Motion Of Gas Research Articles

Forecasting Constraints from Surface Brightness Fluctuations in Galaxy Clusters

Studies of surface brightness (SB) fluctuations in the intracluster medium present an indirect estimate of turbulent pressure support and associated Mach numbers. While high-resolution X-ray spectroscopy can directly constrain line-of-sight gas motions, including those due to turbulence, such observations are relatively expensive and will be limited to nearby, bright clusters. In this respect, SB fluctuations are the most economical means to constrain turbulent motions at large cluster radii across a range of redshifts and masses. To forecast what current and future X-ray and Sunyaev–Zel’dovich facilities may achieve in SB fluctuation studies, I review and synthesize matters of accuracy and precision with respect to calculating power spectra of SB fluctuations, from which turbulent properties are derived. Balancing concerns of power spectrum accuracy and precision across a range of spatial scales, I propose the use of three annuli with [0, 0.4]R 500, [0.4, 1]R 500, and [1, 1.5]R 500. Adopting these three regions, I calculate the uncertainty in the hydrostatic mass bias, σbM , that can be achieved for various instruments in several scenarios. I find that Lynx and AtLAST are competitive in their constraints at R 500, while AtLAST should perform better when constraining σbM at R 200.

Mind the Kinematics Simulation of Planet–Disk Interactions: Time Evolution and Numerical Resolution

Planet–disk interactions can produce kinematic signatures in protoplanetary disks. While recent observations have detected non-Keplerian gas motions in disks, their origins are still being debated. To explore this, we conduct 3D hydrodynamic simulations using the code FARGO3D to study nonaxisymmetric kinematic perturbations at two scale heights induced by Jovian planets in protoplanetary disks, followed by examinations of detectable signals in synthetic CO emission line observations at millimeter wavelengths. We advocate for using residual velocity or channel maps, generated by subtracting an azimuthally averaged background of the disk, to identify planet-induced kinematic perturbations. We investigate the effects of two basic simulation parameters, simulation duration and numerical resolution, on the simulation results. Our findings suggest that a short simulation (e.g., 100 orbits) is insufficient to establish a steady velocity pattern given our chosen viscosity (α = 10−3) and displays plenty of fluctuations on an orbital timescale. Such transient features could be detected in observations. By contrast, a long simulation (e.g., 1000 orbits) is required to reach steady state in kinematic structures. At 1000 orbits, the strongest detectable velocity structures are found in the spiral wakes close to the planet. Through numerical convergence tests, we find hydrodynamics results converge in spiral regions at a resolution of 14 cells per disk scale height or higher. Meanwhile, synthetic observations produced from hydrodynamic simulations at different resolutions are indistinguishable with 0.″1 angular resolution and 10 hr of integration time on Atacama Large Millimeter/submillimeter Array.

Modelling pressure dynamics in a gas pipeline with an in-line sampling

Gas pipelines, whether main, field, or urban, often operate in non-stationary modes. Changes in the operating modes of pumping stations, equipment start-up and shutdown, an in-line sampling or pumping and various factors are causes of instability of pressure, velocity, gas flow rate. Main pipelines are complex engineering systems with the pipeline itself being the main element. Fail-safety is the major factor in the operation of this system. Ensuring operational safety requires studying the movement regimes of the transported medium, particularly study of the dynamics of pressure duringstart-up or shutdown and at specific extraction points. This article aims to build a mathematical model and study the pressure dynamics in a gas pipeline with a sampling point. The theory of non-stationary motion liquid in round pipes has been strongly developed in the works of I. A. Charnyj. These works consider a large complex of engineering tasks taking into account viscous properties of the transported medium and pipe resistance in the hydraulic approximation. In the article on the basis of I. A. Charnyj's researches on the motion of real liquid in circular pipes the equation in partial derivatives of hyperbolic type is compiled. The equation describes the unsteady pressure of a horizontal section of gas pipeline with an extraction point. Using the Dirac delta function allows the formulation of the problem in the form of a single equation. Pressures are set at the ends of a given section, and the initial velocity is related to the Dirac delta function. By applying the finite Fourier sine transform, the partial differential equation is transformed into an ordinary differential equation and solved. Solution of equation is vision of a solution to the initial task. Inverse transform formulas based on Fourier theory allowed us to proceed to the solution of this task. Explicit dependences for the dynamics of unsteady pressure are obtained. The qualitative analysis of the formulas indicates the wave motion of a medium during the initial phase of operation, transitioning into a stationary mode after a brief period. The duration of the transition period depends on factors such as the hydraulic resistance coefficient and the velocity of the transported medium. Coefficient of hydraulic resistance and the velocity of the transported medium are the main factors. An example is considered for a horizontal section under isothermal flow conditions. With assumed numerical parameters, the transition to a stationary state occurs approximately 17 minutes after the process begins, as illustrated in the graphs provided in the article. Engineers can use mathematical models of the liquid and gas motion through pipes in the design of pipelines, as well as in solving tasks that arise during their operation. These tasks include monitoring the condition of the pipeline system, optimizing the operation, accumulation capacity estimates and others.

