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Lin, Jianyu, Hang Ding, Xiyun Lu i Peng Wang. "A Comparison Study of Numerical Methods for Compressible Two-Phase Flows". Advances in Applied Mathematics and Mechanics 9, nr 5 (11.07.2017): 1111–32. http://dx.doi.org/10.4208/aamm.oa-2016-0084.
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AbstractIn this article a comparison study of the numerical methods for compressible two-phase flows is presented. Although many numerical methods have been developed in recent years to deal with the jump conditions at the fluid-fluid interfaces in compressible multiphase flows, there is a lack of a detailed comparison of these methods. With this regard, the transport five equation model, the modified ghost fluid method and the cut-cell method are investigated here as the typical methods in this field. A variety of numerical experiments are conducted to examine their performance in simulating inviscid compressible two-phase flows. Numerical experiments include Richtmyer-Meshkov instability, interaction between a shock and a rectangle SF6 bubble, Rayleigh collapse of a cylindrical gas bubble in water and shock-induced bubble collapse, involving fluids with small or large density difference. Based on the numerical results, the performance of the method is assessed by the convergence order of the method with respect to interface position, mass conservation, interface resolution and computational efficiency.
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Bogoyavlenskij, Oleg. "Invariants and Conserved Quantities for the Helically Symmetric Flows of an Inviscid Gas and Fluid with Variable Density". Zeitschrift für Naturforschung A 74, nr 3 (25.02.2019): 245–51. http://dx.doi.org/10.1515/zna-2018-0504.
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AbstractNew material conservation laws and conserved quantities are derived for the helically symmetric flows of an inviscid compressible gas and an ideal incompressible fluid with variable density$\rho(\mathbf{x},\;t)$.
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Feireisl, Eduard, Antonín Novotný i Hana Petzeltová. "Suitable weak solutions: from compressible viscous to incompressible inviscid fluid flows". Mathematische Annalen 356, nr 2 (25.10.2012): 683–702. http://dx.doi.org/10.1007/s00208-012-0862-5.
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Bogoyavlenskij, Oleg. "Invariants of the Axisymmetric Flows of an Inviscid Gas and Fluid with Variable Density". Zeitschrift für Naturforschung A 73, nr 10 (25.10.2018): 931–37. http://dx.doi.org/10.1515/zna-2018-0229.
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AbstractMaterial conservation laws and integral invariants are constructed for the axisymmetric flows of an inviscid compressible gas and an ideal incompressible fluid with variable density$\rho(\mathbf{x},t)$. The functional independence of the new invariants from helicity is proven.
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Wróblewski, Włodzimierz, Sławomir Dykas i Tadeusz Chmielniak. "Models for water steam condensing flows". Archives of Thermodynamics 33, nr 1 (1.08.2012): 67–86. http://dx.doi.org/10.2478/v10173-012-0003-2.
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Models for water steam condensing flows The paper presents a description of selected models dedicated to steam condensing flow modelling. The models are implemented into an in-house computational fluid dynamics code that has been successfully applied to wet steam flow calculation for many years now. All models use the same condensation model that has been validated against the majority of available experimental data. The state equations for vapour and liquid water, the physical model as well as the numerical techniques of solution to flow governing equations have been presented. For the single-fluid model, the Reynolds-averaged Navier-Stokes equations for vapour/liquid mixture are solved, whereas the two-fluid model solves separate flow governing equations for the compressible, viscous and turbulent vapour phase and for the compressible and inviscid liquid phase. All described models have been compared with relation to the flow through the Laval nozzle.
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Tunney, Adam P., James P. Denier, Trent W. Mattner i John E. Cater. "A new inviscid mode of instability in compressible boundary-layer flows". Journal of Fluid Mechanics 785 (23.11.2015): 301–23. http://dx.doi.org/10.1017/jfm.2015.627.
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The stability of an almost inviscid compressible fluid flowing over a rigid heated surface is considered. We focus on the boundary layer that arises. The effect of surface heating is known to induce a streamwise acceleration in the boundary layer near the surface. This manifests in a streamwise velocity which exhibits a maximum larger than the free-stream velocity (i.e. the streamwise velocity exhibits an ‘overshoot’ region). We explore the impact of this overshoot on the stability of the boundary layer, demonstrating that the compressible form of the classical Rayleigh equation (which governs the development of short wavelength instabilities) possesses a new unstable mode that is a direct consequence of this overshoot. The structure of this new class of modes in the small wavenumber limit is detailed, providing a valuable confirmation of our numerical results obtained from the full inviscid eigenvalue problem.
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Wu, Xinglong, i Qian Zhou. "Onsager’s Energy Conservation of Weak Solutions for a Compressible and Inviscid Fluid". Fractal and Fractional 7, nr 4 (12.04.2023): 324. http://dx.doi.org/10.3390/fractalfract7040324.
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In this article, two classes of sufficient conditions of weak solutions are given to guarantee the energy conservation of the compressible Euler equations. Our strategy is to introduce a test function φ(t)vϵ to derive the total energy. The velocity field v needs to be regularized both in time and space. In contrast to the noncompressible Euler equations, the compressible flows we consider here do not have a divergence-free structure. Therefore, it is necessary to make an additional estimate of the pressure p, which takes advantage of an appropriate commutator. In addition, by using the weak convergence, we show that the energy equality is conserved in a point-wise sense.
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Santos, Maria Angela Vaz dos, i Armando Miguel Awruch. "Numerical Analysis of Compressible Fluids and Elastic Structures Interaction". Applied Mechanics Reviews 48, nr 11S (1.11.1995): S195—S202. http://dx.doi.org/10.1115/1.3005071.
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A finite element algorithm to simulate two dimensional flows of viscous and inviscid compressible fluids for a wide range of Mach numbers is presented in this work. This model is coupled to immersed deformable structures through equilibrium and compatibility conditions in order to analyze its dynamic behavior. For the fluid, time integration is performed by a two-step Taylor-Galerkin explicit scheme and Newmark’s method is used to obtain the dynamic response of the structure. An arbitrary mixed Euler-Lagrange description is used to re-define a new finite element mesh in the presence of the immersed structure displacements. Finally, several examples are included showing the model behavior and possibilities for future expansions.
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Vyas, D. N., i Krishna M. Srivastava. "The stability of stratified shear flows of an inviscid compressible fluid in MHD". Astrophysics and Space Science 192, nr 2 (1992): 309–16. http://dx.doi.org/10.1007/bf00684488.
