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Some Myths & Facts About Temperature Sensing

By Dan Nanigian

Fig 1 Heat flow through a wall; Fig 2 Schematic of typical thermocouple installation

Proper selection of thermocouples and optimization of their performance in specific applications requires a good understanding of the construction, capabilities and limitations of the various types of thermocouples available.

Contact temperature-sensing devices, such a thermocouples, RTDs (resistance temperature detectors), thermistors, bimetallic thermometers and liquid-filled sensors, measure the temperature of their sensing tips; that is, they do not measure the temperature of gases, liquids or solids surrounding the sensing tip unless certain requirements are met. Differences in the thermal properties of the sensor and the media surrounding the sensor (e.g., thermal conductivity, thermal diffusivity and emissivity) can produce large differences in the observed temperature readings. Additionally, isotherms (areas of constant temperature) within the gas, liquid or solid material can produce large differences between observed and actual temperatures. The test engineer (user) must consider these factors before choosing the particular device design. This article describes various situations where temperature measurements are made, and studies temperature-sensor characteristics under dynamic and static conditions. Where appropriate, typical test data are presented to illustrate the performance of temperature sensors under actual tests.

Temperature-measurement applications

Fig 3 Typical peak response curves from various flattened and round wire sensors

Selecting the correct temperature sensor requires a basic knowledge of the temperature profile and the factors that influence the profile within the wall and adjacent gas or liquid. The temperature sensor must measure the desired temperature without disturbing this temperature by its presence, and also must have sufficiently fast response time to follow temperature changes accurately.

Consider a hot gas or liquid on one side of a wall and ambient temperature on the other side. The wall could be a chamber such as a furnace or pipe through which a gas or liquid is flowing. Figure 1 shows the temperature profile across the wall at a given time for a case where the wall is made of one homogenous material such as steel or ceramic. For a wall consisting of several materials, such as steel, insulation and graphite or ceramic, each homogenous material has its own temperature profile across its cross section. The following observations are made from Fig. 1:

• Heat always flows from the hotter medium to the cooler medium
• Heat energy is continuously absorbed by the wall at its hot side and released at the cold side to the cooling medium (e.g., air, water, etc.); under steady-state conditions, heat absorbed must be equal to the heat released or the wall will begin to melt.
• The temperature profile at each interface is asymptotic.
• There is no region where temperature is constant over a given cross section. Constant temperature zones are called isotherms, which occur at right angles (normal) to the plane of heat flow. Adjacent to the hot wall there is a laminar layer of gases, which tend to inhibit the heat flow and serves as an insulator. One could imagine the laminar layer as a layer of heat insulating tape that functions like another material having its own inherent thermal properties, and, therefore, having its own temperature profile across it.

Fig 4 Representative bayonet thermocouple; Fig 5 Modified bayonet thermocouple with ribbon elements

Five distinct areas for temperature measurement in the above example are:

• Exterior wall surface temperature (cool side)
• Interior wall temperature at a specific point
• Wall surface temperature (hot side)
• Local gas/liquid temperature at the interior surface of the wall (hot side)
• Gas temperatures on the hot side of the laminar layer

These areas together with sensor requirements are discussed below.

Exterior wall surface temperature

Fig 6 Essential features of an in-wall design thermocouple for high accuracy

The temperature sensor must be in intimate thermal contact with the wall. Also, the sensor thickness must be small relative to the wall thickness. Ideally, a flat, two-dimensional (2-D) sensor is the best for this application. If the wall is nonmetallic, a small-diameter sheathed thermocouple can be attached by bonding it to the wall. The diameter of the thermocouple must be small compared with the wall thickness. The probe must also be installed so it is in intimate thermal contact with the wall for a distance of 30 times its diameter. For a metal wall, an intrinsic-type thermocouple can be used. Each leg of the two elements should be flattened and welded to the metal wall in close proximity to each other. A schematic of a typical installation is shown in Fig. 2. Typical response curves obtained from various flattened and round wire sensors are shown in Fig. 3. More details on this technique are contained in [1].

Interior metal wall temperature

The temperature sensor must have the same thermal properties (i.e., thermal conductivity and thermal diffusivity) as those of the wall, and it must be accurately located within the wall and make good thermal contact with the bottom of the blind hole. Spring-loaded thermocouples are used for this type of application. Also, the sensor hardware, such as the protection sheath, mounting hardware, etc., must not introduce large conductive paths for heat transfer to occur.

