GB2128338A

GB2128338A - Method and apparatus for measuring the Reynolds Number of a fluid

Info

Publication number: GB2128338A
Application number: GB08324563A
Authority: GB
Inventors: Gerald Anderson; Michael William John Seabrook
Original assignee: Sarasota Automation Ltd
Current assignee: Sarasota Automation Ltd
Priority date: 1982-10-01
Filing date: 1983-09-14
Publication date: 1984-04-26
Also published as: GB2128338B; GB8324563D0; DE3335680A1

Abstract

A method of measuring the Reynolds Number of a fluid or a parameter of the fluid whose value is dependent on the said Reynolds Number, comprises passing the fluid through a conduit (17), mounting at least one electrical heating device (34 35) in said conduit or in a chamber communicating therewith, the or each heating device being arranged to be supplied with electrical power, the amount of which is varied so as to vary its temperature differential with respect to that of the fluid while ensuring that the temperature of the heating device is always above that of the fluid, determining the temperature of the or each heating device at different times during said variation, determining therefrom the power loss of the or each heating device per unit temperature, and employing it to effect a calculation of said Reynolds Number or parameter. Preferably the calculation is effected by determining the difference of power loss of two similar heating devices at different temperatures. <IMAGE>

Description

SPECIFICATION Method and apparatus for measuring the Reynolds Number of a fluid This invention relates to a method and apparatus for measuring the Reynolds Number of a fluid or of measuring a parameter of the fluid (such as mass flow, volume flow or energy flow) whose value is dependent on the said Reynolds Number.

Although the present invention is primarily directed to any novel integer or step, or combination of integers or steps, as herein described and/or as shown in the accompanying drawings, nevertheless, according to one particular aspect of the present invention to which, however, the invention is in no way restricted, there is provided a method of measuring the Reynolds Number of a fluid or of measuring a parameter of the fluid whose value is dependent on the said Reynolds Number, the said method comprising passing the fluid through a conduit, arranging at least one electrical heating device in heat transfer relationship with the fluid in a respective portion of said conduit, supplying the or each heating device with electrical power, effecting a variation in the amount of electrical power to the heating device, or to at least one of the heating devices, so as to vary its temperature differential with respect to that of the fluid while ensuring that the temperature of the heating device is always above that of the fluid, sensing the temperature of the or each heating device at different times during the said variation, determining therefrom the power loss of the or at least one of the heating devices per unit temperature, and employing the said power loss per unit temperature to effect a calculation of the said Reynolds Number or the said parameter.

Preferably there are two similar heating devices in the conduit, and the calculation is effected by determining the difference between the power losses of each of the heating devices when the heating devices are simultaneously operated at different temperatures.

Preferably, each of the two similar heating devices is maintained at a temperature above that of the fluid.

In this case, each heating device is preferably always operated at a temperature of at least 300C above that of the fluid, and the temperatures at which the heating devices are operated do not differ from each other at any time by more than 5 .

Alternatively, one of the heating devices may be allowed to cool to the temperature of the fluid.

Thus the electrical power to one of the heating devices could be shut off for a period to allow it to cool to the temperature of the fluid, in which case the said one heating device would be arranged actually to measure the temperature of the fluid directly as opposed to merely inferring this temperature.

The conduit may comprise a flow sampling tube communicating with a pipe, through which there is a main flow of the fluid, in which case the mass flow of the sample flow may be used to derive the mass flow of the main flow. Alternatively, especially if the main flow is small, the conduit may be constituted merely by said pipe, no use being made of a flow sampling tube.

Preferably each heating device has a positive, substantially linear resistance temperature characteristic. Thus each heating device may be a platinum resistance thermometer.

The or each heating device may be spaced from a support or from another heating device by a space such that the Grashof number of the space does not substantially exceed 2000.

Each of the heating devices may be alternatively operated so as to be relatively hotter and cooler than the other.

The flow sampling tube may have two similar heating devices therein, one of which is disposed in a first portion of the flow sampling tube, the said first portion being of substantially constant crosssectional area, and the other of which is disposed in a second portion of the flow sampling tube, the said second portion being a tapering portion or a portion having substantially constant cross-sectional area which differs from that of the first portion.

