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We consider the vanishing viscosity limit for a model of a general non-Newtonian compressible fluid in R d , d = 2 , 3 . We suppose that the initial data approach a profile determined by the Riemann data generating a planar rarefaction wave for the isentropic Euler system. Under these circumstances the associated sequence of dissipative solutions approaches the corresponding rarefaction wave strongly in the energy norm in the vanishing viscosity limit. The result covers the particular case of a linearly viscous fluid governed by the Navier–Stokes system.

We study an asymptotic analysis of a coupled system of kinetic and fluid equations. More precisely, we deal with the nonlinear Vlasov–Fokker–Planck equation coupled with the compressible isentropic Navier–Stokes system through a drag force in a bounded domain with the specular reflection boundary condition for the kinetic equation and homogeneous Dirichlet boundary condition for the fluid system. We establish a rigorous hydrodynamic limit corresponding to strong noise and local alignment force. The limiting system is a type of two-phase fluid model consisting of the isothermal Euler system and the compressible Navier–Stokes system. Our main strategy relies on the relative entropy argument based on the weak–strong uniqueness principle. For this, we provide a global-in-time existence of weak solutions for the coupled kinetic-fluid system. We also show the existence and uniqueness of strong solutions to the limiting system in a bounded domain with the kinematic boundary condition for the Euler system and Dirichlet boundary condition for the Navier–Stokes system.

In this paper, we are concerned with the uniform regularity estimates of smooth solutions to the isentropic compressible magneto-micropolar system in T3. Under the assumption that , and by applying the classic bilinear commutator and product estimates, the uniform estimates of solutions to the isentropic compressible magneto-micropolar system are established in space, .

Exposing students to hands-on experiments has been a common approach to illustrating complex physical phenomena that have been otherwise modelled solely mathematically. Compressible, isentropic flow in a duct is an example of such a phenomenon, and it is often demonstrated via a de Laval nozzle experiment. We have improved an existing converging/diverging nozzle experiment so that students can modify the location of the normal shock that develops in the diverging portion to better understand the relationship between the shock and the pressure. We have also improved the data acquisition system for this experiment and explained how visualisation of the standing shock is now possible. The results of the updated system demonstrate that the accuracy of the isentropic flow characteristics has not been lost. Through pre- and post-laboratory quizzes, we show the impact on student learning as well.

Shock loss is the primary source of total pressure loss of transonic axial compressors. Reducing the shock by redesigning the geometry of rotor is of great interest for turbomachinery designers. However, the complex flow field involving shock waves, shock-boundary interaction, intense secondary flows, etc., in the compressor makes the design of rotor difficult. The conventional method of design and optimization is computationally intensive and time-costly. This study introduces an inverse design method to design rotor blades corresponding to prescribed isentropic Mach number distributions with no modification of flow-governing equations. An artificial neural network is trained to predict the isentropic Mach number distributions of any deformed blades. Then, with the pattern search optimization, the blade corresponding to the prescribed isentropic Mach number distributions can be achieved. When the aerodynamic parameter database is calculated and the neural network is obtained, this method can design large numbers of blades of changed isentropic Mach number distributions immediately, without modifying the computational fluid dynamics (CFD) flow solver. The design process is fully automatic and efficient. In this study, NASA Rotor 37 is redesigned and optimized as test cases. Some analysis on the influence of blade shape on aerodynamic characteristics of the rotor is represented in this study.

We analyse exact solutions to the Riemann problem for a one-dimensional isentropic and perfectly conducting non-ideal dusty gas flow in the presence of a transverse magnetic field. We give the expression of wave curves as well as the behaviors of these wave curves. A new technique is provided to get a complete list of analytical solutions with the corresponding criteria. Moreover, the numerical solutions to the Riemann problem are also given. It is shown that the analytical solutions match well with the corresponding numerical solutions.

