Effect on step response of various annular fills
As demonstrated, reducing the annular clearance from 0.040 to 0.005 inch reduces the major time constant by almost a factor of 6, even though the mass of the thermowell is increased. Comparative step responses are shown in Figure 11.23.
Example 2: Liquid Flow. Next let us consider flow of an organic liquid. Thermowell has a 0.525-inch OD by 0.260-inch ID. The pencil-type thermocouple has a 0.250-inch OD. Let us look first at the effect of different liquid-flow velocities.
ft/sec ft/sec ft/sec ft/sec t„, sec 25.3 26.3 31.6 61.5
In this particular case, the major time constant changed very little until velocity became very small. Comparative step responses are shown in Figure 11.24. If the thermocouple had been used bare in the first case (10 ft/sec), a single time constant of 0.52 second would have been obtained.
Next let us consider the effect of different annular fills: air, oil, and mercury, all for 10-ft/sec velocity.
AIR OIL MERCURY
For oil the value of thermal conductivity used was 0.079 fi^oQ*^- Step responses are plotted in Figure 11.25.
Consider next the effect of varying thermowell internal diameter while holding the external diameter constant. Again, in this example velocity was maintained at 10 ft/sec and annular fill was air.
0.055 inch 0.005 inch 0.0005 inch t„, sec 228 25.3 3.8
Step responses are given in Figure 11.26.
For large-scale processes, one often hears the arguments that fast temperature measurement is not important because large distillation columns, heat exchangers, and so on are slow. In reality the size of such equipment has little to do with its dynamics, which are determined mostly by the service. For instance, reboilers are very fast, condensers a little less so, liquid—liquid heat exchangers slower yet, and gas—gas exchangers slowest of all—but we frequently find cases in which temperature measurement provides the major lag or lags in a control loop.
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