Transient pressure profiles

Figure 13. Experimental and model transient pressure profiles. Model results are shown with solid lines. Experimental data points (symbols) are connected by dashed lines.

Fig. 2.2 Radius and pressure profiles in the case of Transient Cavitation (Typical profile at frequency of irradiation = 20 kHz, Intensity of irradiation = 0.12 W/m2 and initial radius of the nuclei = 0.001 mm)...

The core is initially completely saturated with aqueous foamer solution with rock adsorption satisfied. Nitrogen and aqueous surfactant solution are then injected at fixed flow rates until steady state is achieved. Transient pressure and aqueous saturation profiles are monitored for a wide range of gas and liquid flows. Only one transient foam displacement is reported here. Additional results are available elsewhere (78-80). 

Only the case of steady coinjection of surfactant solution and gas into a one-dimensional core initially filled with surfactant solution is addressed. Calculated transient foam displacement well represents both the measured wetting liquid saturations and pressure profiles with physically meaningful parameter values. It is predicted and experimentally verified that foam moves in a piston-like fashion through a linear porous medium presaturated with surfactant solution. Moreover, the proposed population-balance predicts the entire spectrum of unique steady foam-flow behavior in the capillary-pressure regime. 

Fig. 17 Transient concentration profiles in y-direction (i.e., along 8-ring channels) measured by interference microscopy for a adsorption and b desorption of methanol in a large crystal of ferrierite for pressure steps 5 -> 10 and 10 5 mbar. The form of the profiles shows that both surface resistance and internal diffusion (along the 8-ring chan-...

The two-phase mixture consisting of diluted (85%) glycerine and of bubbles with radii of Rq= 1.4 and 1.8 cm, respectively, containing a gas mixture of 70%Ar + 30%< 2H2+O2) r was investigated in a vertical shock tube [2,3,8 3. Pressure gauges, equally spaced along the two-phase part of the shock tube, were used to record the pressure profiles which were stored in transient recorders. To reduce scatter, profiles from repeated shots were superimposed. 

Milton et al. (1997) proposed the manometric temperature measurement (MTM) the transient pressure response is mathematically modeled under the assumption that four mechanisms contribute to the pressure rise, namely the direct sublimation of ice through the dried product layer at a constant temperature, the increase in the ice temperature due to continuous heating of the frozen matrix during the measurement, the increase in the temperature at the sublimation interface when a stationary temperature profile is obtained in the frozen layer and, finally, the leaks in the chamber. The four contributions are considered purely additive the values of the thickness and of the thermal gradient are needed but they are not known exactly. The values of the vapor pressure over ice, of the product resistance and the heat transfer coefficient at the vial bottom are determined with regression analysis. 

Conduct steady-state and/or transient study simulations to generate the pressure profile... 

It has been shown that an energy equation can be successfully incorporated into the EHL solver of [14] to obtain mean and surface temperature solutions for both steady state and transient cases. The importance of shear in an EHL contact has also been demonstrated with even small amounts of shear producing temperatures far in excess of those found within the contact under pure rolling conditions. This increase in temperature can also be seen to influence the spike in the pressure profile. 

FIGU RE 7.21 Steady-state simulated partial pressure profiles of gaseous compouuds along the reactor and transient temperature profiles in the commercial reactor at different bed positions. 

Transient cavitation is generally due to gaseous or vapor filled cavities, which are believed to be produced at ultrasonic intensity greater than 10 W/cm2. Transient cavitation involves larger variation in the bubble sizes (maximum size reached by the cavity is few hundred times the initial size) over a time scale of few acoustic cycles. The life time of transient bubble is too small for any mass to flow by diffusion of the gas into or out of the bubble however evaporation and condensation of liquid within the cavity can take place freely. Hence, as there is no gas to act as cushion, the collapse is violent. Bubble dynamics analysis can be easily used to understand whether transient cavitation can occur for a particular set of operating conditions. A typical bubble dynamics profile for the case of transient cavitation has been given in Fig. 2.2. By assuming adiabatic collapse of bubble, the maximum temperature and pressure reached after the collapse can be estimated as follows [2]. 

The bubble formed in stable cavitation contains gas (and very small amount of vapor) at ultrasonic intensity in the range of 1-3 W/cm2. Stable cavitation involves formation of smaller bubbles with non linear oscillations over many acoustic cycles. The typical bubble dynamics profile for the case of stable cavitation has been shown in Fig. 2.3. The phenomenon of growth of bubbles in stable cavitation is due to rectified diffusion [4] where, influx of gas during the rarefaction is higher than the flux of gas going out during compression. The temperature and pressure generated in this type of cavitation is lower as compared to transient cavitation and can be estimated as ... 

In some cases pulse-radiolysis techniques were employed to study the effect of pressure on inorganic reactions. For instance the oxidation of [CuI(phen)2] by dioxygen via the formation of a C -C transient species was studied using this technique (see Section III,A). Other examples include the formation and cleavage of metal-carbon (7-bonds, which formally involve a change in the oxidation state of the metal. A typical example of a volume profile for the formation and cleavage of a Co-CH3 bond is reported in Fig. 21 for the reaction (162)... 

Consider a long circular duct in which an incompressible, constant-property fluid is initially at rest. Suddenly a constant pressure gradient is imposed. The axial momentum equation that describes the transient response of the velocity profile for this situation is... 

Fig. 4.9 Transient nondimensional axial velocity profiles in a long circular duct, responding to a suddenly imposed pressure gradient. The fluid is initially at rest.

The basic mathematical method for power spectrum analysis is the Fourier transformation. By the way. transient fluctuation can be expressed as the sum of the number of simple harmonic waves, which is helpful for understanding fluctuation. A frequency spectrum analysis for pressure signals can yield a profile of the frequencies and that of the amplitude along the frequencies. The basic equation of Fourier transformation can be expressed as... 

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