Choked nozzle

In order to overcome the difficulties associated with the non-choked fuel-flow system and the fixed fuel-flow system, a variable fuel-flow system is introduced the fuel gas produced in a gas generator is injected into a ramburner. The fuel-flow rate is controlled by a control valve attached to the choked nozzle according to the airflow rate induced into the ramburner. An optimized mixture ratio of fuel and air, which is dependent on the flight altitude and flight velocity, is obtained by modulating the combustion rate of the gas-generating pyrolant When a variable fuel-flow-rate system is attached to the choked nozzle of the gas generator, the fuel-flow rate is altered in order to obtain an optimized combustible gas in the ramburner. This class of ducted rockets is termed variable fuel-flow ducted rockets or VFDR . 

The vent mass flow capacity per unit area, Gg, can be obtained using the Omega method (see Annex 8). For gas flow, = 1, and reading from Figure A8.2, the dimensionless mass flow per unit area of a choked nozzle is 0.6. 

Earlier descriptions of the Omega method13,41 defined Omega such that the first term in equations (A8.5)-(A8.10) was equivalent to ao rather than to This led to discrepancies for g> < 4 in calculating G for choked nozzle flow, compared with experimental results. The definitions of Omega given above151 overcome this problem. 

Having obtained Gc, the value of G for choked nozzle flow, Gc can be obtained from the following equation13,4,51 ... 

PRESSURE RATIO, r)c, VERSUS OMEGA FOR A CHOKED NOZZLE... 

The propagation of longitudinal acoustic waves in choked nozzles has been analyzed on the basis of the one-dimensional, time-dependent forms of equations (4-45) and (4-46) by introducing linearizations of the previously indicated type (for example, p = p(l + p )] for the stream wise velocity v as well—that is, v — v(l + i )—and by allowing the mean quantities p, p, and V to vary with the streamwise distance z through the nozzle, in a manner presumed known from a quasi-one-dimensional, steady-flow nozzle analysis [20]. The perturbation equations... 

In the theoretical analysis of shock instability, shock waves that are not too strong are presumed to propagate axially back and forth in a cylindrical chamber, bouncing off a planar combustion zone at one end and a short choked nozzle at the other [101], [102]. The one-dimensional, time-dependent conservation equations for an inviscid ideal gas with constant heat capacities are expanded about a uniform state having constant pressure p and constant velocity v in the axial (z) direction. Since nonlinear effects are addressed, the expansion is carried to second order in a small parameter e that measures the shock strength discontinuities are permitted across the normal shock, but the shock remains isentropic to this order of approximation. Boundary conditions at the propellant surface (z = 0) and at the... 

An example of bulk modes in solid-propellant rockets is afforded by the low-frequency, or L, instability [7]. A characteristic length of importance in rocket design is the ratio of the gas volume in the chamber to the throat area of the nozzle this ratio often is denoted by L, and its ratio to a characteristic exhaust velocity provides an estimate of the residence time of a fluid element in the gas phase inside the chamber. A mass balance for the gas inside a rocket chamber with a choked nozzle is... 

The liquid-nitrogen flow rate was measured with a turbine flowmeter. The total pressure of the jet exhaust Ptj was measured at an orifice in the model plenum chamber by a Precision Pressure Balance transducer. The total temperature of the CO2 exhaust was measured by a thermocouple in the line leading into the vacuum chamber. This thermocouple was downstream of the pressure-regulating valve and therefore measured the total temperature of the CO2 after the expansion to near the jet total pressure. The total temperature and the total pressure of the jet were used in a one-dimensional isentropic flow equation for choked nozzles to calculate the mass flow of CO2. The specific heat ratio used was that corresponding to the total temperature and pressure of the jet. 

The exit Mach number Mo may not exceed unity Mo = 1 corresponds to choked flow sonic conditions may exist only at the pipe exit. The mass velocity G in the charts is the choked mass flux for an isentropic nozzle given by Eq. (6-118). For a pipe of finite length. 

Choked and unchoked flow situations arise in pipes and nozzles in the same fashion for homogeneous equihbrium flashing flow as for gas flow. For nozzle flow from stagnation pressure po to exit pressure pi, the mass flux is given by... 

Critical and Subcritical Flow - The maximum vapor flow through a restriction, such as the nozzle or orifice of a pressure relief valve, will occur when conditions are such that the velocity through the smallest cross-sectional flow area equals the speed of sound in that vapor. This condition is referred to as "critical flow" or "choked flow . 

Flow through chokes and nozzles is a special case of fluid dynamics. For incompressible fluids the problem can be handled by mass conservation and Bernoulli s equation. Bernoulli s equation is solved for the pressure drop across the choke, assuming that the velocity of approach and the vertical displacement are negligible. The velocity term is replaced by the volumetric flow rate times the area at the choke throat to yield... 

Flowrate through a choke, or nozzle, or leak (Equation 4-186) is... 

Dirty or choked spray nozzles in water tower or evaporative condenser, so that the surface is not fully wetted... 

Critical (choked) flow will occur in the nozzle throat when the pressure ratio is... 

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