Formulation of the Riccati equation for the impedance operator in cylindrical coordinates for inhomogeneous anisotropic waveguides with the example of rectilinear anisotropy

Wave Motion ◽  
2015 ◽  
Vol 52 ◽  
pp. 1-14 ◽  
Author(s):  
T.V. Zharnikov ◽  
D.E. Syresin
Keyword(s):  
Riccati Equation ◽  
Cylindrical Coordinates ◽  
Rectilinear Anisotropy ◽  
Impedance Operator

The study of the process of evolution of the jet under outflow of water from the supercritical state through a thin nozzle

2016 ◽  
Vol 11 (1) ◽  
pp. 66-71 ◽  
Author(s):  
R.Kh. Bolotnova ◽  
V.A. Korobchinskaya
Keyword(s):  
Stationary Process ◽  
Supercritical State ◽  
System Of Differential Equations ◽  
Jet Formation ◽  
Cylindrical Coordinates ◽  
Initial Stage ◽  
Supersonic Regime ◽  
Water Outflow ◽  
Thin Nozzle ◽  
Supercritical Temperature

The dynamics of the water outflow from the initial supercritical state through a thin nozzle is studied. To describe the initial stage of non-stationary process outflow the system of differential equations of conservation of mass, momentum and energy in a two-dimensional cylindrical coordinates with axial symmetry is used. The spatial distribution of pressure and velocity of jet formation was received. It was established that a supersonic regime of outflow at supercritical temperature of 650 K is formed, which have a qualitative agreement for the velocity compared with the Bernoulli analytical solution and the experimental data.

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