Two-fluid Theory Research Articles

Influence of embedded structure on two-phase reactive flow characteristics for a small combustion chamber with a moving boundary

In special launch scenarios such as armament and aerospace, the scale of the launch system is severely restricted, which causes unstable combustion of propellant. An embedded structure for the small propulsion system driven by solid propellant is proposed to overcome this problem. This study aims to demonstrate the two-phase flow behaviors and launch safety of the combustion chamber with an embedded structure. A two-dimensional two-phase flow model based on the modified two-fluid theory is developed to describe the detailed two-phase flow behaviors in the combustion chamber during launching. Different from most of the existing studies, the constitutive equations determined from actual physical conditions are used to close the system of continuity equations. The numerical results are compared with that of the experiment to verify the accuracy of the numerical model. On this basis, the launch performance of the embedded structure is investigated. The numerical results indicate that the embedded structure facilitates the ignition process and reduces the risk of excessive pressure, but decreases the muzzle velocity at the same time. In addition, the effect of design parameters on launch safety is further investigated. Design parameters directly affect the launch safety, and the selection of reasonable parameters is a useful method for enhancing the launch performance.

Nonlinear ion acoustic waves in dense magnetoplasmas: Analyzing interaction solutions of the KdV equation using Wronskian formalism for electron trapping with Landau diamagnetism and thermal excitations

Nonlinear ion acoustic waves in the presence of electron trapping with Landau quantization and thermal excitations induced smearing effects of the Fermi step function are investigated using the two-fluid theory in the vicinity of white dwarfs. In spite of the fact that the Kortweg de Vries (KdV) equation is derived within the confines of small amplitude approximation used in the reductive perturbation theory (RPT), it is found to admit solutions that exhibit outstanding capability of wave enhancement and have applications in the nonlinear wave propagation. It is found that enhancing the quantizing magnetic field and the electron thermal effects modify the spatial scale of the formation of the novel nonlinear structures reported for our model. Interestingly, it is found that, unlike the solitary and periodic structures, the choice of space and time coordinates affects the structure of these solutions. Interaction of these solutions with a stable nonlinear structure are also studied.

Relativistic Heat Conduction in the Large-Flux Regime.

We propose a general procedure for evaluating, directly from microphysics, the constitutive relations of heat-conducting fluids in regimes of large fluxes of heat. Our choice of hydrodynamic formalism is Carter's two-fluid theory, which happens to coincide with Öttinger's GENERIC theory for relativistic heat conduction. This is a natural framework, as it should correctly describe the relativistic "inertia of heat" as well as the subtle interplay between reversible and irreversible couplings. We provide two concrete applications of our procedure, where the constitutive relations are evaluated, respectively, from maximum entropy hydrodynamics and Chapman-Enskog theory.

Two-fluid theory of composite bosons and fermions and the quantum Hall proximity effect

Two-fluid theory of composite bosons and fermions and the quantum Hall proximity effect

A prediction-evaluation method for road network energy consumption: Fusion of vehicle energy flow principle and Two-Fluid theory

A prediction-evaluation method for road network energy consumption: Fusion of vehicle energy flow principle and Two-Fluid theory

Evolution from the gradient drift instability to the formation of the spoke potential hump in a partially magnetized plasma

Rotating spokes commonly occur in partially magnetized plasma devices. This work explores the evolution from the gradient drift instability into an m = 1 rotating spoke mode in a magnetically enhanced hollow cathode discharge (with emissive cathode) by means of 2D radial-azimuthal particle-in-cell/Monte Carlo collision simulations. It is shown that the formation of the spoke potential hump region can be explained as a result of the local collapse of the anode sheath due to the gradient drift instability, which is triggered within the anode sheath. The sheath non-neutrality effect on the instability is considered and incorporated in the two-fluid linear theory of gradient drift instability. The unstable modes predicted by the theory are in good agreement with the fluctuation modes developed in the particle simulations.

Calculation of Component Activities for Se-Based Binary Systems by NRTL Equation

The interaction energy parameters of the Nonrandom two-liquid (NRTL) equation for the Bi–Se, Pb–Se, Sb–Se, and Tl–Se binary systems were determined. The difference in the goodness of fit between the systems was discussed for each system. The activities of components at corresponding temperatures for the four binary systems were calculated and discussed using the NRTL equation. The mixing enthalpies and Gibbs free energies of these systems were obtained. The calculations for the four binary systems are in agreement with the experimental data from the literature. It shows that the NRTL equation is reasonable and accurate based on the concept of local composition and two-fluid theory, especially for binary systems containing liquid–liquid equilibria. The results we obtained using the NRTL equation can be very useful in performing vacuum experiments for crude selenium.

