One-dimensional Gas Flow Research Articles

Kinetic modelling of rarefied gas flows with radiation

Two kinetic models are proposed for high-temperature rarefied (or non-equilibrium) gas flows with internal degrees of freedom and radiation. One of the models uses the Boltzmann collision operator to model the translational motion of gas molecules, which has the ability to capture the influence of intermolecular potentials, while the other adopts the relaxation time approximations, which has higher computational efficiency. In our kinetic model equations, not only the transport coefficients such as the shear/bulk viscosity and thermal conductivity but also their underlying relaxation processes are recovered. The non-equilibrium dynamics of gas flow and radiation are tightly coupled, where the transport properties of gas molecules and photons are correlatively dependent. The proposed kinetic models are validated by the direct simulation Monte Carlo method in several non-radiative rarefied gas flows (e.g. the normal shock wave, Fourier flow, Couette flow and the creep flow driven by the Maxwell demon), and the experimental data of planar heat transfer and normal shock waves in nitrogen. Then, the rarefied gas flows with strong radiation are studied based on the kinetic models, not only in the above one-dimensional gas flows, but also in the two-dimensional radiative hypersonic flow passing a cylinder. The characteristics of heat transfer in the tightly coupled fields of gas and radiation are systematically investigated, particularly the influence of the non-equilibrium photon transport and their interactions with gas molecules are revealed. It is found that the radiation makes a profound contribution to the total heat transfer in radiative hypersonic flow at an intermediate photon Knudsen number.

Bimodal star formation in simulations of strongly magnetized giant molecular clouds

ABSTRACT We present the results of a set of radiation magnetohydrodynamic simulations of turbulent molecular clouds in which we vary the initial strength of the magnetic field within a range (1 ≲ μ ≲ 5) consistent with observations of local giant molecular clouds (GMCs). We find that as we increase the strength of the magnetic field, star formation transitions from unimodal (the baseline case, μ = 5, with a single burst of star formation and Salpeter IMF) to bimodal. This effect is clearest in the most strongly magnetized GMC (μ = 1): a first burst of star formation with duration, intensity, and IMF comparable to the baseline case, is followed by a second star formation episode in which only low-mass stars are formed. Overall, due to the second burst of star formation, the strongly magnetized case results in a longer star formation period and a higher efficiency of star formation. The second burst is produced by gas that is not expelled by radiative feedback, instead remains trapped in the GMC by the large-scale B-field, producing a nearly one-dimensional flow of gas along the field lines. The trapped gas has a turbulent and magnetic topology that differs from that of the first phase and strongly suppresses gas accretion onto protostellar cores, reducing their masses. We speculate that this star formation bimodality may be an important ingredient to understand the origin of multiple stellar populations observed in massive globular clusters.

Construction of Exact Solutions of the System of One-Dimensional Gas Dynamics Equations without Gradient Catastrophe

The system of equations that describes one-dimensional polytropic gas flows is considered. The invariants up to the second order of characteristics of the considered system of equations are classified. The method of reducing the Cauchy problems to systems of ordinary differential equations is proposed. Examples of the solutions without gradient catastrophe are constructed using invariants of characteristics supplementary to the Riemann invariants.

Quadrature-based moment methods for kinetic plasma simulations

Quadrature-based moment methods (QBMM) are applied to rarefied gas flow and plasma physics problems represented by the Boltzmann equation or the Vlasov-Poisson system of equations. QBMM are a computationally advantageous alternative to both direct Eulerian and Lagrangian particle solvers, able to provide a noise-free solution to the Boltzmann equation and capture non-equilibrium velocity distribution functions (VDF) without excessive computational cost. To provide a closure of the moment equations, the VDF is assumed to be represented by the sum of weighted kernel functions that are placed at given velocity abscissas. Three QBMM approaches, QMOM (Dirac delta kernels), HyQMOM (hyperbolic QMOM), and EQMOM (Gaussian kernels), are applied to canonical one-dimensional rarefied gas flow and plasma physics problems. A new algorithm for EQMOM that is able to treat pathological VDFs and provide control over large abscissas for more than two nodes is developed. QMOM and EQMOM are suitable for problems where the flow does not have shock-like features (for QMOM) or a discontinuity in the VDF (for EQMOM) and where the VDF is far from non-equilibrium and features strong phase-mixing. HyQMOM is generally applicable to all test problems and yields good representations of both the moments and the VDF. HyQMOM also provides significant wall-time improvement (factor of 10–100) compared to other direct Eulerian solvers.

