WO1991014161A1

WO1991014161A1 - Thermal sensing

Info

Publication number: WO1991014161A1
Application number: PCT/GB1991/000358
Authority: WO
Inventors: Peter Nigel Brett; Julian Mark Moore
Original assignee: Avon Rubber PLC
Current assignee: Avon Technologies PLC
Priority date: 1990-03-09
Filing date: 1991-03-07
Publication date: 1991-09-19
Anticipated expiration: 1992-09-09
Also published as: GB9005286D0

Abstract

In order to determine the temperature of a fluid (2), the fluid (2) is brought into contact with a probe (1', 1'') which contains a plurality of temperature sensors (6, 9, 10; 12) in thermal contact with the body of the probe (1', 1''). The temperature sensors (6, 9, 10; 12) measure the temperature and the results are used to derive a temperature variation function which can then be used to determine the temperature of the fluid (2). In the simplest case, the temperature variation function is a polynominal fitted to the temperatures measured by the temperature sensors (6, 9, 10; 12). Alternatively, a model of the probe (1', 1'') may be generated and this allows a Fourier heat transfer equation to be used to determine the temperature variation function. In a further development, further sensors (12') are used to test the temperature variation function by comparing the temperatures measured by the further sensors (12') with the temperature at the locations of the further sensors (12') predicted by the temperature variation function.

Description

THERMAL SENSING

BACKGROUND OF THE INVENTION FIELD OF THE INVENTION

This invention relates to methods and means for determining temperatures in fluids.

SUMMARY OF THE PRIOR ART

The determination of such temperatures presents particular problems when dealing with systems in which the fluid is subjected to process conditions in which there are rapid changes in temperature- Many serious difficulties are posed when the fluid furthermore is a viscous badly conducting liquid. "Hot spots" or areas of low temperature could easily occur and cause damage or non-uniformity in the product.

A particular example of this is in rubber mixing processes where if there is incomplete or ineffective observation of the temperature in the mixing vessel there may be premature curing or insufficient curing or scorching of the rubber. This is a serious problem in the rubber industry and there are significant scrap costs arising due to rejection for lack of desired quality in the mixed rubber.

Mixing vessels for fluids have of course been fitted with temperature sensors, usually a calibrated thermocouple housed in a probe although infra-red emission sensing devices have also been used. Particularly when determining the temperature of a viscous fluid, it is normally important for the probe to be sturdy, to resist the forces that will be applied to it.

The thermocouple is conventionally regarded as a simple temperature sensor. It is mounted near the tip of a tubular probe sticking into the mouth from the wall of the vessel. However the thermocouple cannot be located at the actual tip which would itself not solve problems due to conduction by the probe. Abrasion itself will tend to heat the probe, causing its own errors. If the couple is set back into the probe then it is strongly affected both by the fact that it is not a point and therefore measures an average temperature over the local area of the probe but also the junction is influenced by the temperature of the material of the probe which is in turn affected by the steep temperature gradient along the probe. Response time to changes (which in the context of rubber mixing may be quite rapid - 20° to 200ºC in two minutes) is also strongly affected by the heat capacity of the probe itself and again by the temperature gradient along it.

Additional sources of measurement error in fluids are due to the heat transfer through the fluid. The heat transfer q (Watts/m²) through the boundary layer of fluid in contact with the probe relies upon a temperature differential between the fluid T_f and probe surface T_s, often modelled on the convective heat transfer law of equation (1): q - h(T_f-T_s) (1) In addition there will be temperature differentials set up throughout the fluid and thus measurement at a point by a single probe will not provide the overall temperature profile. In the case of fluids of poor conductivity, such as rubbery like materials, this effect could lead to substantial errors.

Infra-red sensors have a rapid response but there are difficulties involved if the line of sight is obstructed by a stagnant fluid mass and due to the fact that at least in the case of rubber curing the emissivity of the material changes during the cycle.

It is also known to provide a probe with a body and two spaced apart temperature sensors within and in thermal contact with that body. Then, the body of the probe is heated from a heat source external of the fluid, until the two temperature sensors record the same constant temperature. At such a time, the body of the probe is in heat equilibrium with the fluid, and thus the temperature measured by the sensors should correspond to that of the fluid. The disadvantage of this is that the probe will take a long time to reach the steady state, and thus dynamics temperature determination is not possible. SUMMARY OF THE INVENTION

The present invention seeks to enable more accurate determinations of temperature in fluids.

The invention is based upon the observation that it is not necessary to even attempt to place sensors in contact with the fluid provided (1) there is a plurality of sensors in a probe, and (2) their positions in the probe are known. Then by application of known theories of heat transfer, the temperature of the outside of the probe can be calculated and hence the temperature of the fluid in contact with that surface.

The present invention thus proposes that a temperature variation function be used to obtain the variation of temperature both inside and, by extrapolation using that function, outside the probe.

In a first arrangement temperature readings from a plurality of sensors in an array within a probe body are extrapolated polynominally to give a predicted surface temperature (e.g. at the free end of the probe) from which the fluid temperature can be derived. In the simplest form, the array extends linearly (axially) within an elongate probe.

