Conduction and Temperature Measurement Errors
Thermocouples are widely used for temperature measurements; therefore, the thermocouple will be used as the temperature sensor for this discussion. However, these comments apply to almost any other temperature-measuring device such as RTDs, glass thermometers, bimetallic thermometers, liquid-filled sensors and thermistors. So that we all are on the same page, some basic conditions must be noted before getting into the details of the conduction problem.
- Heat always flows from the hotter medium to the cooler medium.
- A contact measurement device will always indicate its own temperature as it is effected by the conditions to which the sensor is subjected.
- Isotherms (areas of constant temperature) exist in all situations, including gases, liquids and solids.
- With respect to conduction, there is no heat flow between two points of interest if both are at the same temperature and the temperature between them is equal to both.
- Inserting sensors across multiple isotherms creates paths for heat transfer and opportunity for large conduction errors unless certain precautions are observed.
- An accurate temperature does not only mean that the temperature indicated is the correct temperature. It also means that the changes in temperature indicated accurately reflect the actual temperature changes that are occurring.
There are two distinct areas of temperature measurements that need to be addressed separately because each has its own unique characteristics. These are solid walls and gases/liquids.
Solid WallsFor walls (solids), there typically are three temperatures that can be measured:
- The inside-wall surface temperature.
- A given point within a wall (or solid).
- The exterior-wall surface temperature.
Inside-Wall Surface Temperature. When locating the sensor to measure an inside-wall surface temperature, the sensor must be aligned flush with the inside surface. The body of the sensor must have the same thermal properties (thermal diffusivity and conduction) as that of the wall itself in order to not change the temperature of the wall simply due to its presence. This can be accomplished by using a two-dimensional surface thermocouple that has the same thermal properties as that of the test wall (figure 1).
This design uses standard alloy thermocouple elements. However, in the vicinity of the hot measuring junction, the sensing tip details are unique (figure 2). The round wires of the dissimilar metals are ground or formed into thin ribbons of about 0.002" thick. These ribbon elements are electrically insulated from each other and the body of the sensor by sheets of high temperature dielectric insulation of about 0.0002" thick. This sandwich of ribbon elements and high temperature dielectric insulation then is placed between an insert and pressed into a mating hole in the sensor housing.
The excess material is then machined off and the surface of the thermowell is polished with an abrasive cloth until smooth. The process of grinding and polishing the surface forms the hot measuring junction automatically. The high temperature dielectric insulation between the two dissimilar ribbons is so thin that metallic whiskers of one ribbon element bridge across the high temperature dielectric and make hundreds of microscopic friction welded junctions that are parallel to one another, thus forming one composite measuring junction. The junction is formed only on the surface because this is the only place the high temperature dielectric insulation is removed by the sanding operation. Any subsequent erosion of the surface of the thermowell (grinding, flowing gases, plastic, etc.) simply forms new junctions while removing the old junctions. Additionally, the sensing tip can be machined to match most any contour of this interior wall. This self-renewing thermocouple then meets the criteria of having the thermal junction exactly located at the inside surface of the wall.
In a series of controlled tests1, a number of self-renewing thermocouples were used to measure the surface temperature of a phenolic-lined rocket nozzle. All thermocouples were constructed identically except the material of the thermocouple body (thermowell) was varied. Figure 4 shows graphically the results of one test using phenolic and molybdenum thermowells.
Seven seconds after the test began, the two sensors differed by about 2,000oF (1,080oC). Even after 18 sec, they still differed by more than 1,000oF (535oC). Repeated tests produced similar results. Other materials such as stainless steel, tantalum and graphite also were used. In general, the recorded surface temperatures were inversely proportional to the thermal properties of the thermowells. The true surface temperature of the nozzle was that obtained by the thermocouple with a phenolic thermowell because the actual test wall (rocket nozzle) and the thermocouple housing were made from the same material.
A Given Point Within a Wall. This can be measured with the same thermocouple as used for the inside-wall surface temperature. When installing the thermocouple into a blind hole, the sensing tip of the sensor must make good thermal contact with the bottom of the blind hole. This can be accomplished by adding some thermal contact cement to the sensor tip, minimizing temperature discontinuities that may exist because of poor thermal contact. Remember that the sensor will indicate its own temperature.
Exterior Wall Surface. This temperature can be measure accurately with an intrinsic-type thermocouple2 (figure 5). This sensor consists of two ribbon-type thermocouple elements spot-welded or electrically attached to the exterior surface of the wall in proximity of the area of interest. The law of intermediate metals says that a third alloy can be introduced into a thermocouple circuit and create no error as long as the third metal is introduced into both the positive (+) and negative (-) circuits, and the area where applied is of equal temperature. Therefore, by using the metal wall surface as the third metal, and by attaching the individual thermocouple circuits (legs) to the wall, an intrinsic junction is formed. The thermocouple output signal will be that of the average temperature across this intrinsic junction. It is best to keep the two thermocouple wire/circuit connections within very close proximity, therefore minimizing the area of which the temperature is averaged.
Measuring Gases And LiquidsWhen measuring gases and liquids, the sensor must sense the temperature of the gas without disturbing the temperature by its very existence. This can be accomplished by designing the sensing tip to offset conduction errors. Ideally, the sensor must be installed parallel to the isotherms for a distance of at least 20 times the diameter of the sensor. Thus, a 0.25" dia. sensor must be installed for a length of 5" parallel to the isotherms to reduce the conduction error caused by the stem of the sensor. In many applications such as pipelines and furnaces, this is sometimes difficult to accomplish. Figure 6 illustrates the correct and incorrect installations one must consider when adhering to this rule of 20 times sheath diameter insertion with respect to the isotherms in a common furnace configuration.
Many unique designs are possible with a right-angle thermocouple such as within a heated chamber having little or no internal clearance, or perhaps within a tube or pipeline containing flowing gases or liquids. A right-angle design can be used in applications that requires an accurate temperature measurement without having the space to allow for immersion of the sensor. These designs even can be adapted for high temperature use (up to 4,000oF) and supersonic flowing gases. PH