Alternatively, the flow sampling tube may have two similar heating devices therein which are disposed adjacent to each other. Thus, the heating devices may be plate-like members which are disposed parallel to each other.

Alternatively, there may be a portion of the conduit in which the fluid is substantially stagnant, a said heating device being disposed in said portion. Moreover, in addition to the heating device in the said substantially stagnant portion, a heating device may also be disposed in a main portion of the conduit through which the fluid flows. Thus the heating device in the said substantially stagnant portion may be the only heating device whose electrical power is varied so as to vary its temperature differential with respect to that of the fluid. The amount of electrical power supplied to the heating device, or to at least one of the heating devices, may be varied cyclically, the temperature of the respective heating device being determined at a plurality of times during the substantially cylindrical variation.

Preferably, the determination of the said temperature is used to deduce the mean temperature of the respective heating device, the amplitude of variation of its temperature, and the phase lag between temperature and power.

The said amplitude may be corrected by using the said phase lag to give an undamped amplitude, and the latter may be used with the mean temperature to determine the ambient temperature.

A correction may be made to compensate for the effect of the wave which is created by the thermal disturbance of the heating device whose electrical power is varied cyclically.

The invention also comprises apparatus for measuring the Reynolds Number of a fluid or for measuring a parameter of the fluid whose value is dependent on the said Reynolds Number, the said apparatus comprising a conduit, at least one electrical heating device in heat transfer relationship with the fluid in a respective portion of said conduit, means for supplying electrical power to the or each heating device, means for effecting a variation in the amount of electrical power supplied to at least one of said heating devices so as to vary its temperature differential with respect to that of the fluid while ensuring that the temperature of the heating device is always above that of the fluid, means for sensing the temperature of the heating device at different times during the said variation, means for determining therefrom the power loss of the or at least one of the heating devices per unit temperature. and means for employing the said power loss per unit temperature to calculate the said Reynoids Number or the said parameter.

The invention is illustrated, merely by way of example, in the accompanying drawings, in which: Figure 1 is a cross-sectional view of a part of a first embodiment of a flowmeter according to the present invention for measuring the mass flow of a fluid, Figure 2 is a block diagram of another part of the flowmeter of Figure 1, Figure 3 is a diagrammatical perspective view of a part of a second embodiment of a flowmeter according to the present invention for measuring the mass flow of a fluid, Figure 4 is a diagrammatic view of a part of the structure shown in Figure 3, Figure 5 is a view, partly in section, of a part of a third embodiment of a flowmeter according to the present invention for measuring the mass flow of a fluid.

Figure 6 shows graphs of the variation of power and temperature with time of an electrical heating device forming part of the said third embodiment, and Figure 7 is a block diagram of the said third embodiment.

In Figure 1 there is shown a part of a first flowmeter 10 which comprises a stem 11 which is adapted to be mounted in and sealed to a cup-shaped, or "top hat", housing 12. The latter is integral with, or sealed in an opening 13 in a wall 14 of a pipe 1 5 through which may flow a fluid, whose mass flow is to be determined.

Secured to, and sealed to, the stem 11 is a cylindrical housing 1 6 within which there is mounted concentrically a flow sampling tube 1 7. The flow sampling tube 1 7 has a portion 20, whose crosssectional area remains substantially constant axially, and a tapering portion 21 which communicates with the portion 20.The stem 11 has an inlet passage 22 therein which is arranged to receive fluid from the pipe 1 5 which has passed through an annular space 23 between the housings 12, 1 6. This fluid passes successively through the portions 20, 21 and thence through an orifice resistrictor 24 to the interior of a hollow tip or probe 25 which extends to a known position in the pipe 1 5. The construction of the tip or probe 25 is explained more fully in British Patent No. 2,003,659B.

The hollow tip 25 has an output port 26, e.g. at the distal end of the hollow tip 25, to permit the fluid which has passed through the sampling tube 1 7 to be returned to the pipe 1 5.

