Adiabatic Gas Flow Research Articles

Analysis of propagation of normal shocks in Van der Waals gas: Buongiorno model

This paper presents an analytical investigation into the propagation of a normal shock wave in Van der Waals gas flow, employing the Buongiorno model. It explores the dynamics of this flow type under a shock wave, considering modified Rankine–Hugoniot (RH) jump conditions within the Buongiorno model framework. By solving the RH conditions, this study provides a solution for gas flows with varying nanoparticle concentrations, facilitating an examination of parameter variations under discontinuity. The abstract further emphasizes the graphical representation of velocity coefficient and pressure in adiabatic gas flow during a shock wave, considering compressive and exponential waves. The analysis accounts for nanoparticle concentration and non-ideal parameters.

Adiabatic gas transport in the long flow channels

The paper present the determination of the state parameters of natural gas at the pipeline inlet based on knowledge of the pressure and temperature at the receiving point. Natural gas transport will be carried out through an offshore section of a transmission pipeline. The equations of the Fanno flow model will be used to describe the thermodynamic parameters of the gas in the flow lines. The mathematical equations of the flow mentioned above models have been derived from an analysis of the mass, energy and momentum balance equations. They also take into account the viscous friction forces in the transported gas. Based on the carried out calculations, changes in the Mach number, pressure and velocity of methane transported along the analysed pipeline were determined. In addition, the total entropy gain in the analysed methane flow was determined. The novelty of the calculations presented is the use of the Fanno flow model, which considers a realistic adiabatic gas flow. This is in contrast to the isothermal flow model, which assumes an unchanging temperature of the transported gas. In the case under consideration, the adopting model was possible because of the similar temperature values of the gas flowing in the pipeline and the corresponding temperature values of the surrounding seawater. The fundamental advantage of the Fanno flow model is that it satisfies the mass balance of the flowing gas in each cross-section. Thus, the product of the velocity and density of the gas in a pipeline of constant diameter assumes a constant value.

Oblique shock wave in turbulent flow

Abstract The main attention is paid to the analytical analysis of an oblique shock wave in a turbulent adiabatic gas flow. For this purpose, a modified Rankine–Hugoniot model was obtained. On its basis, a solution was derived for the Rankine–Hugoniot conditions for a gas flow with various degrees of turbulence, as well as the equation of the modified Hugoniot adiabat. The behavior of the velocity of an adiabatic turbulent gas flow during its passage through an oblique shock wave at different levels of turbulence is demonstrated. A modification of Prandtl’s law for the velocity coefficients was obtained. The shock polar was also analyzed. The relationship between the angular gas flow and the angle of the shock wave was derived. Finally, the condition for the appearance of an outgoing bow shock wave was obtained.

Shock waves in gas flows with nanoparticles

The paper focuses on the analytical analysis of the propagation of a normal shock wave in an adiabatic gas flow with nanoparticles. A modified Rankine–Hugoniot model was used for this purpose. A solution is obtained for the Rankine–Hugoniot conditions in a gas flow with different nanoparticle concentrations, which makes it possible to analyze the dynamics of variation of the parameters of this type of flow under a shock wave. The variation of velocity, pressure and entropy production of the adiabatic gas flow during a direct shock wave depending on the concentration of nanoparticles in the gas was depicted graphically. It was revealed that increasing the nanoparticle concentration to φ ~ 0.1 weakens the effect of the shock wave, and then, after passing the zone of minimum parameters, the intensity of the shock wave increases.

Analytical simulation of normal shock waves in turbulent flow

The focus of the work is on analytical modeling of normal shock wave propagation in a turbulent adiabatic gas flow. For this, a modified Rankine–Hugoniot model was developed. A solution is obtained for the Rankine–Hugoniot conditions in a turbulent gas flow with different turbulence intensity. Variation of the velocity of an adiabatic turbulent gas flow during its passage through a normal shock wave is elucidated depending on the turbulence intensity. The equation of the modified Hugoniot adiabat is also obtained.