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Yang, Jie, i Song Ping Wu. "An Immersed Boundary Method for Compressible Flows with Complex Boundaries". Applied Mechanics and Materials 477-478 (grudzień 2013): 281–84. http://dx.doi.org/10.4028/www.scientific.net/amm.477-478.281.
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An immersed boundary method based on the ghost-cell approach is presented in this paper. The compressible Navier-Stokes equations are discretized using a flux-splitting method for inviscid fluxes and second-order central-difference for the viscous components. High-order accuracy is achieved by using weighted essentially non-oscillatory (WENO) and Runge-Kutta schemes. Boundary conditions are reconstructed by a serial of linear interpolation and inverse distance weighting interpolation of flow variables in fluid domain. Two classic flow problems (flow over a circular cylinder, and a NACA 0012 airfoil) are simulated using the present immersed boundary method, and the predictions show good agreement with previous computational results.
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Moore, D. W., i D. I. Pullin. "The compressible vortex pair". Journal of Fluid Mechanics 185 (grudzień 1987): 171–204. http://dx.doi.org/10.1017/s0022112087003136.
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We consider the steady self-propagation with respect to the fluid at infinity of two equal symmetrically shaped vortices in a compressible fluid. Each vortex core is modelled by a region of stagnant constant-pressure fluid bounded by closed constant-pressure, constant-speed streamlines of unknown shape. The external flow is assumed to be irrotational inviscid isentropic flow of a perfect gas. The flow is therefore shock free but may be locally supersonic. The nonlinear free-boundary problem for the vortex-pair flow is formulated in the hodograph plane of compressible-flow theory, and a numerical solution method based on finite differences is described. Specific results are presented for a range of parameters which control the flow, namely the Mach number of the pair translational motion and the fluid speed on each vortex bounding streamline. Perturbation-theory predictions are developed, valid for vortices of small core radius when the pair Mach number is much less than unity. These are in good agreement with the hodograph-plane calculations. The numerical and the perturbation-theory results together confirm the recently discovered (Barsony-Nagy, Er-El & Yungster 1987) existence of continuous shock-free transonic compressible flows with embedded vortices. For the vortex-pair geometry studied, solution branches corresponding to physically acceptable flows that could be calculated using the present hodograph-plane numerical method were found to be terminated when either the flow on the streamline of symmetry separating the vortiqes tends to become superonic or when limiting lines appear in the hodograph plane giving a locally multivalued mapping to the physical plane.
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Maicke, Brian A., Orie M. Cecil i Joseph Majdalani. "On the compressible bidirectional vortex in a cyclonically driven Trkalian flow field". Journal of Fluid Mechanics 823 (23.06.2017): 755–86. http://dx.doi.org/10.1017/jfm.2017.310.
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In this study, the Bragg–Hawthorne equation (BHE) is extended in the context of a steady, inviscid and compressible fluid, thus leading to an assortment of partial differential equations that must be solved simultaneously. A solution is pursued by implementing a Rayleigh–Janzen expansion in the square of the reference Mach number. The corresponding formulation is subsequently used to derive a compressible approximation for the Trkalian model of the bidirectional vortex. The approximate solution is compared to a representative computational fluid dynamics simulation in order to validate the modelling assumptions under realistic conditions. The latter is found to exhibit an appreciable steepening of the axial velocity profile, which is accompanied by an axial dependence in the mantle location that is somewhat reminiscent of the radial shifting of mantles reported in some experimental trials and simulations. In this context, flows with a strong swirl intensity do not seem to be significantly affected by the introduction of compressibility. Rather, as the swirl intensity is reduced the effects of compressibility become more noticeable, especially in the axial and radial velocity components. It may also be realized that imparting a progressively larger swirl component stands to promote the axisymmetric distribution of flow field properties, and these include an implicit resistance to dilatational effects in the tangential direction. From a broader perspective, this study provides a viable approximation to the Trkalian motion associated with cyclonic flows, while serving as a limited proof of concept for the compressible Bragg–Hawthorne procedure applied to a steady, axisymmetric and inviscid fluid.
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Zhang, Xueying, Haiyan Tian, Leihsin Kuo i Wen Chen. "A Contact SPH Method with High-Order Limiters for Simulation of Inviscid Compressible Flows". Communications in Computational Physics 14, nr 2 (sierpień 2013): 425–42. http://dx.doi.org/10.4208/cicp.141211.260912a.
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AbstractIn this paper, we study a class of contact smoothed particle hydrodynamics (SPH) by introducing Riemann solvers and using high-order limiters. In particular, a promising concept of WENO interpolation as limiter is presented in the reconstruction process. The physical values relating interactional particles used as the initial values of the Riemann problem can be reconstructed by the Taylor series expansion. The contact solvers of the Riemann problem at contact points are incorporated in SPH approximations. In order to keep the fluid density at the wall rows to be consistent with that of the inner fluid wall boundaries, several lines of dummy particles are placed outside of the solid walls, which are assigned according to the initial configuration. At last, the method is applied to compressible flows with sharp discontinuities such as the collision of two strong shocks and the interaction of two blast waves and so on. The numerical results indicate that the method is capable of handling sharp discontinuity and efficiently reducing unphysical oscillations.
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Timokha, A. N. "The Bateman-type variational formalism for an acoustically-driven drop". Reports of the National Academy of Sciences of Ukraine, nr 3 (11.07.2023): 17–22. http://dx.doi.org/10.15407/dopovidi2023.03.017.
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By employing the Clebsch potentials, the Bateman-type variational formulation for a drop levitating in an acoustic field is proposed when both fluids, liquid drop and external ullage gas, are barotropic, inviscid, compressible and admit rotational flows
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Ly, Nguyen, Zvi Rusak i Shixiao Wang. "Swirling flow states of compressible single-phase supercritical fluids in a rotating finite-length straight circular pipe". Journal of Fluid Mechanics 849 (21.06.2018): 576–614. http://dx.doi.org/10.1017/jfm.2018.394.
