Numerical simulations have been carried out for a supersonic three-dimensional rectangular arc nozzle, where a secondary flow toward the center of the curvature occurs due to the shape of the nozzle. It is known that ...Numerical simulations have been carried out for a supersonic three-dimensional rectangular arc nozzle, where a secondary flow toward the center of the curvature occurs due to the shape of the nozzle. It is known that secondary flow causes longitudinal vortices to form near the wall of the nozzle corner, making the nozzle outlet flow unstable and induces loss of transport energy. When the working fluid is a condensable gas with relatively large latent heat such as moist air or steam, rapid accelerated expansion in the nozzle causes non-equilibrium condensation due to supersaturation. After the release of latent heat during phase transition, nozzle flow continues expanding at an equilibrium saturation condition. In the absence of foreign particles, e.g. ions or dust particles, condensation nuclei are formed in the gas itself causing non-equilibrium homogeneous condensation. Supersonic nozzle flow properties vary considerably due to the occurrence of condensation phenomenon. The objective of this study is to investigate the effect of non-equilibrium homogeneous condensation on the longitudinal vortices which form in the range close to the corner of rectangular arc nozzle numerically.展开更多
A code named LARWM with non-ideal magnetohydrodynamic equations in cylindrical model is used to describe the instability in Tokamak plasma surrounded by a conducting wall with finite resistivity. We mainly take three ...A code named LARWM with non-ideal magnetohydrodynamic equations in cylindrical model is used to describe the instability in Tokamak plasma surrounded by a conducting wall with finite resistivity. We mainly take three factors related to the shear equilibrium plasma flow into consideration to study the stabilizing effect of the shear flow on the resistive wall modes （RWMs）. The three factors are the velocity amplitude of flow, the shear rate of flow on plasma surface, and the inertial energy of equilibrium plasma flow. In addition, a local shear plasma flow is also calculated by the LARWM code. Consequently, it is found that the inertial energy of the shear equilibrium plasma flow has an important role in the stabilization of the RWMs.展开更多
In the traffic equilibrium problem, we introduce capacity constraints of arcs, extend Beckmann’s formula to include these constraints, and give an algorithm for traffic equilibrium flows with capacity constraints on ...In the traffic equilibrium problem, we introduce capacity constraints of arcs, extend Beckmann’s formula to include these constraints, and give an algorithm for traffic equilibrium flows with capacity constraints on arcs. Using an example, we illustrate the application of the algorithm and show that Beckmann’s formula is a sufficient condition only, not a necessary condition, for traffic equilibrium with capacity constraints of arcs.展开更多
The effect of the toroidal flow on the equilibrium of tokamak plasmas is a sensitive point for high performance plasma and its precise control. In this paper the effect is studied numerically using the EFIT （Equilibr...The effect of the toroidal flow on the equilibrium of tokamak plasmas is a sensitive point for high performance plasma and its precise control. In this paper the effect is studied numerically using the EFIT （Equilibrium Fitting） code on EAST （Experimental Advanced Superconducting Tokamak）. Firstly, the numerical calculation exhibits a clear outward shift of pressure contour from the magnetic surfaces in the plasma core and the shift grows with the increase of the toroidal velocity. The peak shift of 8% is observed when the ratio between the plasma velocity and the Alfvdn speed equals to 0.15. Secondly, it is shown that the magnetic surfaces shift outwards from those without flow. With a certain plasma current the safety factor on the magnetic axis decreases as the plasma flow velocity increases. The magnetic shear increases about 10% on the plasma boundary compared with the case without flow.展开更多
Problem of the axisymmetric toroidal equilibrium with pure sheared toroidal flow isinvolved. For standard tokamak equilibrium, general approximate solutions are analytically pur-sued for arbitrary current profile and ...Problem of the axisymmetric toroidal equilibrium with pure sheared toroidal flow isinvolved. For standard tokamak equilibrium, general approximate solutions are analytically pur-sued for arbitrary current profile and non-circular cross-section. Equilibrium properties includingthe fiow-induced density asymmetry are analyzed.展开更多
In this paper, a third-order exponential time differencing scheme, named ETDRK3, was investigated for large time stepping in the computation of hypersonic non-equilibrium flow. The second-order Harten-TVD scheme was u...In this paper, a third-order exponential time differencing scheme, named ETDRK3, was investigated for large time stepping in the computation of hypersonic non-equilibrium flow. The second-order Harten-TVD scheme was used for the spatial discretization. The efficient implementation of the scheme with diagonalization of Jacobin matrix was established and carried out for the semi-cylindrical around flow. Current observations showed that the numerical results were in good agreement with those obtained by the classical explicit three-stage Runge-Kutta scheme (RK3) and implicit LU scheme. Efficiency assessments promised the effectiveness of the ETDRK3 scheme. The rationality of the application of this scheme was proved by its preferable accuracy and efficiency.展开更多
The transition between regular reflection （RR） and Mach reflection （MR） of type V shock-shock interaction on a double-wedge geometry with high temperature non-equilibrium effects is investigated by extended shock-...The transition between regular reflection （RR） and Mach reflection （MR） of type V shock-shock interaction on a double-wedge geometry with high temperature non-equilibrium effects is investigated by extended shock-polar method and numerical simulation. First, the critical angles of transition from detachment criterion and yon Neumann criterion are determined by the extended shock-polar method considering the non-equilibrium effects. Then wave patterns and the transition process are numerically obtained. Results of the critical transition angles from shock-polar calculation and numerical simulation show evident disagreement, indicating transition mechanism between RR and MR of type V interaction is changed. By comparing with the frozen counterpart, it is also found that non-equilibrium effects lead to a larger critical wedge angle and a larger hysteresis interval.展开更多
文摘Numerical simulations have been carried out for a supersonic three-dimensional rectangular arc nozzle, where a secondary flow toward the center of the curvature occurs due to the shape of the nozzle. It is known that secondary flow causes longitudinal vortices to form near the wall of the nozzle corner, making the nozzle outlet flow unstable and induces loss of transport energy. When the working fluid is a condensable gas with relatively large latent heat such as moist air or steam, rapid accelerated expansion in the nozzle causes non-equilibrium condensation due to supersaturation. After the release of latent heat during phase transition, nozzle flow continues expanding at an equilibrium saturation condition. In the absence of foreign particles, e.g. ions or dust particles, condensation nuclei are formed in the gas itself causing non-equilibrium homogeneous condensation. Supersonic nozzle flow properties vary considerably due to the occurrence of condensation phenomenon. The objective of this study is to investigate the effect of non-equilibrium homogeneous condensation on the longitudinal vortices which form in the range close to the corner of rectangular arc nozzle numerically.
