Standing wave design

Mallmann, T., Burris, B., Ma, Z., Wang, N.-H. Standing wave design for nonlinear SMB systems for fructose purification, AIChE/., 1998, 44, 2628-2646. 

Ma and Wang [32] proposed a new approach which they called the Standing Wave Design (SWD) for the optimization of the experimental conditions of the SMB separation of a binary mixture, using an SMB system for which they assume a linear... 

Valid for standing wave design Cq discharge coefficient of the nozzle... 

The maximum pressure from an explosion of a hydrocarbon and air is 7 x initial pressure, unless it occurs in a long pipe where a standing wave can be set up. It may be cheaper to design some small vessels to withstand an explosion than to provide a safety relief system. It is typical to specify %" as minimum plate thickness (for carbon steel only). 

To minimize pipe vibrations it is necessary to design pipe runs so that the "acoustic length of the pipe run does not create a standing wave that... 

Fig. 13.21 shows another example of oscillatory burning of an RDX-AP composite propellant containing 0.40% A1 particles. The combustion pressure chosen for the burning was 4.5 MPa. The DC component trace indicates that the onset of the instability is 0.31 s after ignition, and that the instability lasts for 0.67 s. The pressure instability then suddenly ceases and the pressure returns to the designed pressure of 4.5 MPa. Close examination of the anomalous bandpass-filtered pressure traces reveals that the excited frequencies in the circular port are between 10 kHz and 30 kHz. The AC components below 10 kHz and above 30 kHz are not excited, as shown in Fig. 13.21. The frequency spectrum of the observed combustion instability is shown in Fig. 13.22. Here, the calculated frequency of the standing waves in the rocket motor is shown as a function of the inner diameter of the port and frequency. The sonic speed is assumed to be 1000 m s and I = 0.25 m. The most excited frequency is 25 kHz, followed by 18 kHz and 32 kHz. When the observed frequencies are compared with the calculated acoustic frequencies shown in Fig. 13.23, the dominant frequency is seen to be that of the first radial mode, with possible inclusion of the second and third tangential modes. The increased DC pressure between 0.31 s and 0.67 s is considered to be caused by a velocity-coupled oscillatory combustion. Such a velocity-coupled oscillation tends to induce erosive burning along the port surface. The maximum amplitude of the AC component pressure is 3.67 MPa between 20 kHz and 30 kHz. - ...

Another interesting effect that plays a role in the design of the proper housing for QCM in liquid is the generation of compressional standing waves. This can be observed when the crystal oscillates in parallel with a vessel wall in close proximity, which acts as a reflector (Fig. 4.10 Janshoff et al., 2000 Schneider and Martin, 1995). The effect can be observed over the distance of the reflector surface (e.g., 100pm Lin and Ward, 1995 Schneider and Martin, 1995). 

The design of the assembly is shown in Fig. 12.19. The quartz wafer is sandwiched between two electrodes that apply an oscillating electric field, resulting in a standing wave within the wafer and in mechanical oscillation at resonant frequencies, generally in the range from 2 MHz to 20 MHz. A wafer of thickness 320 jum oscillates at around 5 MHz. At this... 

The cavity supports an infinite number of standing wave patterns, called modes, which are designated TEMnpq, where n, p and q are integers. The microwave electric field distribution can be calculated for any mode, from a formula given by Balle and Flygare [14]. However, the dominant modes are those of the type TEM0oq and for these the resonant frequencies are... 

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