Transonic Shocks for the Full Compressible Euler System in a General Two-Dimensional De Laval Nozzle

Li, Jun; Xin, Zhouping; Yin, Huicheng

doi:10.1007/s00205-012-0580-x

Cited by 69 publications

(74 citation statements)

References 29 publications

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“…Moreover, interesting decompositions for hyperbolic and elliptic modes of 3-D Euler system are also presented by [6] and [7]. There are also some interesting results in a 2-D de Laval nozzles [16] and a conic divergent nozzle [13][14][15]. For subsonic flow in an infinite nozzle, one may refer to [9] and the reference therein.…”

Section: Introduction and Main Resultsmentioning

confidence: 93%

Transonic shock in finitely long nozzle with porous medium boundary condition

Duan

Weng

2011

Journal of Differential Equations

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In this paper, we investigate the 2-D Euler equations with complex boundary conditions. For the entrance and exit of finitely long nozzle, we use the supersonic incoming flow condition and the end pressure condition, respectively. In addition, for the nozzle wall, the lower one is solid and the upper one is permitted to have leakage. We establish the well-posedness if appropriate seepage discharge is given. We also obtain the shock position by solving a free boundary problem without assuming the shock must go through a fixed point.

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Section: Introduction and Main Resultsmentioning

confidence: 93%

Transonic shock in finitely long nozzle with porous medium boundary condition

Duan

Weng

2011

Journal of Differential Equations

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“…The steady transonic flows were studied by many mathematicians, see [4,7,8,[15][16][17]22,23] and the references therein. The irrotational subsonic-sonic flows in multidimensional convergent nozzles were studied in [18].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…By now, we have established the unique existence of a subsonic solution in an axisymmetric nozzle with large vorticity, provided that the axial velocity and the entropy are given in the upstream satisfying (14)- (16), for the mass flux m 0 ≥ m 0 . Next, we will show the existence of a critical incoming mass flux, see Theorem 1.4.…”

Section: Asymptotic Behavior and Uniquenessmentioning

confidence: 96%

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Subsonic non-isentropic Euler flows with large vorticity in axisymmetric nozzles

Duan

Luo

2015

Journal of Mathematical Analysis and Applications

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In this paper, we investigate the effects of vorticity for smooth subsonic nonisentropic Euler flows in infinitely long axisymmetric nozzles. It is a sequel to B. Duan and Z. Luo (2013) [13] on non-isentropic Euler system. In [13], the authors obtained the unique existence of a smooth subsonic solution with restriction on the smallness of Bernoulli's function in the upstream. The smallness assumption is sufficient to prevent the appearance of singularity, however, it leads that the vorticity is also small. The purpose of this paper is to remove such restriction on the smallness of the vorticity.

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“…Recently, the isentropic case is studied in [13].On the other hand, there are a huge amount of literatures to investigate the well posedness of the compressible transonic shock problem in convergent-divergent nozzles. We would like to point out the references [14-16] for irrotational flows and [17][18][19][20][21][22] for compressible inviscid flows. The main contribution in the mentioned works indicates that some special transonic shock solution (called background transonic solution) is stable under the small perturbation of the receiver pressure at the exhaust of the nozzles and the position of the shock surface is monotonic with respect to the receiver pressure.…”

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confidence: 99%

Subsonic non‐isentropic ideal gas with large vorticity in nozzles

Chao

2015

Math Methods in App Sciences

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This paper investigates the steady subsonic inviscid flows with large vorticities through two-dimensional infinitely long nozzles. We establish the existence and uniqueness of the smooth subsonic ideal flows, which are governed by a twodimensional complete Euler system. More precisely, given the horizontal velocity with possible large oscillation and the entropy of the incoming flows at the entrance of the nozzles, it was shown that there exists a critical value; if the mass flux of the incoming flows is larger than the critical one, then there exists a unique smooth subsonic polytropic gas through the given smooth infinitely long nozzles. Furthermore, the maximal speed of the flows approaches to the sonic speed, as the mass flux goes to the critical value. The results improve the previous work for steady subsonic flows with small vorticities and for subsonic irrotational flows and indicate that the large vorticity is admissible for the smooth subsonic ideal flows in nozzles. This paper gives a rigorous proof to the well posedness of the smooth subsonic problem first posed back in the basic survey of Lipman Bers for inviscid flows with large vorticities.

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Transonic Shocks for the Full Compressible Euler System in a General Two-Dimensional De Laval Nozzle

Cited by 69 publications

References 29 publications

Transonic shock in finitely long nozzle with porous medium boundary condition

Transonic shock in finitely long nozzle with porous medium boundary condition

Subsonic non-isentropic Euler flows with large vorticity in axisymmetric nozzles

Subsonic non‐isentropic ideal gas with large vorticity in nozzles

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