41. Flow of gases and steam through difusers

(a) subsonic diffuser shortly diffuser; (b) supersonic diffuser. A [m²] flow area of diffuser; c [m·s^-1] velocity of gas; Ma [-] Mach number; A* [m²] critical flow area of supersonic diffuser, here velocity of gas is reached speed of sound (critical state of gas). Subscript i denotes state at inlet of the diffuser, subscript e denotes state at exit of the diffuser.

v [m³·kg^-1] specific volume; ε*_c [-] critical pressure ratio; κ [-] isentropic index.

left inside subsonic diffuser; right inside supsonic diffuser. z [J·kg^-1] losses – required increasing of inlet kinetic energy of gas for cover of losses*; Δp_z [Pa] pressure drop – difference of stagnation pressures. Subscript iz denotes isentropic compression – compression without losses.

g [m·s^-2] gravitational acceleration; y_{i, e} [J·kg^-1] specific total energy of liquid at inlet and at exit;
z_i-e [J·kg^-1] specific internal losses of diffuser; h [m] horizontal level of axis; g·h [J·kg^-1] specific potential energy.

n [-] polytropic index. Polytropic index is equal isentropic index n=κ for case ideal compression. The equation is derived under simplifying assumptions that velocity of gas has main axis direction – the velocity is deflected from axis direction at walls in realy. The derivation is shown in the Appendix 432.

(a) stepped supersonic diffuser; (b), (c) stepped supersonic diffuser with downstream shock waves - as if reflected from the diffuser wall - which naturally directs the velocity vector in the axial direction and reduces losses [1, p. 409]. RV shock waves.

Condensing turbine about 25 MW at speed 3 000 min^-1, one controlled steam extraction at 0,25 MPa for 80 t·h^-1, pressure admission steam is 2 MPa at 390 °C, Made in PBS. Figure: [1].

1 radial compressor impeller radiálního kompresoru; 2 diffuser blades with supersonic profile.

vlevo general scheme of ejector or injector; vpravo example of a steam ejector as the vacuum pump of a condenser [6]. p motive steam; v suction gas (mix of steam and inertial gas); 1 suction section; 2 diffuser throat (mixture section); 3 exit diffuzer. The function of the ejectors or injectors is based on the transmission of a portion of the kinetic energy of the motive fluid to the suction fluid. This happens approximately in the throat of the diffuser. Prior to this, however, it is necessary to suck in the suction fluid into the motive fluid jet exiting the nozzle (in this case the Laval nozzle), which happens at the boundary of the suction and mixing zone due to turbulence at the stream interface. In the diffuser part of the machine, kinetic energy is transformed into pressure energy.

μ [-] ejection respectively injection ratio [1, p. 419]. u [J·kg^-1] the specific internal thermal energy. The index p indicates the motive and the index v the sucktion working fluid. Δ is a change mark, for example, Δ(p/ρ)_p means a change in the pressure energy of the motive between the inlet and the outlet. The derivation of the equation when neglecting the change in potential energy is given  Appendix 404. The ejector and injector are also calculated in [7], [1], [8], [9].

Problem 3.410

a inlet throutling area; b outlet throutling area. 1 supersonic diffuser; 2 combustion chamber and fuel injection to subsonic flow of compressed air; 3 expansion of exhaust gas inside nozzle.

(a) description of function; (b) experimental unmanned aircraft X-43A with Scramjet*. 1 supersonic diffuser; 2 combustion chamber inside throutling and inlet of fuel to sonic flow; 3 expansion of exhaust through nozzle; 4 shock waves; 5 expansion waves.