A New Mapped WENO Method for Hyperbolic Problems

In this study, a new family of rational mapping functions gRM(ω;k,m,s) is introduced for seventh-order WENO schemes. gRM is a more general family of mapping functions, which includes other mapping functions such as gM and gIM as special cases. The mapped WENO scheme WENO-IM(2,0.1), which uses gIM, performs excellently at fifth order but rather poorly at seventh order. The reason for this loss of accuracy was found to be the over-amplification of very small weights by the mapping process, which can be traced back to the large slope of gIM at ω = 0. For m > 1, gRM can be designed to have a unit slope at ω = 0, which will preserve small weights with little to no amplification. It has been demonstrated through several one-dimensional linear advection test cases that the mapped WENO scheme WENO-RM(6,3,2 × 103), which uses the mapping function gRM(ω;6,3,2 × 103), outperforms both WENO-M and WENO-IM(2,0.1) at seventh order. The proposed scheme also performs better at a number of one-dimensional inviscid gas flow problems compared to other popular WENO schemes such as the WENO-Z scheme.

The Riemann problem for one-dimensional dusty gas dynamics with external forces

This article concerns the study of the Riemann Problem (RP) for a non-homogeneous system governing the one-dimensional compressible flow of dusty gas, where the external forces are assumed to be continuous function of time. The elementary wave solutions such as rarefaction wave, shock wave, and contact discontinuity are rigorously determined. The effect of dust particles on the density and flow velocity and shock speed is examined, and their consequences on the solution of the Riemann Problem are discussed. Moreover, we discussed the condition for the existence of vacuum appears in the solution of the Riemann Problem.

Similarity solutions for strong shock waves in non-ideal magnetogasdynamics under the effect of monochromatic radiation

This manuscript aims to deal with the one-dimensional unsteady flow of non-ideal gas with monochromatic radiation under the influence of a magnetic field, where the invariance method of the Lie group of transformations is applied in a cylindrically symmetric motion. The density is assumed to be uniform in the undisturbed medium. The radiation flux is considered to move through the non-ideal gas. The self-similar solutions of the considered model are obtained for the power-law and the exponential-law shock paths. The effects of the adiabatic exponent, radiation parameter, ambient magnetic field, and the parameter of non-idealness on the flow variables are shown graphically. Numerical calculations are performed to obtain the self-similar solutions.

The analytical solutions to one-dimensional non-ideal dusty gas flow

The analytical solutions to one-dimensional non-ideal dusty gas flow

Analytical solutions for one-dimensional diabatic flows with wall friction

Abstract

Exact solutions for quasi-one-dimensional compressible viscous flows in conical nozzles

Abstract

Quotients of Euler Equations on Space Curves

Quotients of partial differential equations are discussed. The quotient equation for the Euler system describing a one-dimensional gas flow on a space curve is found. An example of using the quotient to solve the Euler system is given. Using virial expansion of the Planck potential, we reduce the quotient equation to a series of systems of ordinary differential equations (ODEs). Possible solutions of the ODE system are discussed.

Singularities in Euler Flows: Multivalued Solutions, Shockwaves, and Phase Transitions

In this paper, we analyze various types of critical phenomena in one-dimensional gas flows described by Euler equations. We give a geometrical interpretation of thermodynamics with a special emphasis on phase transitions. We use ideas from the geometrical theory of partial differential equations (PDEs), in particular symmetries and differential constraints, to find solutions to the Euler system. Solutions obtained are multivalued and have singularities of projection to the plane of independent variables. We analyze the propagation of the shockwave front along with phase transitions.

