Velocity detachment

The detached section of ions sets off along the TOP analyzer, with the ions having velocities proportional to the square roots of their m/z values. 

Based on 23 data points for 3 systems. Average absolute deviation 26%. Use with surface area of drop after detachment occurs, = velocity through nozzle <3 = iuterfacial tension. 

After detachment of the flame from the walls, the narrow ever-diminishing hot product zone behind the flame moves owing to the free convection in the centrifugal acceleration field toward the axis of rotation, with a speed scaling with circumferential velocity at the flame location, which reduces the observed flame speed to very low values, and in some cases negative ones. 

In Chapter 6.4, J. Chomiak and J. Jarosinski discuss the mechanism of flame propagation and quenching in a rofating cylindrical vessel. They explain the observed phenomenon of quenching in ferms of the formation of fhe so-called Ekman layers, which are responsible for the detachment of flames from the walls and the reduction of fheir width. Reduction of the flame speed with increasing angular velocity of rofation is explained in terms of free convection effects driven by centrifugal acceleration. 

We are currently working on detached systems in the old open clusters NGC 2243, NGC 188 and NGC 6791. Presently we have the most complete and best data available for NGC 188 (see Fig. 1 and caption for more details) and NGC 2243. In both clusters the detached system is located close to the cluster turnoff and consists of two quite similar stars. In NGC 6791 we were able to determine the period for the system called V20 [1] and have subsequently obtained photometry for this system covering both eclipses. Due to the faintness (V = 17.34) we have not yet obtained radial velocities for the system which is comprised of a star very close to the cluster turnoff and a main-sequence star approximately 2.2 magnitudes (V) fainter. 

Fig. 1. The color-magnitude diagram of NGC 188 from [2] with the location of the detached eclipsing binary V12 [3] overplotted. From radial-velocity measurements we find (assuming an inclination of 90 degrees since we do not yet have photometry of the eclipses) that the masses of the two components are 1.06 and 1.08 solar masses. We estimate that we will be able to reach a precision of 1% in the mass estimate. We are in the process of acquiring eclipse photometry such that the radii and orbital inclination can be determined. Since both components are very close to the cluster turnoff their masses and radii can be directly used to give a very accurate age estimate for the cluster by comparing to isochrones in the (mass, radius) plane and requiring that they both lie on the same isochrone.

Fig. 5 shows the simulated air-bubble formation and rising behavior in water. For the first three bubbles, the formation process is characterized by three distinct stages of expansion, detachment, and deformation. In comparison with the bubble formation in the air-hydrocarbon fluid (Paratherm) system, the coalescence of the first two bubbles occurs much earlier in the air-water system. Note that the physical properties of the Paratherm are p — 870kg/m3, Pi — 0.032 Pa - s, and a — 0.029 N/m at 25 °C and 0.1 MPa. This is due to the fact that, compared to that in the air-Paratherm system, the first bubble in the air-water system is much larger in size and hence higher in rise velocity leading... 

The actual construction details of blowout panels is beyond the scope of the text. A detached blowout panel moving at high velocity can cause considerable damage. Therefore a mechanism must be provided to retain the panel during the deflagration process. Furthermore, thermal insulation of panels is also required. Construction details are available in manufacturers literature. 

Taylod205 also conducted mathematical analysis of the generation of ripples by wind blowing over a viscous fluid. Using a relationship between the growth of the amplitude of disturbance waves and the surface stress, Taylor derived a criterion for the instability of waves. In Taylor s instability theory, the disintegration of a liquid sheet/film is visualized as a process in which droplets are detached from the liquid surface with a wave of optimum amplitude. The diameter of the most frequent droplets is then formulated as a function of air velocity over the liquid surface, liquid density, surface tension and viscosity, as well as air density. 

The mechanical breakup mode occurs around the rims of the sheet where the air-liquid relative velocity is low, forming relatively large droplets. At low relative velocities, aerodynamic forces are much smaller than surface tension and inertia forces. Thus, the breakup of the liquid rims is purely mechanical and follows the Rayleigh mechanism for liquid column/jet breakup. For the same air pressure, the droplets detached from the rims become smaller as the liquid flow rate is increased. 

The equation of motion is more useful in the above form when expressed in terms of v, the velocity of the base, because the condition of detachment pertains to the bubble base and not to the bubble center. Equation (25) can be written as... 

Depending on its subtraction from or addition to the buoyancy force, the continuous phase velocity can either increase or decrease the bubble volume. Normally, this velocity is such that the bubble detaches prematurely from the nozzle tip. Maier (M2) has shown that the shear force experienced by the bubble, which causes its premature detachment, is a maximum when the continuous phase flows at right angles to the nozzle axis. 

The model is based on the assumption that the drop detachment does not take place until the velocity v of the drop is larger than the velocity of the dispersed phase in the nozzle, and also until the buoyancy force equals the force due to interfacial tension. 

When the static drop stage is passed, the drop starts rising with varying velocity, but still maintaining its connection with the nozzle through a neck. As further liquid is pumped into the drop during the time of detachment tc also, the final drop volume becomes... 

At vanishingly small flow rates, the drops get detached at the nozzle tip. As the flow rate is increased, the jetting point is reached where a very short continuous neck of liquid exists between the nozzle tip and the point of detachment. Further increase in the flow rate lengthens the jet, whereas still further increase to the critical velocity gives the jet a ruffled appearance. Beyond this region, the jet recedes to the nozzle tip. 

At low flow velocity of the dispersed phase, the interfacial tension does not influence the droplet diameter but it affects the time-scale parameters for droplet formation [35-37] the detachment time becomes shorter at high interfacial tension (low surfactant concentration) [38]. 

Figure 19.3 Influence of equivalence ratio on antinodal RMS pressure fluctuation annular flow arrangement, bulk mean velocity in main flow, Um = 7-5 m/s bulk mean velocity in pilot stream. Up = 8 m/s Re j = UmD/v = 40,000, axial separation between annular ring and step, A = 0.513. 1 — 4 m = 0.62 2 — 0.70 3 — 0.76 dashed line corresponds to flame detachment...

---