Observational signatures of circumbinary discs II: Kinematic signatures in velocity residuals

Abstract Kinematic studies of protoplanetary discs are a valuable method for uncovering hidden companions. In the first paper of this series, we presented five morphological and kinematic criteria that aid in asserting the binary nature of a protoplanetary disc. In this work we study the kinematic signatures of circumbinary discs in the residuals of their velocity maps. We show that Doppler-flips, spiral arms, eccentric gas motion, fast flows inside of the cavity, and vortex-like kinematic signatures are commonly observed. Unlike in the planetary mass companion case, Doppler-flips in circumbinary discs are not necessarily centred on a companion, and can extend towards the cavity edge. We then compare the kinematic signatures in our simulations with observations and see similarities to the Doppler-flip signal in HD 100546 and the vortex-like kinematic signatures in HD 142527. Our analysis also reveals kinematic evidence for binarity in several protoplantary disks typically regarded as circumstellar rather than circumbinary, including AB Aurigae and HD 100546.

3D Radiation-hydrodynamical Simulations of Shadows on Transition Disks

Shadows are often observed in transition disks, which can result from obscuring by materials closer to the star, such as a misaligned inner disk. While shadows leave apparent darkened emission as observational signatures, they have significant dynamical impact on the disk. We carry out 3D radiation-hydrodynamical simulations to study shadows in transition disks and find that the temperature drop due to the shadow acts as an asymmetric driving force, leading to spirals in the cavity. These spirals have zero pattern speed following the fixed shadow. The pitch angle is given by tan−1(c s /v ϕ ) (6° if h/r = 0.1). These spirals transport mass through the cavity efficiently, with α ∼ 10−2 in our simulation. Besides spirals, the cavity edge can also form vortices and flocculent streamers. When present, these features could disturb the shadow-induced spirals. By carrying out Monte Carlo radiative transfer simulations, we show that these features resemble those observed in near-infrared scattered light images. In the vertical direction, the vertical gravity is no longer balanced by the pressure gradient alone. Instead, an azimuthal convective acceleration term balances the gravity–pressure difference, leading to azimuthally periodic upward and downward gas motion reaching 10% of the sound speed, which can be probed by Atacama Large Millimeter/submillimeter Array line observations.

An atlas of gas motions in the TNG-Cluster simulation: From cluster cores to the outskirts

Galaxy clusters are unique laboratories for studying astrophysical processes and their impact on halo gas kinematics. Despite their importance, the full complexity of gas motion within and around these clusters remains poorly known. This paper is part of a series presenting the first results from the new TNG-Cluster simulation, a suite comprising 352 high-mass galaxy clusters including the full cosmological context, mergers and accretion, baryonic processes and feedback, and magnetic fields. Studying the dynamics and coherence of gas flows, we find that gas motions in galaxy cluster cores and intermediate regions are largely balanced between inflows and outflows, exhibiting a Gaussian distribution centered at zero velocity. In the outskirts, even the net velocity distribution becomes asymmetric, featuring a double peak where the second peak reflects cosmic accretion. Across all cluster regions, the resulting net flow distribution reveals complex gas dynamics. These are strongly correlated with halo properties: at a given total cluster mass, unrelaxed, late-forming halos with fewer massive black holes and lower accretion rates exhibit a more dynamic behavior. Our analysis shows no clear relationship between line-of-sight and radial gas velocities, suggesting that line-of-sight velocity alone is insufficient to distinguish between inflowing and outflowing gas. Additional properties, such as temperature, can help break this degeneracy. A velocity structure function (VSF) analysis indicates more coherent gas motion in the outskirts and more disturbed kinematics toward halo centers. In all cluster regions, the VSF shows a slope close to the theoretical models of Kolmogorov (∼1/3), except within 50 kpc of the cluster centers, where the slope is significantly steeper. The outcome of TNG-Cluster broadly aligns with observations of the VSF of multiphase gas across different scales in galaxy clusters, ranging from ∼1 kpc to megaparsec scales.