We present first principles predictions of the absolute entropy of a silicate liquid (CaSiO3) over a wide pressure-temperature range encompassing the Earth’s mantle (2000–6000 K, 0–270 GPa). The results are derived from molecular dynamics simulations based on density functional theory and the two-phase thermodynamic (2PT) method, which divides the vibrational density of states into solid-like and gas-like parts, and which we describe in detail. The heat capacity derived from the absolute entropy agrees well with experimental measurements at low pressure. We find that the vibrational contribution accounts for more than 75% of the total entropy over the range of our study. We find that the two-body approximation to the excess entropy (relative to the ideal gas), which is computed with knowledge only of the radial distribution function, is excellent over most of the range considered, except at the lowest pressures and temperatures. We also compute the entropy of CaSiO3 perovskite and use the entropy of liquid and solid phases to determine their absolute free energies and the melting curve. The melting curve agrees well with experiment and independent theoretical determinations based on Clausius-Clapeyron integration and the ZW method, showing a melting temperature of 5600 K at the Earth’s core-mantle boundary. We find a nearly universal scaling of the self-diffusion coefficients with the excess entropy D ∗ = 0.9 exp 1.2 S ex , where D* is the self-diffusion coefficient suitably non-dimensionalized using macroscopic thermodynamic properties, and Sex is the excess entropy in units of the Boltzmann constant per atom. We use our results to estimate the temperature distribution in an isentropic, molten silicate Earth, finding 4.4 kJ/kg/K to be the lowest entropy that is completely molten, and producing a temperature at the core-mantle boundary of 6000 K.

We investigate the asymptotic behavior of solutions to the initial boundary value problem for the micropolar fluid model in a half line ℝ+ ≔ (0, ∞). Inspired by the relationship between a micropolar fluid model and Navier-Stokes equations, we prove that the composite wave consisting of the transonic boundary layer solution, the 1-rarefaction wave, the viscous 2-contact wave and the 3-rarefaction wave for the inflow problem on the micropolar fluid model is time-asymptotically stable under some smallness conditions. Meanwhile, we obtain the global existence of solutions based on the basic energy method.

The present study reports densities, ρ, speeds of sound, u, molar heat capacities, CP of binary piperidine or 1-methylpiperidine (1) + 2- or 3- or 4-picolines (2) mixtures over entire composition range by varying temperature range from 293.15 to 308.15 K with step of 5 K interval. Experimental data have been used to access excess molar volumes, VE, excess isentropic compressibilities, $$\kappa_{{\rm S}}^{\text{E}}$$ and excess heat capacities, $$C_{{\rm P}}^{\text{E}}$$ . The VE, $$\kappa_{{\rm S}}^{\text{E}}$$ and $$C_{{\rm P}}^{\text{E}}$$ data have been fitted to Redlich–Kister polynomial equation to evaluate the adjustable parameters and standard deviations. The $$C_{{\rm P}}^{\text{E}}$$ data of piperidine (1) + 2- or 3- or 4-picolines (2); 1-methylpiperidine (1) + 3- or 4-picolines (2) are positive and those for 1-methylpiperidine (1) + 2-picoline (2) mixture, sign and magnitude of $$C_{{\rm P}}^{\text{E}}$$ values change with increase in mole fraction of 1-methylpiperidine. Further, VE and $$\kappa_{{\rm S}}^{\text{E}}$$ of 1-methylpiperidine (1) + 2- or 3- or 4-picolines (2); piperidine (1) + 2- or 3-picolines (2) are negative; and those for piperidine (1) + 4-picoline (2) are positive across full range of composition. The VE, $$\kappa_{{\rm S}}^{\text{E}}$$ and $$C_{{\rm P}}^{\text{E}}$$ data have been utilized to test the applicability of Graph theory. It has been observed that VE, $$\kappa_{{\rm S}}^{\text{E}}$$ and $$C_{{\rm P}}^{\text{E}}$$ values calculated from the Graph theory compare reasonably well with their corresponding experimental values. The Quantum mechanical calculations and IR spectral studies on the aforesaid mixtures support the presence of various molecular entities (estimated by analyses of VE data) in pure and mixed state.

We are concerned with the vanishing flux-approximation limits of solutions to the isentropic relativistic Euler equations governing isothermal perfect fluid flows. The Riemann problem with a two-parameter flux approximation including pressure term is first solved. Then, we study the limits of solutions when the pressure and two-parameter flux approximation vanish, respectively. It is shown that, any two-shock-wave Riemann solution converges to a delta-shock solution of the pressureless relativistic Euler equations, and the intermediate density between these two shocks tends to a weighted δ-measure that forms a delta shock wave. By contract, any two-rarefaction-wave solution tends to a two-contact-discontinuity solution of the pressureless relativistic Euler equations, and the intermediate state in between tends to a vacuum state.