Dynamic virial theorem at nonequilibrium and applications

We show that a variety of nonequilibrium dynamics of interacting many-body systems are universally characterized by an elegant relation, which we call the dynamic virial theorem. The out-of-equilibrium dynamics of quantum correlations is entirely governed by Tan' s contact. It gives rise to a series of observable consequences and is closely related to experiments with ultracold atoms. In particular, we show that the dynamic virial theorem provides an experimentally accessible verification of the maximum energy growth theorem [R. Qi et al., Phys. Rev. Lett. 126, 240401 (2021)], which is encoded in the evolution of the atomic cloud size during expansion. In addition, the dynamic virial theorem leads to a simple thermodynamic relation of strongly interacting quantum gases in the framework of two-fluid hydrodynamic theory, which holds in a wide range of temperature. This thermodynamic relation is a type of out-of-equilibrium analog of Tan's pressure relation at equilibrium. Our results provide a fundamental understanding of the generic behaviors of interacting many-body systems at nonequilibrium and are readily examined in experiments with ultracold atoms.

Temporal Aggregated Analysis of GPS Trajectory Data Using Two-Fluid Model

The market for on-demand mobility services is growing worldwide. These services include, for example, ride-hailing, ride-sharing, and car-sharing. Large-scale fleets of such services collect GPS trajectory (probe vehicle) data constantly everywhere in the network. At a certain penetration rate, this data becomes representative of the entire road network. It can give valuable insights into traffic dynamics and the evolution of congestion. In this paper, we use such GPS trajectory data from Chengdu, China, to investigate the stability and recurrence of macroscopic traffic patterns. Using the two-fluid theory, we find that the two-fluid coefficients are robust on between-day variation, not only supporting the theory itself but also emphasizing that the general evolution of traffic is a robust pattern. We investigate the deviations from the model using time series analysis of the residuals of the two-fluid model. Here, we find evidence for daily and weekly seasonality in the residuals, indicating that congestion patterns are convincingly recurring. These patterns can be used for network-wide traffic state prediction. We conclude that GPS trajectory data from large on-demand mobility fleets is a promising data source for observing traffic patterns in urban road networks once the data becomes representative.

Considerations of A Two-Fluid Heliospheric Plasma Dynamics Under Dominant Electron Pressure

Electrons in plasma physics mostly are the underestimated species, since usually they only have to guarantee electric quasineutrality, but don’t count in terms of mass-, momentum-, and energy flows. This is different in space plasmas like the heliospheric plasma, especially the plasma downstream of the solar wind termination shock. Here it has become evident more recently that electrons dominate the plasma pressure and, connected with that, the plasma energy flow. Under these conditions a two-fluid plasma theory is needed to adequately describe fields and flows. We first here develop a pure two-fluid thermodynamics of such two-fluid plasmas and then study the actual situation in case of the heliospheric plasma that the electron pressure is dominating over the proton pressure. Under such auspices the electron pressure determines the mass- and momentum flows of the plasma and in fact decreases with the decrease of bulk velocity of the flow

Two-fluid kinetic theory for dilute polymer solutions.

We provide a Boltzmann-type kinetic description for dilute polymer solutions based on two-fluid theory. This Boltzmann-type description uses a quasiequilibrium based relaxation mechanism to model collisions between a polymer dumbbell and a solvent molecule. The model reproduces the desired macroscopic equationsfor the polymer-solvent mixture. The proposed kinetic scheme leads to a numerical algorithm which is along the lines of the lattice Boltzmann method. Finally, the algorithm is applied to describe the evolution of a perturbed Kolmogorov flow profile, whereby we recover the major elastic effect exhibited by a polymer solution, specifically, the suppression of the original inertial instability.