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Steady states of inviscid, compressible and axisymmetric swirling flows of a single-phase, inert, thermodynamically supercritical fluid in a rotating, finite-length, straight, long circular pipe are studied. The fluid thermodynamic behaviour is modelled by the van der Waals equation of state. A nonlinear partial differential equation for the solution of the flow streamfunction is derived from the fluid equations of motion in terms of the inlet flow specific total enthalpy, specific entropy and circulation functions. This equation reflects the complicated, nonlinear thermo-physical interactions in the flows, specifically when the inlet state temperature and density profiles vary around the critical thermodynamic point, flow compressibility is significant and the inlet swirl ratio is high. Several types of solutions of the resulting nonlinear ordinary differential equation for the axially independent case describe the flow outlet state when the pipe is sufficiently long. The approach is applied to an inlet flow described by a solid-body rotation with uniform profiles of the axial velocity and temperature. The solutions are used to form the bifurcation diagrams of steady compressible flows of real fluids as the inlet swirl level and the centreline inlet density are increased at a fixed inlet Mach number and temperature. Focus is on heavy-molecule fluids with low values of $R/C_{v}$. Computed results provide theoretical predictions of the critical swirl levels for the exchange of stability of the columnar state and for the appearance of non-columnar states and of vortex breakdown states as a function of inlet centreline density. The difference in the dynamical behaviour between that of a calorically perfect gas and of a real gas is explored. The analysis sheds new fundamental light on the complex dynamics of high-Reynolds-number, compressible, subsonic swirling flows of real gases.
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Chakraborty, B. B., Dinesh Khattar i Suman Verma. "On integrals and invariants for inviscid, compressible, two-dimensional flows under gravity". Fluid Dynamics Research 26, nr 3 (marzec 2000): 141–47. http://dx.doi.org/10.1016/s0169-5983(99)00019-2.
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FEDORCHENKO, A. T. "A model of unsteady subsonic flow with acoustics excluded". Journal of Fluid Mechanics 334 (10.03.1997): 135–55. http://dx.doi.org/10.1017/s0022112096004417.
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Diverse subsonic initial-boundary-value problems (flows in a closed volume initiated by blowing or suction through permeable walls, flows with continuously distributed sources, viscous flows with substantial heat fluxes, etc.) are considered, to show that they cannot be solved by using the classical theory of incompressible fluid motion which involves the equation div u = 0. Application of the most general theory of compressible fluid flow may not be best in such cases, because then we encounter difficulties in accurately resolving the complex acoustic phenomena as well as in assigning the proper boundary conditions. With this in mind a new non-local mathematical model, where div u ≠ 0 in the general case, is proposed for the simulation of unsteady subsonic flows in a bounded domain with continuously distributed sources of mass, momentum and entropy, also taking into account the effects of viscosity and heat conductivity when necessary. The exclusion of sound waves is one of the most important features of this model which represents a fundamental extension of the conventional model of incompressible fluid flow. The model has been built up by modifying both the general system of equations for the motion of compressible fluid (viscous or inviscid as required) and the appropriate set of boundary conditions. Some particular cases of this model are discussed. A series of exact time-dependent solutions, one- and two-dimensional, is presented to illustrate the model.
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Branda˜o, Mauricio Pazini. "New Theoretical Developments in Aeroacoustics and Aerodynamics". Applied Mechanics Reviews 46, nr 11S (1.11.1993): S79—S91. http://dx.doi.org/10.1115/1.3122661.
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The Acoustic Analogy is studied regarding its application to Aerodynamics. The concept of generalized derivatives is reviewed and extended. As consequences, new versions of the generalized continuity, momentum, energy, and energy momentum conservation equations are presented. These conservation laws form a basis for theoretical ideas regarding three-dimensional, linear and non-linear, potential and non-potential, steady and unsteady flows of incompressible and compressible, inviscid and viscous fluids. Extensions made in the definition of generalized derivatives relate fluid properties to new surface terms linked to tangential flow. In integral form, some of these relations recall the classical circulation and downwash integrals of Aerodynamics. An iterative solution technique of the resulting singular integral equations is proposed.
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CARLENZOLI, CLAUDIO, i PAOLA ZANOLLI. "DOMAIN DECOMPOSITION APPROXIMATION TO A GENERALIZED STOKES PROBLEM BY SPECTRAL METHODS". Mathematical Models and Methods in Applied Sciences 01, nr 04 (grudzień 1991): 501–15. http://dx.doi.org/10.1142/s0218202591000253.
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We consider here the approximation of a generalized Stokes problem by spectral methods in the collocation form. This problem is of particular interest when Navier-Stokes equations for viscous compressible flows are investigated. We also analyze a coupling of a viscous model with an inviscid one; precisely, we split the computational domain in two parts and in one of them we eliminate the viscous coefficient from the Stokes equations. Such an approach can be worthwhile in the study of compressible fluids around rigid profiles with critical layers. Finally we consider some numerical results with the aim of showing the excellent accuracy of the spectral approximations, as well as the efficiency of an iterative algorithm that we propose in order to alternate viscous and inviscid numerical solvers.
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COSGROVE, JASON M., i LAWRENCE K. FORBES. "SELECTIVE WITHDRAWAL OF A TWO-LAYER VISCOUS FLUID". ANZIAM Journal 53, nr 4 (kwiecień 2012): 253–77. http://dx.doi.org/10.1017/s1446181112000259.
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AbstractSelective withdrawal of a two-layer fluid is considered. The fluid layers are weakly compressible, miscible and viscous and therefore flow rotationally. The lower, denser fluid flows with constant velocity out through one or more drain holes in the bottom of a rectangular tank. The drain is opened impulsively and the subsequent draw-down produces waves in the interface which travel outward to the edges of the tank and are reflected back with a $18{0}^{\circ } $ change of phase. The points on the interface that have the highest absolute gradient form regions of high vorticity in the tank, enabling mixing of the fluids. An inviscid linearized interface is computed and compared to contour plots of density for the viscous solution. The two agree closely at early times in the withdrawal process, but as time increases, nonlinear and viscous effects take over. The time at which the lighter fluid starts to flow out of the tank is dependent on the number of drains, their width, and the fluid flow rate and density, and is investigated here.
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Ahmed, Fareed, Faheem Ahmed i Yong Yang. "Numerical Solution of Multidimensional Compressible Flow by High Order Nodal Discontinuous Galerkin Method". Applied Mechanics and Materials 392 (wrzesień 2013): 100–104. http://dx.doi.org/10.4028/www.scientific.net/amm.392.100.
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In this paper we present a robust, high order method for numerical solution of multidimensional compressible inviscid flow equations. Our scheme is based on Nodal Discontinuous Galerkin Finite Element Method (NDG-FEM). This method utilizes the favorable features of Finite Volume Method (FVM) and Finite Element Method (FEM). In this method, space discretization is carried out by finite element discontinuous approximations. The resulting semi discrete differential equations were solved using explicit Runge-Kutta (ERK) method. In order to compute fluxes at element interfaces, we have used Roe Approximate scheme. In this article, we demonstrate the use of exponential filter to remove Gibbs oscillations near the shock waves. Numerical predictions for two dimensional compressible fluid flows are presented here. The solution was obtained with overall order of accuracy of 3. The numerical results obtained are compared with experimental and finite volume method results.