By introducing an isentropic Euler system with a new version of extended Chaplygin gas equation of state, we study two kinds of occurrence mechanism on the phenomenon of concentration and the formation of delta shock waves in the zero-exponent limit of solutions to the extended Chaplygin gas equations as the two exponents tend to zero wholly or partly. The Riemann problem is first solved. Then, we show that, as both the two exponents tend to zero, that is, the extended Chaplygin gas pressure tends to a constant, any two-shock-wave Riemann solution of the extended Chaplygin gas equations converges to a delta-shock solution to the zero-pressure flow system, and the intermediate density between the two shocks tends to a weighted δ-measure which forms a delta shock wave; any two-rarefaction-wave Riemann solution tends to a two-contact-discontinuity solution to the zero-pressure flow system, and the nonvacuum intermediate state in between tends to a vacuum. It is also shown that, as one of the exponents goes to zero, namely, the extended Chaplygin gas pressure approaches to some special generalized Chaplygin gas pressure, any two-shock-wave Riemann solution tends to a delta-shock solution to the generalized Chaplygin gas equations.

We investigate the sharp time decay rates of the solution \begin{document}$ U $\end{document} for the compressible Navier-Stokes system (1.1) in \begin{document}$ {\mathop{\mathbb R\kern 0pt}\nolimits}^3 $\end{document} to the constant equilibrium \begin{document}$ (\bar\rho>0, 0) $\end{document} when the initial data is a small smooth perturbation of \begin{document}$ (\bar\rho,0) $\end{document} . Let \begin{document}$ \widetilde U $\end{document} be the solution to the corresponding linearized equations with the same initial data. Under a mild non-degenerate condition on initial perturbations, we show that \begin{document}$ \|U-\widetilde U\|_{L^2} $\end{document} decays at least at the rate of \begin{document}$ (1+t)^{-\frac54} $\end{document} , which is faster than the rate \begin{document}$ (1+t)^{-\frac34} $\end{document} for the \begin{document}$ \widetilde U $\end{document} to its equilibrium \begin{document}$ (\bar\rho ,0) $\end{document} . Our method is based on a combination of the linear sharp decay rate obtained from the spectral analysis and the energy estimates.

Three-dimensional ideal gas flows behind a detached bow shock wave near the nonsymmetrical nose part of a bluff body in a uniform supersonic flow are investigated. The vector lines of the vector product of the velocity and entropy gradient are considered on isentropic surfaces, which are stream surfaces starting on closed lines located on the shock wave and covering the leading point of the shock wave. It is shown that if these vector lines encircle the isentropic surface they are closed. This means that an orthogonal curvilinear coordinate system in which the coordinate lines coincide with the streamlines may be constructed on each isentropic surface.

The present work performs the isentropic analysis and numerical simulation of high-pressure hydrogen jets to study the hydrogen leakage. The exit parameters and the flow characteristics are studied with the ideal gas assumption and real gas effects. The jet exit parameters calculated by the real gas thermodynamic model are different from the results obtained by the ideal gas assumption at high initial pressure based on the isentropic analysis. The ideal gas and the real gas equation of state results in the differences of Mach disk parameters at high initial pressures. The ideal gas assumption underestimates the Mach disk distance by 8% and overestimates the Mach disk diameter by 15% at the initial pressure of 50 MPa. The exit mass flow rates computed from the isentropic expansion assumption agree well with the numerical simulations. The results show that it is reasonable to evaluate mass flow rates of high-pressure hydrogen jets by the isentropic expansion assumption.

A dispersion relation for magnetoacoustic waves in partially ionized heat-releasing plasma in an external magnetic field is derived in a compact form. The increments of slow and fast modified magnetoacoustic waves are calculated in the case of isentropic instability; their strong dependence on the degree of ionization and frequency of ion—neutral collisions is showed.