Quasi-Static and Dynamic Photon Bubbles in Cold Atom Clouds

Turbulent radiation flow is ubiquitous in many physical systems where light–matter interaction becomes relevant. Photon bubble instabilities, in particular, have been identified as a possible source of turbulent radiation transport in astrophysical objects such as massive stars and black hole accretion disks. Here, we report on the experimental observation of a photon bubble instability in cold atomic gases, in the presence of multiple scattering of light. Two different regimes are identified, namely, the growth and formation of quasi-static structures of depleted atom density and increased photon number, akin to photon bubbles in astrophysical objects, and the destabilisation of these structures in a second regime of photon bubble turbulence. A two-fluid theory is developed to model the coupled atom–photon gas and to describe both the saturation of the instability in the regime of quasi-static bubbles and the low-frequency turbulent phase associated with the growth and collapse of photon bubbles inside the atomic sample. We also employ statistical dimensionality reduction techniques to describe the low-dimensional nature of the turbulent regime. The experimental results reported here, along with the theoretical model we have developed, may shed light on analogue photon bubble instabilities in astrophysical scenarios. Our findings are consistent with recent analyses based on spatially resolved pump–probe measurements.

Kinematic stability and simulations of the variational two-fluid model for slug flow

The two-fluid short-wave theory (TF-SWT) mode of the one-dimensional two-fluid model (TFM) [A. Clausse and M. Lopez de Bertodano, “Natural modes of the two-fluid model of two-phase flow,” Phys. Fluids 33, 033324 (2021)] showed that the incompressible kinematic and Kelvin–Helmholtz instabilities are the source of the long-standing ill-posed question. Here, the stability of the short wave mode is analyzed to obtain an unstable incompressible well-posed TFM for vertical slug flow, where inertial coupling and drag play the key role. Then, a computational method is implemented to perform non-linear simulations of slug waves. Linear stability analyses, i.e., characteristics and dispersion, of a variational TF-SWT for vertical slug flows are presented. The current TFM is constituted with a lumped-parameter model of inertial coupling between the Taylor bubble and the liquid. A characteristic analysis shows that this conservative model is parabolic, and it provides a base upon which other models can be constructed, including short-wave damping mechanisms, like vortex dynamics. The dispersion analysis shows that depending on the interfacial drag, the problem can be kinematic unstable. A new kinematic condition in terms of the inertial coupling and the interfacial drag is derived that is consistent with previous theoretical and experimental results. The material waves, which are predicted by linear stability theory, then develop into nonlinear slug waveforms that are captured by the numerical simulations. These and the horizontal stratified flow waves of previous research illustrate the TFM capability to model interfacial structures that behave like waves. Otherwise, when the physics of the TF-SWT waves is ignored, the model is ill-posed.

Electrostatic weak turbulence theory for warm magnetized plasmas

Electrostatic weak turbulence theory for plasmas immersed in an ambient magnetic field is developed by employing a hybrid two-fluid and kinetic theories. The nonlinear susceptibility response function is calculated with the use of warm two-fluid equations. The linear dispersion relations for longitudinal electrostatic waves in magnetized plasmas are also obtained within the warm two-fluid theoretical scheme. However, dissipations that arise from linear and nonlinear wave–particle interactions cannot be discussed with the macroscopic two-fluid theory. To compute such collisionless dissipation effects, linearized kinetic theory is utilized. Moreover, a particle kinetic equation, which is necessary for a self-consistent description of the problem, is derived from the quasilinear kinetic theory. The final set of equations directly generalizes the electrostatic weak turbulence theory in unmagnetized plasmas, which could be applied for a variety of problems including the electron beam–plasma interactions in magnetized plasma environments.

Turbulent field fluctuations in gyrokinetic and fluid plasmas

A key uncertainty in the design and development of magnetic confinement fusion energy reactors is predicting edge plasma turbulence. An essential step in overcoming this uncertainty is the validation in accuracy of reduced turbulent transport models. Drift-reduced Braginskii two-fluid theory is one such set of reduced equations that has for decades simulated boundary plasmas in experiment, but significant questions exist regarding its predictive ability. To this end, using a novel physics-informed deep learning framework, we demonstrate the first ever direct quantitative comparisons of turbulent field fluctuations between electrostatic two-fluid theory and electromagnetic gyrokinetic modeling with good overall agreement found in magnetized helical plasmas at low normalized pressure. This framework presents a new technique for the numerical validation and discovery of reduced global plasma turbulence models.