Mounted in apertures 30, 31 in the portions 20, 21 respectively are ceramic mounts 32,33 respectively. The ceramic mounts 32, 33 respectively carry plate-like electrical heating devices 34, 35 of substantially the same shape and other characteristics. Each of the plate-like electrical heating devices 34, 35 is mounted at each of its ends on an alumina block 36 so as to be spaced from its respective ceramic mount by a narrow gap 37. Each of the heating devices 34,35 is constituted by a platinum resistance thermometer comprising a printed pattern of platinum on an alumina substrate.The heating device 34 is connected by a pair of lead wires 40 to a power source constituted by a current generator 41 (Figure 2), while the heating device 35 is connected by a pair of lead wires 42 to the power source constituted by a current generator 43.

Referring to Figure 2, the current through each of the heating devices 34, 35 is controlled by a digital to analog current converter 44, while the voltage developed across each of the heating devices 34, 35 is measured by an analog to digital converter 45, both of the converters 44, 45 being controlled and read by a microcomputer 46.

The microcomputer 46 is so programmed that, in operation one of the heating devices 34, 35 is maintained at a first temperature differential, e.g. 500 C, above the temperature of the fluid for a predetermined period, e.g. one minute, while the other heating device is simultaneously maintained at a second temperature differential, e.g. 480C, above the temperature of the fluid for the said predetermined period, and then the said one and the said other heating device is respectively maintained at the second and first temperature differential for the said predetermined period.

Alternatively, this variatoin in the temperature differentials could be effected sinusoidally instead of stepwise.

Each said predetermined period should preferably be long enough to allow the transient heat, which is required to raise the thermal mass of the heating device to its new temperature, to die away. If a shorter predetermined period than this were selected, then the equations which are mentioned below would have to have additional terms therein and this would make the calculations more difficult. Thus, for example, those equations which contain a Q, term would have to have an additional dQ qdt differential term added, where razz which represents the thermal mass of the heating device, would need to be determined by calibration.

If desired, the heating devices 34, 35 may be alternatively operated at the first and second temperature differentials a plurality of times. As will be appreciated, the difference between the first and second temperature differentials is quite small and does not normally exceed 50C, so that the heating devices 34, 35 may be regarded as being driven at a substantially fixed temperature differential above the temperature of both the fluid and of the flow sampling tube 1 7.

The microcomputer 46 calculate both the power dissipated (V x i) and the resistance R, i.e. V/i, and hence the temperature of each of the heating devices 34, 35. The current can be changed slightly and the resulting change in power and temperature can be used to determine the temperature of the fluid and flow sampling tube 1 7. The heating devices 34, 35 are both mounted in the flow path through the flow sampling tube 1 7.The local flow around each of the heating devices 34, 35 is governed by the cross-sectional area of the flow sampling tube 1 7 at each of the heating devices 34, 35, and since the heating device 35 is mounted in the tapering portion 21 the linear flow of the fluid passing the heating device 35 will be a factor Ra times that passing the other heating device 34, Ra being the ratio of the cross-sectional areas of the flow sampling tube 1 7 at the heating device 34, 35 respectively. The conduction and radiation losses from each of the heating devices 34, 35 are similar and so to a first order these terms can be canacelled by subtraction.

If the voltage and current supplied to a heating device when the latter is at the said first temperature differential is respectively V, and i" and if the voltage and current supplied to a heating device when the latter is at the said second temperature differential is respectively V2 and i2, and if to a first order R = A + BT where A and B are constants of the heating devices, so that, for example, for a PT100 platinum resistance thermometer, A = 100 ohms, and B = 0.385 ohms/ C, then T, = (V1/i1 - A)/B, and T2 = (V2/i2 - A)/B (1) where T1 and T2 are the temperatures of the heating device at the times of the first and second temperature differentials.

Also Power, Power2 (2) (T, - Tfluid) (T2 - TtIuId) where Power, and Power2 are respectively the power supplied to the heating devices 34, 35 at T, and T2, while Fluid is the temperature of the fluid passing through the flow sampling tube 1 7.

Therefore Fluid = (V2i2T1 - V1i1T2)/(V2i2 - V1i1) (3) Each of the heating devices 34,35 is operated in this way and TflUid at each heating device can therefore be accurately calculated, enabling temperture gradients in the flow sampling tube 17 to be overcome and enabling the local temperature of the fluid to be inferred without further measurement.