The type of thermocouple assembly shown in Fig. 4 with in pocket depth installations up to 1.5 in. (38 mm) has inherent errors caused by the depth of the pocket, nipple cap, air currents in the vicinity of the heated cylinder and the position of the thermocouple relative to the top, bottom or side of the heated cylinder. Bayonet-type thermocouples show the following errors in controlled tests [2]:

• Air drafts from open doors and windows, air circulating around heated cylinders and cooling air caused errors of up to 90 F (~50 C) in thermocouples installed in pocket depths of 0.5 in. (13 mm) using conventional-style twist-lock nipples.
• Errors from 7 to 36 F (~4 to 20 C) were observed simply by positioning the thermocouple in the top, bottom or side of a heated cylinder. An error in measurement was also noted with respect to the type of nipple used to install the thermocouple in the wall. All thermocouples in this test were also at pocket depths of 0.5 in.

• Fig 7 Self-renewing thermocouple consisting of flat ribbons, mica insulation and a sensing junction formed by abrasion

  Errors of 18 F (~10 C) were measured in pocket depths of 0.5 in. In pocket depths of 1.5 in., the error was reduced to about 4 F (~2 C).
• The additive effects of these errors can easily create an overall error of 90 F or more in shallow-depth applications of conventional bayonet-type thermocouples. Therefore, a more precise temperature sensor is needed, particularly in applications where the pocket depth is 1.5 in. or less.

Fig 8 Self-renewing thermocouple response time as temperature and pressure from a shock wave pass sensors; Fig 9 Transient application using self-renewing thermocouple for plastics injection molding

New designs have been developed for shallow pocket depths. A right-angle ribbon type (one of the newer designs) was specifically developed to eliminate conduction errors caused by temperature gradients [3]. The design is a thermally isolated, or adiabatic, probe, which measures the actual local temperature independent of conduction effects. Controlled-gradient tests show no measurable errors in temperature, and response times are a few milliseconds. Figure 5 illustrates a modified bayonet thermocouple with ribbon elements. Typical applications of the spring-loaded thermocouples include thick-walled chambers and cylinders such as gun barrels, injection molding machines, extruders, etc.

Interior nonmetallic-wall temperatures

To determine thermal properties and heat flux in certain experiments, the temperature history of an interior point in low-conductivity materials is frequently obtained from a thermocouple appropriately installed in the material. Large errors can be produced by the presence of the thermocouple itself if certain precautions are not observed. The errors are pronounced when the thermocouple is installed in materials such as Teflon‚, nylon, phenolic, silica phenolic and similar low-conductivity materials.

Fig 10 Transient application using self-renewing thermocouple for glass molding

The parameter to consider is the ratio of the thermal conductivity of the base material to that of the thermocouple assembly. If the ratio is significantly less than 1.0, temperature errors as large as 700 F (385 C) can be created [4]. In transient cases, even larger errors are produced. Methods to reduce the error include:

• Designing a thermocouple assembly having a thermal conductivity matching that of the measured material
• Reducing the radius of the thermocouple wire, or increasing the surface area/cross-sectional area ratio
• Placing the thermocouple and adjacent lead wire parallel to the plane of heat flow

Fig 11 Shallow immersion probe (ribbon thermocouple) for use in gas or liquid

Figure 6 shows the essential features of a thermocouple specifically designed to meet these requirements. The thermowell material is the same as that of the test wall. The thermal junction and extension leads in the immediate vicinity of the junction are of ribbon form, which yields the largest possible surface area/cross-sectional area ratio for a given wire size. Both the junction and the lead wires are in the same plane.

The thermocouple, when installed so the probe is normal to the plane of heat flow, produces the most accurate in-wall temperature histories in low-conductivity materials. The sensor can be made in any standard pair of elements with fiberglass insulation, from No. 24 gage down to No. 36 gage wires. The probe length and diameter are optional, limited only by the machinability of the material used; a 0.1875-in. (~5 mm) diameter wire is convenient for most materials. All probes should be potted into the mating hole with suitable bonding agents.