One-Dimensional Gas Flow Analysis of the Intake and Exhaust System of a Single Cylinder Diesel Engine

In order to design a diesel engine system and to predict its performance, it is necessary to analyze the gas flow of the intake and exhaust system. Gas flow analysis in a three-dimensional (3D) format needs a high-resolution workstation and an enormous amount of time for analysis. Calculation using the method of characteristics (MOC), which is a gas flow analysis in a one-dimensional (1D) format, has a fast calculation time and can be analyzed with a low-resolution workstation. However, there is a problem with poor accuracy in certain areas. It was assumed that the reason was that 1D could not implement the shape. The error that occurs in the shape of the bent pipe used in the intake and exhaust ports of the diesel engine was analyzed and to find a solution to the low accuracy, the results of the experiment and 1D analysis were compared. The discharge coefficient was calculated using the average mass flow rate, and as a result of applying it, the accuracy was improved for the maximum negative pressure by 0.56–1.93% and the maximum pressure by 3.11–7.86% among the intake pipe pressure results. The difference in phase of the exhaust pipe pressure did not improve. It is considered as a limitation of 1D analysis that does not improve even by applying the discharge coefficient. In the future, we intend to implement a bent pipe that cannot be realized in 1D using a 3D format and to prepare a method to supplement the reliability by using 1D–3D coupling.

Interaction of waves in one-dimensional dusty gas flow

Abstract The present study uses the theory of weakly nonlinear geometrical acoustics to derive the high-frequency small amplitude asymptotic solution of the one-dimensional quasilinear hyperbolic system of partial differential equations characterizing compressible, unsteady flow with generalized geometry in ideal gas flow with dust particles. The method of multiple time scales is applied to derive the transport equations for the amplitude of resonantly interacting high-frequency waves in a dusty gas. These transport equations are used for the qualitative analysis of nonlinear wave interaction process and self-interaction of nonlinear waves which exist in the system under study. Further, the evolutionary behavior of weak shock waves propagating in ideal gas flow with dust particles is examined here. The progressive wave nature of nonresonant waves terminating into the shock wave and its location is also studied. Further, we analyze the effect of the small solid particles on the propagation of shock wave.

Development of a method of extended cells for the formulation of boundary conditions in numerical integration of gas dynamics equations in the domains of a curvilinear shape

A method of extended cells for the formulation of boundary conditions in the numerical integration of the Euler equations in domains with curvilinear boundaries for the cases of one-dimensional and two-dimensional compressible gas flows has been proposed in this study. The proposed method is based on the use of the explicit Godunov type finite volume method on a regular rectangular Cartesian grid. The essence of the extended cell method is that when integrating the basic equations of gas dynamics in a fractional cell, numerical fluxes are calculated through the sides of the new extended cell. This new cell is constructed tangentially to the curved boundary and has a size no less than the cell size in the regular domain. Parameters inside the new cell are calculated as mean integral values over the area of the neighboring regular cells included in it. In this case, when choosing a time step in accordance with the Courant condition, the stability of the method in the main computational domain is preserved both when integrating fractional cells and when integrating regular cells. Thanks to this approach, the proposed method has low requirements for computing resources, the ability to generalize for three-dimensional space and increase the order of accuracy without major modifications of the algorithm. To test the proposed method, solutions were obtained for the generally accepted test problems of gas dynamics: normal and double Mach reflection of a shock wave from a plane wall. The choice of the time step was made in accordance with the Courant condition in regular finite volumes. The results obtained have made it possible to assess the convergence of the proposed method and their comparison with the results of calculations using other methods have shown a good quantitative and qualitative agreement

Gas Heating Mechanisms in Atmospheric Pressure Helium Dielectric-Barrier Discharges Driven by a kHz Power Source