The heat loss Q, for one of the heating devices 34, 35 is as follows: Q, = a1K(Ts1 -Tg1) (Re") + 1K(Ts1 -Tg1) + #1(Ts1 - Tb1) + 8, (Ts14-Tb4) (4) Where Ts, is the temperature of the said one heating device, Tg1 is the temperature of the fluid local, to the said one heating device, Tb, is the temperature of the ceramic mount local to the said one heating device, K is the thermal conductivity of the fluid, y, 1' Pi' and 81 are constants depending upon the shape of the said one heating device and the parts to which it is connected, Re is the Reynolds number of the fluid and n is a factor which depends upon the shape of the heating devices and has a value between 0.45 and 0.5.

The first of the terms in the above expression (4) arises from the fact that each of the heating devices is in the stream of fluid passing through the flow sampling tube 17 and is therefore subject to forced convection, whereby there is heat loss which is proportional to the Reynolds number of the fluid; the second of the terms therein arises from the heat conduction through the thin film of fluid between the heating device and the adjacent ceramic mount, this heat conduction occurring because of the temperature difference between the heating device and the fluid; the third of the terms therein arises from the heat conduction through the alumina blocks 36 and ceramic mounts 32, 33; while the fourth of the terms therein arises from the radiation from the heating device which occurs because the heating device is hotter than the flow sampling tube 17.

As will be appreciated, the heating devices 34, 35 are operating in substantially the same conditions except that the local velocity of the fluid passing the heating device 35 is much greater than that passing the heating device 34.

Thus provided Tb, and Tga are the same or very nearly the same, which is very likely, and provided that it is arranged that (Z2, p2l Y2 and 6,, which are the constants relating to the other heating device and the parts to which it is connected, are respectively, substantially the same as the constants a,, p1 y, and S,, which is ensured by matching the heating devices, then it is possible to divide the above expression through by the term (Ts, -- Tg,) since the latter term can be obtained from equation (2) above.So divided and taking account of the heat losses Q1, Q2 Of each of the heating devices 34,35 then Qg Q2 = aK(Re1 - Re2) (5) (Ts1 -Tg1) (Ts2-Tg2) when Ts2 and Tg2 are respectively the temperature of the other heating devices and of the fluid local thereto, and Re, and Re2 are the Reynolds Numbers of the fluid adjacent to the heating devices 34, 35 respectively, although there will be a small error if the radiation terms are not equal, i.e. Tg, + Tg2.

Thus by the method described above the true temperature differential of each of the heating devices with respect to the fluid will have been calculated, it will be divided by the heat loss of each of the heating devices, and provided that the heating devices are very similar geometrically, then the above mentioned second third and fourth terms of equation (4) will be cancelled out, leaving only the first of the said terms of equation (4) which is proportional to the thermal conductivity K of the fluid and to the Reynolds Number of the fluid.

With respect, moreover, to equation (5) above, Re, and Re2 depend upon the relative cross-sectional areas of the flow sampling tube 1 7 adjacent the respective heating devices 34, 35. If the ratio of these cross-sectional areas is Ra, then Re, Re2= (6) Ra Therefore the power loss (mW) per unit temperature (OC) of each of the heating devices 34, 35, i.e. its dissipation constant, is given by the expression Dissipation constant difference (mW/ C) = a K Re1 (1 - 1 (7) Ran Thus the dissipation constant depends on the fluid thermal conductivity, the Reynolds Number of the fluid and the ratio Ra.

The Reynolds Number terms may be removed from expression (5) as follows:

Where Ts and Tg are the mean temperatures respectively of the heating devices and of the fluid local to these devices.

Rearranging expression (8), this gives

This value of K is used by the microcomputer 46 to calculate the value of the Reynolds Number Re from equation (7). This Reynolds Number will be that of the fluid passing through the flow sampling tube 17 and therefore will be proportional to that of the fluid passing through the pipe 1 5.

The values a, /3, y, and S are all determined by calibration at the manufacturing stage by passing two gases of known different thermal conductivity through the flowmeter and measuring the heat loss of the heating devices when operated at two different known temperatures and with a known fluid temperature. Moreover, since the heating devices are constituted by platinum resistance thermometers, the value of Ts will be known exactly from its resistance.

