The Experts below are selected from a list of 192 Experts worldwide ranked by ideXlab platform
Christophe Bailly - One of the best experts on this subject based on the ideXlab platform.
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Numerical study of self-induced tranSonic Flow oscillations behind a sudden duct enlargement
Physics of Fluids, 2009Co-Authors: Thomas Emmert, Philippe Lafon, Christophe BaillyAbstract:A Sonic Flow in a plane duct passing an abrupt increase in cross section is studied using compressible large-eddy simulations. Different Flow patterns are likely to appear in this configuration according to the ratio between the downstream ambient pressure and the upstream reservoir pressure. For low pressure ratios, the Flow is entirely superSonic in the channel and a steady symmetrical shock pattern is observed. For higher pressure ratios, the Flow can be attached to one side of the channel with a jet-like shock cell structure, or can be characterized by strong oscillations of a single normal shock located near the sudden expansion, known as base-pressure oscillations in literature. A hysteresis phenomenon is found experimentally and the state reached by the tranSonic Flow depends on the path followed by the pressure ratio. Moreover, a coupling of these base-pressure oscillations with the quarter-wavelength resonance of the duct can occur. All these regimes are numerically investigated and the results are favorably compared to available experimental data. A case of frequency locking of this self-excited mechanism is also reproduced, in agreement with a modeling of the resonator. The governing equations are solved using high-order central finite differences combined with an overset grid approach. The large-eddy simulations are based on a relaxation filtering and a nonlinear shock-capturing scheme is also implemented for shock waves.
Thomas Emmert - One of the best experts on this subject based on the ideXlab platform.
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Numerical study of self-induced tranSonic Flow oscillations behind a sudden duct enlargement
Physics of Fluids, 2009Co-Authors: Thomas Emmert, Philippe Lafon, Christophe BaillyAbstract:A Sonic Flow in a plane duct passing an abrupt increase in cross section is studied using compressible large-eddy simulations. Different Flow patterns are likely to appear in this configuration according to the ratio between the downstream ambient pressure and the upstream reservoir pressure. For low pressure ratios, the Flow is entirely superSonic in the channel and a steady symmetrical shock pattern is observed. For higher pressure ratios, the Flow can be attached to one side of the channel with a jet-like shock cell structure, or can be characterized by strong oscillations of a single normal shock located near the sudden expansion, known as base-pressure oscillations in literature. A hysteresis phenomenon is found experimentally and the state reached by the tranSonic Flow depends on the path followed by the pressure ratio. Moreover, a coupling of these base-pressure oscillations with the quarter-wavelength resonance of the duct can occur. All these regimes are numerically investigated and the results are favorably compared to available experimental data. A case of frequency locking of this self-excited mechanism is also reproduced, in agreement with a modeling of the resonator. The governing equations are solved using high-order central finite differences combined with an overset grid approach. The large-eddy simulations are based on a relaxation filtering and a nonlinear shock-capturing scheme is also implemented for shock waves.
Philippe Lafon - One of the best experts on this subject based on the ideXlab platform.
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Numerical study of self-induced tranSonic Flow oscillations behind a sudden duct enlargement
Physics of Fluids, 2009Co-Authors: Thomas Emmert, Philippe Lafon, Christophe BaillyAbstract:A Sonic Flow in a plane duct passing an abrupt increase in cross section is studied using compressible large-eddy simulations. Different Flow patterns are likely to appear in this configuration according to the ratio between the downstream ambient pressure and the upstream reservoir pressure. For low pressure ratios, the Flow is entirely superSonic in the channel and a steady symmetrical shock pattern is observed. For higher pressure ratios, the Flow can be attached to one side of the channel with a jet-like shock cell structure, or can be characterized by strong oscillations of a single normal shock located near the sudden expansion, known as base-pressure oscillations in literature. A hysteresis phenomenon is found experimentally and the state reached by the tranSonic Flow depends on the path followed by the pressure ratio. Moreover, a coupling of these base-pressure oscillations with the quarter-wavelength resonance of the duct can occur. All these regimes are numerically investigated and the results are favorably compared to available experimental data. A case of frequency locking of this self-excited mechanism is also reproduced, in agreement with a modeling of the resonator. The governing equations are solved using high-order central finite differences combined with an overset grid approach. The large-eddy simulations are based on a relaxation filtering and a nonlinear shock-capturing scheme is also implemented for shock waves.
Zhouping Xin - One of the best experts on this subject based on the ideXlab platform.
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Regular subSonic-Sonic Flows in general nozzles
Advances in Mathematics, 2021Co-Authors: Chunpeng Wang, Zhouping XinAbstract:Abstract This paper concerns subSonic-Sonic potential Flows in general two dimensional nozzles. For finitely long symmetric nozzles, we formulate the subSonic-Sonic Flow problem by prescribing the Flow angle at the inlet and the outlet. It is shown that this problem admits a unique Lipschitz continuous subSonic-Sonic Flow, and the Sonic points of the Flow must occur at the wall or the throat. This is the first result on the well-posedness for general subSonic-Sonic Flow problems. More importantly, the location of Sonic points is classified completely. Indeed, it is shown that there exists a critical value depending only on the length and the geometry of the nozzle such that the Flow is Sonic on the whole throat if the height of the nozzle is not greater than this critical value, while the Sonic points must be located at the wall if the height is greater than this value. Furthermore, the critical height is positive iff the nozzle is suitably flat near the throat. As a direct application of this theory, we can obtain conditions on whether there is a smooth tranSonic Flow of Meyer type whose Sonic points are all exceptional in de Laval nozzles.