Numerical investigation of in-cylinder gas motion dynamics in a heavy-duty direct injection hydrogen internal combustion engine

Mixture homogenization is one of the most important parameter for hydrogen internal combustion engines (H2ICE) to achieve near-zero NOx emissions and stable combustion, especially when premixed combustion strategy is used. On the other hand, inhomogeneities are inevitable due to the limited duration for mixing. This is more prominent in H2ICEs; those adopts low pressure direct injection (LPDI) system. Optimizing an engine to achieve higher level of homogeneity requires profound understanding of in-cylinder gas motion and mixing dynamics.To establish deeper comprehension of gas motion inside the cylinder, a 13-L LPDI H2ICE was modelled, and effect of different parameters were investigated by a holistic 1D-3D simulation methodology. While boundary conditions of operating point were obtained from the 1D simulations, different swirl numbers (SN), piston shapes and injector cap designs were simulated with 3D-CFD. Simulation results were analyzed based on uniquely defined parameters like homogeneity index (HI) and symmetricity of motion (SOM), as well as standard parameters like turbulence kinetic energy (TKE), and 3D visualizations of equivalence ratio iso-surfaces. Analysis showed that, there is a negative correlation between SN and HI under investigated conditions. Moreover, it was found that piston shapes which are promoting the tumble motion, improved average TKE by 31% and HI by 28% over base piston. This study aims to be a reference for the in-cylinder gas motion design of ultra-lean LPDI H2ICEs, where the target is retrofitting an existing diesel engine and attaining the best HI, SOM and TKE values at rated power conditions.

Gas Kinematics and Dynamics of Carina Pillars: A Case Study of G287.76-0.87

We study the kinematics of a pillar, namely G287.76-0.87, using three rotational lines of 12CO(5-4), 12CO(8-7), 12CO(11-10), and a fine structure line of [O i] 63 μm in southern Carina observed by SOFIA/GREAT. This pillar is irradiated by the associated massive star cluster Trumpler 16, which includes η Carina. Our analysis shows that the relative velocity of the pillar with respect to this ionization source is small, ∼1 km s−1, and the gas motion in the tail is more turbulent than in the head. We also performed analytical calculations to estimate the gas column density in local thermal equilibrium (LTE) conditions, which yields N CO as (∼0.2–5) × 1017 cm−2. We further constrain the gas’s physical properties in non-LTE conditions using RADEX. The non-LTE estimations result in nH2≃105cm−3 and N CO ≃ 1016 cm−2. We found that the thermal pressure within the G287.76-0.87 pillar is sufficiently high to make it stable for the surrounding hot gas and radiation feedback if the winds are not active. While they are active, stellar winds from the clustered stars sculpt the surrounding molecular cloud into pillars within the giant bubble around η Carina.

Probing Dust and Gas Properties Using Ringed Disks

How rapidly a planet grows in mass and how far it may park from the host star depend sensitively on two nondimensional parameters: Stokes number St and turbulent α. Yet these parameters remain highly uncertain, being difficult or impossible to measure directly. Here, we demonstrate how the ringed disks can be leveraged to obtain St and α separately by constructing a simple toy model that combines the dust radial equation of motion under aerodynamic drag and coupling to gas motion with the measured distribution of dust masses in Class 0/I disks. Focusing on known systems with well-resolved dust rings, we find that the ranges of St and α that are consistent with the measured properties of the rings are small: 10−4 ≲ St ≲ 10−2 and 10−5 ≲ α ≲ 10−3. These low St and α ensure the observed rings are stable against clumping. Even in one marginal case where the formation of bound clumps is possible, further mass growth by pebble accretion is inhibited. Furthermore, the derived low α is consistent with the nearly inviscid regime where type I migration can be prematurely halted. Our analysis predicts a minimal planet population beyond ∼tens of au, where we observe dust rings and significantly more vigorous planet formation inside ∼10 au, consistent with current exo-giant statistics. We close with discussions on the implications of our results on small planet statistics at large orbital distances.