Thus since the Reynolds Number of the fluid passing through the pipe 1 5 can be calculated, provided the viscosity of this fluid remains constant, the mass flow of the fluid through the pipe 1 5 can be calculated since the Reynolds Number is directly proportional to the mass flow of the fluid divided by its viscosity. All the above calculations are of course made by the microcomputer 46 which is appropriately programmed for the purpose.

The flowmeter described above has the following advantages: (1) As the heating devices 34, 35 operate at a substantially constant temperature differential above the fluid temperature notwithstanding the technique for varying this temperature slightly which is described above, there is no fundamental upper limit on the temperature of operation of the flowmeter which may thus be used up to say 8000 C. This is in contrast to previously known flowmeters in which the temperature of a reference heating device in a relatively stagnant region was maintained at a predetermined working temperature and power was supplied to a main flow heating device to adjust it to a temperature equal to that of the reference heating device.Thus in the known-device there was an upper limit (e.g. 2000C) to the temperature of the fluid, which temperature needed to be substantially below the said predetermined working temperature.

(2) The heating devices 34, 35 are constituted by platinum resistance thermometers which have a positive linear resistance temperature coefficient which is advantageous as it avoids any problems of cold start-up. In contrast, the heating devices of the said known flowmeter were thermistors which have a negative resistance-temperature coefficient which is not self-starting as it cannot draw sufficient power to heat itself up and reduce its resistance when used at low temperatures, e.g. below -200C.

(3) The flowmeter described above does not use a reference heating device in a relatively stagnant region and complications due to temperature changes, density changes and condensation changes arising from the use of such a relatively stagnant region therefore do not occur. Such complications give a large source of error in the known flowmeters.

(4) The flowmeter described above can readily be used with an appropriately programmed commercially available microcomputer, e.g. the Sarasota Automation 900 Series microcomputer.

(5) The flowmeter described above compensates completely correctly for changes in the thermal conductivity of the fluid.

(6) The technique for varying the temperature differential of the heating devices described above makes it possible to compensate for thermal gradients along the flow sampling tube 1 7 and from the centre to the wall of the pipe 1 5, since the correct local temperature is determined in each place.

In the flowmeter described above, the spaces between the heating devices 34, 35 and their respective ceramic mounts 32, 33 is kept as small as possible (e.g. to a value not exceeding 1.0 mm and typically to a value of 0.25 mm in order to ensure that the heat losses from the heating devices 34, 35 are primarily by conduction rather than by natural convection, since this substantially improves the accuracy of the flowmeter. Thus it is desirable to arrange that the Grashof Number of each said space which represents the heat loss due to natural convection, should not substantially exceed 2000. Since the spaces between the heating devices 34, 35 and their respective ceramic mounts 32, 33 are made as small as possible, there is a risk that these spaces will be fouled up by dirt or condensation.However, since both the heating devices 34, 35 are in the main flow through the flow sampling tube 17, in contrast to one of them being in a relatively stagnant region, there will tend to be automatic flushing of the said spaces. Moreover, the condensation can be removed by raising the temperature of the heating devices 34, 35 so as to "boil off" the condensation.

Fouling or condensation can be detected by observing whether the value of K which is obtained from the use of equation (9) exceeds that of any known gas or exceeds that of any gas expected to exist in the fluid stream.

The flowmeter described above, however, is not suitable for very low flows, e.g. a flow of about 1 5 cms/sec through the portion 20, since this will cause natural convection heat loss to occur from the heating device 34 at a time when forced convection heat loss is occurring from the heating device 35, and this will mean that the mass flow readings produced by the flowmeter will not be accurate at such low flows as the heat loss will no longer be in accordance with that set forth in equation (4). Such low flows, however, are capable of being properly measured by the flowmeter of Figures 3 and 4.

The flowmeter of Figures 3 and 4 is generally similar to that of Figures 1 and 2 and is operated in a generally similar manner and therefore will not be described in detail. In the flowmeter of Figures 3 and 4, however, use is made of a flow sampling tube 50 which is perfectly cylindrical throughout and which thus does not have a tapering portion 21. Mounted in the centre of the flow sampling tube 50 is an assembly 51 comprising two platinum resistance thermometer type heating devices 52, 53 which are identical in construction to the heating devices 34, 35. The heating devices 52, 53 are thus plate-like members which are arranged parallel to each other and are spaced apart by a narrow gap a (Figure 4).