Even this simple arrangement has been found to improve substantially upon the performance of the prior art single sensor probe, and also may permit dynamic temperature measurements to be made, since the present invention does not rely on the establishment of stable temperature conditions.

In a second arrangement, temperatures determined by a plurality of sensors distributed within the probe are analysed so as to yield temperatures at a network of notional nodes, some of which correspond to the surface of the probe.

In order to test the temperature variation function, it is possible to derive that function using only some of the sensors within the probe.Assumptions have to be made about the thermal behaviour of the probe and sensors, and those assumptions can then be tested by comparing the temperature measured by further sensors, other than those used to derive the temperature variation function, with the temperature which the temperature variation function predicts at the location of those further sensors. If the actual and derived temperatures do not match, the assumptions may then be varied.

Alternatively, or in addition, the assumptions used in deriving the temperature variation function may be used to create a mathematical model (e.g. in a computer) of the probe. This then permits that model to be pre-tested under laboratory conditions, e.g. by placing the probe in an environment of known temperature and investigating the temperatures measured by the sensors and comparing the resultant temperature. This operation may be achieved mathematically if an accurate model is derived. BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the present invention will now be described in detail, by way of example, with reference to the accompanying drawings, in which:

Figure 1 shows a prior art probe;

Figure 2 shows a first embodiment of the present invention, together with a graph derived from it;

Figure 3 shows a second embodiment, showing also notional nodes;

Figure 4 is a schematic diagram of logic devices associated with either embodiment; and

Figure 5 is a flow-chart showing steps in a method according to the present invention.

DETAILED DESCRIPTION

Looking first at the prior art, a probe 1 sticks into the chamber 2 of a mixing vessel from its wall 3. At the tip of the probe 4 there is a mounted a thermal sensor device 5 such as a thermocouple.

The actual thermocouple itself will not usually be at the exposed surface and therefore will give a reading affected both by the axial length of the sensor device 5 and by the conductivity of the probe

1 and wall 3.

Figure 2 shows a probe 1' with sensors 6-10 distributed along it within its body, and a thermal contact with that body. The body needs to be sufficiently sturdy to resist forces applied to it by the fluid and may thus be e.g. of metal. The schematic graph which is also part of this figure shows how the values 6'-10' may readily be extrapolated to give a temperature reading 11a which is a predicted tip temperature for the probe from which for a given fluid temperature lib can be further extrapolated.

Figure 3 shows a schematic embodiment suitable for the application of an adapted method. The wall 3 has a probe 1" projecting inwardly from it.

Temperature sensors are provided in the body of the probe at the positions indicated by solid circles 12. In order that fluid temperatures at the probe surface can be derived from an array of sensor temperatures within the probe, it is essential to acquire an accurate appreciation of the probe properties. This can be achieved by constructing a model of the probe by performing experiments in controlled environments, before it is put into operation, as will be described later.

The hollow circles 13, one set of which lie on the surface of the body 1", represent notional nodes for the prediction of the probe surface temperature in the manner which will be described.

The figure further shows how angular coordinates x, θ and r are applied to the body of the probe, with x being a distance ordinate originating at the tip of the probe.

The embodiment of Fig. 3 may be simplified, either by reducing the number of sensors 12, or by limiting the dimensions analysed. In the latter case, it would be necessary to adopt at least the dimension corrisponding to the major temperature gradient.

Figure 4 shows schematically how the probe 1' or 1" is connected by sensor cables 14 to an amplifier unit 15 and then to a signal and logic processing unit 16 in which a temperature prediction scheme and also the desired batch control data are applied to give an output 17 of data for control of the actual temperature in the vessel.

Fourier's equation of heat transfer may be written for example in polar coordinates in equation (2)

wherein c is the specific heat capacity of the material of the probe, k is its thermal conductivity and ρ is its density (see Fourier's Equation of heat transfer in 3D: in Patankar S.V., Numerical Heat Transfer and Fluid Flow, McGraw Hill, 1980).

Normally this equation is used to determine temperatures within a body the surface temperatures of which are known.

However here, the temperature of the sensors 12 and their position being accurately known, these may be used as boundary values to the solution of equations to determine temperatures at the surface of the probe.

If the probe is (as would be preferred) radially symmetrical and it can be assumed that the surface temperature is uniform around one circumference, then equation (2) may be reduced to equation (3):-

In either case, an accurate real time estimation of the local fluid temperature can then be made by application of equation (1). However, the value of heat transfer coefficient h is not necessarily a known parameter, in such cases an adaptive scheme to vary the value of h could be applied. This would vary h until the predicted fluid temperature matched an appropriate distribution pattern and the predicted values of temperatures at measured points, (not employed as a boundary to the solution), are confirmed.

That confirmation may be achieved by providing further sensors 12' in the probe 1" of Fig. 3, which further sensors 12' are not used to derive the distribution pattern (temperature variation function). Instead, the temperature variation function is used to predict the temperature at the location of those further sensors (12'). That predicted temperature may then be compared with the actual temperature measured by those further sensors (12') to test the assumption used in obtaining the temperature variation function.

