline operating conditions demonstrate that the optimal valve spacing depends systematically on attenuation characteristics, activation thresholds, and allowable response times. The analytical solution further predicts a narrow quasi-invariant valve activation interval of approximately 112–116 s, which is theoretically explained through the dominant acoustic–diffusive balance of the proposed model. Verification against an independent finite difference solution shows excellent agreement, with the maximum relative deviation remaining below 1%, thereby confirming the accuracy and numerical consistency of the analytical formulation. The proposed framework provides a physically interpretable and computationally efficient tool for leakage assessment, emergency valve design, and safety-oriented analysis of conventional natural gas transmission pipelines. Full article

This study develops an analytical and computational framework for coupled transient gas redistribution induced by simultaneous localized injection and withdrawal in transmission pipelines. The aim is to describe source–sink interactions within a single transmission system, unlike conventional approaches that treat inflow and outflow processes independently. The governing equations of one-dimensional non-stationary isothermal compressible gas flow are transformed into a diffusion-type formulation using Charny regularization. The pipeline is divided into three interacting regions connected through pressure-continuity and mass-flux coupling conditions. Closed-form Laplace-domain solutions are derived for the dimensionless pressure field, and a practical Laplace-domain approximation is used for computational evaluation of transient pressure profiles. The results reveal a characteristic balancing point separating injection-dominated and withdrawal-dominated regions and show rapid convergence toward a quasi-steady redistribution regime. A pressure-deviation-based objective function is introduced to evaluate hydraulic disturbance, and the optimization analysis shows that the minimum disturbance occurs under a near-balanced source–sink operating condition. The obtained pressure profiles, asymptotic behavior, and regional redistribution patterns confirm the physical consistency of the proposed model. The framework provides a mathematically interpretable basis for analyzing coupled redistribution dynamics, hydraulic stabilization, and asymptotic equilibrium in gas transmission systems. Full article

Thermally driven heat pumps primarily use thermal energy to drive a compression cycle. The thermal energy can be waste heat, natural-gas combustion, or solar, helping increase efficiency and reduce greenhouse-gas emissions. We study a thermal compressor heat pump (TCHP) in which Stirling-type thermal compressors (TCs) are heat-driven rather than electrically driven, delivering a nominal heat capacity of 8 kW with CO₂ as the refrigerant. Unlike most existing dynamic models of CO₂ cycles, which focus on electrically driven or single-stage systems, this work targets a heat-driven multi-stage configuration and includes transient validation. Like any vapor compression cycle (VCC), a TCHP requires a dynamic model for control and optimization; its predictive reliability must be validated on experimental data. We therefore describe the test bench and performance expressions, collect steady-state and transient datasets, and derive a hybrid dynamic model: finite-volume (FV) differential equations for slow components and quasi-static submodels (linear regressions and correlations) for fast elements. The contribution of this work is the development and experimental validation of a hybrid FV model for a multi-stage heat-driven CO₂ TCHP. Validation against both steady-state and transient datasets shows good agreement. On 15 steady-state operating points, the model reproduces pressures within ∼1 bar mean absolute error (MAE) and system-level performance (total recovered heat, $CO{P}_{\mathrm{th}}$) within ∼6% mean absolute percentage error (MAPE), with $R^2\gtrsim 0.8$; component heat-rate predictions are within ∼20% MAPE. Under transient step tests on expansion valve openings and burner fan speed, the thermal COP and total recovered heat track within $4\%$ MAPE (up to $R^2=0.96$), pressures within $1.5$ bar MAE, and the evaporator heat rate within 14–$22\%$ MAPE. Full article

The SHB fault-controlled condensate gas reservoir is the largest ultra-deep carbonate gas reservoir in China, and the accuracy of dynamic reserve calculation is an important basis for developing the development plan. The fault-controlled condensate gas reservoir has some problems, such as “ultra-deep, ultra-high temperature, supercritical”, strong heterogeneity of reservoir space, and difficulty in obtaining real underground reservoir parameters, which seriously affect the results of dynamic reserve evaluation. Combining the quasi-steady flow equation and the flow resistance of a gas well, a new flow material balance method based on the original apparent formation pressure and daily production data is proposed to effectively calculate the dynamic reserves of a gas reservoir. By comparing the calculation results of various dynamic reserves calculation methods for the SHB condensate gas reservoir, it is proven that this method can effectively calculate the dynamic reserves of gas wells and has important guiding significance for the calculation of dynamic reserves of fault control body condensate gas reservoirs. Full article