Wall surface temperature (hot side)

A surface thermocouple must match the thermal properties of the wall, must not disturb the surface contour of the wall, must be two-dimensional, must have low millisecond response time and the thermal junction must be self-renewing if ablation and/or erosion are present.

The self-renewing thermocouple shown in Fig. 7 meets these requirements [5]. This unique thermocouple design [2] uses flat ribbons, mica insulation and a sensing junction formed by abrasion. The design has a two-dimensional surface measuring junction with microsecond response times to surface temperature fluctuations. The sensor thermowell can be made of any machinable material, thus matching the thermal properties of the wall precisely.

The thermal junction is formed by performing a simple abrasive action across the sensing surface using a medium-grit size abrasive paper. The sanding and polishing action produces thousands of microscopic hot-weld junctions that join one ribbon to the other ribbon. Since the thermal junction is formed via an abrasive action, any additional erosion from use simply removes the old junctions while simultaneously forming new junctions. Thus, the thermal-sensor design has a self-renewing feature, which is useful in applications where the wall is subject to wear.

Figure 8 shows temperature and pressure versus time of a shock wave as it passes the location of the two sensors. A shock wave is generated by evacuating the shock tube, filling the tube with a combustible gas and igniting the gas electrically at the closed end of the tube. The measured response time of the self-renewing thermocouple in this test was 8 microseconds, which is equivalent to a rate of 28 x 10(2) F/sec (15.5 x 10(6) C/s). This unique thermocouple has been used in many transient applications. Typical examples of temperatures recorded by this thermocouple are shown in Figs. 9 and 10.

Gas or liquid temperatures inside the chamber

The gas region begins at the boundary layer at the surface of the hot wall and extends to the opposite wall. In steady-state flow, gas temperatures follow a bell-shaped profile; that is, it is coolest at the wall surfaces and reaches a maximum at the center of the flowing gas. (In cryogenic flow, the opposite occurs; that is, the cryogenic gas or liquid is coolest at the center of the flow and warmest at the wall surfaces.) In furnaces or closed chambers, the gas is not moving, but there are isotherms within the gas (this will be discussed in Part 2 of this article).

To accurately measure the gas temperatures, the sensor must meet two requirements:

• The sensing tip of the sensor must not disturb the local temperature of the gas by its presence.
• The sensor must lie in the plane of an isotherm.

Special types of ribbon thermocouples meet these requirements as shown in Fig. 11. Note that the ribbons and junction are heated simultaneously, and conduction along the stem is eliminated. If round wires or round metal sheaths are used in the sensor design, the tip of the sensor must be bent into an “L” shape for a distance equal to at least 20 diameters of the sheath.

Array of temperature sensors

Time constants

The time constant of a temperature sensor (or any other sensor) is defined as the time required for the sensor to respond to 63.2% of its total output signal when subjected to a step-change in temperature. Sensor response time is not the same as the time constant, but is a measure of how long it takes for the sensor to reach its full output. Thus, response time can be defined as five time constants (Fig. 1), which is based on the fact that the temperature sensor is subjected to a step change in temperature.

A step change in temperature occurs very rarely in the physical world (some examples are shock waves, explosions, gun barrel tests, internal combustion engines, and injection molding). However, these are not truly step changes when measured using a fast responding sensor. Thus, a different term is needed to define more accurately what occurs in the physical world. Nanmac uses “rise time” to define the time required for the test event to reach its full output. For example, a particular temperature event might take one second to reach its full output even though the time constant of the temperature sensor may be only one microsecond. A temperature sensor cannot reach its full output before the rise time of the event reaches its full output.

Response times

Response in static air. Air response tests can be performed in static and moving air. The response time of a thermocouple suddenly immersed into hot air depends on the diameter of the thermocouple wires if all other variables are held constant. Figure 2 illustrates the typical response times of exposed bare wire thermocouples.

Fig 1 Total response time is defined as five time constants

Bath response time. Most temperature sensors have a protection sheath (such as stainless steel, Inconel, ceramic and molybdenum) surrounding the sensing elements and the required electrical insulation. The time constant of an assembled temperature sensor depends on the overall response time of all its components. If all but one variable are held constant, the effect of that variable on sensor response times can be determined graphically (e.g., effect of sensor diameter graphically illustrated in Fig. 3). Similar relationships can be determined for other variables such as sheath types, type and amount of insulation, wire size and properties, size of measuring junction, physical shape of the sensor (round, elliptical, or flat) etc.