In this paper, we consider the Cauchy problem of the original three-dimensional non-isentropic compressible Euler equations. Among the two main results, a class of finite-time blowup conditions without assumptions on γ > 1 and η ( 0 ) ≔ ∫ R 3 ρ e S ( 0 , x ) ∕ γ ( 0 , x ) − ρ e S ∕ γ d x is established. It is shown that together with the requirement on the sign of initial momentum, sufficiently strong F ( 0 ) will develop finite-time singularity and the C 1 solutions cannot exist globally. Here, F ( t ) = ∫ R 3 [ α ( t ) + f ( r ) ] x ⋅ ρ u d x is a newly introduced functional weighted by a sum of a time-dependent parameter function α ( t ) and a radius-dependent parameter function f ( t ) satisfying some mild conditions. As one of the applications, it is analysed that stronger α implies that the necessary conditions for solutions of the original three-dimensional non-isentropic compressible Euler equations to exist on or before a given finite time is looser.

In this paper, the local well-posedness of strong solutions to the Cauchy problem of the isentropic compressible Navier-Stokes equations is proved with the initial date being allowed to have vacuum. The main contribution of this paper is that the well-posedness is established without assuming any compatibility condition on the initial data, which was widely used before in many literatures concerning the well-posedness of compressible Navier-Stokes equations in the presence of vacuum.

We show that the compressible Euler system for isentropic gas flow admits unbounded solutions. The examples are radial flows of similarity type and describe a spherically symmetric and continuous w...

In this paper, we are concerned with the large-time behavior of solutions to the Cauchy problem on the non-isentropic compressible micropolar fluid. For the initial data near the given equilibrium we prove the global well-posedness of classical solutions and obtain the optimal algebraic rate of convergence in the three-dimensional whole space. Moreover, it turns out that the density, the velocity and the temperature tend to the corresponding equilibrium state with rate \begin{document}$ (1+t)^{-3 / 4} $\end{document} in \begin{document}$ L^{2} $\end{document} norm and the micro-rotational velocity tends to the equilibrium state with the faster rate \begin{document}$ (1+t)^{-5 / 4} $\end{document} in \begin{document}$ L^{2} $\end{document} norm. The proof is based on the detailed analysis of the Green function and time-weighted energy estimates.

The thermodynamic property data for solid phase I of benzene are reviewed and utilized to develop a new fundamental equation of state (EOS) based on Helmholtz energy, following the methodology used for solid phase I of CO2 by Trusler [J. Phys. Chem. Ref. Data 40, 043105 (2011)]. With temperature and molar volume as independent variables, the EOS is able to calculate all thermodynamic properties of solid benzene at temperatures up to 470 K and at pressures up to 1800 MPa. The model is constructed using the quasi-harmonic approximation, incorporating a Debye oscillator distribution for the vibrons, four discrete modes for the librons, and a further 30 distinct modes for the internal vibrations of the benzene molecule. An anharmonic term is used to account for inevitable deviations from the quasi-harmonic model, which are particularly important near the triple point. The new EOS is able to describe the available experimental data to a level comparable with the likely experimental uncertainties. The estimated relative standard uncertainties of the EOS are 0.2% and 1.5% for molar volume on the sublimation curve and in the compressed solid region, respectively; 8%–1% for isobaric heat capacity on the sublimation curve between 4 K and 278 K; 4% for thermal expansivity; 1% for isentropic bulk modulus; 1% for enthalpy of sublimation and melting; and 3% and 4% for the computed sublimation and melting pressures, respectively. The EOS behaves in a physically reasonable manner at temperatures approaching absolute zero and also at very high pressures.

We are concerned with a two-phase fluid model in $${\mathbb {R}}^3$$ . This model was first derived by Choi (SIAM J. Math. Anal. 48: 3090–3122, 2016) by taking the hydrodynamic limit from the Vlasov–Fokker–Planck/isentropic Navier–Stokes equations with strong local alignment forces. Under the assumption that the $$H^3$$ norm of the initial data is small but its higher-order Sobolev norm can be arbitrarily large, the global existence and uniqueness of classical solutions are obtained by an energy method. Moreover, if in addition, the initial data norm of the $$\dot{H}^{-s}(0\le s