Furthermore, the assumptions may be pre-tested using a mathematical model and/or by locating the probe under known temperature conditions, so that the predicted external temperature, using the temperature variation function, may be compared with the known temperature.

Thus, as shown in Fig. 5, the basic steps of operation, using the present invention, are to bring the probe into contact with the fluid (step 100), to measure temperatures using the sensors 6, 9, 10, 12 (step 101), derive a temperature variation function (step 102), and thereby predict the temperature of the fluid (step 103). Furthermore, as shown in Fig. 5, a mathematical model of the probe may first be created (step 104), which is tested under known conditions (step 105) if the rest shows the model is not accurate, the parameters of the model are revised (step 106), and processing returns to step 104, the creation of the model. If, on the other hand, the model behaves correctly under known conditions at step 105, then the probe can then be used (step 100).

The other optional steps, mentioned above, are to use the further sensors 12' to test the temperature variation function derived at step 102. To do this, the temperature at those further sensors 12' is predicted using the temperature variation function (step 107), and the predicted temperature is then compared with the actual temperature measured by those further sensors 12', at step 108. If that comparison shows that the temperature predicted is not as accurate, the assumptions underlying the temperature variation function are revised (step 109), and processing returns to step 102. If, on the other hand, the predicted and actual temperature of the sensors corresponds so that the temperature variation function is accurate, that temperature variation may then be used to obtain the temperature of the fluid, at step 103.

One exemplary sequence for determining a conductive heat transfer coefficient may be quoted:-

1. Given the form/pattern of a suitable temperature distribution within the fluid in close proximity with the surface of the probe (e.g. uniform).

2. Given a first value of convective heat transfer coefficient (h).

3. Apply the analytical scheme to compute temperatures.

4. Using the values of temperature and temperature gradients predicted by an analytical scheme at the surface of the probe, use equation 1 to determine fluid temperature values corresponding to nodal points.

5. Examine the distribution of predicted temperatures within the fluid.

6. Adjust h appropriately.

7. Recompute temperatures of the fluid as in (3) and (4) above.

8. Same as (5) and, if necessary, (6) and repeat loop.

The solution of the equation (2) or (3) may be achieved, using the scheme of Figure 3 to predict temperature at each node 13 from the temperatures measured at each sensor 12.

Application of a Finite Element or Finite Difference Scheme solves for all temperatures simultaneously from a series of simultaneous equations. For example, Crank Nicholson's Implicit Method (Smith, G.D., Numerical Solutions of Partial Differential Equations, Oxford University Press, 1969) is a finite difference scheme that is formulated from a star configuration of nodes. The differences in time Δt, axial position Δx, and radius Δr about t, x and r respectively, are related by the general formula given in equation 4.

where α and β are dimensionless coefficients.

Greater resolution is obtained by increasing node density. However, care is needed when selecting nodal spacing as the scheme is more accurate if the following ratios are less than unity

Solutions at physical boundaries are dealt with by using the well documented method of virtual points (ref 8).

Even though there are other schemes that could be implemented including a finite element method, the novel principle of this proposed sensing device is preserved.

Claims

1. A method of determining the temperature of a fluid (2) comprising:

bringing the fluid (2) into contact with a probe (1', 1"), the probe having a probe body and a plurality of spaced-apart temperature sensors

(6, 9, 10; 12) within and in thermal contact with the probe body; and

measuring the temperatures detected by each of the temperature sensors (6,9,10;12);

characterised in that:

the method further includes:

deriving at least one temperature variation function representing the variation of temperature both within and outside the probe (1', 1"), on the basis of the temperature detected by at least some of the temperature sensors (6,9,10;12); and

obtaining a temperature of the fluid proximate the probe (1', 1") on the basis of the at least one temperature variation function.

2. A method according to claim 1, wherein prior to the step of obtaining the temperature of the fluid (2) the temperatures measured by further temperature sensors (12') are compared with temperatures derived from the temperature variation function corresponding to the location of the further temperature sensors (12') thereby to test the at least one temperature variation function, said further sensors (12') being other than said at least some of the temperature sensors (6, 9, 10; 12).

3. A method according to claim 1 or claim 2, wherein a mathematical model of said probe and fluid is generated, and said mathematical model is used in the derivation of the at least one variation function.

4. A method according to claim 3, wherein, prior to the bringing of the fluid (2) into contact with the probe (1', 1"), the mathematical model is tested under known temperature conditions.

5. A method according to any one of the preceding claims, wherein the at least one temperature variation function is a polynomial function.

6. A method according to any one of claims 1 to 4, wherein the at least one temperature variation function is a Fourier heat transfer function.

7. A method according to any one of claims 1 to 4, wherein a plurality of temperature variation functions are derived by finite element analysis.

8. A method according to any one of the preceding claims, wherein the probe (1') extends axially into the fluid (2), and the temperature sensors (6,9,10) are arranged linearly in the probe body, parallel to the axis of the probe.

9. A method according to any one of claims 1 to 7, wherein the probe (1") extends axially into the fluid (2) and the temperature sensors (12) are arranged on an array extending parallel and perpendicular to the axis of the probe.