Nozzle Choking

Suppose that we connect a high-pressure reservoir full of air to a low-pressure reservoir full of jair by means of a converging nozzle. We assume that by suitable pumps, etc., we can maintain the pressure in each reservoir at any value we select and that we have some method of measuring the mass flow rate of gas passing through the nozzle. See Fig. 8.8. 

At first the pressure in both reservoirs is the same high pressure P. Since there is no pressure gradient across the nozzle, there is no flow. Then holding the pressure in the high-pressure reservoir constant at F, we begin to lower pressure P2 in the low-pressure reservoir. For each value of P2 we measure the mass flow rate m, and we plot m versus PJP The results are shown in Fig. 8.9. 

We observe that the mass flow rate increases steadily as we lower P2, until P2/Pi equals 0.5283, and then further lowering of P2 does not increase the mass flow rate. If we refer to App. A.5, we see that if the assumptions of isentropic, one-dimensional, steady flow apply, then this pressure ratio corresponds exactly to the sonic velocity (M = l) at the throat of the nozzle. Lowering the downstream pressure more does not increase the mass flow rate, because the flow that the value of 

The shout jnever leaves the spot where she made it (in the upstream direction). The sound signal, that there is a sharp pressure drop downstream of the nozzle, can never be communicated to the gas upstream of the nozzle. Thus, once the flow becomes sonic at the throat, nothing we can do downstream will increase the mass flow rate at that point. This situation, in which the flow at the throat is sonic, is called choking. One speaks of the nozzle as being choked because no more mass can get through it without a change in upstream conditions. The adjustment of the lower pressure takes place downstream of the throat by a rarefaction which is neither an isentropic nor a one-dimensional process and is not covered by the one-dimensional equations we develop in this chapter. 

Some device for measuring mass flow rate 

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The value of FB in equation (A6.4) depends on whether or hot flow is choked in the safety valve nozzle. Choking occurs if ... 

Choking. A common expression for use of the constricted nozzle(, choke ) to control the flow of gas from a rocket engine thrust chamber by building up pressure inside the chamber until the upper limit of mass flow is reached, or when the speed of sound is reached in the duct... 

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... 

If the back pressure is reduced below P, there is no increase in the flow rate through the nozzle, ie the flow is choked. In a convergent nozzle it is impossible for the gas speed to exceed the speed of sound. This case is... 

It is only in regime 1 that the flow rate depends on the back pressure. It will be noticed that this is only a small part of the nozzle s range of operation. Once the sonic speed has been reached at the throat (at the pressure P ), the flow becomes choked and the flow rate remains constant, for constant supply conditions, and is independent of the back pressure. 

The combustion gas of an internal burning of a propellant flows along the port of the propellant If the nozzle attached to a rocket motor is removed, the pressure in the port becomes equal to atmospheric pressure and no sonic velocity is attained at the rear-end of the port. Then, no thrust is generated by the combustion of the propellant However, if the mass burning rate of the propellant is high enough to choke the flow at the rear-end of the port, the pressure in the port is increased and the flow reaches sonic velocity. The increased pressure in the port is converted into thrust. The thrust F is represented by... 

When the gas injection nozzle is in an unchoked condition, the pressure in the gas generator is equal to the combustion chamber pressure, i. e., pg = p The gas generation rate is determined by the pressure in the combustion chamber. When the gas injection nozzle is in a choked condition, the burning rate is determined by the gas injection nozzle area, A g, and then the pressure in the gas generator, pg, is determined by... 

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 . 

Gives a forceful emission of fire and sparks especially when used in a tube with a choke or nozzle. 

Can be used in a tube without a choke or nozzle, to give bright silver sparks. 

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