The present work investigates contributions of different heating mechanisms and power efficiency of atmospheric-pressure helium dielectric-barrier discharges (APHeDBDs) containing a small amount of N2 for temperature measurements by developing the numerical methodology combining the one-dimensional (1D) plasma fluid model (PFM) and 3D gas flow model (GFM) with simulated results validated by measurements including the discharge power consumption and temperature distribution. The discharge dynamics are modeled by the 1D PFM for evaluating the average heating source considering elastic collision, ion Joule heating, and exothermic reactions as the source term of energy equation solved in the 3D GFM. The simulated current density reaches 29 A m−2 which is close to that measured as 35 A m−2. The simulated power consumption is 2.0 W which is in good agreement with the average measured power consumption as 2.1 W. The simulated average gas temperature in the reactive zone is around 346 K which is also close to the rotational temperature determined. The analysis shows that elastic collision and ion Joule heating are dominant heating mechanisms contributing 23.9% and 65.8% to the heating source, respectively. Among ion species, N2+ and N4+ are dominant species contributing 44.1% and 50.7% to the heating source of ion Joule heating, respectively. The simulated average total heating source is around 5.6 × 105 W m−3 with the maximum reaching 3.5 × 106 W m−3 in the sheath region due to the contribution of ion Joule heating.

Pulsed very high-frequency plasma-enhanced chemical vapor deposition of silicon films for low-temperature (120 °C) thin film transistors

With the aim of improving silicon (Si) film quality deposited by atmospheric-pressure (AP) plasma-enhanced chemical vapor deposition at a low substrate temperature of 120 °C, we examine the difference between continuous wave and pulsed plasmas for deposition characteristics depending on H2 and SiH4 flow rates and inpur VHF power. A specifically designed parallel-plate-type electrode system is used to generate the AP plasma, which is excited by 150 MHz very high-frequency (VHF) electric power. Hydrogen and monosilane diluted with helium are used as the process gases. The electrode system enables us to form turbulence-free one-dimensional gas flow in the plasma zone, thereby ensuring a deposition process without contamination of the substrate surface with dust particles. The electrical property of the deposited Si layers was evaluated by fabricating bottom-gate thin film transistors (TFTs). The performance of the bottom-gate TFTs revealed that the a-Si TFTs, i.e. those channel layers prepared with a pulse duty cycle of 10%, exhibit reasonably high field effect mobilities of around 1 cm2 · V–1 · s–1, suggesting that the pulse modulation of input VHF power is highly effective in achieving a plasma chemistry suitable for high-quality Si growths at low temperatures.

Similarity solutions for strong shock waves in magnetogasdynamics under a gravitational field

In the present paper, we use a Lie group of transformations to obtain a class of similarity solutions to a problem of cylindrically symmetric strong shock waves propagating through one-dimensional, unsteady, and isothermal flow of a self-gravitating ideal gas under the influence of azimuthal magnetic field. The density of the ambient medium is assumed to be non-uniform ahead of the shock. The generators of the Lie group of transformations involve arbitrary constants which yield four different cases of possible solutions. Out of all possibilities, only two cases hold similarity solutions. One is with a power law shock path, and the other one is with an exponential law shock path. We present a detailed investigation for the case of power law shock path. Numerical computations have been performed to find out the flow patterns in the flow-field behind the shock. Also, we have analyzed the effects of variation in adiabatic index, ambient density exponent, gravitational parameter, and Alfven-Mach number on the flow variables behind the shock. All computations have been done using the software package MATLAB.

Solution of the Riemann problem for an ideal polytropic dusty gas in magnetogasdynamics

Abstract The main aim of this paper is, to obtain the analytical solution of the Riemann problem for a quasi-linear system of equations, which describe the one-dimensional unsteady flow of an ideal polytropic dusty gas in magnetogasdynamics without any restriction on the initial data. By using the Rankine-Hugoniot (R-H) and Lax conditions, the explicit expressions of elementary wave solutions (i. e., shock waves, simple waves and contact discontinuities) are derived. In the flow field, the velocity and density distributions for the compressive and rarefaction waves are discussed and shown graphically. It is also shown how the presence of small solid particles and magnetic field affect the velocity and density across the elementary waves. It is an interesting fact about this study that the results obtained for the Riemann problem are in closed form.

A Typical Dropping Cusp Singularity of Solutions to Equations of a One-Dimensional Isentropic Gas Flow

Solutions are considered for the system of nonlinear equations of a one-dimensional isentropic gas flow with low densities. A typical singularity of these solutions corresponding to a cusp catastrophe is described. A model solution with such a singularity was obtained for the special case of shallow-water equations. Within the terms of this model solution, an asymptotic solution is obtained for the system of nonlinear equations of a one-dimensional isentropic gas flow.