Evidence for non-zero turbulence in the protoplanetary disc around IM Lup

ABSTRACT The amount of turbulence in protoplanetary discs around young stars is critical for determining the efficiency, timeline, and outcomes of planet formation. It is also difficult to measure. Observations are still limited, but direct measurements of the non-thermal, turbulent gas motion are possible with the Atacama Large Millimeter/submillimeter Array (ALMA). Using CO(2–1)/$^{13}$CO(2–1)/C$^{18}$O(2–1) ALMA observations of the disc around IM Lup at $\sim 0.4$ arcsec ($\sim$60 au) resolution we find evidence of significant turbulence, at the level of $\delta v_{\rm turb}=(0.18-0.30)$c$_\mathrm{ s}$. This result is robust against systematic uncertainties (e.g. amplitude flux calibration, mid-plane gas temperature, disc self-gravity). We find that gravito-turbulence as the source of the gas motion is unlikely based on the lack of an imprint on the rotation curve from a massive disc, while magneto-rotational instabilities and hydrodynamic instabilities are still possible, depending on the unknown magnetic field strength and the cooling time-scale in the outer disc.

Simultaneous improvements of thermal efficiencies and smoke emissions in semi-premixed diesel combustion with dual-injectors and a spatially divided combustion chamber

To simultaneously establish the high thermal efficiencies and the low smoke emissions in the semi-premixed diesel combustion with a twin peaked heat release consisting of the first-stage premixed combustion and the second-stage spray diffusive combustion, a combination of dual-injectors and a newly designed divided combustion chamber was proposed and the combustion characteristics were investigated. The divided chamber with a lip at the middle of the side wall can prevent the second fuel spray from entering the burned region of the premixture from the first-stage injection, realizing a suitable spatial distribution of spray flames and suppressing the soot formation. The dual-injectors can independently provide the fuel sprays into the upper and the lower layers of the divided chamber with the optional quantities and timings for the first and second injections, establishing the optimum combustion phasing. The distributions of the equivalence ratios and the soot formation characteristics in the divided chamber as well as in an ordinary re-entrant chamber as a reference were analysed with CFD simulations, showing that the soot formation is smaller in the divided chamber. The second-stage spray diffusive combustion is improved as well as the late afterburning and the combustion duration are reduced with the suppression of interference between the spray flames in the divided chamber. The cooling loss in the divided chamber is smaller due to the weaker gas motion and the lower heat transfer coefficient. The experiments also showed that the thermal efficiencies are better and the smoke emissions are lower in the divided chamber at medium loads. However, at higher loads, the smoke emissions increase due to the offset injector arrangement, and the CFD analysis showed that lower smoke emissions can be expected with optimization of the injector arrangement to locate the injector for the second fuel injection at the centre of cylinder.

Nonlinear instability of surface waves between viscous–liquid and subsonic‐gas layers subject to uniform oblique magnetic field

AbstractNonlinear instability of surface waves between viscous–liquid and inviscid‐gas layers is discussed. The two fluids are magnetic and subjected to uniform oblique magnetic field. The gas is subsonic and the viscosity is introduced by viscous potential approximation. The evolution equations near and on the marginal state are derived by means of multiple scales technique. The stability criteria of the waves are obtained by the modulation idea. Many special cases of dispersion equation as well as solvability conditions correspond well the similar ones in the literature. Various numerical applications have been investigated to reveal the parameters effects on the system stability. Linear results show dual influences for magnetic field, sum of inclination angles and permeability ratio whereas the wavelength, gas motion, and inclination angle in the liquid tend to destabilize the flow. Nonlinear applications reveal dual role for the gas thickness, while it has a linear stable‐role. Moreover, nonlinearity shows dual roles for viscosity and liquid thickness, which have no influences according to linear theory. The investigation of stability using nonlinear theory seems more accurate to describe the (un)stable influences comparing with the linear one. The current work may be useful to give more accurate comprehension of stability process as well as to obtain the required conditions of stability by designing suitable devices, which control the model parameters.