This study seeks to improve the performance of a low-temperature differential free-piston Stirling air conditioner (FPSAC). To achieve this, a novel approach is proposed, which replaces the conventional simple harmonic drive with a multi-harmonic drive. This modification aims to optimize the motion of the driving piston, bringing it closer to the ideal movement pattern. The research involves both thermodynamic and dynamic coupling simulations of the FPSAC, complemented by experimental verification of its key performance parameters. A thermodynamic model for the gas medium, employing a quasi-one-dimensional dynamic approach for compressible fluids, and a nonlinear two-dimensional vibration dynamic model for the solid piston are developed, focusing on the low-temperature differential FPSAC physical model. The finite difference method is employed to numerically simulate the entire system, including the electromagnetic thrust of the multi-harmonic-driven linear oscillating motor, fluid transport equations, and the nonlinear dynamic equations of the power and gas control pistons. Variations in displacement, velocity, and pressure for each control volume at any given time are obtained, along with the indicator and temperature–entropy diagrams after the system stabilizes. The simulation results show that, in cooling mode, assuming no heat loss or mechanical friction, the Stirling cooler operates at a frequency of 80 Hz. Using the COP_sin value for the simple harmonic drive as a baseline, performance is improved by altering the driving method. Under the multi-harmonic drive, the COP_c5 increased by 10.03% and COP_c7 by 14.23%. In heating mode, the COP under the multi-harmonic drive improved by 0.51% for COP_h5 and 2.61% for COP_h7. Performance experiments were conducted on the low-temperature differential FPSAC, and the key parameter test results showed good agreement with the simulation outcomes. The maximum deviation at the trough was found to be less than 2.45%, while at the peak, the maximum error did not exceed 3.61%. When compared to the simple harmonic drive, the application of the multi-harmonic drive significantly enhances the overall efficiency of the FPSAC, demonstrating its superior performance. The simulation analysis and experimental results indicate a significant improvement in the coefficient of performance of the Stirling cooler under the multi-harmonic drive at the same power level, demonstrating that the multi-harmonic drive is an effective approach for enhancing FPSAC performance. Furthermore, it should be noted that the method proposed in this study is applicable to other types of low-temperature differential free-piston Stirling air conditioners. Full article

Computer software that simulates the thermodynamic and gas dynamic properties of internal combustion engines can play a significant role in the design and optimization of internal combustion engines. In the present work, a quasi-dimensional numerical model for two-stroke engines is presented. Particular attention was paid to reporting in-cylinder models, combustion (turbulent with flame development and flame–wall interaction), and turbulence (K-k-$ϵ$ model), with the addition of tumble- and squish-generated turbulence that is quite common in such engines. The aim was to reduce the role of the calibration constants, which are fundamental for correlating the models with the experiments, and relations for calculating the tumble ratio and turbulent scales were reported. A one-dimensional model for manifolds is also presented (solving the Euler equations), using the second-order Roe Riemann solver with some improvements, paying particular attention to the source terms, such as area variation. Additionally, a new approach to the end-pipe boundaries, which would reduce the mass conservation error, is reported. The engines tested were two kart two-stroke engines, used for racing purposes: the IAME X30 engine and the IAME Screamer III KZ engine. A comparison between the model results and the experimental data was made, and good accordance was observed, with a root mean square error of about 0.5 kW and providing good accuracy in evaluating changes, such as the combustion chamber squish area and the exhaust pipe length. Full article

Polyurethane microcellular elastomers (PUME) are good at impact protection and energy absorption, and belong to rate sensitive- and strain history-dependent materials. In this study, PUME with different densities of 800 kg/m³, 600 kg/m³ and 400 kg/m³ were prepared, then the compressive responses of PUME in the strain rate range of 0.001 s⁻¹ to 3400 s⁻¹ were systemically investigated. By studying the energy absorption and efficiency diagram of PUME, the compressive properties of materials with different densities under compressive impact load were described, which showed that PUME with a density of 600 kg/m³ had better performance. A visco–hyperelasticity–air constitutive model was established to describe the large deformation response of PUME at high strain rates. The model included three components: hyperelastic part, viscoelastic part and gas pressure part. Quasi-static and dynamic compression tests were used to determine the constitutive relations of seven parameters. The samples with a density of 600 kg/m³ at different strain rates were fitted by MATLAB software, and the constitutive model parameters were obtained. The comparison between the constitutive equation and the experimental results showed that there was a good consistency. The constitutive model can provide data support for simulation analysis and application of PUME as energy absorbing protective facilities. Full article