The heating device 52 is connected to its power source (not shown) by wire leads 54, 55 while the heating device 53 is connected to its power source by wire leads 56, 57. The heating devices 52, 53 are spaced from each other by end spacers 60, 61 and the assembly 51 is mounted in the flow sampling tube 50 by supports 62, 63. As will readily be appreciated, in the construction shown in Figures 3 and 4, the heating devices 52, 53 will go simultaneously into natural convection at low flows. At other flows, however, the heating devices 52, 53 will lose heat to the fluid stream by forced convection. As will be appreciated, the side of each of the heating devices 52, 53 remote from the other is open to the flow of the fluid through the flow sampling tube 50, while a stagnant pocket of fluid is created in the narrow gap a.

The assembly 51 is made as symmetrical as possible, and the side of each heating device 52, 53 remote from the other will lose heat to the fluid stream by forced convection. If both heating devices 52, 53 are at the same temperature, no heat flows from one to the other, although each of them will lose heat by forced convection to the fluid which passes them by virtue of forced convection and they will also lose heat to the flow sampling tube 50 by radiation and conduction.

If, however, they are at different temperatures, then in addition to the heat loss by forced convection, conduction and radiation, heat flows from the hotter device to the colder device by conduction through the fluid in the gap a, through the end spacers 60, 61 and supports 62, 63 and by radiation. At the same time, the cooler device loses heat at a reduced rate by forced convection, by radiation and by fluid conduction.The microcomputer 46 can be employed to vary the temperature differentials of the heating devices 52, 53 with respect to the temperature of the fluid in the manner described above, e.g. by holding the temperature differential of the heating device 52 at 500C for one minute while simultaneously holding the temperature differential of the heating device 53 at 480C for this period, and then holding the temperature differentials of the heating devices 52, 53 at 480C, 500C respectively for the next minute, or by varying them sinusoidally in antiphase about a mean temperature.

In this state, the steady state heat losses Q,, Q2 from the hotter and cooler heating devices respectively are as follows: Q, = aK(Ts1 - Tg) Re" + K(Ts1 - Ts2) + (Ts14 - Ts24) + y(Ts1 - Ts2) + E(TS14 - TB4) (10) where E is a constant depending on the surface area of the heating device and the surrounding geometry, and TB is the body temperature, i.e. the temperature of the wall of the flow sampling tube 17.

In equation (10), the first term arises from forced convection, the second term arises from conduction through the fluid from one heating device to the other, the third term arises from radiation through the fluid from one heating device to the other, the fourth term arises from conduction through the blocks 36, and the fifth term arises from radiation from one of the heating devices to the wall of the flow sampling tube 17.

Q2=#K(Ts - Tg)Ren - K(Ts1 -Ts2) (TSi4T524)Y(T5lT52)+(Ts24TB4) (11) Since the value of Tg can be obtained by varying the temperature differential as explained above, if each side of the equations (10) and (11) are divided through by (Ts1 -Tg) and (Ts2-Tg) respectively, then Q1 Q2 + 2aK Re" + 2E(Ts + T8)(Ts2 + TB2) (12) (Ts1-Tg) (Ts2-Tg) where Ts is (Ts1 + Ts2)/2.

The radiation term can be calibrated out as a zero offset.

Again by subtraction.

Q, Q2 2/3K + 2S(Ts + TB)(Ts2 + T82) + 2y (13) (Ts1-Tg) (Ts2-Tg) The values of , y and S can be found by using gases of different thermal conductivity and calibrating at different fluid temperatures. Consequently the value of K can be calculated from equation (13). This value of K can then be used in equation (12) to give a true Reynoids Number from which the mass flow may be deduced by knowledge of the viscosity of the fluid.

No natural convection will occur between the heating devices 52, 53 provided that the Grashof Number is less than 2000, that is (Ts1 - Ts2) p X3 -- < 2000.

Ts p where p is the density and FL is the viscosity of the fluid, and x is the distance from which the heating devices are separated from each other.

This is readily achieved for a wide range of cases over a wide range of pressures and temperatures by ensuring that x is about 0.25 mm, although at high temperatures reduced spacing will be required.

