Gas speed

When the gas speed is sufficiently high, the separation factor corresponding to a given value of the cut is essentially independent of the gas velocity and, hence, at high speeds, is given (104) to a good approximation as... 

He considered that the rapid flame propagation could be achieved with the same mechanism as vortex breakdown. Figure 4.2.2 schematically shows his vortex bursting mechanism [4,5]. When a combustible mixture rotates, Ihe pressure on the axis of rotation becomes lower than the ambient pressure. The amount of pressure decrease is equal to max in Rankine s combined vor-fex, in which p denotes fhe unburned gas density and Vg denotes the maximum tangential velocity of the vortex. However, when combustion occurs, the pressure on the axis of rofafion increases in the burned gas owing to the decrease in the density, and becomes close to the ambient pressure. Thus, there appears a pressure jump AP across the flame on fhe axis of rotation. This pressure jump may cause a rapid movement of the hot burned gas. By considering the momentum flux conservation across the flame, fhe following expression for the burned gas speed was derived ... 

A choked flow takes place when the pressure ratio p2/Pi of gas through an orifice is very small. In the choked flow, the gas speed beyond the orifice is close to the sound velocity, and a change of p2 does not modify the flow rate. This regime finds application in the production of molecular beams. 

If the upstream pressure Pt is kept constant and the downstream pressure P2 is gradually reduced, the flow rate will gradually increase. However, as P2— 0 the density p—>0 and consequently the mass flow rate must approach zero if the gas speed u remains finite. Thus, at some value of P2 satisfying the condition 0mass flow rate must reach a maximum. 

A simple interpretation of this choking condition is as follows. The gas flows as a result of the pressure difference P — P2. When the gas speed reaches the speed at which a pressure wave propagates relative to the gas, any pressure wave generated will be unable to travel upstream but will remain stationary relative to the pipe. Thus, if the pressure in the reservoir into which the gas discharges is reduced below Pw, the fact cannot be transmitted upstream and so the flow rate will not change. 

Putting k = y in equation 6.75 gives the gas speed at the maximum flow rate as VyPWVW. That this is the correct result for adiabatic flow can be confirmed from equations 6.63 and 6.64. Differentiating equation 6.63 with respect to P2 gives... 

If the back pressure is reduced below P, there is no increase in the flow rate through the nozzle, ie the flow is choked. In a convergent nozzle it is impossible for the gas speed to exceed the speed of sound. This case is... 

Nitrogen contained in a large tank at a pressure P = 200000 Pa and a temperature of 300 K flows steadily under adiabatic conditions into a second tank through a converging nozzle with a throat diameter of 15 mm. The pressure in the second tank and at the throat of the nozzle is P, = 140000 Pa. Calculate the mass flow rate, M, of nitrogen assuming frictionless flow and ideal gas behaviour. Also calculate the gas speed at the nozzle and establish that the flow is subsonic. The relative molecular mass of nitrogen is 28.02 and the ratio of the specific heat capacities y is 1.39. 

Thus, the gas speed at the throat is less than the sonic speed there. The flow is subsonic throughout the nozzle. This result is to be expected because the pressure ratio is 0.7 and the critical pressure ratio (for y = 1.39) is 0.53. 

Under these conditions, the gas speed is the sonic speed c and the pressure wave may be assumed to propagate at the sonic speed so that equation 10.41 can be written as... 

Assumption (2) is justified by the high electrical conductivity of the current collectors, compared to those of the electrodes. Assumption (3) derives from the low gas speed in the SOFC gas channels, where the density variation is not related to com-pressions/expansions [6], Assumption (4) is introduced because in anode-supported SOFCs, radiative heat transfer can be neglected compared to convective heat transfer phenomena [7, 8], Finally, assumption (5) is made for simplicity considering the high electronic conductivity of the electrode, compared to the ionic conductivity, which reduces the ability of oxygen ions to migrate through the electrodes. 

The boundary conditions presented in this section are those representing an experimental campaign performed on a single cell. These external boundary conditions for voltage, temperature, species concentration and gas speed are defined as follows ... 

Fig. 4.30 In contrast to the (non-reac-tive) Taylor model, the tracer gas speed for a reacting gas is unequal to the carrier gas speed. This can be derived from the exponential term in the solution of the concentration of the tracer gas cA at the channel exit.

The vent opening should be as large as possible in order to avoid high gas speeds, which can lead to product being drawn into the vent. In practice, three vent inserts are used to ensure effective devolatilization on the one hand and to prevent product from discharging into the vent on the other hand (see Fig. 4.15) ... 

A smaller inner diameter (e.g., 0.1 mm) can also be used, but with the inconvenience of limiting the work to more diluted samples in order to avoid column overload. On the other hand, this type of column permits carrier gas speeds higher than with columns of inner diameters in the range 0.2-0.3 mm. Columns with inner diameters equal to 0.1 mm exhibit fewer plates with the increment of the carrier gas speed, in contrast to the columns with equivalent characteristics, but of... 

In this part, the results of the simulation of the leakage are presented for a pipe which of 250 meter in length and with a hole (orifice) of 1 cm2 area on the surface, by using a grid system with 100 nodes. It is also considered that the hole is in the middle of the pipe length and it is assumed that the initial gas pressure and initial gas speed are 30 bar and 41 ft/s, respectively [4], It is considered that the upstream boundary condition is the reservoir with constant pressure and the downstream boundary condition is stated with three forms ... 

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