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Song, Charles C. S., i Mingshun Yuan. "A Weakly Compressible Flow Model and Rapid Convergence Methods". Journal of Fluids Engineering 110, nr 4 (1.12.1988): 441–45. http://dx.doi.org/10.1115/1.3243575.
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A weakly compressible flow model for small Mach number flows is applied to the computation of steady and unsteady inviscid flows. The equations of continuity and motion are decoupled from the energy equation, but, unlike the equations for incompressible fluids, these equations retain the ability to represent rapidly changing flows such as hydraulic transients and hydroacoustics. Two methods to speed up the process of convergence when an explicit method is used to calculate steady incompressible flows are proposed. The first method which is quite similar to the artificial compressiblity method is to assume an arbitrarily small sound speed (equivalent to large Mach number) to speed up the convergence. Any positive finite number may be used for M. One disadvantage of this method is the contamination of the steady flow solution by acoustic noise that may reverberate in the flow field for some time after the steady flow has been essentially established. The second method is based on the concept of valve stroking or boundary control. Certain boundary stroking functions that will unify the hydroacoustic and hydrodynamic processes can be found by using the inverse method of classical hydraulic transients. This method yields uncontaminated steady flow solution very rapidly independent of the Mach number.
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Billet, G., J. Huard, P. Chevalier i P. Laval. "Experimental and Numerical Study of the Response of an Axial Compressor to Distorted Inlet Flow". Journal of Fluids Engineering 110, nr 4 (1.12.1988): 355–60. http://dx.doi.org/10.1115/1.3243563.
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A model representing the response of fixed or rotating axial compressor blade-rows is coupled to a 3-D numerical simulation of the flow outside the blade rows. The code can be used to study nonuniform compressible 3-D flows through turbomachines. The fluid is assumed to be inviscid in the space outside the rows, while the viscous effects are taken into account inside. Numerical results are compared with experimental data obtained on a test stand with steady distorted inflow. This comparison shows that this numerical approach is capable of predicting the response of the compressor. This work is part of a larger project aimed at predicting the response of a compressor to a nonuniform inlet flow that is periodic in time, or fully unsteady.
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Hejranfar, K., i M. H. Azampour. "Simulation of 2D fluid–structure interaction in inviscid compressible flows using a cell-vertex central difference finite volume method". Journal of Fluids and Structures 67 (listopad 2016): 190–218. http://dx.doi.org/10.1016/j.jfluidstructs.2016.09.009.
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Blom, F. J., i P. Leyland. "Analysis of Fluid-Structure Interaction by Means of Dynamic Unstructured Meshes". Journal of Fluids Engineering 120, nr 4 (1.12.1998): 792–98. http://dx.doi.org/10.1115/1.2820740.
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This paper presents a computational analysis on forced vibration and fluid-structure interaction in compressible flow regimes. A so-called staggered approach is pursued where the fluid and structure are integrated in time by distinct solvers. Their interaction is then taken into account by a coupling algorithm. The unsteady fluid motion is simulated by means of an explicit time-accurate solver. For the fluid-structure interaction problems which are considered here the effects due to the viscosity can be neglected. The fluid is hence modeled by the Euler equations for compressible inviscid flow. Unstructured grids are used to discretise the fluid domain. These grids are particularly suited to simulate unsteady flows over complex geometries by their capacity of being dynamically refined and unrefined. Dynamic mesh adaptation is used to enhance the computational precision with minimal CPU and memory constraints. Fluid-structure interaction involves moving boundaries. Therefore the Arbitrary Lagrange Euler method (ALE-method) is adopted to solve the Euler equations on a moving domain. The deformation of the mesh is controlled by means of a spring analogy in conjunction with a boundary correction to circumvent the principle of Saint Venant. To take advantage of the differences between fluid and structure time scales, the fluid calculation is subcycled within the structural time step. Numerical results are presented for large rotation, pitching oscillation and aeroelastic motion of the NACA0012 airfoil. The boundary deformation is validated by comparing the numerical solution for a flat plate under supersonic flow with the analytical solution.
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Krishnan, Mithun, Anurag Ray i Ravi Peetala. "Numerical Analysis of High Speed Flow Applications using Various Flux Schemes". Trends in Sciences 19, nr 18 (30.08.2022): 5813. http://dx.doi.org/10.48048/tis.2022.5813.
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Numerical analysis using computational fluid dynamics is an affordable and effective method with increasing relevance every day in research and engineering problems. Choosing an appropriate convective discretization scheme is paramount importance for obtaining more accurate solutions using CFD methods. The present study compares two commonly used numerical convective schemes, the upwind scheme of Advection Upstream Splitting Method (AUSM) and the central schemes of Kurganov-Noelle-Petrova and Kurganov-Tadmor scheme (K-T) have been made to find the better central scheme. These two schemes are validated with inviscid 1D and 2D problems such as Sod’s shock tube, forward facing step in a Mach 3 tunnel, 15 Degree ramp in a Mach 2 supersonic tunnel, the Mach-reflection problem and scramjet engine operating under high Mach number. The AUSM and K-T schemes are robust enough to capture all the features of compressible flows. Comparison of results obtained by these 2 schemes is presented using density contours and surface property changes. It has been observed that both the schemes are robust enough to capture the flow features of the problems and that they have better accuracy for different conditions.
HIGHLIGHTS
This paper focuses on two convective flux discretization techniques i.e. the upwind scheme of AUSM and the central schemes of K-T and KNP
Inviscid simulations for various problems in the supersonic as well as hypersonic regime were used in Sod’s 1-Dimensional Shock Tube, flow over forward facing step in supersonic wind tunnel and Mach 5 flow thorough scramjet engine
The AUSM and K-T schemes are robust enough to capture all the features of compressible flows. It has been observed that both the schemes are robust enough to capture the flow features of the problems and that they have better accuracy for different conditions
GRAPHICAL ABSTRACT
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d’Agostino, Luca, i Fabio Burzagli. "On the Stability of Parallel Bubbly Cavitating Flows". Journal of Fluids Engineering 122, nr 3 (25.04.2000): 471–80. http://dx.doi.org/10.1115/1.1287036.
