Diverging compression

When an airplane exceeds the speed of sound, we say that it breaks the sound barrier. In so doing, it generates a sonic wave or pressure wave-front. When steam and gas flow into the converging section of the jet diffuser shown in Fig. 16.1, the same thing happens. The gradually converging sides of the diffuser increase the velocity of the steam and gas, as the vapor enters the diffuser throat up to, and even above, the speed of sound. This creates a pressure wavefront, or sonic boost. This sonic boost, will multiply the pressure of the flowing steam and gas by a factor of perhaps 3 or 4. 

Note something really important at this point. If, for any reason, the velocity of the steam and gas falls below the speed of sound in the diffuser throat, the sonic pressure boost would disappear. 

As the steam and gas leave the diffuser throat, the flow then enters the gradually diverging sides of the diffuser. The velocity of the steam and gas is reduced. The kinetic energy of the flowing stream is partially converted to pressure as the steam and gas slow down. This increase in 

While smaller than the sonic boost, the velocity boost is more reliable. Even though the velocity in the diffuser throat in Fig. 16.1 falls well below the speed of sound, the increase in pressure in the diverging portion of the diffuser is only slightly reduced. 

The overall pressure boost of a steam jet is obtained by multiplying the sonic boost effect times the velocity boost effect. The overall boost is called the jet s compression ratio. 

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This equation is analogous to the compressibility equation for fluids and diverges with the same exponent y as the critical temperaUire is approached from above ... 

A third exponent y, usually called the susceptibility exponent from its application to the magnetic susceptibility x in magnetic systems, governs what m pure-fluid systems is the isothennal compressibility k, and what in mixtures is the osmotic compressibility, and detennines how fast these quantities diverge as the critical point is approached (i.e. as > 1). 

If the finite size of the system is ignored (after all, A is probably 10 or greater), the compressibility is essentially infinite at the critical point, and then so are the fluctuations. In reality, however, the compressibility diverges more sharply than classical theory allows (the exponent y is significantly greater dian 1), and thus so do the fluctuations. 

The field-density concept is especially usefiil in recognizing the parallelism of path in different physical situations. The criterion is the number of densities held constant the number of fields is irrelevant. A path to the critical point that holds only fields constant produces a strong divergence a path with one density held constant yields a weak divergence a path with two or more densities held constant is nondivergent. Thus the compressibility Kj,oi a one-component fluid shows a strong divergence, while Cj in the one-component fluid is comparable to (constant pressure and composition) in the two-component fluid and shows a weak... 

Fig. 9. Compressible flow in a converging—diverging no22le where A represents no flow, C subsonic flow, and F through H supersonic flow. See text.

Fig. 17-9. Formation of a subsidence inversion in subsiding (sinking) air. Note the vertical compression of the sinking layer which is usually accompanied by horizontal divergence.

On the loaded side of a slab subjected to an intense reflected blast wave, a region of the slab will fail if the intensity of the compressive wave transmitted into the slab exceeds the dynamic compressive strength of the material. For an intense wave striking a thin concrete slab, the failure region can extend through the slab, and a sizeable area turned to rubble which can fall or be ejected from the slab. For a thicker slab or localized loaded area, spherical divergence of the stress wave can cause it to decay in amplitude within the slab so that only part of the loaded face side is crushed by direct compression. 

Pressure profiles for compressible flow through a convergent-divergent nozzle... 

For the delivery of atomization gas, different types of nozzles have been employed, such as straight, converging, and converging-diverging nozzles. Two major types of atomizers, i.e., free-fall and close-coupled atomizers, have been used, in which gas flows may be subsonic, sonic, or supersonic, depending on process parameters and gas nozzle designs. In sonic or supersonic flows, the mass flow rate of atomization gas can be calculated with the following equation based on the compressible fluid dynamics ... 

The result that the divergence of flow velocity (V u) is zero is general as long as the fluid is uniform and incompressible. Liquid and "solid" fluids are approximately incompressible. However, gas is compressible and hence V u 0 for gas. 

At temperatures much higher than Za, the polymer fluid formally undergoes a fluid-gas transition where the isothermal compressibility Kr diverges, but this high temperature regime is normally inaccessible in polymer systems because of thermal decomposition. 

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