Effects of displacement current on wave dispersion relation and polarization properties in auroral plasmas

In-situ observations from the FREJA magnetospheric research satellite and the Fast Auroral SnapshoT satellite have shown that plasma waves are frequently observed in the auroral plasma, which are believed to be fundamentally important in wave energy dissipation and particle energization. However, the effects of a displacement current on these waves have not been examined. Based on the two-fluid theory, we investigate the dispersion relation and polarization properties of fast, Alfvén, and slow modes in the presence of a displacement current, and the effects of the displacement current on these waves are also considered. The results show that the wave frequency, polarization, magnetic helicity and other properties for the fast and Alfvén modes are highly sensitive to the normalized Alfvén velocity vA /c, plasma beta β, and propagation angle θ, while for the slow mode the dependence is minor. In particular, for both fast and Alfvén modes, the magnetic helicity is obviously different with and without the displacement current, especially for the Alfvén mode with the helicity reversals from right-handed to left-handed when vA /c increases from 0 to 0.3. The charge-neutral condition of both fast and Alfvén modes with frequencies larger than the proton cyclotron frequency is invalid in the presence of the displacement current. Moreover, the presence of the displacement current leads to relatively large magnetic compressibility for the Alfvén mode and relatively large electron compressibility for the fast mode. These results can be useful for a comprehensive understanding of the wave properties and the physics of particle energization phenomena in auroral plasmas.

Uncovering turbulent plasma dynamics via deep learning from partial observations.

One of the most intensely studied aspects of magnetic confinement fusion is edge plasma turbulence which is critical to reactor performance and operation. Drift-reduced Braginskii two-fluid theory has for decades been widely applied to model boundary plasmas with varying success. Towards better understanding edge turbulence in both theory and experiment, we demonstrate that a physics-informed deep learning framework constrained by partial differential equations can accurately learn turbulent fields consistent with the two-fluid theory from partial observations of electron pressure which is not otherwise possible using conventional equilibrium models. This technique presents a paradigm for the advanced design of plasma diagnostics and validation of magnetized plasma turbulence theories in challenging thermonuclear environments.

How Many Cars in the City Are Too Many? Towards Finding the Optimal Modal Split for a Multi-Modal Urban Road Network

Interactions among different modes or vehicle classes in urban road networks affect the network performance in different and complex ways. Thus, an answer to the question of “how many cars are too many for a city?” is not trivial. However, multi-modal macroscopic fundamental diagrams (MFD) offer a novel opportunity to answer this question. So far, no methodology exists to estimate multi-modal MFDs resulting from arbitrary multi-modal interactions. In this paper, we propose a methodology to capture additional delays in the shape of the MFD and derive an approach for estimating multi-modal MFDs thereof. The influence on the MFD shape is established using the two-fluid theory of urban traffic by defining pairwise copula functions between travel times of each mode. In contrast to many existing approaches, the presented approach retains individual mode's speed information. We show the applicability of the approach with a tri-modal case of bicycles, buses, and cars with empirical data from Amsterdam (The Netherlands) and London (United Kingdom). Although the approach is not limited to this specific tri-modal case, we use the example to discuss the initial policy question by deriving optimal modal splits for a given accumulation of travelers. Last, we compare the new approach to existing estimation methods for bi-modal MFDs describing car and bus traffic.

Prediction of thermodynamic properties of organic mixtures: Combining molecular simulations with classical thermodynamics

The binary interaction parameters of the nonrandom two liquid (NRTL) thermodynamic model are predicted for several organic mixtures using molecular simulations. Based on the theoretical framework of the two-fluid theory, the binary interaction parameters are expressed in terms of the interaction energies, size of the molecules, and size of the local molecular domains; these quantities are calculated from molecular simulations. We show that our technique is robust in terms of its predictions involving organic mixtures with compatible chemical characteristics while we propose possible modifications in the case of mixtures involving incompatible chemical components or significant size disparity, where there is a notable difference between the interaction parameters calculated from simulations and those obtained from experimental data regression. We further demonstrate that the binary interaction parameters calculated from data regression are not unique and that molecular simulations can guide the parameter selection process by identifying physically relevant binary interaction parameters. Requiring only the local molecular structure information from molecular simulations, the method offers fast and reliable prediction of phase equilibrium properties, especially in cases where limited experimental data are available.

A general metriplectic framework with application to dissipative extended magnetohydrodynamics

General equations for conservative yet dissipative (entropy producing) extended magnetohydrodynamics are derived from two-fluid theory. Keeping all terms generates unusual cross-effects, such as thermophoresis and a current viscosity that mixes with the usual velocity viscosity. While the Poisson bracket of the ideal version of this model has already been discovered, we determine its metriplectic counterpart that describes the dissipation. This is done using a new and general thermodynamic point of view to derive dissipative brackets, a means of derivation that is natural for understanding and creating dissipative dynamics without appealing to underlying kinetic theory orderings. Finally, the formalism is used to study dissipation in the Lagrangian variable picture where, in the context of extended magnetohydrodynamics, non-local dissipative brackets naturally emerge.