21.7Process/instrument suitability

The primary consideration for selecting a proper temperature sensing element for any application is the expected temperature range. Mechanical (bi-metal) and filled-system temperature sensors are limited to relatively low process temperatures, and cannot relay signals very far from the point of measurement.

Thermocouples are by far the most rugged and wide-ranging of the contact-type temperature sensors. Accuracies vary with thermocouple type and installation quality.

RTDs are more fragile than thermocouples, but they require no reference compensation and are inherently more linear.

Optical sensors lack the ability to measure temperature of fluids inside vessels unless a transparent window is provided in the vessel for light emissions to reach the sensor. Otherwise, the best an optical sensor can do is report the skin temperature of a vessel. For monitoring surface temperatures of solid objects, especially objects that would be impractical or even dangerous to contact (e.g. electrical insulators on high-voltage power lines), optical sensors are the only appropriate solution.

Chemical reactivity is a concern for contact-type sensors. If the sensing element is held inside a thermowell, that thermowell must be selected for minimum reaction with the process fluid(s). Bare thermocouples are particularly vulnerable to chemical reactions given the nature of most thermocouple metals (iron, nickel, copper, etc.), and must be carefully chosen for the particular process chemistry to avoid reliability problems later.

21.8Review of fundamental principles

Shown here is a partial listing of principles applied in the subject matter of this chapter, given for the purpose of expanding the reader’s view of this chapter’s concepts and of their general interrelationships with concepts elsewhere in the book. Your abilities as a problem-solver and as a life-long learner will be greatly enhanced by mastering the applications of these principles to a wide variety of topics, the more varied the better.

•Kirchho ’s Voltage Law: the algebraic sum of all voltages in a loop is equal to zero. Relevant to thermocouple circuit calculations, where the reference junction voltage always opposes the measurement junction voltage. Also relevant to RTD circuits when determining the amount of voltage sensed by the instrument compared to the amount of voltage dropped by the RTD resistance element.

•Ideal Gas Law: P V = nRT , describing the relationship between gas pressure, chamber volume, gas quantity (in moles), and gas temperature. Relevant to Class III filled-bulb temperature sensors, where the increased pressure of an enclosed gas corresponds to the temperature of that gas.

•Self-balancing opamp circuits: all self-balancing operational amplifier circuits work on the principle of negative feedback maintaining a nearly zero di erential input voltage to the opamp. Making the “simplifying assumption” that the opamp’s di erential input voltage is exactly zero assists in circuit analysis, as does the assumption that the input terminals draw negligible current.

•Stefan-Boltzmann Law: dQdt = eσAT 4, that all objects warmer than absolute zero radiate thermal energy (photons). Relevant to non-contact pyrometry, where the intensity of the received radiation is proportional to the fourth power of the object’s absolute temperature.

•Time constant: (τ ), defined as the amount of time it takes a system to change 63.2% of the way from where it began to where it will eventually stabilize. The system will be within 1% of its final value after 5 time constants’ worth of time has passed (5τ ). Relevant to temperature lags caused by sensor mass and thermowells.

•Inverse square law: the strength of a field radiating away from a point-source diminishes proportionately to the square of the distance from the source. Relevant to determining the amount of radiant energy intercepted by a sensor when monitoring a point-source of heat.

References

Baker, Bonnie C., “Precision Temperature-Sensing With RTD Circuits”, application note AN687, Microchip Technology Incorporated, 2003.

Beckerath, Alexander von; Eberlein, Anselm; Julien, Hermann; Kersten, Peter; and Kreutzer, Jochem, WIKA-Handbook, Pressure and Temperature Measurement, WIKA Alexander Wiegand GmbH & Co., Klingenberg, Germany, 1995.

Darling, Charles Robert, Pyrometry – A Practical Treatise on the Measurement of High Temperatures, E. & F.N. Spon, Ltd, London, 1911.

Fribance, Austin E., Industrial Instrumentation Fundamentals, McGraw-Hill Book Company, New York, NY, 1962.

Irwin, J. David, The Industrial Electronics Handbook, CRC Press, Boca Raton, FL, 1997.

Kallen, Howard P., Handbook of Instrumentation and Controls, McGraw-Hill Book Company, Inc., New York, NY, 1961.

Lipt´ak, B´ela G. et al., Instrument Engineers’ Handbook – Process Measurement and Analysis Volume I, Fourth Edition, CRC Press, New York, NY, 2003.

“Model 444 Alphaline Temperature Transmitters”, Document 00809-0100-4263, Revision AA, Rosemount, Inc., 1998

“Radiamatic Detectors and Accessories”, Specification document 23-75-03-03, Honeywell, Inc., Fort Washington, PA, 1992.

“Temperature - Electromotive Force (EMF) Tables for Standardized Thermocouples”, Pyromation, Inc.

“Temperature Measurement – Thermocouples”, ISA-MC96.1-1982, Instrument Society of America, Research Triangle Park, NC, 1982.

Since this accelerating force is applied on the cross-sectional area of the fluid plug, we may express it as a pressure, the definition of pressure being force per unit area:

F = ρV a

FA = ρ VA a

P = ρ VA a

Since the rules of algebra required we divide both sides of the force equation by area, it left us with a fraction of volume over area ( VA ) on the right-hand side of the equation. This fraction has a physical meaning, since we know the volume of a cylinder divided by the area of its circular face is simply the length of that cylinder:

P = ρ VA a

P = ρla

When we apply this to the illustration of the fluid mass, it makes sense: the pressure described by the equation is actually a di erential 3 pressure drop from one side of the fluid mass to the other, with the length variable (l) describing the spacing between the di erential pressure ports:

Length (l)

Pressure drop

(P)

This tells us we can accelerate a “plug” of fluid by applying a di erence of pressure across its length. The amount of pressure we apply will be in direct proportion to the density of the fluid and its rate of acceleration. Conversely, we may measure a fluid’s rate of acceleration by measuring the pressure developed across a distance over which it accelerates.

We may easily force a fluid to accelerate by altering its natural flow path. The di erence of pressure generated by this acceleration will indirectly indicate the rate of acceleration. Since the acceleration we see from a change in flow path is a direct function of how fast the fluid was originally moving, the acceleration (and therefore the pressure drop) indirectly indicates fluid flow rate.

3What really matters in Newton’s Second Law equation is the resultant force causing the acceleration. This is the vector sum of all forces acting on the mass. Likewise, what really matters in this scenario is the resultant pressure acting on the fluid plug, and this resultant pressure is the di erence of pressure between one face of the plug and the other, since those two pressures impart two forces on the fluid mass in direct opposition to each other.

Another way we may accelerate a fluid is to force it to turn a corner through a pipe fitting called an elbow. This will generate radial acceleration, causing a pressure di erence between the outside and inside of the elbow which may be measured by a di erential pressure transmitter:

Pipe elbow

H L

The pressure tap located on the outside of the elbow’s turn registers a greater pressure than the tap located on the inside of the elbow’s turn, due to the inertial force of the fluid’s mass being “flung” to the outside of the turn as it rounds the corner.

rates, and derive mathematical relationships between fluid pressure and flow rate starting from basic physical conservation laws.