Propagative compression

FIGURE 5.7 Comparison of spatially uniform compression to propagative compression. 

In fluidized bed reactors and regenerators, the magnitude of compressed gas pressure varies whether the compression is made slowly or rapidly. A gas that is compressed slowly such that the pressure rises uniformly in a control volume is known as slow, or spatially uniform, compression. A rapidly compressed gas, such as by a rapid piston motion, is known as propagative compression. Figure 5.7 shows the schematics of both spatially uniform and propagative compression. 

Likewise, for rapid, or propagative, compression, you have the following ... 

Thus, you can see that the propagative compression results in a final pressure are 2.3 times that produced by spatially uniform compression. There is the added effect of shock with propagative compression that can enhance forces exerted on internal vessel components. 

The transmission times can be used to determine the depth to the defects. As yet the use of this kind of testing in concrete is based on the rektilinear propagation of compression waves from the surface. No directional transducers for use on concrete are known to exist. 

Some of the tests and criterion used to define fire resistance may be found in the Hterature (9). Additionally, the compression—ignition and hot manifold tests as defined in MIL-H-19457 and MIL-H-5606, respectively the Wick test as defined by Federal Standards 791, Method 352 flash point and fire point as defined in ASTM D92 autoignition temperature as defined in ASTM D2155 and linear flame propagation rate are defined in ASTM D5306 are used. 

This frequency is a measure of the vibration rate of the electrons relative to the ions which are considered stationary. Eor tme plasma behavior, plasma frequency, COp, must exceed the particle-coUision rate, This plays a central role in the interactions of electromagnetic waves with plasmas. The frequencies of electron plasma waves depend on the plasma frequency and the thermal electron velocity. They propagate in plasmas because the presence of the plasma oscillation at any one point is communicated to nearby regions by the thermal motion. The frequencies of ion plasma waves, also called ion acoustic or plasma sound waves, depend on the electron and ion temperatures as well as on the ion mass. Both electron and ion waves, ie, electrostatic waves, are longitudinal in nature that is, they consist of compressions and rarefactions (areas of lower density, eg, the area between two compression waves) along the direction of motion. 

V/c is the ratio of fluid velocity to the speed of sound or aeoustie veloeity, c. The speed of sound is the propagation velocity of infinitesimal pressure disturbances and is derived from a momentum balance. The compression caused by the pressure wave is adiabatic and frictionless, and therefore isentropic. 

Water Hammer When hquid flowing in a pipe is suddenly decelerated to zero velocity by a fast-closing valve, a pressure wave propagates upstream to the pipe inlet, where it is reflected a pounding of the hne commonly known as water hammer is often produced. For an instantaneous flow stoppage of a truly incompressible fluid in an inelastic pipe, the pressure rise would be infinite. Finite compressibility of the flmd and elasticity of the pipe limit the pressure rise to a finite value. The Joukowstd formula gives the maximum pressure... 

Noise Control Sound is a fluctuation of air pressure that can be detected by the human ear. Sound travels through any fluid (e.g., the air) as a compression/expansion wave. This wave travels radially outward in all directions from the sound source. The pressure wave induces an oscillating motion in the transmitting medium that is superimposed on any other net motion it may have. These waves are reflec ted, refracted, scattered, and absorbed as they encounter solid objects. Sound is transmitted through sohds in a complex array of types of elastic waves. Sound is charac terized by its amplitude, frequency, phase, and direction of propagation. 

Decomposition Flame Arresters Above certain minimum pipe diameters, temperatures, and pressures, some gases may propagate decomposition flames in the absence of oxidant. Special in-line arresters have been developed (Fig. 26-27). Both deflagration and detonation flames of acetylene have been arrested by hydrauhc valve arresters, packed beds (which can be additionally water-wetted), and arrays of parallel sintered metal elements. Information on hydraulic and packed-bed arresters can be found in the Compressed Gas Association Pamphlet G1.3, Acetylene Transmission for Chemical Synthesis. Special arresters have also been used for ethylene in 1000- to 1500-psi transmission lines and for ethylene oxide in process units. Since ethylene is not known to detonate in the absence of oxidant, these arresters were designed for in-line deflagration application. 

Shock-compression processes are encountered when material bodies are subjected to rapid impulsive loading, whose time of load application is short compared to the time for the body to respond inertially. The inertial responses are stress pulses propagating through the body to communicate the presence of loads to interior points. In our everyday experience, such loadings are the result of impact or explosion. To the untrained observer, such events evoke an image of utter chaos and confusion. Nevertheless, what is experienced by the human senses are the rigid-body effects the time and pressure resolution are not sufficient to sense the wave phenomena. 

For a shock wave in a solid, the analogous picture is shown schematically in Fig. 2.6(a). Consider a compression wave on which there are two small compressional disturbances, one ahead of the other. The first wavelet moves with respect to its surroundings at the local sound speed of Aj, which depends on the pressure at that point. Since the medium through which it is propagating is moving with respect to stationary coordinates at a particle velocity Uj, the actual speed of the disturbance in the laboratory reference frame is Aj - -Ui- Similarly, the second disturbance advances at fl2 + 2- Thus the second wavelet overtakes the first, since both sound speed and particle velocity increase with pressure. Just as a shallow water wave steepens, so does the shock. Unlike the surf, a shock wave is not subject to gravitational instabilities, so there is no way for it to overturn. 

Throughout this book, a shock pulse (a steady compression wave followed by an expansion wave) will be represented as a profile, such as in Fig. 2.6. In Fig. 2.8 we show a series of P-x snapshots of pressure versus propagation distance x for an initially square pulse, at a series of times t. For a fluid with... 

When an isotropic material is subjected to planar shock compression, it experiences a relatively large compressive strain in the direction of the shock propagation, but zero strain in the two lateral directions. Any real planar shock has a limited lateral extent, of course. Nevertheless, the finite lateral dimensions can affect the uniaxial strain nature of a planar shock only after the edge effects have had time to propagate from a lateral boundary to the point in question. Edge effects travel at the speed of sound in the compressed material. Measurements taken before the arrival of edge effects are the same as if the lateral dimensions were infinite, and such early measurements are crucial to shock-compression science. It is the independence of lateral dimensions which so greatly simplifies the translation of planar shock-wave experimental data into fundamental material property information. 

An important application of the impedance match method is demonstrated by the pressure-particle velocity curves of Fig. 4.9 for various explosives. Using the above method, the pressure in shock waves in various explosives is inferred from the intersection of the explosive Hugoniot with the explosive product release isentropes and reflected shock-compression Hugoniots (Zel dovich and Kompaneets, 1960). The amplitudes of explosively induced shock waves which can be propagated into nonreacting materials are calculable using results such as those of Fig. 4.9. 

Figure 4.11. Diagrammatic sketches of atomic lattice rearrangements as a result of dynamic compression, which give rise to (a) elastic shock, (b) deformational shock, and (c) shock-induced phase change. In the case of an elastic shock in an isotropic medium, the lateral stress is a factor v/(l — v) less than the stress in the shock propagation direction. Here v is Poisson s ratio. In cases (b) and (c) stresses are assumed equal in all directions if the shock stress amplitude is much greater than the material strength.

At this point it is useful to define the velocity of a sound (/ or b) wave propagating in a moving medium, which may also be compressed. The velocity with respect to stations moving with the medium is termed Lagrangian, C. The position of a station (for the purpose of calculating the velocity) is taken to be specified by its initial position. Sound velocity with respect to distances, measured with respect to the laboratory, is termed Eulerian, C . 

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