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This paper illustrates the effects of the dynamics of bubbles with arbitrary vapor-gas contents on the inviscid and viscous stability of two-dimensional parallel bubbly flows of low void fraction. The linear perturbation equations derived for the stability analysis include the effects of bubble compressibility, inertia, and energy dissipation due to the viscosity of the liquid and the transfer of heat and mass as a consequence of compression/expansion of the noncondensable gas and evaporation/condensation of the vapor contained in the bubbles. Numerical solution of the spatial stability problem for two-dimensional inviscid shear layers and Blasius boundary layers confirms that the presence of the dispersed phase is generally in favor of stability. Significant deviations from the classical results for compressible and incompressible single phase fluids are observed, especially when the occurrence of large compliant and/or resonant oscillations of the bubbles greatly enhances their dynamic coupling with the perturbation field. More importantly, the present analysis points out some major differences in the stability of parallel flows with noncondensable gas bubbles with respect to cavitating flows containing bubbles with a dominant content of vapor. Unconditional stability is predicted in the travelling bubble cavitation limit for low pressures and high vapor mass fraction of the bubble contents. Results are shown to illustrate these effects for some representative flow configurations and conditions. [S0098-2202(00)00603-9]
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Re, B., C. Dobrzynski i A. Guardone. "Assessment of grid adaptation criteria for steady, two-dimensional, inviscid flows in non-ideal compressible fluids". Applied Mathematics and Computation 319 (luty 2018): 337–54. http://dx.doi.org/10.1016/j.amc.2017.03.049.
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Goldstein, M. E., M. Z. Afsar i S. J. Leib. "Non-homogeneous rapid distortion theory on transversely sheared mean flows". Journal of Fluid Mechanics 736 (8.11.2013): 532–69. http://dx.doi.org/10.1017/jfm.2013.518.
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AbstractThis paper is concerned with the small-amplitude unsteady motion of an inviscid non-heat-conducting compressible fluid on a transversely sheared mean flow. It extends previous analyses (Goldstein,J. Fluid Mech., vol. 84, 1978b, pp. 305–329; Goldstein,J. Fluid Mech., vol. 91, 1979a, pp. 601–632), which show that the hydrodynamic component of the motion is determined by two arbitrary convected quantities in the absence of solid surfaces and hydrodynamic instabilities. These results can be used to specify appropriate upstream boundary conditions for unsteady surface interaction problems on transversely sheared mean flows in the same way that the vortical component of the Kovasznay (J. Aero. Sci., vol. 20, 1953, pp. 657–674) decomposition is used to specify these conditions for surface interaction problems on uniform mean flows. But unlike Kovasznay’s result, the arbitrary convected quantities no longer bear a simple relation to the physical variables. A major purpose of this paper is to complete the formalism developed in Goldstein’s earlier two papers by obtaining the necessary relations between these quantities and the measurable flow variables. The results are important because they enable the complete extension of non-homogeneous rapid distortion theory to transversely sheared mean flows. Another purpose of the paper is to derive a generalization of the famous Ffowcs Williams and Hall (J. Fluid Mech., vol. 40, 1970, pp. 657–670) formula for the sound produced by the interaction of turbulence with an edge, which is frequently used as a starting point for predicting sound generation by turbulence–solid surface interactions. We illustrate the utility of this result by using it to calculate the sound radiation produced by the interaction of a two-dimensional jet with the downstream edge of a flat plate.
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Tailleux, Rémi. "On the Determination of the 3D Velocity Field in Terms of Conserved Variables in a Compressible Ocean". Fluids 8, nr 3 (8.03.2023): 94. http://dx.doi.org/10.3390/fluids8030094.
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Explicit expressions of the 3D velocity field in terms of the conserved quantities of ideal fluid thermocline theory, namely the Bernoulli function, density, and potential vorticity, are generalised in this paper to a compressible ocean with a realistic nonlinear equation of state. The most general such expression is the ‘inactive wind’ solution, an exact nonlinear solution of the inviscid compressible Navier–Stokes equation that satisfies the continuity equation as a consequence of Ertel’s potential vorticity theorem. However, due to the non-uniqueness of the choice of the Bernoulli function, such expressions are not unique and primarily differ in the magnitude of their vertical velocity component. Due to the thermobaric nonlinearity of the equation of state, the expression for the 3D velocity field of a compressible ocean is found to resemble its ideal fluid counterpart only if constructed using the available form of the Bernoulli function, the Bernoulli equivalent of Lorenz’s available potential energy (APE). APE theory also naturally defines a quasi-material, approximately neutral density variable known as the Lorenz reference density. This density variable, in turn, defines a potential vorticity variable that is minimally affected by thermobaric production, thus providing all the necessary tools for extending most results of ideal fluid thermocline theory to a compressible ocean.
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Pei, Weicheng, Yuyan Jiang i Shu Li. "High-Order CFD Solvers on Three-Dimensional Unstructured Meshes: Parallel Implementation of RKDG Method with WENO Limiter and Momentum Sources". Aerospace 9, nr 7 (11.07.2022): 372. http://dx.doi.org/10.3390/aerospace9070372.
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In aerospace engineering, high-order computational fluid dynamics (CFD) solvers suitable for three-dimensional unstructured meshes are less developed than expected. The Runge–Kutta discontinuous Galerkin (RKDG) finite element method with compact weighted essentially non-oscillatory (WENO) limiters is one of the candidates, which might give high-order solutions on unstructured meshes. In this article, we provide an efficient parallel implementation of this method for simulating inviscid compressible flows. The implemented solvers are tested on lower-dimensional model problems and real three-dimensional engineering problems. Results of lower-dimensional problems validate the correctness and accuracy of these solvers. The capability of capturing complex flow structures even on coarse meshes is shown in the results of three-dimensional applications. For solving problems containing rotary wings, an unsteady momentum source model is incorporated into the solvers. Such a finite element/momentum source hybrid method eliminates the reliance on advanced mesh techniques, which might provide an efficient tool for studying rotorcraft aerodynamics.
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Ren, Jie, Olaf Marxen i Rene Pecnik. "Boundary-layer stability of supercritical fluids in the vicinity of the Widom line". Journal of Fluid Mechanics 871 (28.05.2019): 831–64. http://dx.doi.org/10.1017/jfm.2019.348.
