Gas velocity vectors

In Fig 10.16 b) instantaneous fields of the dry H2 mole fraction and the gas velocity vectors after 10 seconds simulation time are shown. That is, the reactions were turned on 5 seconds after the flow was initiated. The hydrogen production is fast in the inlet zone and the hydrogen produced are transported toward the exit. 

Fig. 10.16. Simulation of a chemical reactive mixture, (a) Instantaneous fields of the solids volume fraction and the particle velocity vectors after 50 seconds, (b) Contour plot of an instantaneous dry H2 mole fraction field during start up of the process, 5 seconds after the reactants enter the column and 10 seconds after the start up of the flow. The consistent gas velocity vector field is given in the same plot.

The eddy diffusion term. A, describes the effect of peak broadening caused by the presence of particles in the column. It exists only for packed columns. Because of the particles, the molecules travel different paths thus their elution is carried out at different times, as illustrated in Figure 8.8. It depends on the particle diameter, sphericity, and how the column is packed. Eddy diffusion is independent of the gas velocity vector, HETP = A. The initial peak as it enters the column is narrow and taller. As it exits the column the peak becomes much broader and the height decreases. 

In Fig. 4.1 lb instantaneous fields of the dry H2 mole fraction and the gas velocity vectors after 10 s simulation time are shown. That is, the reactions were turned on 5 s after the flow was initiated. The hydrogen production is fast in the inlet zone and the hydrogen produced are transported toward the exit. It is also seen that the gas bubbles created in the bottom of the vessel have a tendency to move toward the center of the tube and rise at a radial position halfway between the wall and the center. These bubbles carry some of the solids in their wakes producing the solids circulation pattern seen in (a). There are no experimental data available for this process yet, so no firm validation has been performed. Nevertheless, the flow pattern is deemed to be reasonable and the chemical conversion is in fair agreement with those obtained in fixed bed simulations [125]. 

Now each such particle adds its change in momentum, as given above, to the total change of momentum of the gas in time t. The total change in momentum of the gas is obtained by multiplying Af by the change in momentum per particle and integratmg over all allowed values of tlie velocity vector, namely, those for which V n< 0. That is... 

Ocily n. - 1 of the n equations (4.1) are independent, since both sides vanish on suinming over r, so a further relation between the velocity vectors V is required. It is provided by the overall momentum balance for the mixture, and a well known result of dilute gas kinetic theory shows that this takes the form of the Navier-Stokes equation... 

Velocity vectors of the gas flow measured using laser Doppler anemometry inside a closed chamber during the formation of a tulip flame. Images of the flame are also shown, though the velocity measurements required many repeated runs, hence, the image is only representative. The chamber has square cross sections of 38.1mm on the side. The traces in the velocity fields are the flame locations based on velocity data dropout. The vorticity generated as the flame changes shape appears clearly in the velocity vectors. 

Transient computations of methane, ethane, and propane gas-jet diffusion flames in Ig and Oy have been performed using the numerical code developed by Katta [30,46], with a detailed reaction mechanism [47,48] (33 species and 112 elementary steps) for these fuels and a simple radiation heat-loss model [49], for the high fuel-flow condition. The results for methane and ethane can be obtained from earlier studies [44,45]. For propane. Figure 8.1.5 shows the calculated flame structure in Ig and Og. The variables on the right half include, velocity vectors (v), isotherms (T), total heat-release rate ( j), and the local equivalence ratio (( locai) while on the left half the total molar flux vectors of atomic hydrogen (M ), oxygen mole fraction oxygen consumption rate... 

The maj or limitation of the TAB model i s that it can only keep track of one oscillation mode, while in reality there are many oscillation modes. Thus, more accurately, the Taylor analogy should be between an oscillating droplet and a sequence of spring-mass systems, one for each mode of oscillations. The TAB model keeps track only of the fundamental mode corresponding to the lowest order spherical zonal harmonic 5541 whose axi s i s aligned with the relative velocity vector between the droplet and gas. Thi s is the longest-lived and therefore the most important mode of oscillations. Nevertheless, for large Weber numbers, other modes are certainly excited and contribute to droplet breakup. Despite this... 

Figure 5.4. Calculated gas velocity field near a close-coupled atomizer velocity vectors (right) and stream lines (left) (Atomization gas Ar, Ma = 1 at nozzle exit.). (Reprinted with permission from Ref. 325.)...

Figure 7. Velocity vectors and gas density contours under very low humidity operation (a) in the middle and (b) at the exit of a 10 cm PEFC. ...

Intermolecular collisions do not cause large deviations from the ideal gas law at STP for molecules such as N2 or He, which are well above their boiling points, but they do dramatically decrease the average distance molecules travel to a number which is far less than would be predicted from the average molecular speed. Collisions randomize the velocity vector many times in the nominal round trip time, leading to diffusional effects as discussed in Chapter 4. If all of the molecules start at time t = 0 at the position x = 0, the concentration distribution C(x,t) at later times is a Gaussian ... 

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