Under-expanded flow

When a supersonic flow emerges from a rocket nozzle, several oblique shock waves and expansion waves are formed along the nozzle flow. These waves are formed repeatedly and form a brilliant diamond-Uke array, as shown in Fig. C-5. When an under-expanded flow, i. e., having pressure higher than the ambient pressure is formed at the nozzle exit, an expansion wave is formed to decrease the pressure. This expansion wave is reflected at the interface between the flow stream and the ambient air and a shock wave is formed. This process is repeated several times to form a diamond array, as shown in Fig. C-6 (a). 

The first quantitative attempt (K12) in this direction was made with vertical orifices, under constant flow conditions. Here, the bubble formation is considered to be occurring in two distinct steps. In the first stage, the bubble is assumed to expand at the tip, moving vertically at the same time. As the bubble is formed at an angle to the vertical, a vertical component of the surface tension force will be operative during this stage. The first stage is... 

Figure C-6. Structures of (a) an under-expanded nozzle flow and (b) an over-expanded nozzle flow.

The working capillary-1 with ID of 0.3 mm and length of 216 mm is made from stainless steel. The capillary-1 is soldered to the extension tube-6. The fluid under study flows to a cold zone through the extension tube-6. Capillary-1 with extension tube-6 located in the high temperature and high pressure autoclave-4. The extension tube-6 is connected to a movable cylinder-9, which in turn is connected to the fixed cylinder-11 by means of the flexible tube-10. Both cylinders (9 and 11) are supplied with identical expanded bottles, employed to stabilize the fluid efflux through the capillary. The input and output sections of the capillary have conical extensions. All parts of the experimental installation in contact with the sample are made out of stainless steel. 

A comparison of the theoretical exit pressure for an isen-tropic nozzle with the level of the ambient back-pressure. For isentropic exit pressures below the ambient, the flow is over-expanded for isentropic exit pressures exceeding the ambient value, the flow is under-expanded when the pressures are matched, the flow is perfectly expanded . 

The gas flow (nitrogen N2) through conventional straight bore holes or apertures during expansion of gas from an atomizer nozzle is that of under-expanded jets if the atomization pressure is above the critical value 0.189 MPa. In this case the gas exits the nozzle at a Mach number Ma = UJc = 1. The state of gas at the nozzle exit, that is at the Inlet in Figs. 18.15 and 18.16, can be determined by the stagnation conditions in the atomizer as follows ... 

Fig. 18.18 Left, numerical simulation of the flow field near the nozzle for an under-expanded jet (slice) Right, axial velocity component distribution at the centre-line of the jet, comparison between simulation and experiment, experimental data adapted from Heck [26]...

Natural water drive occurs when the underlying aquifer is both large (typically greater than ten times the oil volume) and the water is able to flow Into the oil column, i.e. it has a communication path and sufficient permeability. If these conditions are satisfied, then once production from the oil column creates a pressure drop the aquifer responds by expanding, and water moves into the oil column to replace the voidage created by production. Since the water compressibility is low, the volume of water must be large to make this process effective, hence the need for the large connected aquifer. 

Under normal operations, the existing differential pressure governor is switehed to manual and the double slide valve is wide open. This valve must be suffieiently opened so that, even in the event of an emergeney expander trip, the entire flue gas flow ean pass through the double slide valve without the regenerator diseharge pressure inereasing to nonpermissible levels. 

However, when an expander has to operate at mismatehed eondi-tions, the aetual mismateh usually oeeurs in the inlet butterfly valve, whieh attempts to maintain regenerator pressure. Fortunately, proeessing parameters ean also be modulated under different produetion eapaeities. In sueh eireumstanees, it is important to keep the volume flow in the normal range to maintain system effieieney. For an ideal gas, the eonditional equation is ... 

The availability of large and fast computers, in combination with numerical techniques to compute transient, turbulent flow, has made it possible to simulate the process of turbulent, premixed combustion in a gas explosion in more detail. Hjertager (1982) was the first to develop a code for the computation of transient, compressible, turbulent, reactive flow. Its basic concept can be described as follows A gas explosion is a reactive fluid which expands under the influence of energy addition. Energy is supplied by combustion, which is modeled as a one-step conversion process of reactants into combustion products. The conversion (combustion)... 

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