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We investigate the hydrodynamic stability of compressible boundary layers over adiabatic walls with fluids at supercritical pressure in the proximity of the Widom line (also known as the pseudo-critical line). Depending on the free-stream temperature and the Eckert number that determines the viscous heating, the boundary-layer temperature profile can be either sub-, trans- or supercritical with respect to the pseudo-critical temperature, $T_{pc}$. When transitioning from sub- to supercritical temperatures, a seemingly continuous phase change from a compressible liquid to a dense vapour occurs, accompanied by highly non-ideal changes in thermophysical properties. Using linear stability theory (LST) and direct numerical simulations (DNS), several key features are observed. In the sub- and supercritical temperature regimes, the boundary layer is substantially stabilized the closer the free-stream temperature is to $T_{pc}$ and the higher the Eckert number. In the transcritical case, when the temperature profile crosses $T_{pc}$, the flow is significantly destabilized and a co-existence of dual unstable modes (Mode II in addition to Mode I) is found. For high Eckert numbers, the growth rate of Mode II is one order of magnitude larger than Mode I. An inviscid analysis shows that the newly observed Mode II cannot be attributed to Mack’s second mode (trapped acoustic waves), which is characteristic in high-speed boundary-layer flows with ideal gases. Furthermore, the generalized Rayleigh criterion (also applicable for non-ideal gases) unveils that, in contrast to the trans- and supercritical regimes, the subcritical regime does not contain an inviscid instability mechanism.
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Costiuc, I., L. Costiuc i A. Chiru. "Investigations of pressure field along a channel of a pressure wave supercharger". IOP Conference Series: Materials Science and Engineering 1220, nr 1 (1.01.2022): 012023. http://dx.doi.org/10.1088/1757-899x/1220/1/012023.
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Abstract The aim of the paper is a numerical investigation of the evolution of the pressure field along the wave rotor channels of a pressure wave ICE supercharger. In the present literature, most of the studies are considering the fluids as incompressible and inviscid in a 2D field. The present study is using the compressible and viscous terms in the unsteady Lattice Boltzmann method for fluid in a 3D field. The geometry was drawn in CAD software using measurements made on a real model of the CX-93 pressure wave supercharger. The simulation was conducted using a code for native unsteady LBM approach to reproduce data such as pressures, temperature and mass flows, which are usually hard to be measured in a real pressure wave supercharger. The computational domain was modelled as a moving rotational domain with adaptive refinement. Results such as velocity, pressure and temperature field in the rotor channels were obtained for exhaust gas inlet pressure of 0.292 MPa and 721 K temperature at different rotational speeds. The air inlet state considered was: 0,096 MPa and 313 K. The simulated values obtained are similar to the reported experimental results found in the literature showing a good concordance with the model.
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Doshi, Parshwanath S., Rajesh Ranjan i Datta V. Gaitonde. "Global and local modal characteristics of supersonic open cavity flows". Physics of Fluids 34, nr 3 (marzec 2022): 034104. http://dx.doi.org/10.1063/5.0082808.
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Flows past cavities at high-speeds have become increasingly important in applications such as flame-holding and propulsion unstart control. Recently maturated linear techniques have helped discern the underlying mechanisms in the subsonic and low supersonic speed regime ([Formula: see text]). Here, we combine these linear methods with fully non-linear two- and three-dimensional simulations to assimilate the significant changes observed when the Mach number is increased further to the [Formula: see text] range. The resolvent method is first employed to analyze cavity-shear layer coupled oscillations and modal characteristics, which are found to differ in key respects from those reported at lower Mach numbers. At higher speeds, more 2D coupled modes are obtained with the dominant modes containing secondary waves displaying elaborate patterns. The role of the shear layer on the cavity dynamics is then examined with local spatial stability analyses. In addition to the well-known Kelvin–Helmholtz instability encountered in the subsonic and transonic regimes, forward-propagating ( k+) supersonic shear layer instabilities are detected at higher speeds. These are associated with Mach wave reflections between the shear layer and the cavity floor and may introduce higher order coupled modes. Furthermore, 3D modal analysis indicates a shift toward the dominance of 3D modes compared to 2D modes; although consistent with compressible free shear layer observations, 2D cavity modes remain significant to higher convective Mach number. When the Reynolds number is increased, resolvent-based mode shapes and frequencies continue to compare favorably with Dynamic Mode Decomposition of large-eddy simulations because of inviscid instability dominance.
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Costiuc, I., i L. Costiuc. "Numerical investigation of a pressure wave supercharger". IOP Conference Series: Materials Science and Engineering 1220, nr 1 (1.01.2022): 012022. http://dx.doi.org/10.1088/1757-899x/1220/1/012022.
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Abstract The paper aims at a numerical investigation of the evolution of velocity, pressure and temperature field along the wave rotor channels for a pressure wave supercharger. Since in literature most of the studies are made considering the working fluid as incompressible and inviscid in a 2D field, the present study is using the compressible and viscous terms in unsteady Navier-Stokes equations for fluid in 3D field. The geometry was drawn in CAD software using measurements made on a real model of the CX-93 pressure wave supercharger. The simulation was conducted using a CFD code for unsteady 3D k-e, k-co model approach to reproduce data such as pressures, temperature and mass flows which are usually measured in real engine pressure wave supercharging. The computational domain for uRANS was modeled as a moving rotational domain with adaptive meshing. Results such as velocity, pressure and temperature field in the rotor channels were obtained for exhaust gas inlet pressure of 0.28 MPa and 1465 K temperature at different rotational speeds. The air inlet state considered was: 0,098 MPa and 293 K. Supercharging by means of a pressure wave supercharger, in order to improve the performance of an internal combustion engine, appears to be a promising solution since the exhaust gas generates a benefice boost of intake air with significant advantages when compared to the conventional turbocharging. The numerical modelling of the complex phenomena occurring within the narrow channels might be a useful tool for improving the pressure exchange between the working fluids, either by modifying the input parameters or by optimizing the geometry of the rotor, ports or pockets.
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Jahanbakhshi, Reza, i Cyrus K. Madnia. "The effect of heat release on the entrainment in a turbulent mixing layer". Journal of Fluid Mechanics 844 (3.04.2018): 92–126. http://dx.doi.org/10.1017/jfm.2018.122.