Probing the eccentricity in protostellar discs: Modelling kinematics and morphologies

Context. Protostellar discs are mostly modelled as circular structures of gas and dust orbiting a protostar. However, a number of physical mechanisms, for example, the presence of a (sub)stellar companion or initial axial asymmetry, can cause the gas and dust orbital motion to become eccentric. Theoretical studies have revealed that, when present, disc eccentricity is expected to occur with predictable profiles that can be long-lasting and potentially observable in protostellar systems. Aims. We construct an analytical model predicting the typical features of the kinematics and morphology of eccentric protostellar discs, with the final goal of characterising the observational appearance of eccentricity in discs. Methods. We validate the model using a numerical simulation of a circumbinary disc (where the binary makes the disc eccentric). We finally post-process the simulation with Monte Carlo radiative transfer to study how eccentric features would appear through the ‘eyes’ of ALMA. Results. Besides the motion of the material on eccentric Keplerian orbits in the disc orbital plane, the most characteristic eccentric feature emerging from the analytical model is strong vertical motion with a typical anti-symmetric pattern (with respect to the disc line of pericentres). A circumbinary disc with a ≈ 40 au eccentric cavity (ecav = 0.2), carved by an abin = 15 au binary, placed at a distance d = 130 pc, is expected to host in its upper emission surface vertical oscillations up to vz ~ 400 m s−1 close to the cavity edge, that is to say, well within ALMA spectral and spatial resolution capabilities. A residual spiral pattern in the vertical velocity Δvz ~ 150 m s−1 of the simulation cannot be captured by the theoretical model, we speculate it to be possibly linked to the presence of a companion in the system.

X-ray-inferred kinematics of the core intracluster medium in Perseus-like clusters: Insights from the TNG-Cluster simulation

The intracluster medium (ICM) of galaxy clusters encodes the impact of the physical processes that shape these massive halos, including feedback from central supermassive black holes (SMBHs). In this study, we examine the gas thermodynamics, kinematics, and the effects of SMBH feedback on the core of Perseus-like galaxy clusters with a new simulation suite: TNG-Cluster. We first make a selection of simulated clusters similar to Perseus based on the total mass and inner ICM properties, such as their cool-core nature. We identify 30 Perseus-like systems among the 352 TNG-Cluster halos at z = 0. Many exhibit thermodynamical profiles and X-ray morphologies with disturbed features such as ripples, bubbles, and shock fronts that are qualitatively similar to X-ray observations of Perseus. To study observable gas motions, we generate XRISM mock X-ray observations and conduct a spectral analysis of the synthetic data. In agreement with existing Hitomi measurements, TNG-Cluster predicts subsonic gas turbulence in the central regions of Perseus-like clusters, with a typical line-of-sight velocity dispersion of 200 km s−1. This implies that turbulent pressure contributes < 10% to the dominant thermal pressure. In TNG-Cluster, such low (inferred) values of ICM velocity dispersion coexist with high-velocity outflows and bulk motions of relatively small amounts of super-virial hot gas, moving up to thousands of km s−1. However, detecting these outflows in observations may prove challenging due to their anisotropic nature and projection effects. Driven by SMBH feedback, such outflows are responsible for many morphological disturbances in the X-ray maps of cluster cores. They also increase both the inferred and intrinsic ICM velocity dispersion. This effect is somewhat stronger when velocity dispersion is measured from higher-energy lines.