Shock Waves in Euler Flows of Gases

Non-stationary Euler flows of gases are studied. The system of differential equations describing such flows can be represented by means of 2-forms on zero-jet space and we get some exact solutions by means of such a representation. Solutions obtained are multivalued and we provide a method of finding caustics, as well as wave front displacement. The method can be applied to any model of thermodynamic state as well as to any thermodynamic process. We illustrate the method on adiabatic ideal gas flows.

Analytical Study of Weak Shock Waves in Gas with dust particles

In the present paper, the exact solution of quasilinear hyperbolic system of equations governing the propagation of weak shock waves in a one-dimensional dusty adiabatic gas flow with generalized geometries is derived. Here, the density behind the shock front is assumed to vary according to a power law of the distance. An analytical expression for the total energy carried by weak shock wave in dusty gas is also derived.

A Comparison of Data Reduction Methods for Average Friction Factor Calculation of Adiabatic Gas Flows in Microchannels.

In this paper, a combined numerical and experimental approach for the estimation of the average friction factor along adiabatic microchannels with compressible gas flows is presented. Pressure-drop experiments are performed for a rectangular microchannel with a hydraulic diameter of 295 μm by varying Reynolds number up to 17,000. In parallel, the calculation of friction factor has been repeated numerically and results are compared with the experimental work. The validated numerical model was also used to gain an insight of flow physics by varying the aspect ratio and hydraulic diameter of rectangular microchannels with respect to the channel tested experimentally. This was done with an aim of verifying the role of minor loss coefficients for the estimation of the average friction factor. To have laminar, transitional, and turbulent regimes captured, numerical analysis has been performed by varying Reynolds number from 200 to 20,000. Comparison of numerically and experimentally calculated gas flow characteristics has shown that adiabatic wall treatment (Fanno flow) results in better agreement of average friction factor values with conventional theory than the isothermal treatment of gas along the microchannel. The use of a constant value for minor loss coefficients available in the literature is not recommended for microflows as they change from one assembly to the other and their accurate estimation for compressible flows requires a coupling of numerical analysis with experimental data reduction. Results presented in this work demonstrate how an adiabatic wall treatment along the length of the channel coupled with the assumption of an isentropic flow from manifold to microchannel inlet results in a self-sustained experimental data reduction method for the accurate estimation of friction factor values even in presence of significant compressibility effects. Results also demonstrate that both the assumption of perfect expansion and consequently wrong estimation of average temperature between inlet and outlet of a microchannel can be responsible for an apparent increase in experimental average friction factor in choked flow regime.

Exact Solution of the Weak Shock Wave in Non-ideal Gas

In the present paper the exact solution of quasilinear hyperbolic system of equations governing the propagation of weak shock waves in a one dimensional non-ideal adiabatic gas flow with generalized geometries is derived. Here the density ahead of the shock front is assumed to vary according to a power law of the distance. The effect of van der Waals parameter on the radius of weak shock wave is analyzed. An analytical expression for the total energy carried by weak shock wave in non-ideal gas is also derived.

Numerical simulation of a two‐stage pulse tube refrigerator based on adiabatic model

AbstractCryocoolers are devices that are capable of achieving and maintaining cryogenic temperatures for a number of applications such as high‐energy physics, cooling of superconducting magnets, sensors, high‐vacuum production, cryotronics, cryonics, and so on. All the above applications need coolers with high reliability, efficiency, low maintenance, and low cost. The absence of moving parts at the cryogenic temperatures makes the pulse tube (PT) coolers quite suitable for the above applications. In spite of considerable developments in the area of PT cryocoolers, many of the fundamental processes responsible for the cold production are not fully understood. In this work, we present the results of numerical simulations of two‐stage pulse tube refrigerators (PTR) using adiabatic flow of gas through the pulse tube system. A two‐stage PTR is the improved version of single‐stage system to achieve temperature close to 4 K. Assuming adiabatic gas flow through PTs, the algebraic equations for pressure, mass flow, and volumes at different locations have been derived and solved by a MATLAB based program. Using the above, the performance of PTR has been optimized for different operational parameters. The cooling powers predicted by the model have been compared with the experimental data, and they are in good agreement with each other.

