Global smooth axisymmetric Euler flows with rotating effect in an infinitely long axisymmetric nozzle

2022 ◽  
Author(s):  
Zihao Zhang
Keyword(s):  
Axisymmetric Nozzle ◽  
Euler Flows

scholarly journals Global subsonic Euler flows in an infinitely long axisymmetric nozzle

2011 ◽  
Vol 250 (2) ◽  
pp. 813-847 ◽  
Author(s):  
Lili Du ◽  
Ben Duan
Keyword(s):  
Axisymmetric Nozzle ◽  
Euler Flows

scholarly journals Note on the uniqueness of subsonic Euler flows in an axisymmetric nozzle

2012 ◽  
Vol 25 (2) ◽  
pp. 153-156 ◽  
Author(s):  
Lili Du ◽  
Ben Duan
Keyword(s):  
Axisymmetric Nozzle ◽  
Euler Flows

Numerical simulation of a vectored axisymmetric nozzle

2020 ◽  
Author(s):  
Roberto Marsilio ◽  
Michele Ferlauto ◽  
M. Hadi Hamedi-Estakhrsar
Keyword(s):  
Numerical Simulation ◽  
Axisymmetric Nozzle

scholarly journals Adjoint-based optimisation of detonation initiation by a focusing shock wave

Shock Waves ◽  
2021 ◽  
Author(s):  
S. Bengoechea ◽  
J. Reiss ◽  
M. Lemke ◽  
J. Sesterhenn
Keyword(s):  
Shock Wave ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Detonation Initiation ◽  
Axisymmetric Nozzle ◽  
Exponential Factor ◽  
Pulsed Detonation Engine ◽  
Pulsed Detonation ◽  
Detonation Engine ◽  
Adjoint Approach

AbstractAn optimisation study of a shock-wave-focusing geometry is presented in this work. The configuration serves as a reliable and deterministic detonation initiator in a pulsed detonation engine. The combustion chamber consists of a circular pipe with one convergent–divergent axisymmetric nozzle, acting as a focusing device for an incoming shock wave. Geometrical changes are proposed to reduce the minimum shock wave strength necessary for a successful detonation initiation. For that purpose, the adjoint approach is applied. The sensitivity of the initiation to flow variations delivered by this method is used to reshape the obstacle’s form. The thermodynamics is described by a higher-order temperature-dependent polynomial, avoiding the large errors of the constant adiabatic exponent assumption. The chemical reaction of stoichiometric premixed hydrogen-air is modelled by means of a one-step kinetics with a variable pre-exponential factor. This factor is adapted to reproduce the induction time of a complex kinetics model. The optimisation results in a 5% decrease of the incident shock wave threshold for the successful detonation initiation.

On the application of the Kelvin–Arnol'd energy principle to the stability of forced two-dimensional inviscid flows

1998 ◽  
Vol 356 ◽  
pp. 221-257 ◽  
Author(s):  
P. A. DAVIDSON
Keyword(s):  
Magnetic Field ◽  
Nonlinear Stability ◽  
Broad Class ◽  
Mhd Flow ◽  
Two Dimensional ◽  
Energy Principle ◽  
Inviscid Flows ◽  
Virtual Displacement ◽  
Euler Flows ◽  
Universal Procedure

Arnol'd developed two distinct yet closely related approaches to the linear stability of Euler flows. One is widely used for two-dimensional flows and involves constructing a conserved functional whose first variation vanishes and whose second variation determines the linear (and nonlinear) stability of the motion. The second method is a refinement of Kelvin's energy principle which states that stable steady Euler flows represent extremums in energy under a virtual displacement of the vorticity field. The conserved-functional (or energy-Casimir) method has been extended by several authors to more complex flows, such as planar MHD flow. In this paper we generalize the Kelvin–Arnol'd energy method to two-dimensional inviscid flows subject to a body force of the form −ϕ∇f. Here ϕ is a materially conserved quantity and f an arbitrary function of position and of ϕ. This encompasses a broad class of conservative flows, such as natural-convection planar and poloidal MHD flow with the magnetic field trapped in the plane of the motion, flows driven by electrostatic forces, swirling recirculating flow, self-gravitating flows and poloidal MHD flow subject to an azimuthal magnetic field. We show that stable steady motions represent extremums in energy under a virtual displacement of ϕ and of the vorticity field. That is, d1E=0 at equilibrium and whenever d2E is positive or negative definite the flow is (linearly) stable. We also show that unstable normal modes must have a spatial structure which satisfies d2E=0. This provides a single stability test for a broad class of flows, and we describe a simple universal procedure for implementing this test. In passing, a new test for linear stability is developed. That is, we demonstrate that stability is ensured (for flows of the type considered here) whenever the Lagrangian of the flow is a maximum under a virtual displacement of the particle trajectories, the displacement being of the type normally associated with Hamilton's principle. A simple universal procedure for applying this test is also given. We apply our general stability criteria to a range of flows and recover some familiar results. We also extend these ideas to flows which are subject to more than one type of body force. For example, a new stability criterion is obtained (without the use of Casimirs) for natural convection in the presence of a magnetic field. Nonlinear stability is also considered. Specifically, we develop a nonlinear stability criterion for planar MHD flows which are subject to isomagnetic perturbations. This differs from previous criteria in that we are able to extend the linear criterion into the nonlinear regime. We also show how to extend the Kelvin–Arnol'd method to finite-amplitude perturbations.

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