The reversible adiabatic equation for ideal gas (T $${\text{V}}_{\text{m}}^{\gamma{-1}}$$ = C) is one of the most important equations in thermodynamics. But there is still a lack of theoretical explanation of the constant C at present. Since the reversible adiabatic process is isentropic process, the constant C could be expressed as a function of entropy through the statistical thermodynamic method. According to the different heat capacities and heat capacity ratios, the molecules of ideal gas are divided into three sorts that are monatomic molecules, linear polyatomic molecules (which include the diatomic molecules) and nonlinear polyatomic molecules. Although the calculation formulas for entropy of different kinds of molecules are very different, their expressions of constant C are similar. All of them could be expressed as C = N × exp(Sm/CV,m), where N is structure parameter. The reversible adiabatic equation was extended to a more general equation T $${\text{V}}_{\text{m}}^{\gamma-1}$$ = N × exp(Sm/CV,m), which could be applied to any process for ideal gas.

Contrary to classical thermodynamics, which deals with systems in thermal equilibrium, partially ionized gases generally do not reach thermal equilibrium. Nonextensive statistical mechanics has helped extend classical thermodynamics to nonequilibrium ionized gas. However, the fundamental question on whether the statistics of non-Maxwellian electrons satisfy the laws of thermodynamics has not been resolved. Here, we verify the thermodynamic laws of reversible and adiabatic processes for a magnetically expanding ionized gas. Together with the experimental evidence of the non-Maxwellian electron distribution, the \ensuremath{\kappa} distribution, which measures the thermal equilibrium states, shows the Tsallis entropy to be nearly constant and the polytropic index to be close to adiabatic values along a divergent magnetic field. These results verify that the collisionless magnetic expansion of a nonequilibrium plasma is reversible and adiabatic, and an isentropic process is the origin of the high-energy tail of the energy distribution far downstream.

The linearized Euler equations (LEE) provide an accurate — yet computationally efficient — description of propagation and damping of acoustic waves in geometrically complex, non-uniform reactive mean flows like those found in gas turbine combustion chambers. However, direct application of the LEE to perfectly premixed combustors with highly turbulent flows overestimates entropy waves as the LEE solution inherently contains coupled acoustic, vortical and entropy modes. In the present work, the LEE are decomposed into isentropic and non-isentropic parts ultimately obtaining a simplified set of isentropic LEE, in which only acoustic and vortical modes propagate. In the isentropic LEE, only continuity and momentum equations need to be solved. The energy equation is replaced by the isentropic relation between acoustic pressure and density. From the decomposition, the unsteady heat release term, which acts as a source in the energy equation, naturally arises as a source in the continuity equation. This way, the thermoacoustic coupling is still preserved in the isentropic formulation. The derived isentropic set of equations is first tested with a one-dimensional benchmark configuration consisting of a mean flow temperature jump, non-uniform mean flow velocity and unsteady heat release sources. Solutions of the non-isentropic and isentropic set of LEE are compared and the avoidance of entropy waves proved. Finally, isentropic LEE are used for reproducing the frequency of the self-excited first transversal mode of a lab-scale swirl-stabilized premixed combustor. Furthermore, isentropic and non-isentropic LEE solutions are compared. The non-isentropic LEE yield too high levels of entropy at the combustor exit that may explain the increased damping rate of the non-isentropic LEE solution compared to the isentropic LEE solution. This shows the relevance of isentropic LEE for correctly predicting thermoacoustic stability limits at high frequencies in relevant industrial applications.

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.

Based on the classical 1-D isentropic theory, the relationship between the critical blocking ratio and the critical incoming flow Mach number in the evacuated tube is deduced in this paper. Next, a...

This article studies a Riemann problem for the so-called “[Formula: see text]-system”[Formula: see text], [Formula: see text], which rules one-dimensional isentropic thermoelastic media. Such study is made using a product of distributions that allows us to extend both the classical solution concept and a weak solution concept. By considering [Formula: see text] as an entire function that takes real values on the real axis, this product also extends for certain distributions [Formula: see text] the meaning of [Formula: see text]. Under certain conditions, this Riemann problem has solutions that are [Formula: see text]-shock waves. Furthermore, those [Formula: see text]-shock waves satisfy the so-called generalized Rankine–Hugoniot conditions.

