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Proactive Reservoir Management
Published in Ashok K. Pathak, Petroleum Reservoir Management, 2021
Acoustic emissions technique can capture the rarefaction waves that are caused by leaks in pipes. Rarefaction is the opposite phenomenon of compression. It comes into play when oil and gas moving through pipelines under pressure release through leaks.
What Is Sound? Seven Important Characteristics
Published in Timothy A. Dittmar, Audio Engineering 101, 2013
Imagine dropping a stone in water. The stone (source) will create a series of ripples in the water. The ripples (waves) are created by areas of dense molecules that are being pushed together as sparse molecules expand, thus creating flatter areas. Sound travels just like this, by compression and rarefaction. Compression is the area where dense molecules are pushed together and rarefaction is the area where fewer molecules are pulled apart, or expanded, in the wave. The compression area is higher in pressure and the rarefaction area is lower in pressure.
Physical Foundation of Interior Ballistics
Published in Donald E. Carlucci, Sidney S. Jacobson, Ballistics, 2018
Donald E. Carlucci, Sidney S. Jacobson
A rarefaction wave, sometimes known as an expansion or relief wave, is the means by which nature handles a sudden drop in pressure. As we stated earlier, compression waves (also known as condensations) eventually coalesce into shocks that are analyzed as step discontinuities in pressure. This coalescence was brought about by the fact that the local velocity increases with increasing pressure. In a rarefaction, the opposite is true. A rarefaction increases over time because the pressure at the head of the wave is greater than that at the tail of the wave. In the case of our shock tube, the head of the rarefaction will propagate at the local speed of sound in the material (a4 in Figure 2.29), while the tail will propagate at a velocity (u3 ‑ a3) that is equal to (up ‑ a2). This is schematically depicted in Figure 2.32. Throughout the rarefaction wave, the velocity continuously decreases between these two values. Because of this continuous decrease in velocity, it is common to model the decrease as a series of wavelets. The more wavelets we include, the smoother the curve. If we use Figure 2.32 to trace a particle path after the bursting of the diaphragm, we see that the particle would not move until the head of the rarefaction wave passed by it. After the passage of the head of the wave, the velocity would continuously increase until the passage of the tail of the wave, after which it would be moving at velocity up. The length of the rarefaction can be determined at any time by scribing a horizontal line through the diagram. If we do this at two points in time on the diagram, we can see how the length of the wave increases.
The Riemann problem for a spray model
Published in Applicable Analysis, 2023
Mai Duc Thanh, Duong Xuan Vinh
Let us defined the following notations : i-wave from connect to . It can be i-shock wave () or i-rarefaction wave ().: an i-wave from to , followed by an j-wave from to .
Elucidating the mechanism of defect formation in the 7050-T7451 aluminum alloy by laser shock peening
Published in Waves in Random and Complex Media, 2022
Liangchen Ge, Haotian Chen, Guoran Hua, Boyuan Xu, Zongjun Tian
The 3000 MPa shock pressure with the largest stress–strain difference was selected for transient analysis, and the distribution of this stress–strain difference at different times (63, 68, and 80 ns) is shown in Figure 7. According to the stress distribution, the rarefaction wave was not formed at 63 ns, and the compressive stress on the surface of the alloy was the lowest at –6580.973 MPa. At 68 ns, the formed rarefaction wave caught up with the shock wave front. The rarefaction wave also caught up with the shock wave 99.96 µm from the alloy surface, where the stress difference was 2233.88 MPa. At 80 ns, the maximum compressive stress at 296.22 µm was –1653.09 MPa, and the minimum compressive stress of 368.093 MPa appeared on the surface of the alloy; the stress difference was reduced to 2021.183 MPa. According to the strain distribution, the rarefaction wave was not formed at 63 ns, and the compression strain was generated at the position where the shock wave front passed under the action of the elastic-plastic wave. At 68 ns, the surface compressive strain gradually decreased, with the maximum compressive strain of 24.52 µm appearing at 197.32 µm. The surface strain decreased even further at 80 ns to a maximum compressive strain of –20.89 µm at 296.22 µm. Because the strain rate of the material was less than the pulse width, there was a certain time difference between the strain change and the stress change. Therefore, the maximum stress–strain difference was obtained at 68 ns.
The limits of Riemann solutions to the relativistic van der Waals fluid
Published in Applicable Analysis, 2021
Thus, the first goal of this paper is to solve the Riemann problem for the relativistic van der Waals fluid (1), (2). According to the principle of special relativity, the velocity of relativistic fluid should be less than c, the speed of light. Thus, the physically relevant region of solution to the relativistic van der Waals fluid (1) and (2) in this paper is which is obviously quite different from that of the isothermal and polytropic gas. In the region , we consider the following Riemann initial data for (1) and (2), where and are arbitrary constants. In fact, the study of Riemann problem for relativistic flow plays a vital role in the field of mathematics and physics as well as in engineering. By means of the Lorentz transformation, the specific expression of the shock wave is formulated and the geometric properties of rarefaction wave and shock wave curves are analyzed. Then, by the method of analyzing in the phase plane, we establish the existence and uniqueness of Riemann solutions with five different structures. See Section 3 below.