The right response

Ian Henry of AJ Thermosensors looks at the effect of sensor response time on the accuracy and performance of temperature critical processes.

The measurement of temperature in most industrial processes relies on a temperature sensitive device such as a thermocouple or resistance thermometer placed in the process, usually in a fluid. Sensors might be fitted through the wall of a liquid filled pipe or through the side of a furnace into the gas or air atmosphere inside.

Where temperatures are reasonably constant, or change only slowly, the sensor can be assumed to be at the same temperature as the fluid surrounding it in almost all cases. However, if the sensor is not permanently in the process, but inserted manually when required, or when temperatures change rapidly, this assumption can lead to serious errors.

TIME AND TEMPERATURE

Consider the response of a temperature over time to a step change in temperature. Where the temperature itself steps up, the sensor’s response is an exponential curve up to the new temperature. There are two main factors to consider – one is the shape of the curve and the other is the overall response time compared to the rate of change of the temperature that is to be measured.

The shape of the curve is a function of fundamental thermodynamics and therefore not something that can be easily influenced. Since heat flow is proportional to temperature difference, the rate of heat flow and therefore the rate of sensor temperature rise falls rapidly as the aiming point is approached.

In practice the result is not actually a true exponential because the temperature under measurement never undergoes a true step function, but to a first approximation the error after a given number of time constants is given by e-x, where x is the number of time constants.

In terms of a given application with perhaps a 1000 degrees C process temperature step change, the error will still be 18 degrees C after four time constants, and six time constants have to elapse before the error is within 3 degrees C.

The second factor, the actual time involved, is a function of the thermal mass of the sensor, the thermal mass of the medium and the conductivity between the two.

To illustrate the point, consider placing a heavy duty industrial thermosensor housed in a rugged stainless steel pocket in a refrigerator for a couple of hours and then bringing it into a room. Clearly, it would then take a long time to accurately measure room temperature.

To make a more meaningful assessment, the factors involved in the actual heat transfer from the surrounding medium to the sensor need to be examined. In the extreme example above, the thermal mass of the sensor is large; hence, a large amount of energy is needed to raise its temperature. The thermal mass of the medium, in this case air, is low and the conductivity between the two is low as well because still air is a poor conductor of heat.

To improve the situation, the thermal mass of the sensor could be reduced, or the thermal mass of the medium and the conductivity between the two could be increased.

To effect these changes, the sensor could be removed from its protective stainless steel pocket. In addition, a fan could be used to move air over the sensor, increasing heat transfer. Also, placing the sensor into water at room temperature could speed things up substantially because water has a higher thermal mass. Then, however, it has to be ensured that the water is really at room temperature.

Some of the most common methods of affecting sensor speed are shown in Table 1. Taking the sensor out of its protective pocket highlights the most commonly encountered trade off – speed versus ruggedness. The golden rule is that to increase the speed of the sensor, the thermal mass must be kept down. Regrettably, this will reduce the strength of the sensor too.

If the process is steady state, or changes very slowly, and the sensor is permanently installed, then response speed should not be an issue. If, on the other hand, the temperature to be measured is in a vacuum or the temperature changes faster than 5 degrees C per minute in gas or 50 degrees C per minute in a liquid such as water, or if the sensor is not permanently installed, then sensor response speed does need to be considered.

To decide on a suitable response speed, the rule of thumb shown above can be used. It should contain response lag errors to around 1%, but must be applied with caution because there are many variables to consider.

Having applied the rule of thumb, it is important to find a sensor with the appropriate time constant. Table 2 gives some typical ranges for commonly encountered sensor types. Obviously, without specifying precise dimensions and materials, the figures are of necessity a wide range, but are useful to narrow the choice.

Manufacturers should be able to provide more details of performance for mass produced sensors. However, it is worth bearing in mind that many sensors are custom made, and short of making one and testing it, makers may have no means to provide you with the information you need.

Checking out sensor speed

Using the rule of thumb below can help decide on a suitable response speed for a sensor:

TCs <=TP10 x Eacc x6

where TCs is the required sensor time constant (in a representative medium), TP10 is the shortest time in seconds for the process temperature to change by 10% of its range and Eacc is the acceptable error. As an example, we could consider a stirred reaction vessel filled with process fluids at different temperatures. Suppose that it is important to control the cooling water jacket to prevent an exothermic reaction from running away. Suppose also that temperature change of over 100 degrees C/min is encountered when the vessel is charged rapidly with volumes of liquid at different temperatures. Instantaneous measurement error should be no more than 1% of the 200 degrees C range. Thus, TP10 is 12 seconds, Ecc is 0.05. Then TCs must be less than 3.6secs in stirred water.

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