The present paper is concerned with the existence and stability of smooth stationary solutions to the multidimensional isentropic bipolar hydrodynamic model for semiconductors in a bounded domain Ω ∈ R N ( N = 1 , 2 , 3 ) with insulating boundary conditions. The existence of non-constant steady smooth solutions is firstly obtained by the calculus of variations and the maximum principle. It is further shown that the particle densities converge exponentially fast to the steady state solutions.

This paper studies a fluid–particle interaction model for the evolution of particles dispersed in fluid. This coupled model consists of the Smoluchowski equation for the particle part, and 2D isentropic compressible Navier–Stokes equations for the fluid part. The global existence of strong solutions to the Cauchy problem of the coupled system with large initial data which may contain vacuum is established.

In this paper, we establish the existence and uniqueness of local strong solutions to the kinetic Cucker–Smale model coupled with the isentropic compressible Navier–Stokes equations in the whole space. Moreover, the blowup mechanism for strong solutions to the coupled system is also investigated.

The Riemann problem for isentropic van der Waals fluid flows in a nozzle with discontinuous cross-section is investigated. The pressure, expressed as a function of the density, is increasing and admits two inflection points. The model is not strictly hyperbolic, and the characteristic fields are not genuinely nonlinear. Since the model is written in Eulerian coordinates, it is hard to directly examine the Liu entropy condition. There may exist up to four stationary jumps from a given state. After imposing the admissibility criterion, two admissible stationary jumps may also co-exist. This leads to the multiple solutions of the Riemann problem for van der Waals fluids.

In this article, we study the global L∞ entropy solutions for the Cauchy problem of system of isentropic gas dynamics in a divergent nozzle with a friction. Especially when the adiabatic exponent γ = 3, we apply for the maximum principle to obtain the L∞ estimates w(ρδ,e, uδ,e) ≤ B(t) and z(ρδ,e, uδ,e) ≤ B(t) for the viscosity solutions (ρδ,e, uδ,e), where B(t) is a nonnegative bounded function for any finite time t. This work, in the special case γ ≥ 3, extends the previous works, which provided the global entropy solutions for the same Cauchy problem with the restriction w(ρδ,e, uδ,e) ≤ 0 or z(ρδ,e, uδ,e) ≤ 0.

In this paper, we study the formation of finite-time singularities of smooth solutions to the compressible Euler equations with damping in arbitrary dimensions for isentropic, polytropic fluid flows. The radial component of initial momentum is assumed to be large enough and the smooth solutions are assumed to be decay at far fields, but it is not required that the initial velocity field has a compact support. It is shown that the smooth solutions to the Cauchy problem will break down in a finite time. Our result partially complements the work for the compactly supported initial velocity field (Sideris et al., 2003).

For the example of the JetCat P-200RX turbojet engine, optimization of the diffuser and straightening unit of a compact centrifugal compressor is considered, on the basis of a mathematical model of viscous turbulent air flow. The goal of optimization is to increase the isentropic (adiabatic) efficiency of the compressor.

The purpose of this paper is to investigate uniformly global smooth solutions to the Cauchy problem for a non-isentropic Euler–Maxwell system with velocity dissipation and small physical parameters. As the parameters go to zero, we prove that the quasi-neutral limit of the non-isentropic Euler–Maxwell system is the e-MHD system and the linear transport equation for temperature, while its non-relativistic quasi-neutral limit is the incompressible Euler equation and the linear transport equation for temperature. The uniform energy estimates are achieved through controlling the divergence and the curl of the velocity, the electric and magnetic fields.

The concentration phenomenon of the kinetic energy, $$\rho |\mathbf{u}|^2$$ , associated to isentropic compressible Navier–Stokes equations, is addressed in $${\mathbb {R}}^n$$ with $$n=2,3$$ and the adiabatic constant $$\gamma \in [1,\frac{n}{2}]$$ . Except for a space-time set with a Hausdorff dimension of less than or equal to $$\Gamma (n)+1$$ with $$\begin{aligned} \Gamma (n)=\max \left\{ \gamma (n), n-\frac{n\gamma }{\gamma (n)+1}\right\} \quad {\text {and}}\quad \gamma (n)=\frac{n(n-1)-n\gamma }{n-\gamma }, \end{aligned}$$ no concentration phenomenon occurs.