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Optimal Hölder Continuity for a Class of Degenerate Elliptic Problems with an Application to SubSonic-Sonic Flows
Communications in Partial Differential Equations, 2010Co-Authors: Chunpeng Wang, Zhouping XinAbstract:In this paper, we first study a class of elliptic equations with anisotropic boundary degeneracy. Besides establishing the existence, uniqueness and comparison principle, we obtain the optimal Holder estimates for weak solutions by the estimates in the Campanato space. Based on such Holder estimates, we then investigate subSonic-Sonic Flows with singularities at the Sonic curves in a symmetric convergent nozzle with straight wall for an approximate model of the potential Flow equation. It is proved that the perturbation problem of the symmetric subSonic-Sonic Flow is solvable and the symmetric subSonic-Sonic Flow is stable.
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Global subSonic and subSonic-Sonic Flows through infinitely long nozzles
Indiana University Mathematics Journal, 2007Co-Authors: Chunjing Xie, Zhouping XinAbstract:In this paper, we study global subSonic and subSonicSonic Flows through a general infinitely long nozzle. First, it is proved that there exists a critical value for the incoming mass flux so that a global uniformly subSonic Flow exists in the nozzle as long as the incoming mass flux is less than the critical value. More importantly, we establish some uniform estimates for the deflection angles and the minimum speed of the subSonic Flows by combining hodograph transformation and the comparison principle for elliptic equations. With the help of these properties and a compensated compactness framework, we get the existence of a global subSonic-Sonic Flow solution in the case of the critical incoming mass flux.
Chunpeng Wang - One of the best experts on this subject based on the ideXlab platform.
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Regular subSonic-Sonic Flows in general nozzles
Advances in Mathematics, 2021Co-Authors: Chunpeng Wang, Zhouping XinAbstract:Abstract This paper concerns subSonic-Sonic potential Flows in general two dimensional nozzles. For finitely long symmetric nozzles, we formulate the subSonic-Sonic Flow problem by prescribing the Flow angle at the inlet and the outlet. It is shown that this problem admits a unique Lipschitz continuous subSonic-Sonic Flow, and the Sonic points of the Flow must occur at the wall or the throat. This is the first result on the well-posedness for general subSonic-Sonic Flow problems. More importantly, the location of Sonic points is classified completely. Indeed, it is shown that there exists a critical value depending only on the length and the geometry of the nozzle such that the Flow is Sonic on the whole throat if the height of the nozzle is not greater than this critical value, while the Sonic points must be located at the wall if the height is greater than this value. Furthermore, the critical height is positive iff the nozzle is suitably flat near the throat. As a direct application of this theory, we can obtain conditions on whether there is a smooth tranSonic Flow of Meyer type whose Sonic points are all exceptional in de Laval nozzles.
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Continuous subSonic-Sonic Flows in convergent nozzles with straight solid walls
Nonlinearity, 2016Co-Authors: Yuanyuan Nie, Chunpeng WangAbstract:This paper concerns continuous subSonic-Sonic potential Flows in a two-dimensional convergent nozzle with straight solid walls. It is shown that for the given inlet, which is a perturbation of an arc centered at the vertex of the nozzle, and the given incoming Flow angle which is a perturbation of the angle of the inner normal of the inlet, and the given incoming mass flux belonging to an open interval depending only on the adiabatic exponent and the length of the arc, there is a unique continuous subSonic-Sonic Flow from the given inlet with the given incoming Flow angle and the given incoming mass flux. Furthermore, the Sonic curve of this Flow is a free boundary, where the Flow is singular in the sense that the speed is only Holder continuous and the acceleration blows up at the Sonic state. The perturbation problem is solved in the potential plane, where the Flow is governed by a degenerate elliptic problem with two free boundaries, on one of which the equation is degenerate and on the other of which the boundary condition is nonlocal.
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Continuous subSonic-Sonic Flows in a general nozzle
Journal of Differential Equations, 2015Co-Authors: Chunpeng WangAbstract:Abstract This paper concerns continuous subSonic–Sonic potential Flows in a two dimensional finite nozzle with a general upper wall and a straight lower wall. We give a class of nozzles where continuous subSonic–Sonic Flows may exist. Consider a continuous subSonic–Sonic Flow in such a nozzle after rescaling the upper wall in a small scale. It is shown that for a given inlet and a fixed point at the upper wall, there exists uniquely a continuous subSonic–Sonic Flow whose velocity vector is along the normal direction at the inlet and the Sonic curve, which satisfies the slip conditions on the nozzle walls and whose Sonic curve intersects the upper wall at the fixed point. Furthermore, the Sonic curve of this Flow is a free boundary, where the Flow is singular in the sense that the speed is only C 1 / 2 Holder continuous and the acceleration blows up at the Sonic state. As the scale tends to zero, the precise convergent rate of the continuous subSonic–Sonic Flow converging to the Sonic state is also determined.
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Optimal Hölder Continuity for a Class of Degenerate Elliptic Problems with an Application to SubSonic-Sonic Flows
Communications in Partial Differential Equations, 2010Co-Authors: Chunpeng Wang, Zhouping XinAbstract:In this paper, we first study a class of elliptic equations with anisotropic boundary degeneracy. Besides establishing the existence, uniqueness and comparison principle, we obtain the optimal Holder estimates for weak solutions by the estimates in the Campanato space. Based on such Holder estimates, we then investigate subSonic-Sonic Flows with singularities at the Sonic curves in a symmetric convergent nozzle with straight wall for an approximate model of the potential Flow equation. It is proved that the perturbation problem of the symmetric subSonic-Sonic Flow is solvable and the symmetric subSonic-Sonic Flow is stable.