Optimum velocity ratio

Figure 4-116. Optimum velocity ratio for expander stage.

Figure 4-110 depicts an efficiency curve versus velocity ratio for a reaction-type expander. The optimum efficiency will occur at a velocity ratio of. 63. For a velocity ratio considerable greater or less than. 63 a significant efficiency penalty can be expected. Considering the effects on the parameters mentioned above, it is easy to see the importance the velocity ratio has on the performance of the expander. 

As mentioned earlier, because the number of stages has a significant effect in determining the velocity ratio, consider the effect the gas conditions have in determining tlie optimum number of stages. To make this determination, the following parameters should be considered ... 

Equation (13) is the first important equation for open tubular column design. It is seen that the optimum radius, with which the column will operate at the optimum velocity for the given inlet pressure, increases rapidly as an inverse function of the separation ratio (cc-1) and inversely as the square root of the inlet pressure. Again it must be remembered that, when calculating (ropt)5 the dimensions of the applied pressure (P) must be appropriate for the dimensions in which the viscosity (r)) is measured. 

Table 1, values for the optimum velocity can be calculated for different values of the separation ratio of the critical pair. The results are shown in Figure 3. 

Figure 3. Graph of Optimum Velocity against Separation Ratio of the Critical Pair...

Although the optimum column radius increases linearly with the separation ratio of the critical pair, this simple relationship is moderated by the ratio of the square of the optimum radius to the optimum velocity, both of which are functions of (a). 

As the optimum column radius is inversely proportional to (a-1), and (uopt) is inversely proportional to (ropt)> the simple linear relationship between optimum velocity and the separation ratio is to be expected. The high velocities employed for... 

The optimum velocity changes linearly from about 1 cm/sec. to 800 cm/sec. and the minimum plate height from 200 pm to about 10 pm over the same separation ratio... 

The observations that the thrust coefficient has its maximum value near the stoichiometric mixture ratio, see figure V. A. 6.,is consistent with the foregoing expectations. Since specific impulse is proportional to the product of the characteristic velocity and the thrust coefficient, it is expected and observed that the optimum mixture ratio in terms of the specific impulse should fall between the optimum mixture ratios for the characteristic velocity and for the thrust coefficient. It is noted that the characteristic velocity is the dominant member of the pair, a property which adds further to the utility of the characteristic velocity as a performance parameter to rocket propulsion development. 

The approximate efficiency of a capillary column operated at its optimum velocity (assuming the inlet/outlet pressure ratio is small) is given by the Golay equation. 

The simplification is a result of the assumption that the coefficients of axial dispersion and of mass transfer kinetics are equal for the two components. The ratio of the two optimum velocities is... 

It is clear that the major factor controlling the particle diameter will be the separation ratio (a), which reflects the difficulty of the separation. The more difficult the separation, the more theoretical plates are needed, and thus the column must be longer. However, to use a longer column, the particle diameter must be increased to allow the optimum velocity to be realized without exceeding the maximum system pressure. The effect of the capacity ratio of the first solute of the critical pair on the optimum particle diameter is complex. Extracting the function of the capacity ratio (f(k )) from equation (1),... 

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