Hyperbolic heat conduction, effective temperature, and third law for nonequilibrium systems with heat flux.

Some analogies between different nonequilibrium heat conduction models, particularly random walk, the discrete variable model, and the Boltzmann transport equation with the single relaxation time approximation, have been discussed. We show that, under an assumption of a finite value of the heat carrier velocity, these models lead to the hyperbolic heat conduction equation and the modified Fourier law with relaxation term. Corresponding effective temperature and entropy have been introduced and analyzed. It has been demonstrated that the effective temperature, defined as a geometric mean of the kinetic temperatures of the heat carriers moving in opposite directions, acts as a criterion for thermalization and is a nonlinear function of the kinetic temperature and heat flux. It is shown that, under highly nonequilibrium conditions when the heat flux tends to its maximum possible value, the effective temperature, heat capacity, and local entropy go to zero even at a nonzero equilibrium temperature. This provides a possible generalization of the third law to nonequilibrium situations. Analogies and differences between the proposed effective temperature and some other definitions of a temperature in nonequilibrium state, particularly for active systems, disordered semiconductors under electric field, and adiabatic gas flow, have been shown and discussed. Illustrative examples of the behavior of the effective temperature and entropy during nonequilibrium heat conduction in a monatomic gas and a strong shockwave have been analyzed.

Shock-wave-like structures induced by an exothermic neutralization reaction in miscible fluids.

We report shock-wave-like structures that are strikingly different from previously observed fingering instabilities, which occur in a two-layer system of miscible fluids reacting by a second-order reaction A+B→S in a vertical Hele-Shaw cell. While the traditional analysis expects the occurrence of a diffusion-controlled convection, we show both experimentally and theoretically that the exothermic neutralization reaction can also trigger a wave with a perfectly planar front and nearly discontinuous change in density across the front. This wave propagates fast compared with the characteristic diffusion times and separates the motionless fluid and the area with anomalously intense convective mixing. We explain its mechanism and introduce a new dimensionless parameter, which allows to predict the appearance of such a pattern in other systems. Moreover, we show that our governing equations, taken in the inviscid limit, are formally analogous to well-known shallow-water equations and adiabatic gas flow equations. Based on this analogy, we define the critical velocity for the onset of the shock wave which is found to be in the perfect agreement with the experiments.

Finite Element Modeling and Analysis of Powder Stream in Low Pressure Cold Spray Process

Low pressure cold gas dynamic spray (LPCGDS) is a coating process that utilize low pressure gas (5–10 bars instead of 25–30 bars) and the radial injection of powder instead of axial injection with the particle range (1–50 μm). In the LPCGDS process, pressurized compressed gas is accelerated to the critical velocity, which depends on length of the divergent section of nozzle, the propellant gas and particle characteristics, and the diameters ratio of the inlet and outer diameters. This paper presents finite element modeling (FEM) of powder stream in supersonic nozzle wherein adiabatic gas flow and expansion of gas occurs in uniform manner and the same is used to evaluate the resultant temperature and velocity contours during coating process. FEM analyses were performed using commercial finite volume package, ANSYS CFD FLUENT. The results are helpful to predict the characteristics of powder stream at the exit of the supersonic nozzle.

Efficiency of energy separation at compressible gas flow in a planar duct

The method of energy separation in a high-speed flow proposed by A.I. Leontyev is investigated numerically. The adiabatic compressible gas flow (of a helium-xenon mixture) with a low Prandtl number in a planar narrow duct and a flow with heat exchange in a duct partitioned by a heat-conducting wall are analysed. The temperature recovery factor on the adiabatic wall, degree of cooling the low-speed flow part, temperature efficiency, and the adiabatic efficiency in a duct with heat exchange are estimated. The data are obtained for the first time, which make it possible to compare the efficiency of energy separation in a high-speed flow with the efficiency of similar processes in vortex tubes and other setups of gas-dynamic energy separation.

