Critical expansion rates

The phenomenon of critical flow is well known for the case of single-phase compressible flow through nozzles or orifices. When the differential pressure over the restriction is increased beyond a certain critical value, the mass flow rate ceases to increase. At that point it has reached its maximum possible value, called the critical flow rate, and the flow is characterized by the attainment of the critical state of the fluid at the throat of the restriction. This state is readily calculable for an isen-tropic expansion from gas dynamics. Since a two-phase gas-liquid mixture is a compressible fluid, a similar phenomenon may be expected to occur for such flows. In fact, two-phase critical flows have been observed, but they are more complicated than single-phase flows because of the liquid flashing as the pressure decreases along the flow path. The phase change may cause the flow pattern transition, and departure from phase equilibrium can be anticipated when the expansion is rapid. Interest in critical two-phase flow arises from the importance of predicting dis-... 

The subscript s denotes an isentropic path for ideal nozzle flow. For ideal gas with Pok = constant, substitution of this isentropic expansion law into Eq. (23-98) yields the following critical pressure ratio PJP and critical flow rate Gc ... 

Other theories give fragment size as a function of a hypothesized critical expansion velocity (Rinehard and Pearson, Ref 13), or based upon a critical strain rate, a mechanism related to radial, not tangential, stress gradient across the cylinder wall (Garg and Siekmann, Ref 14, and Taylor, Ref 15). Mott, however, gives a more tractable mathematical treatment suited to first-order engineering, as compared to the others. Mott s equations are... 

Experiments with the refrigerants R12 and R22 were performed with the annular nozzle A1 having a similar profile as nozzle B1. The expansion rates were comparable with those of the CO -expansions in nozzle B1. The results for R12 are shown in Fig.6 Wilson points could be determined only in the range between 50 and 90 per cent of the critical pressure. Above the upper limit, about 6 K below the critical temperature, the Wilson line cannot be distinguished from the saturation line. This is reasonable because of the rapidly decreasing values of... 

The general concensus Is that the steep Increase In pressure beyond a critical flow rate Is a direct consequence of viscoelasticity In relation to the unsteadiness of the flow field In a porous medium. During flow the molecules can become extended, and this Is particularly the case In converglng/dlverging extenslonal flows, such as the fluid experiences In pore throats In a reservoir rock. If the fluid relaxation time Is small with respect to the time It takes to pass through a contraction or expansion, the fluid will accommodate quickly and no elastic effects are observed. If, on the other hand, relaxation time Is relatively large, elastic effects become dominant, resulting In excessive pressure Increase. 

With disk diameters above 5.25 in., all parameters, eg, water absorption and thermal expansion, become more critical which aggravates the expansion or warp of disks. If in the future disk rotation speeds have to be increased significantly to boost data transfer rates, higher demands will be placed on warp (tilt angle) and modulus to avoid creeping (ie, irreversible elongation in radial direction). A survey of the requirement profile for the substrate material of optical disks is given in Table 5 (182,186,187,189). 

It will be seen when the pressure ratio Pi/Pi is less than the critical value (wr — 0.607) the flow rate becomes independent of the downstream pressure P2. The fluid at the orifice is then flowing at the velocity of a small pressure wave and the velocity of the pressure wave relative to the orifice is zero. That is the upstream fluid cannot be influenced by the pressure in the downstream reservoir. Thus, the pressure falls to the critical value at the orifice, and further expansion to the downstream pressure takes place in the reservoir with the generation of a shock wave, as discussed in Section 4.6. 

The versatility and accuracy of the oxygen consumption method in heat release measurement was demonstrated. The critical measurements include flow rates and species concentrations. Some assumptions need to be invoked about (a) heat release per unit oxygen consumed and (b) chemical expansion factor, when flow rate into the system is not known. Errors in these assumptions are acceptable. As shown, the oxygen consumption method can be applied successfully in a fire endurance test to obtain heat release rates. Heat release rates can be useful for evaluating the performance of assemblies and can provide measures of heat contribution by the assemblies. The implementation of the heat release rate measurement in fire endurance testing depends on the design of the furnace. If the furnace has a stack or duct system in which gas flow and species concentrations can be measured, the calorimetry method is feasible. The information obtained can be useful in understanding the fire environment in which assemblies are tested. 

Post-installed bolts will be required at times for attachment of equipment which may be subjected to large accelerations during a blast. Expansion anchors should be avoided for most blast design applications unless the load levels are low. Typically "wedge" type anchors are qualified for dynamic loads although most of these ratings are for vibratory loads and are based on cyclic tests at low stress levels. These should only be used where ultimate loads are less than the rated capacity with a margin of safely. Epoxy anchors have shown excellent dynamic capacity and may be considered for critical applications. 

Additional fluid-lift capability was planned through a combination of increased gas-lift capacity and installation of submersible pumps. Gas-lift system expansion was critical for future flexibility of the system to allow target production rate modifications on the basis of reservoir performance. Most field gaslift compressors used to supplement plant compression were to be shut in as soon as gas-lift system expansions were completed. 

---