This paper deals with the creation of parallel algorithms implementing macro-and microscopic traffic flow models on modern supercomputers. High-performance computing contributes to the development of intelligent transportation systems based on information technologies and aimed at the effective regulation of traffic in large cities. As a macroscopic approach, the quasi-gas-dynamic traffic model approximated by explicit finite-difference schemes is proposed. One- and two-dimensional variants of the system are considered, and the concept of lateral velocity and different equations for obtaining it are discussed. The microscopic approach is represented by the multilane cellular automata model. The previously developed model is extended to reproduce synchronized flow in accordance with Kerner’s three-phase theory. The new version starts from the Kerner–Klenov–Schreckenberg–Wolf model and operates with the concept of the synchronization gap. Macroscopic models are relevant for determining the common characteristics of road traffic, while microscopic models are useful for a detailed description of cars’ movement. Both approaches possess inner parallelism. The parallel algorithms are based on the geometrical parallelism principle with different boundary conditions at interfaces of the subdomains. Sufficiently high speedups were reached when up to 100 processors were involved in calculations. The proposed algorithms can serve as the core of ITS. Full article

In the paper, we study a design and stability of contrast-independent partially explicit time discretizations for Quasi-Gas-Dynamics (QGD) Equations in multiscale high-contrast media. In our previous works, we have introduced contrast-independent partially explicit time discretizations. In this paper, we extend these ideas to multiscale QGD problems. Because of high contrast, explicit methods require a very small time stepping. By designing appropriate spatial splitting and temporal splitting, partially explicit methods remove this constraint. The proposed partially explicit time discretization consists of two steps. First, we split the space into contrast dependent (fast) and contrast independent (slow) components on a coarse grid that is much larger compared to spatial heterogeneities. Secondly, we design a temporal splitting algorithm in a such way that it is stable and the time step is independent of the contrast and only depends on the coarse mesh size. Using proposed method, a few degrees of freedom are treated implicitly and the approach is mostly explicit. We prove that the proposed splitting is unconditionally stable under some suitable conditions formulated for the second space (slow). We present numerical results and show that the proposed methods provide results similar to implicit methods with the time step that is independent of the contrast. Full article

The article presents a numerical study of the large-amplitude, acoustically-driven streaming flow for different frequencies of the acoustic wave and different temperature gradients between hot and cold surfaces. The geometries studied were mainly two-dimensional rectangular resonators of different lengths, but also one three-dimensional rectangular resonator and one long and narrow channel, representative of a typical U-shaped resistance thermometer. The applied numerical model was based on the Navier–Stokes compressible equations, the ideal gas model, and finite volume discretization. The oscillating wall of the considered geometries was modeled as a dynamically moving boundary of the numerical mesh. The length of the resonators was adjusted to one period of the acoustic wave. The research confirmed that baroclinic acoustic streaming flow was largely independent of frequency, and its intensity increased with the temperature gradient between the hot and cold surface. Interestingly, a slight maximum was observed for some oscillation frequencies. In the case of the long and narrow channel, acoustic streaming manifested itself as a long row of counter-rotating vortices that varied slightly along the channel. 3D calculations showed that a three-dimensional pair of streaming vortices had formed in the resonator. Examination of the flow in selected cross-sections showed that the intensity of streaming gradually decreased as it approached the side walls of the resonator creating a quasi-parabolic profile. The future development of the research will focus on fully 3D calculations and precise identification of the influence of the bounding walls on the streaming flow. Full article

We deal with 2D and 3D barotropic gas dynamics system of equations with two viscous regularizations: so-called quasi-gas dynamics (QGD) and quasi-hydrodynamics (QHD) ones. The system is linearized on a constant solution with any velocity, and an explicit two-level in time and symmetric three-point in each spatial direction finite-difference scheme on the uniform rectangular mesh is considered for the linearized system. We study $L^2$-dissipativity of solutions to the Cauchy problem for this scheme by the spectral method and present a criterion in the form of a matrix inequality containing symbols of symmetric matrices of convective and regularizing terms. Analyzing these inequality and matrices, we also derive explicit sufficient conditions and necessary conditions in the Courant-type form which are rather close to each other. For the QHD regularization, such conditions are derived for the first time in 2D and 3D cases, whereas, for the QGD regularization, they improve those that have recently been obtained. Explicit formulas for a scheme parameter that guarantee taking the maximal time step are given for these conditions. An important moment is a new choice of an “average” spatial mesh step ensuring the independence of the conditions from the ratios of the spatial mesh steps and, for the QGD regularization, from the Mach number as well. Full article

This paper presents the Eulerian–Lagrangian approach for numerical modeling of high-speed gas-droplet flows and aeroacoustics. The proposed hybrid approach is implemented using the OpenFOAM library and two different methods. The first method is based on a hybrid convective terms approximation method employing a Kurganov–Tadmor and PIMPLE scheme. The second method employs the regularized or quasi-gas dynamic equations. The Lagrangian part of the flow description uses the OpenFOAM cloud model. Within this model, the injected droplets are simulated as packages (parcels) of particles with constant mass and diameter within each parcel. According to this model, parcels moving in the gas flow could undergo deceleration, heating, evaporation, and breakup due to hydrodynamic instabilities. The far-field acoustic noise is predicted using Ffowcs Williams and Hawking’s analogy. The Lagrangian model is verified using the cases with droplet evaporation and motion. Numerical investigation of water microjet injection into the hot ideally expanded jet allowed studying acoustic properties and flow structures, which emerged due to the interaction of gas and liquid. Simulation results showed that water injection with a mass flow rate equal to 13% of the gas jet mass flow rate reduced the noise by approximately 2 dB. This result was in good coincidence with the experimental observations, where maximum noise reduction was about 1.6 dB. Full article