The two-dimensional (2D) pseudo-steady isothermal flow, which is isentropic and irrotational, around a convex corner is studied. The self-similar solutions for the supersonic flow around the convex corner are constructed, where the properties of the centered simple wave are used for the 2D isentropic irrotational pseudo-steady Euler equations. The geometric procedures of the center simple waves are given. It is proven that the supersonic flow turns the convex corner by an incomplete centered expansion wave or an incomplete centered compression wave, depending on the conditions of the downstream state.

The characterization of aerothermodynamic performance and components interactions are of great importance to improve the design of multi-stage axial turbines. The steady and unsteady flow simulations were carried out to investigate the performance maps and the vane-rotor interaction in a two-stage high-pressure (hp) axial turbine. The obtained results show that the expansion properties are controlled mainly by the first stage nozzle guide vane (NGV). Besides, the aerodynamic characteristics of the second stage vanes and blades are affected by the impingements of wakes from upstream stage, hence lesser isentropic efficiency compared with an isolated stage. Moreover, the secondary flows, tip leakage flow and vortices emanating from the first rotor are convected downstream, thereby inducing considerable flow deviations and losses. The clocking of vane/blade rows has revealed variations in aerodynamic loading and isentropic efficiency. Indeed, the maximum isentropic efficiency clocking position corresponds to upstream wakes close to the leading edge of second stage vanes, while the minimum efficiency clocking position corresponds to wakes passing midway. The unsteady flow computations and FFT analysis revealed different modes of components interaction identified in terms of the passing frequencies (BPF) of the two rotors and their combinations.

In this paper, we consider limit behaviors of Riemann solutions to the isentropic Euler equations for a non-ideal gas (i.e. van der Waals gas) as the pressure vanishes. Firstly, the Riemann problem of the isentropic Euler equations for van der Waals gas is solved. Then it is proved that, as the pressure vanishes, any Riemann solution containing two shock waves to the isentropic Euler equation for van der Waals gas converges to the delta shock solution to the transport equations and any Riemann solution containing two rarefaction waves tends to the vacuum state solution to the transport equations. Finally, some numerical simulations completely coinciding with the theoretical analysis are demonstrated.

In this study, an aeroacoustic fluid model for slightly-compressible isentropic flows is developed and evaluated for its compressibility effects in the context of fluid-structure interactions. This model considers computational feasibility and accuracy by adding compressibility terms directly on the incompressible form of Navier–Stokes equation. Rather than solving for the full compressible form, our slightly-compressible form significantly reduces the complications in establishing stabilization and implementation of its finite element procedure, and yet still captures the fluctuating acoustic waves expected in the compressible form. Using this approach, we demonstrate that generations and propagations of acoustic waves can be accurately captured, without the inclusion of a fully compressible representation of the fluid. Upon the successful verification of its accuracy against analytical and known solutions, we then evaluate the fluid compressibility effect on fluid-structure interactions. Our results show that comparing to an incompressible fluid, a deformable solid generates sound waves while it is driven by the flow and vibrates in the fluid. A periodic volume change in the fluid is also observed, which can be considered as a sound source.

The isentropic motion of a perfect ideal gas on a constant homogeneous supersonic background is considered. A two-dimensional stationary potential problem of gas dynamics is solved to study the interaction of three traveling waves whose amplitudes and phases are slowly varying in the direction of the background flow in the case when the sum of “harmonic” phases is exactly equal to zero. The equations of amplitude and phase variation are derived and their solutions are analyzed analytically. The question of what boundary conditions should be satisfied is discussed.

The propagation of waves in a thermally unstable medium with a magnetic field is considered. The characteristic perturbation growth and wave breaking times have been found in the approximation of weak nonlinearity and small deviations from adiabaticity; the wave profiles at the breaking time are presented. We show that the development of instability is suppressed as the wave propagation direction changes from longitudinal to transverse relative to the magnetic field. Our studies have been carried out for the atomic zones of photodissociation regions, for which we have previously determined the conditions for the development of an isentropic thermal instability mode.