The sensing tip must absorb heat faster than heat is conducted away to increase in temperature. Also, the heat capacity of the medium must be large compared with the heat conducted away by the sensor so the step change can be maintained during the test. In air tests, the temperature of the air surrounding the probe decreases as soon as heat is applied to the sensor until more heat flows into this region from the undisturbed air region, which takes a considerable length of time in still air. The time decreases as the air mass flow rate increases as shown in the table.

Air flow effects on response time

In liquid tests, the heat capacity of the liquid is much greater than air, so the heat input into the sensor is much greater. Thus, the superimposed temperature change more closely approaches a step function.

In liquid metal (or contacting a hot plate), the heat capacity of the metal is much greater than those of gas or liquid, so the temperature change approaches a step change even more. Thus, these tests produce the fastest response times for a given temperature sensor.

Time constants

Fig 2 Exposed wire thermocouples in air; T = 200F

The time constant of a temperature sensor affects the accuracy of temperature measurements in transient applications as illustrated by the following examples.

Example 1. Measure the temperature of a hot plate, bearing wall, etc. by contacting the sensor to the hot wall for three seconds duration. From the sensors point of view, this is a three-second transient. Because it takes five time constants to reach 99% of its output, the time constant of this sensor can be no slower than 600 milliseconds.

Example 2. Measure the temperature of a cyclical application such as in injection molding. In a typical molding cycle of ten seconds, it takes about 1.5 seconds to fill the mold with hot plastic. The remainder of the cycle time is used for curing the part, opening the mold, ejecting the part and then closing the mold to begin the next cycle. Thus, the transient portion of the cycle is only 1.5 seconds, and a sensor having a time constant of 300 milliseconds is required.

It is not sufficient to immerse a temperature sensor in a container of hot water to determine its time constant. Laminar layers adjacent to the cool probe, the speed at which the probe is immersed into the water and the heat transfer coefficient of the water mask the response time. Such a test gives a rise time, which for a sensor having a fast response time, simply changes proportionally with the probe’s velocity through the water. A more accurate measure of response time can be obtained by slowly heating the sensing tip with a small torch and quickly removing the heat source while its output is increasing. The time lag between the instant the heat source is removed and the output of the sensor begins to decrease is a good indication of the sensor’s response time.

Two types of errors produced when using a temperature sensor with inadequate re-sponse times in transient applications are: 1) the peak temperature is either missed completely or greatly reduced; and 2) peak temperature is delayed, inaccurately indicating when the peak temperature occurred. In many industrial processes, true peak temperature and/or when it occurs are critical to control process efficiently.

Ribbon thermocouples in hot-water tests. Figure 4 shows temperature versus time data obtained by manually immersing a right-angle thermocouple from ice water to boiling water then back to ice water.

Response tests in moving air. The effect of moving air on temperature sensor response time also must be considered. When sensor response time in air is specified, it is necessary to indicate the air mass flow rate under which the test will be conducted, or the data is meaningless.

Other factors affecting response times

Sensor response times can be greatly affected by two variables even if the diameter of the two elements are the same, and the orientation of the probe with respect to the isotherms is the same, then the thermocouple with the lowest combined thermal conductivity will produce the fastest response time. Thus, a Chromel-Alumel (Type K) thermocouple has a much faster response time than a Cu-Constantan (Type T) thermocouple of the same diameter and construction. Type T is much faster if the probe is installed parallel to the plane of heat flow.

Conduction problems and isotherms

Fig 3 Response time for sheathed thermocouples: Fig 4 Ribbon thermocouple in hot-water test

A thermocouple installed in a furnace is subject to large errors caused by conduction along the stem. Because heat is always conducted from a hotter medium to a cooler medium, it is very important to eliminate (or minimize) the error caused by conduction along the sensor stem, which usually contains a metallic sheath, electrical insulation and wire. The sensor measures the temperature of its sensing tip after the tip reaches an equilibrium temperature; that is, when heat input to the sensing tip offsets the heat losses (conduction along the stem through the wall and thus to the outside environment). This stem effect must be eliminated to obtain the true temperature of the interior of the furnace.