The Carnot cycle and the attendant notions of reversibility and entropy are examined. It is shown how the modern view of these concepts still corresponds to the ideas Clausius laid down in the nineteenth century. As such, they reflect the outmoded idea, current at the time, that heat is motion. It is shown how this view of heat led Clausius to develop the entropy of a body based on the work that could be performed in a reversible process rather than the work that is actually performed in an irreversible process. In consequence, Clausius built into entropy a conflict with energy conservation, which is concerned with actual changes in energy. In this paper, reversibility and irreversibility are investigated by means of a macroscopic formulation of internal mechanisms of damping based on rate equations for the distribution of energy within a gas. It is shown that work processes involving a step change in external pressure, however small, are intrinsically irreversible. However, under idealised conditions of zero damping the gas inside a piston expands and traces out a trajectory through the space of equilibrium states. Therefore, the entropy change due to heat flow from the reservoir matches the entropy change of the equilibrium states. This trajectory can be traced out in reverse as the piston reverses direction, but if the external conditions are adjusted appropriately, the gas can be made to trace out a Carnot cycle in P-V space. The cycle is dynamic as opposed to quasi-static as the piston has kinetic energy equal in difference to the work performed internally and externally. Full article

So far, the torrefaction process has been merely discussed based on the physical and chemical characteristics of the final product, but the mechanism has not been yet pondered and investigated. Thus far, microwave torrefaction has been predominately used for thermal pre-treatment; therefore, a paradigm shift in the methodology has been introduced by using a Joule heating system. The article mainly focuses on the thermal engineering aspect of the torrefaction process. The densified black pine underwent thermal pre-treatment at a temperature of 523 K. The furnace used for torrefaction was initially improvised to carry out thermal degradation at quasi-static/dynamic conditions. A 3D PDE thermal model was developed to determine the numerical solution and temperature distribution across a black pine pellet. To compare the effect of the linear ramping profile, time-dependent as well as fixed Dirichlet conditions were applied to the proposed model. The mass distribution, duration of the torrefaction process, the effect of Nusselt and Reynold’s number of inert gas, and thermal history are some of the factors whose influence on the numerical solution was investigated. The simulation of thermal pre-treatment and its effect on the heat transfer characteristic was examined with help of a PDE thermal model, whereas the numerical solution of diffusion of the product of reactions was determined by solving the partial differential equations with the help of the discretisation method (PDEPE). The densification of black pine was performed in a ring die, whereas initial milling of biomass was carried out using a 1.5 mm sieve size. The system was found to have a homogeneous distribution in energy and temperature with time, whereas the amplitude of heat flux along the radial direction was reduced by 15% if the same pellet underwent torrefaction for a duration of 5 min in dynamic mode. Similarly, a 64.46% drop in amplitude of heat flux along the azimuth plane could be seen while performing torrefaction in a time-dependent thermal history. However, the relative amplitude of the heat flux at the centre of the pellet was estimated to be lowered by 98.41% along the vertical axis for heating a pellet in a quasi-static condition. The net change in the mass fraction of carbon dioxide across the boundary film was seen to be 40% higher than that of carbon monoxide. The rate of change of mass fraction of carbon monoxide across the boundary film was increased by 7–11% with the increase in torrefaction time. A 6.8% rise in the evaporation of water was noticed during the first half interval of torrefaction (from 5 min to 10 min). In the second half, from 10 min to 15 min, it was merely increased by 5.8%. A relative drop of 17.24% in water evaporation was estimated in the dynamic state of the system. Full article

We investigate the formation dynamics of sonic horizons in a Bose gas confined in a (quasi) one-dimensional trap. This system is one of the most promising realizations of the analogue gravity paradigm and has already been successfully studied experimentally. Taking advantage of the exact solution of the one-dimensional, hard-core, Bose model (Tonks–Girardeau gas), we show that by switching on a step potential, either a sonic, black-hole-like horizon or a black/white hole pair may form, according to the initial velocity of the fluid. Our simulations never suggest the formation of an isolated white-hole horizon, although a stable stationary solution of the dynamical equations with those properties is analytically found. Moreover, we show that the semiclassical dynamics, based on the Gross–Pitaevskii equation, conforms to the exact solution only in the case of fully subsonic flows while a stationary solution exhibiting a supersonic transition is never reached dynamically. Full article