Velocity pressure amplitude

The most important parameter in the analysis of pressure-coupled combustion instability is the acoustic admittance Y, which is the ratio of the amplitude of the acoustic velocity V to the amplitude of the acoustic pressure amplitude of the acoustic velocity V to the amplitude of the acoustic pressure P ... 

These reflection and transmission coefficients relate the pressure amplitude in the reflected wave, and the amplitude of the appropriate stress component in each transmitted wave, to the pressure amplitude in the incident wave. The pressure amplitude in the incident wave is a natural parameter to work with, because it is a scalar quantity, whereas the displacement amplitude is a vector. The displacement amplitude reflection coefficient has the opposite sign to (6.90) or (6.94) the displacement amplitude transmission coefficients can be obtained from (6.91) and (6.92) by dividing by the appropriate longitudinal or shear impedance in the solid and multiplying by the impedance in the fluid. The impedances actually relate force per unit area to displacement velocity, but displacement velocity is related to displacement by a factor to which is the same for each of the incident, reflected, and transmitted waves, and so it all comes to the same thing in the end. In some mathematical texts the reflection... 

The character of the solution is independent of the concrete form of the pressure decrease law at the piston it(t), described by the dimensionless function f(t/r), only if / decreases fast enough for large values of t/r. In particular, it is unimportant whether / increases continuously or discon-tinuously at t < r. Even for a continuous increase of the gas pressure, a shock wave will form with a pressure amplitude of the order of the maximum pressure P at the piston. The shock wave velocity here is of order D yjP/p0, so that some small mass of gas, of order Dp0r r is subjected to a shock compression of amplitude P. After the pressure at the piston goes to zero this gas, extending into the vacuum, attains a velocity of order u0 y/P/p0, and at the time t it will be located at a point x — u0t tyfP/p0. So, for example, if f(t/r) = 1 at 0 < t < t/r < 1 and... 

These probes can be used to measure the pressure amplitude in the system [19]. In principle the local acoustic power can be obtained by measuring the pressure amplitude P, the velocity v of an imaginary particle submitted to the field, and their... 

The second factor, as mentioned in the previous section, refers to the propagation pattern of the flame front. In the model experiments, due to the geometry applied, the pressure waves propagated as planar waves which induce the highest related pressure amplitudes. In real structures, two- or three-dimensional flame fronts will occur, with lower pressure peak values at the same flame propagation velocities. 

Node A point or region in a standing wave in which a given characteristic of the wave motion, such as particle velocity or displacement, or pressure amplitude, has a minimum or zero value. 

Fig. 5.11 Relative pressure amplitude P IPq and combustion wave velocity of H2 + O2 mixtures in the obstructed tube versus the equivalence ratio (j)...

Some of the data obtained in the tube stuffed with 19-mm diameter steel spheres [12,18] are presented in Fig. 5.11. Curves 1, 2, 3 and 4 denote the process velocity at initial pressures of Fo = 0.1,0.2,0.5 and 0.9 MPa, curves 5,6,7 and 8 are relative pressure amplitude Pi/Po at the same Pq values. Obstacles installed in the tube do not interrupt the detonation process when the initial pressure is 0.5 MPa, however the velocity and the pressure of the process is slightly lower that those in the unobstructed tube. It is typical, in the obstructed tube, that the detonation pressure is independent of mixture composition over a wide range. 

With these governing equations and boundary conditions in place, and if the input pressure distribution that drives the flow field is known, it is possible to develop a formal solution for the axial velocity. For an oscillatory flow, the input pressure would normally be expected to be of a sinusoidal form P(x,r,t) = const e (o. Following Reference 29, the method of characteristics shows the pressure distribution throughout the tube to be P x,r,t) = A x,r)e where c is the wave speed in the fluid and A is the pressure amplitude. Since the fluid must be taken to be viscous, c is not equal to Cq, the inviscid fluid wave speed. Instead, c = Cq (2/(1 - with z a parameter of the problem that depends on a, (O, v, a,... 

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. 

McQueen et al. (1982) demonstrated that by placing a series of high-impedance transparent fluids (called optical analyzers) over the sample at a series of thicknesses less than d in the target that the overtaking rarefaction (sound) velocity can be accurately obtained. Arrival of rarefaction waves rapidly reduce the shock pressure. These wave arrivals could be very readily detected by the change in light radiance caused by the onset of a decrease in shock amplitude when the rarefaction wave caught up to the shock front. The... 

For the average pressure wave velocity in the pipe, compute the distance at which the amplitude falls to 1/e of its original value, the distance at which it falls at one-half of its original value (half depth) and the attenuation in dB/1,000 ft. Compute also the amplitude at surface. Bottomhole amplitude peak to peak 200 psi frequencies 0.2, 12 and 24 Hz. 

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