Dynamics of Gas Motion in Pipe with Permeable Wall

Dynamics of Gas Motion in Pipe with Permeable Wall

Matrix methods and teaching the fundamentals of fluid and gas mechanics in higher education institutions

Problem. The instruction of physical and mathematical disciplines in higher education institutions employing cutting-edge methods and universal approaches, which seamlessly integrate scientific and engineering activities of future specialists, remains one of the pertinent and priority tasks. The utilization of multidimensional or even infinite-dimensional spaces has become an effective and nearly indispensable tool in mathematical modeling of physical phenomena. This circumstance is directly linked to the increasing level of abstraction and the refinement of mathematical methods. The use of geometric methods inherent in vector algebra and vector analysis as the foundation for studying mechanics, despite their illustrative nature, is losing its relevance. Methods built upon matrix formalism are evolving as substitutes. The matrix framework enables the exploitation of phase space advantages to derive canonical equations of motion for continuous media and electromagnetic field equations in covariant forms. The electromagnetic potential acquires mechanical significance, allowing the utilization of electromechanical analogies at a fundamental level rather than on a merely formal basis, as done in classical electrodynamics. Goal. The aim of this research is to study and justify the advantages of matrix methods for deriving equations of motion for fluids and gases from the canonical equations of mechanics by utilizing a continuum model in phase and physical space. The research is directed towards demonstrating the connection between the internal microscopic and macroscopic motion of fluids and gases, as well as highlighting the potential of matrix formalism both in terms of modeling and the utilization of computational tools. Methodology. The methodological basis for selecting matrix methods lies in the application of tensor analysis and its generalizations for modeling the motion of fluids and gases in physical and phase space. Results. It has been demonstrated that the matrix method, previously applied to classical and relativistic mechanics, allows for the consideration of the molecular structure of the environment by folding the multidimensional phase space of the mechanical system, represented by a particle of the medium, and thereby deriving equations of motion for fluids and gases from the canonical equations of classical mechanics and the equations of momentum balance of the medium. Originality. The combination of canonical equations as a result of applying the conservation law of matter in the form of balance equations in phase space and momentum balance equations in physical space allows for elucidating the relationship between macroscopic and microscopic motions of the medium, as well as the mathematical structure of the equations of motion for fluids and gases. Practical value. The proposed method allows, while remaining within the standard mathematical training offered by technical educational institutions, to effectively formalize the equations of motion for fluids and gases and provide them with an invariant form. By guiding oneself through invariance, both fundamental laws (such as the law of universal gravitation) and partial laws (the generalized Newton's law) can be obtained.

The Scatter Matters: Circumgalactic Metal Content in the Context of the M–σ Relation

The interaction between supermassive black hole (SMBH) feedback and the circumgalactic medium (CGM) continues to be an open question in galaxy evolution. In our study, we use smoothed particle hydrodynamics simulations to explore the impact of SMBH feedback on galactic metal retention and the motion of metals and gas into and through the CGM of L* galaxies. We examine 140 galaxies from the 25 Mpc cosmological volume Romulus25, with stellar masses between log(M */M ⊙) = 9.5–11.5. We measure the fraction of metals remaining in the interstellar medium (ISM) and CGM of each galaxy and calculate the expected mass of each SMBH based on the M BH–σ relation (Kormendy & Ho 2013). The deviation of each SMBH from its expected mass, ΔM BH, is compared to the potential of its host via σ. We find that SMBHs with accreted mass above M BH–σ are more effective at removing metals from the ISM than undermassive SMBHs in star-forming galaxies. Overall, overmassive SMBHs suppress the total star formation of their host galaxies and more effectively move metals from the ISM into the CGM. However, we see little to no evacuation of gas from the CGM out of their halos, in contrast with other simulations. Finally, we predict that C iv column densities in the CGM of L* galaxies are unlikely to depend on host galaxy SMBH mass. Our results show that the scatter in the low-mass end of the M BH–σ relation may indicate how effective an SMBH is in the local redistribution of mass in its host galaxy.

Submodels of 2-d model of the motion of fluid or gas in a porous medium with an external non-stationary source or absorption

