Steady Subsonic Ideal Flows Through an Infinitely Long Nozzle with Large Vorticity

Li, Du; Xie, Chunjing; Xin, Zhouping

doi:10.1007/s00220-014-1951-y

Cited by 82 publications

(62 citation statements)

References 16 publications

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“…Then, given positive axial velocity U 0 (r), entropy function E(r), and suitable incoming mass flux m 0 in the upstream, we obtain the unique existence of an axisymmetric subsonic solution (ρ, U, V, W, p) ∈ C 1,α (Ω 0 ) 5 for the non-isentropic Euler system (7) with swirl velocity W ≡ 0 in Ω 0 . The solution satisfies the solid wall condition (9), the symmetric condition (10), the mass flux condition (11), and the uniformly subsonic condition…”

Section: Introduction and Main Resultsmentioning

confidence: 97%

“…However, because of the possible appearance of supersonic bubbles and other singularities, the wellposedness of subsonic-sonic flows with large vorticity is unclear. Recently, Du, Xie and Xin [11] established the unique existence of a smooth subsonic isentropic solution in a two dimensional infinitely long nozzle for given horizontal velocity of the incoming flows in the upstream with possible large vorticity, please also see [3]. In this paper, without requirements on isentropic and small vorticity conditions, we focus on the three dimensional steady non-isentropic Euler system (1) in an infinitely long axisymmetric nozzle Ω 0 ,…”

Section: Introduction and Main Resultsmentioning

confidence: 98%

“…satisfying the non-isentropic Euler system (7), the solid wall condition (9), the symmetric condition (10), the condition (11), and…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…, there are non-isentropic solutions with mass flux m 0 which satisfy system (7), conditions (11), (17), the asymptotic behaviors (19)- (20) and…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…Letting l → ∞, we have Next, without proof, we give the following proposition to show that the axial velocity is positive, which is necessary to show the equivalence between the non-isentropic Euler system (8) (17), (19)- (20), and satisfying the mass flux condition (11).…”

Section: Asymptotic Behavior and Uniquenessmentioning

confidence: 97%

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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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Section: Introduction and Main Resultsmentioning

confidence: 97%

Section: Introduction and Main Resultsmentioning

confidence: 98%

“…satisfying the non-isentropic Euler system (7), the solid wall condition (9), the symmetric condition (10), the condition (11), and…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…, there are non-isentropic solutions with mass flux m 0 which satisfy system (7), conditions (11), (17), the asymptotic behaviors (19)- (20) and…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Section: Asymptotic Behavior and Uniquenessmentioning

confidence: 97%

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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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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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The optimal convergence rates of non‐isentropic subsonic Euler flows through the infinitely long three‐dimensional axisymmetric nozzles

2020

Math Methods in App Sciences

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This paper is concerned about the optimal convergence rates of non‐isentropic subsonic flows at far fields in three‐dimensional infinitely long axisymmetric nozzles. By using the stream function formulation for the compressible Euler equations, the subsonic Euler flows are equivalent to a quasilinear elliptic equation of the stream function. The key points to prove the convergence rates of subsonic flows at far fields are the choice of compared functions and the maximum principles.

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Steady Subsonic Ideal Flows Through an Infinitely Long Nozzle with Large Vorticity

Cited by 82 publications

References 16 publications

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

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

Subsonic non‐isentropic ideal gas with large vorticity in nozzles

The optimal convergence rates of non‐isentropic subsonic Euler flows through the infinitely long three‐dimensional axisymmetric nozzles

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