基金the National Natural Science Foundation of China(Grant Nos.11105065 and 11275041)the National Basic Research Program of China(Grant Nos.2008CB717801,2008CB787103,2009GB105004,and 2010GB106002)
文摘A code named LARWM with non-ideal magnetohydrodynamic equations in cylindrical model is used to describe the instability in Tokamak plasma surrounded by a conducting wall with finite resistivity. We mainly take three factors related to the shear equilibrium plasma flow into consideration to study the stabilizing effect of the shear flow on the resistive wall modes （RWMs）. The three factors are the velocity amplitude of flow, the shear rate of flow on plasma surface, and the inertial energy of equilibrium plasma flow. In addition, a local shear plasma flow is also calculated by the LARWM code. Consequently, it is found that the inertial energy of the shear equilibrium plasma flow has an important role in the stabilization of the RWMs.
文摘In the traffic equilibrium problem, we introduce capacity constraints of arcs, extend Beckmann’s formula to include these constraints, and give an algorithm for traffic equilibrium flows with capacity constraints on arcs. Using an example, we illustrate the application of the algorithm and show that Beckmann’s formula is a sufficient condition only, not a necessary condition, for traffic equilibrium with capacity constraints of arcs.
基金supported by National Natural Science Foundation of China (No. 10475077)
文摘The effect of the toroidal flow on the equilibrium of tokamak plasmas is a sensitive point for high performance plasma and its precise control. In this paper the effect is studied numerically using the EFIT （Equilibrium Fitting） code on EAST （Experimental Advanced Superconducting Tokamak）. Firstly, the numerical calculation exhibits a clear outward shift of pressure contour from the magnetic surfaces in the plasma core and the shift grows with the increase of the toroidal velocity. The peak shift of 8% is observed when the ratio between the plasma velocity and the Alfvdn speed equals to 0.15. Secondly, it is shown that the magnetic surfaces shift outwards from those without flow. With a certain plasma current the safety factor on the magnetic axis decreases as the plasma flow velocity increases. The magnetic shear increases about 10% on the plasma boundary compared with the case without flow.
基金National Science Foundation (19975015) and the China Nuclear Science Foundation(Y7l00C030l).
文摘Problem of the axisymmetric toroidal equilibrium with pure sheared toroidal flow isinvolved. For standard tokamak equilibrium, general approximate solutions are analytically pur-sued for arbitrary current profile and non-circular cross-section. Equilibrium properties includingthe fiow-induced density asymmetry are analyzed.
文摘In this paper, a third-order exponential time differencing scheme, named ETDRK3, was investigated for large time stepping in the computation of hypersonic non-equilibrium flow. The second-order Harten-TVD scheme was used for the spatial discretization. The efficient implementation of the scheme with diagonalization of Jacobin matrix was established and carried out for the semi-cylindrical around flow. Current observations showed that the numerical results were in good agreement with those obtained by the classical explicit three-stage Runge-Kutta scheme (RK3) and implicit LU scheme. Efficiency assessments promised the effectiveness of the ETDRK3 scheme. The rationality of the application of this scheme was proved by its preferable accuracy and efficiency.
文摘The transition between regular reflection （RR） and Mach reflection （MR） of type V shock-shock interaction on a double-wedge geometry with high temperature non-equilibrium effects is investigated by extended shock-polar method and numerical simulation. First, the critical angles of transition from detachment criterion and yon Neumann criterion are determined by the extended shock-polar method considering the non-equilibrium effects. Then wave patterns and the transition process are numerically obtained. Results of the critical transition angles from shock-polar calculation and numerical simulation show evident disagreement, indicating transition mechanism between RR and MR of type V interaction is changed. By comparing with the frozen counterpart, it is also found that non-equilibrium effects lead to a larger critical wedge angle and a larger hysteresis interval.