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Direct numerical simulations of a temporally evolving compressible reacting mixing layer have been performed to study the entrainment of the irrotational flow into the turbulent region across the turbulent/non-turbulent interface (TNTI). In order to study the effects of heat release and interaction of the flame with the TNTI on turbulence several cases with different heat release levels, $Q$, and stoichiometric mixture fractions are chosen for the simulations with the highest opted value for $Q$ corresponding to hydrogen combustion in air. The combustion is mimicked by a one-step irreversible global reaction, and infinitely fast chemistry approximation is used to compute the species mass fractions. Entrainment is studied via two mechanisms: nibbling, considered as the vorticity transport across the TNTI, and engulfment, the drawing of the pockets of the outside irrotational fluid into the turbulent region. As the level of heat release increases, the total entrained mass flow rate into the mixing layer decreases. In a reacting mixing layer by increasing the heat release rate, the mass flow rate due to nibbling is shown to decrease mostly due to a reduction of the local entrainment velocity, while the surface area of the TNTI does not change significantly. It is also observed that nibbling is a viscous dominated mechanism in non-reacting flows, whereas it is mostly carried out by inviscid terms in reacting flows with high level of heat release. The contribution of the engulfment to entrainment is small for the non-reacting mixing layers, while mass flow rate due to engulfment can constitute close to 40 % of the total entrainment in reacting cases. This increase is primarily related to a decrease of entrained mass flow rate due to nibbling, while the entrained mass flow rate due to engulfment does not change significantly in reacting cases. It is shown that the total entrained mass flow rate in reacting and non-reacting compressible mixing layers can be estimated from an expression containing the convective Mach number and the density change due to heat release.
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Gilbert, Andrew D., i Jacques Vanneste. "Geometric generalised Lagrangian-mean theories". Journal of Fluid Mechanics 839 (25.01.2018): 95–134. http://dx.doi.org/10.1017/jfm.2017.913.
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Many fluctuation-driven phenomena in fluids can be analysed effectively using the generalised Lagrangian-mean (GLM) theory of Andrews & McIntyre (J. Fluid Mech., vol. 89, 1978, pp. 609–646) This finite-amplitude theory relies on particle-following averaging to incorporate the constraints imposed by the material conservation of certain quantities in inviscid regimes. Its original formulation, in terms of Cartesian coordinates, relies implicitly on an assumed Euclidean structure; as a result, it does not have a geometrically intrinsic, coordinate-free interpretation on curved manifolds, and suffers from undesirable features. Motivated by this, we develop a geometric generalisation of GLM that we formulate intrinsically using coordinate-free notation. One benefit is that the theory applies to arbitrary Riemannian manifolds; another is that it establishes a clear distinction between results that stem directly from geometric consistency and those that depend on particular choices. Starting from a decomposition of an ensemble of flow maps into mean and perturbation, we define the Lagrangian-mean momentum as the average of the pull-back of the momentum one-form by the perturbation flow maps. We show that it obeys a simple equation which guarantees the conservation of Kelvin’s circulation, irrespective of the specific definition of the mean flow map. The Lagrangian-mean momentum is the integrand in Kelvin’s circulation and distinct from the mean velocity (the time derivative of the mean flow map) which advects the contour of integration. A pseudomomentum consistent with that in GLM can then be defined by subtracting the Lagrangian-mean momentum from the one-form obtained from the mean velocity using the manifold’s metric. The definition of the mean flow map is based on choices made for reasons of convenience or aesthetics. We discuss four possible definitions: a direct extension of standard GLM, a definition based on optimal transportation, a definition based on a geodesic distance in the group of volume-preserving diffeomorphisms, and the ‘glm’ definition proposed by Soward & Roberts (J. Fluid Mech., vol. 661, 2010, pp. 45–72). Assuming small-amplitude perturbations, we carry out order-by-order calculations to obtain explicit expressions for the mean velocity and Lagrangian-mean momentum at leading order. We also show how the wave-action conservation of GLM extends to the geometric setting. To make the paper self-contained, we introduce in some detail the tools of differential geometry and main ideas of geometric fluid dynamics on which we rely. These include variational formulations which we use for alternative derivations of some key results. We mostly focus on the Euler equations for incompressible inviscid fluids but sketch out extensions to the rotating–stratified Boussinesq, compressible Euler, and magnetohydrodynamic equations. We illustrate our results with an application to the interaction of inertia-gravity waves with balanced mean flows in rotating–stratified fluids.
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Kamali Moghadam, R., N. Sahranavard Fard i H. Jalali. "New Approach of Axisymmetric Compressible Finite-Volume Lattice Boltzmann Method for Numerical Simulation of Supersonic Inviscid Flow". Fluid Dynamics 56, nr 1 (styczeń 2021): 121–33. http://dx.doi.org/10.1134/s0015462821010080.
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Stoyanovskaya, Olga P., Vitaliy V. Grigoryev, Anastasiya N. Suslenkova, Maxim N. Davydov i Nikolay V. Snytnikov. "Two-Phase Gas and Dust Free Expansion: Three-Dimensional Benchmark Problem for CFD Codes". Fluids 7, nr 2 (24.01.2022): 51. http://dx.doi.org/10.3390/fluids7020051.
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In the computational mechanics of multiphase dispersed flows, there is an issue of computing the interaction between phases in a mixture of a carrier fluid and dispersed inclusions. The problem is that an accurate dynamics simulation of a mixture of gas and finely dispersed solids with intense interphase interaction requires much more computational power compared to pure gas or a mixture with moderate interaction between phases. To tackle this problem, effective numerical methods are being searched for to ensure adequate computational cost, accuracy, and stability of the results at an arbitrary intensity of momentum and energy exchange between phases. Thus, to assess the approximation, dispersive, dissipative, and asymptotic properties of numerical methods, benchmark solutions of relevant test problems are required. Such solutions are known for one-dimensional problems with linear plane waves. We introduce a novel analytical solution for the nonlinear problem of spherically symmetric expansion of a gas and dust ball into a vacuum. Therein, the dynamics of carrier and dispersed phases are modeled using equations for a compressible inviscid gas. Solid particles do not have intrinsic pressure and are assumed to be monodisperse. The carrier and dispersed phases exchange momentum. In the derived solution, the velocities of gas and dust clouds depend linearly on the radii. The results were reproduced at high, moderate, and low momentum exchange between phases using the SPH-IDIC (Smoothed Particle Hydrodynamics with Implicit Drag in Cell) method implemented based on the open-source OpenFPM library. We reported an example of using the solution as a benchmark for CFD (computational fluid dynamics) models verification and for the evaluation of numerical methods. Our benchmark solution generator developed in the free Scilab environment is publicly available.
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Si, Nan, i Alan Brown. "A Framework of Runge–Kutta, Discontinuous Galerkin, Level Set and Direct Ghost Fluid Methods for the Multi-Dimensional Simulation of Underwater Explosions". Fluids 7, nr 1 (29.12.2021): 13. http://dx.doi.org/10.3390/fluids7010013.
