The Polytropic Approach in Modelling Compressible Flows Through Constant Cross-Section Pipes

A compressible flow with wall friction has been predicted in a constant cross-section duct by means of a barotropic modelling approach, and new analytical formulas have been proposed that also allow any possible heat transfer to the walls to be taken into account. A comparison between the distributions of the steady-state flow properties, pertaining to the new formulas, and to those of a classic Fanno analysis has been performed. In order to better understand the limits of the polytropic approach in nearly chocked flow applications, a numerical code, which adopts a variable polytropic coefficient along the duct, has been developed. The steady-state numerical distributions along the pipe, obtained for either a viscous adiabatic or an inviscid diabatic flow by means of this approach, coincide with those of the Fanno and Rayleigh models for Mach numbers up to 1. A constant polytropic exponent can be adopted for a Fanno flow that is far from choking conditions, while it cannot be adopted for the simulation of a Rayleigh flow, even when the flow is not close to choking conditions. Finally, under the assumption of diabatic flows with wall friction, the polytropic approach, with a constant polytropic exponent, is shown to be able to accurately approximate cases in which no local maximum is present for the temperature along the duct. The Mach number value at the location where the local maximum temperature possibly occurs has been obtained by means of a new analytical formula.

What if the neutron star maximum mass is beyond ∼2.3 M⊙?

ABSTRACT By assuming the formation of a black hole soon after the merger event of GW170817, the maximum mass of non-rotating stable neutron star, MTOV ≃ 2.3 M⊙, is proposed by numerical relativity, but there is no solid evidence to rule out MTOV > 2.3 M⊙ from the point of both microphysical and astrophysical views. It is naturally expected that the equation of state (EOS) would become stiffer beyond a specific density to explain massive pulsars. We consider the possibility of EOSs with MTOV > 2.3 M⊙, investigating the stiffness and the transition density in a polytropic model, for two kinds of neutron stars (i.e. gravity-bound and strong-bound stars on surface). Only two parameters are input in both cases: (ρt, γ) for gravity-bound neutron stars, while (ρs, γ) for strong-bound strange stars, with ρt the transition density, ρs the surface density, and γ the polytropic exponent. In the matter of MTOV > 2.3 M⊙ for the maximum mass and 70 ≤ Λ1.4 ≤ 580 for the tidal deformability, it is found that the smallest ρt and γ should be ∼0.50 ρ0 and ∼2.65 for neutron stars, respectively, whereas for strange star, we have γ > 1.40 if ρs > 1.0 ρ0 (ρ0 is the nuclear saturation density). These parametric results could guide further research of the real EOS with any foundation of microphysics if a pulsar mass higher than 2.3 M⊙ is measured in the future, especially for an essential comparison of allowed parameter space between gravity-bound and strong-bound compact stars.

Fully Transient Model of a Hydraulic Accumulator

Hydraulic piston accumulators play a major role especially within the field of stationary hydraulics. The calculation of the amount of hydraulic energy which can be stored in such an accumulator is crucial when it comes to a precise system design. The knowledge of the temperature within the accumulator is required in order to calculate the amount of energy to be stored. This paper presents a simulation approach with the goal to simulate the gaseous phase within a piston accumulator and to present results for the polytropic exponent without conducting costly experiments. The temperature, pressure, density and velocity profiles inside of the gaseous phase as well as the temperature profile inside the boundaries are calculated transiently in order to achieve that goal. The effects of dissipation, heat transfer and transient wall temperature are added to the simulation routine continuously and their effects on the results are discussed in detail.

Numerical Simulation of a Supersonic Ejector for Vacuum Generation with Explicit and Implicit Solver in Openfoam

Supersonic ejectors are used extensively in all kind of applications: compression of refrigerants in cooling systems, pumping of volatile fluids or in vacuum generation. In vacuum generation, also known as zero-secondary flow, the ejector has a transient behaviour. In this paper, a numerical and experimental research of a supersonic compressible air nozzle is performed in order to investigate and to simulate its behaviour. The CFD toolbox OpenFOAM 6 was used, with two density-based solvers: explicit solver rhoCentralFoam, which implements Kurganov Central-upwind schemes, and implicit solver HiSA, which implements the AUSM+up upwind scheme. The behaviour of the transient evacuation ranges between adiabatic polytropic exponent at the beginning of the process and isothermal at the end. A model for the computation of the transient polytropic exponent is proposed. During the evacuation, two regimes are encountered in the second nozzle. In the supercritic regime, the secondary is choked and sonic flow is reached. In the subcritic regime, the secondary flow is subsonic. The final agreement is good with the two different solvers, although simulation tends to slightly overestimate flow rate for large values region.

Nonlinear Estimation of Variables for Heat Release Calculation Using a Gradient Method

Advanced combustion such as the partially premixed combustion (PPC) is characterized by high energy efficiency. However, they are sensitive to the inlet condition and injection of a combustion engine. Therefore, it is essential to use combustion feedback. The accuracy of the feedback variables, derived from the cylinder pressure signal, is crucial for effective combustion feedback control. This paper proposes a nonlinear least-squares regression method to estimate the pressure offsets and variable polytropic exponent in heat release calculation automatically. The combustion feedback variables derived from the auto-tuned heat-release rate were applied to a heavy-duty compression ignition (CI) engine burning with gasoline fuel.

Analytic growth rate of gravitational instability in self-gravitating planar polytropes

Gravitational instability is a key process that may lead to fragmentation of gaseous structures (sheets, filaments, haloes) in astrophysics and cosmology. We introduce here a method to derive analytic expressions for the growth rate of gravitational instability in a plane stratified medium. First, the main strength of our approach is to reduce this intrinsically fourth-order eigenvalue problem to a sequence of second-order problems. Second, an interesting by-product is that the unstable part of the spectrum is computed by making use of its stable part. Third, as an example, we consider a pressure-confined, static, self-gravitating slab of a fluid with an arbitrary polytropic exponent, with either free or rigid boundary conditions. The method can naturally be generalised to analyse the stability of richer, more complex systems. Finally, our analytical results are in excellent agreement with numerical solutions. Their second-order expansions provide a valuable insight into how the rate and wavenumber of maximal instability behave as functions of the polytropic exponent and the external pressure (or, equivalently, the column density of the slab).

On the Variation of the Polytropic Exponent in a High Pressure Fan Impeller

Fan impellers are usually designed considering that the pumped air is incompressible and homogeneous, i.e. its density remains constant. When the incompressibility hypothesis can lead to significant errors, as in the case of high pressure fans, the analysis of the air flow can be made by considering that the air undergoes a polytropic process of constant polytropic exponent. In this paper, the concept of polytropic process of variable exponent depending on impeller radius is introduced, in order to better approximate the phenomena that take place inside blade passages. Numerical results obtained for an impeller of a high pressure fan without spiral casing suggest that the pumped air undergoes two different processes: an expansion in the first part of the impeller and the usual compression in the second part. The two processes are reflected in the strong variation of the polytropic exponent, which shows a vertical asymptote where the change of the process takes place. The results also suggest that high pressure fan impellers could consist of two stages, each stage being designed according to the process that takes place inside it: expansion or compression.