Thus, a 0.25 in. (~6 mm) diameter sensor must be installed parallel to the isotherms for a distance of 20 times its diameter, or 5 in. (127 mm) to offset conduction error. Ideally, sensor orientation should be considered during the design stage of the furnace, not after. Generally, accurate temperature measurement is achieved by installing the sensor parallel to the longitudinal axis of the workload for a distance equal to 20 times the sensor diameter. It is easy to determine if there is a significant error in the installation by temporarily installing a smaller diameter thermocouple into the same location under the same conditions. If there is a conduction error caused by stem effect, the smaller diameter sensor will indicate a higher temperature. Errors as high as 300 F (165 C) have been observed in heat-treating applications. Figures 5 and 6 illustrate correct and incorrect temperature-sensor installations in furnaces.

Thermal properties of the thermowell

Fig 5 Furnace with bottom heaters

In an experiment designed to determine the effect of thermal properties of the thermowell on the recorded temperature, several identical thermocouples were constructed using various materials (combinations of phenolic, stainless steel and molybdenum) in the thermowell, keeping all other conditions the same. The thermocouples were installed flush with the inner surface of a rocket motor nozzle containing phenolic insulation.

Figure 7 shows the results of one test in which a phenolic probe and molybdenum probe were used in the same test. The sensors differed by about 2000 F (1080 C) seven seconds after the test started, and still differed by 1000 F (535 C) after 18 seconds. Repeated tests produced similar results. Other materials such as stainless steel, tantalum, graphite, etc. also were used. Generally, recorded surface temperatures were inversely proportional to the thermal properties of the thermowells. The true surface temperature of the nozzle was obtained using a thermocouple with a phenolic thermowell.

Using only a Mo-sheathed Type C thermocouple would show that the highest surface temperature of the phenolic wall was only 3090 F (1700 C), and specifications based on this data would produce catastrophic results.

Recording-system errors

Fig 6 Furnace with heaters on all sides

In addition to sensor errors, there are other errors created by the recording system including connectors, extension wires, reference junctions, amplifiers, controllers, etc. To illustrate, the errors possible using a high-temperature Type C thermocouple (W5%Re vs. W26%Re) are itemized.

The ANSI standard limits of error for a Type C thermocouple is +/-1% between 800 and 4200 F (430 and 2320 C), thus Type C elements can be “off” by a maximum of +/-42 F (+/-23 C) and still be acceptable for use at 4200 F. ANSI established the acceptable maximum deviation (limits of error) for all thermocouple types from NIST calibrations. This is the first source of error in temperature measurements.

Fig 7 Effects of thermowell materials

Additional sources of errors are introduced when calibrated ANSI Type C wires are assembled into a thermocouple including the welded junction, two-hole insulators and protection sheath. Several more sources of error are introduced when the assembled thermocouple is installed into a heated chamber or furnace including conduction errors due to temperature gradients within the chamber wall, response time errors if transients are occurring and radiation errors due to cold walls. Finally, a few more sources of error are introduced when the output of the assembled thermocouple is recorded including reference-junction, transmitter, amplifier and other errors; compensated lead-wire errors and recorder or controller errors.

 Because all of the above errors are included in every installation, minimizing them requires paying very careful attention to details. If each source of error cannot be isolated and measured, the measuring system is not capable of detecting them. Errors are either electronic or thermal.

Electronic errors at 2730 F (1500 C) include:

• Wire calibration error: +/-1% = +/-15 C
• Extension wire error: +/- 0.5% = +/-7.5 C
• Typical ref. junction error: +/-1 C
• Typical recorder error: +/-0.5% or +/-7.5 C

The maximum possible electronic error is +/-31 C at 1500 C (+/-56 F at 2730 F). All of these errors fortunately are not always accumulative, because some errors cancel out others.

Thermal errors include:

• Stem-effect error caused by conduction from the tip of the sensor to the wall. This error is most pronounced when there are large temperature differences between the wall and the tip of the sensor.
• Radiation error caused by temperature differences between the tip of the thermocouple (including its protection sheath) and the inside walls and/or the workpiece or load in the furnace.

By Dan Nanigian, NANMAC Corp.