Transient modeling of gas flow in pipelines following catastrophic failure

This paper simulates transient compressible adiabatic gas flows in a long pipeline following a catastrophic failure using an implicit high order finite difference scheme as a discretisation technique for convective terms. A rupture is assumed to be occurred accidentally at a distance from the feeding point of a pipeline where the pipeline being divided into two distinct sections, high and low pressure segment. The results show that at early times after the rupture, considerable pressure loss will occur at the breakpoint with a chocked flow at this point. After expansion waves reach the closed end of the pipe, a reversal flow will constitute in the pipe. In the high pressure segment, the gas feeding continues and flow rate reaches a steady state chocked flow. In the low pressure segment, the flow rate decreases towards zero until the entire gas of the low pressure segment be evacuated.

Assessment of CFD Modeling via Flow Visualization in Cold Spray Process

The two-phase flow properties of copper particle laden nitrogen are computationally modeled and compared with the data obtained from the experiments, determining the achievable degree of consistency between model and reality. Two common, commercial nozzles are studied. A two-way coupled Lagrangian scheme along with the RSM turbulence model is used to track the particles and to model the interactions between the gas and the particulate phase. Significant agreement is found for the geometrical gas flow structure, the resulting particle velocities, and the dependence of the two-phase flow on the particulate phase mass loading. The particle velocities decrease with increasing mass loading, even for modest powder feed rates of <3 g/s. The velocity drop occurs even when the gas flow rate is kept constant. Adiabatic gas flow models neglecting the energy consumption by the particles are thus inaccurate, except for very dilute suspensions with low technical relevance. For the cases modeled, the experiments evidence the high predictive power of the chosen CFD approach.

Mach-uniformity through the coupled pressure and temperature correction algorithm

We present a new type of algorithm: the coupled pressure and temperature correction algorithm. It is situated in between the fully coupled and the fully segregated approach, and is constructed such that Mach-uniform accuracy and efficiency are obtained. The essential idea is the separation of the convective and the acoustic/thermodynamic phenomena: a convective predictor is followed by an acoustic/thermodynamic corrector. For a general case, the corrector consists of a coupled solution of the energy and the continuity equations for both pressure and temperature corrections. For the special case of an adiabatic perfect gas flow, the algorithm reduces to a fully segregated method, with a pressure-correction equation based on the energy equation. Various test cases are considered, which confirm that Mach-uniformity is obtained.

The Cauchy Problem for Hyperbolic Conservation Laws with Three Equations

Ž . where a , b , t are nonnegative constants. When b s 0, system 1.1 can be w x used to model the adiabatic gas flow through porous media 5 , where is specific volume, u denotes velocity, s stands for entropy, and s denotes pressure. Its form in Euler coordinates is also a model of isothermal w x unsteady two phase flow in pipelines 1 . In this paper we study the global generalized solution for this case. The case b / 0, when written in Euler

Transonic inviscid disc flows in the Schwarzschild metric - I

The coupled hydrodynamic equations governing equatorial flows applicable to inviscid disc accretion in the Schwarzschild metric are solved analytically and numerically. Here, we concentrate on the transonic solutions, that represent physically allowed accretion on to black holes. A polytropic equation linking gas pressure and density is assumed, and solutions are obtained for different conditions, such as isothermal and adiabatic gas flows. The dependence of those solutions on the angular momentum is explored. Under certain conditions, when there exist multiple possible sonic points, the numerical simulation automatically zeros in to the unique transonic solution passing through one of the sonic points.

Some one-dimensional unsteady adiabatic gas flows with plane symmetry

A method for the approximate analytic investigation of one-dimensional adiabatic gas flows in the form of arbitrary small perturbations of a simple wave is proposed. A class of exact solutions which, in particular, describes the flows arising from the short intense impact of a piston moving under gas pressure is obtained.