The motion of fluid or gas in a porous medium is the main object of investigation of underground hydromechanics. The model describing this motion was called “Porous medium”.In our paper, we study a general 2-d model of the motion of fluid or gas in porous medium with an external non-stationary source or absorption. As the main research method, we use the method of group (symmetry) analysis, which is one of the most effective ways to obtain information about the properties of solutions to differential equations that define a physical model. A group classification of the differential equation defining studied physical model is carried out. As a result, all basic models with different symmetry properties are obtained. For the basic model, which admits the widest group a classification of all its invariant submodels is performed and all invariant submodels, defined by invariant solutions of rank 1 are studied. All solutions found have physical meaning.The set of explicitly found solutions forms a 47-parametric family of exact solutions. Each solution in this family depends on an arbitrary function defining an external non-stationary source or absorption. For each solution, for the specific values of the parameters on which it depends and for this specific function, we obtained a graph of the pressure distribution.Other solutions are used to describe the movement of a liquid or gas if either the pressure and its rate of change, or the pressure and one of its gradient components, are given at an initial time at a fixed point. The set of these solutions depends on 13 parameters and a function defining an external non-stationary source or absorption. For specific values of this function and specific values of the parameters on which each solution depends, the existence and uniqueness of a solution to the corresponding boundary value problem under some additional conditions has been established. Each such problem is solved numerically. The results of these decisions we reflected in the graphs.The significance of obtained solutions lies in the fact that we have obtained a database consisting of two multiparameter families of invariant solutions of rank 1 of the equation describing the motion of fluid or gas in a porous medium in the presence of an external non-stationary source or absorption. Every solution depends on an empirically determined function. These solutions describe specific physical processes. They can also be used as test solutions in numerical calculations related to the study of the motion of fluid or gas in a porous medium during fluids filtering, engineering surveys in the construction of building structures and in the extraction of shale oil or gas.

Dynamic coupling effects of injection on spray and mixture formation in an asymmetrically vibrating combustion engine

Enhanced methods of energy conversion present a viable solution for addressing energy load challenges. This study introduces a vibrating combustion engine designed to enhance energy conversion efficiency by harnessing flexible dynamics and variable asymmetric motion. However, the consideration of its unique dynamic effects has emerged as a pivotal challenge in fuel-air mixing and combustion research. This study introduces a fuel spray and mixing simulation method that facilitates the reciprocal exchange of coupling parameters between the combustion and dynamics models. It iterates the simulation outcomes of motion and combustion to predict mixture formation. Subsequently, the method is employed to explore the impact of injection position on fuel spray and mixture formation. Results show that there is an optimum injection position for the operation frequency, and retarding or advancing leads to slow compression and weak gas motion for fuel spray and mixing, although retarded injection provides high in-cylinder gas pressure and temperature. The early injection generally causes long penetration, small droplet diameter, slight impingement, and fast evaporation, unless it is too early. The results further indicate that when IAP = 6 mm, a more uniform mixture can be attained at the beginning of combustion, leading to a thermal efficiency of up to 42.9% for the engine.

Mixing is easy: New insights for cosmochemical evolution from pre-stellar core collapse

Signposts of early planet formation are ubiquitous in substructured young discs. Dense, hot, and high-pressure regions that formed during the gravitational collapse process, integral to star formation, facilitate dynamical mixing of dust within the protostellar disc. This provides an incentive to constrain the role of gas and dust interaction and resolve potential zones of dust concentration during star and disc formation stages. We explore whether the thermal and dynamical conditions that developed during protostellar disc formation can generate gas flows that efficiently mix and transport the well-coupled gas and dust components. We simulated the collapse of dusty molecular cloud cores with the hydrodynamics code PLUTO augmented with radiation transport and self-gravity. We used a two-dimensional axisymmetric geometry and followed the azimuthal component of the velocity. The dust was treated as Lagrangian particles that are subject to drag from the gas, whose motion is computed on a Eulerian grid. We considered 1, 10, and 100 micron-sized neutral, spherical dust grains. Importantly, the equation of state accurately includes molecular hydrogen dissociation. We focus on molecular cloud core masses of 1 and 3 $M_ odot $ and explore the effects of different initial rotation rates and cloud core sizes. Our study underlines mechanisms for the early transport of dust from the inner hot disc regions via the occurrence of two transient gas motions, namely meridional flow and outflow. The vortical flow fosters dynamical mixing and retention of dust, while the thermal pressure driven outflow replenishes dust in the outer disc. Notably, these phenomena occur regardless of the initial cloud core mass, size, and rotation rate. Young dynamical precursors to planet-forming discs exhibit regions with complex hydrodynamical gas features and high-temperature structures. These can play a crucial role in concentrating dust for subsequent growth into protoplanets. Dust transport, especially, from sub-au scales surrounding the protostar to the outer relatively cooler parts, offers an efficient pathway for thermal reprocessing during pre-stellar core collapse.