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This work describes the development of a hybrid framework of Runge–Kutta (RK), discontinuous Galerkin (DG), level set (LS) and direct ghost fluid (DGFM) methods for the simulation of near-field and early-time underwater explosions (UNDEX) in early-stage ship design. UNDEX problems provide a series of challenging issues to be solved. The multi-dimensional, multi-phase, compressible and inviscid fluid-governing equations must be solved numerically. The shock front in the solution field must be captured accurately while maintaining the total variation diminishing (TVD) properties. The interface between the explosive gas and water must be tracked without letting the numerical diffusion across the material interface lead to spurious pressure oscillations and thus the failure of the simulation. The non-reflecting boundary condition (NRBC) must effectively absorb the wave and prevent it from reflecting back into the fluid. Furthermore, the CFD solver must have the capability of dealing with fluid–structure interactions (FSI) where both the fluid and structural domains respond with significant deformation. These issues necessitate a hybrid model. In-house CFD solvers (UNDEXVT) are developed to test the applicability of this framework. In this development, code verification and validation are performed. Different methods of implementing non-reflecting boundary conditions (NRBCs) are compared. The simulation results of single and multi-dimensional cases that possess near-field and early-time UNDEX features—such as shock and rarefaction waves in the fluid, the explosion bubble, and the variation of its radius over time—are presented. Continuing research on two-way coupled FSI with large deformation is introduced, and together with a more complete description of the direct ghost fluid method (DGFM) in this framework will be described in subsequent papers.
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Marchant, M. J., i N. P. Weatherill. "Adaptivity techniques for compressible inviscid flows". Computer Methods in Applied Mechanics and Engineering 106, nr 1-2 (lipiec 1993): 83–106. http://dx.doi.org/10.1016/0045-7825(93)90186-2.
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Hu, Langhua, Siyang Yang i Guo-Wei Wei. "Simulation of Inviscid Compressible Flows Using PDE Transform". Communications in Computational Physics 16, nr 5 (listopad 2014): 1201–38. http://dx.doi.org/10.4208/cicp.031113.160514a.
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AbstractThe solution of systems of hyperbolic conservation laws remains an interesting and challenging task due to the diversity of physical origins and complexity of the physical situations. The present work introduces the use of the partial differential equation (PDE) transform, paired with the Fourier pseudospectral method (FPM), as a new approach for hyperbolic conservation law problems. The PDE transform, based on the scheme of adaptive high order evolution PDEs, has recently been applied to decompose signals, images, surfaces and data to various target functional mode functions such as trend, edge, texture, feature, trait, noise, etc. Like wavelet transform, the PDE transform has controllable time-frequency localization and perfect reconstruction. A fast PDE transform implemented by the fast Fourier Transform (FFT) is introduced to avoid stability constraint of integrating high order PDEs. The parameters of the PDE transform are adaptively computed to optimize the weighted total variation during the time integration of conservation law equations. A variety of standard benchmark problems of hyperbolic conservation laws is employed to systematically validate the performance of the present PDE transform based FPM. The impact of two PDE transform parameters, i.e., the highest order and the propagation time, is carefully studied to deliver the best effect of suppressing Gibbs’ oscillations. The PDE orders of 2-6 are used for hyperbolic conservation laws of low oscillatory solutions, while the PDE orders of 8-12 are often required for problems involving highly oscillatory solutions, such as shock-entropy wave interactions. The present results are compared with those in the literature. It is found that the present approach not only works well for problems that favor low order shock capturing schemes, but also exhibits superb behavior for problems that require the use of high order shock capturing methods.
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Zhang, Y., i M. Oberlack. "Inviscid instability of compressible exponential boundary layer flows". AIP Advances 11, nr 10 (1.10.2021): 105308. http://dx.doi.org/10.1063/5.0062795.
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Djordjevic, V. D., i L. G. Redekopp. "Linear stability analysis of nonhomentropic, inviscid compressible flows". Physics of Fluids 31, nr 11 (1988): 3239. http://dx.doi.org/10.1063/1.866934.
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Padmini, M., i M. Subbiah. "Stability of Non-Homentropic, Inviscid, Compressible Shear Flows". Journal of Mathematical Analysis and Applications 241, nr 1 (styczeń 2000): 56–72. http://dx.doi.org/10.1006/jmaa.1999.6616.
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Liu, Cheng, i Changhong Hu. "An immersed boundary solver for inviscid compressible flows". International Journal for Numerical Methods in Fluids 85, nr 11 (20.06.2017): 619–40. http://dx.doi.org/10.1002/fld.4399.
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Tao, Zhao-Ling. "Variational Approach to the Inviscid Compressible Fluid". Acta Applicandae Mathematicae 100, nr 3 (11.01.2008): 291–94. http://dx.doi.org/10.1007/s10440-007-9187-x.
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Anco, Stephen C., Amanullah Dar i Nazim Tufail. "Conserved integrals for inviscid compressible fluid flow in Riemannian manifolds". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, nr 2182 (październik 2015): 20150223. http://dx.doi.org/10.1098/rspa.2015.0223.
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An explicit determination of all local conservation laws of kinematic type on moving domains and moving surfaces is presented for the Euler equations of inviscid compressible fluid flow in curved Riemannian manifolds in n >1 dimensions. All corresponding kinematic constants of motion are also determined, along with all Hamiltonian kinematic symmetries and kinematic Casimirs which arise from the Hamiltonian structure of the inviscid compressible fluid equations.
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OCKENDON, H., J. R. OCKENDON i S. A. E. G. FALLE. "The Fanno model for turbulent compressible flow". Journal of Fluid Mechanics 445 (16.10.2001): 187–206. http://dx.doi.org/10.1017/s0022112001005584.
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The paper considers the derivation and properties of the Fanno model for nearly unidirectional turbulent flow of gas in a tube. The model is relevant to many industrial processes. Approximate solutions are derived and numerically validated for evolving flows of initially small amplitude, and these solutions reveal the prevalence of localized large-time behaviour, which is in contrast to inviscid acoustic theory. The properties of large-amplitude travelling waves are summarized, which are also surprising when compared to those of inviscid theory.
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Xia, Nan. "Investigation of the stability of inviscid compressible swirling flows". Aerospace Science and Technology 6, nr 2 (luty 2002): 99–103. http://dx.doi.org/10.1016/s1270-9638(02)01155-0.
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