However, in this case, even if Q2 = 0 and Ts1 - Tg = 500then Ts1 - Ts2 is only about 40 so that highly accurate measurement of temperature is necessary. However, it is easier to measure changes in temperature if each of the heating devices 52, 53 is alternatively made hotter and cooler than the other.

Thus, for example, the heating device 52 may be hotter than the heating device 53 for the first minute and then the heating device 53 may be hotter than the heating device 52 for the second minute. In fact such alternate operation of the heating device 52, 53 at one minute intervals may be continuous or may be repeated only intermittently. By taking mean readings of the heating devices 52, 53 problems arising from their not being quite square in the flow sample tube 50 can be overcome.

The flowmeter illustrated in Figures 3 and 4 has the following advantages: (1) The flowmeter illustrated for use at low flows since both the heating devices 52, 53 go into natural convection together at low flows.

(2) In spite of the deliberate variation in the temperatures of the heating devices 52, 53 the sum of the two signals therefrom gives a flow signal having no deliberate alternating components.

In either the construction of Figures 1 and 2 or Figures 3 and 4, the microcomputer 46 can be programmed to indicate when K is outside a given range, since this will indicate that the narrow gaps 37, a are fouling up and that the flowmeter is in need of cleaning. Moreover, the assembly 51, like the assembly of the heating devices 34, 35 should ideally be provided as shown with four wire leads 56, 57 to determine the power and resistance correctly.

In the apparatus described above, the mass flow of the main flow through the pipe 1 5 is derived by determining the mass flow of the sample flow which passes through the flow sampling tube 1 7.

However, if the main flow were sufficiently small, e.g. because the diameter of the pipe 15 is -" (0.64 cms), then the flow sampling tube 17 need not be employed and at least one of the heating devices may be located in the pipe 1 5.

In Figure 5 there is shown a probe 64 which forms part of a third embodiment of a flowmeter according to the present invention. The probe extends through and is sealed in a wall 67, of a housing or pocket 68 which is attached to a wall 65 of a pipe 66 through which may flow a fluid whose mass flow is to be determined.

The probe 64 has a conduit 70 therein. The conduit 70 has an inlet 72, into which may pass fluid (e.g. gas) from the pocket 68, and an outlet 71 from which the fluid may return to the pipe 66. The conduit 70 also has a portion 73 which extends outwardly of the inlet 72 and which therefore contains relatively stagnant fluid. In the end of the portion 73 remote from the inlet 72 there is mounted a reference heating device 74, while a main flow heating device 75 is disposed in the main flow of fluid passing through the conduit 70. The reference heating device 74 is spaced from the inlet 72 by a distance equal to at least twice the diameter of the pocket 68 (although, for purposes of simplification this is not shown in Figure 5). Each of the heating devices 74, 75 may be a platinum resistance thermometer.The heating devices 74, 75 are mounted in the probe 64 by supports 76, 77 respectively.

The reference heating device 74 and the main flow heating device 75 are supplied by a database 80 of a micro-computer 81 (Figure 7) with voitages such that the temperature of each of the heating devices 74, 75 is always above that of the fluid passing through the conduit 70. There is no deliberate cyclical perturbation of the power supply to the main flow heating device 75, the voltage supplied to the main flow heating device 75 being such as to maintain the latter at a substantially constant temperature differential, which is the same as the mean differential of the reference heating device 74, e.g. 500C above the temperature of the fluid passing through the conduit 70. It should be remembered that, although everything else remains steady, power has to increase with flow to maintain the temperature differential.Thus in equation (4) above Q, increases as Re increases. However, the voltage supplied to the reference heating device 74, while also maintaining the latter at a mean temperature which is approximately the same as the said constant temperature differential, varies sinusoid ally throughout a predetermined cycle, e.g. of 48 seconds. As shown in Figure 6, this sinusoidal variation in the power supply to the reference heating device 74 will cause the temperature of the latter to vary sinusoidally after a time lag.

If readings of the temperature of the reference heating device 74 are taken every second during such a 48 second cycle, then the micro-computer 81 can carry out the following calculations:

where W (which is the same as #mean referred to below) is the average temperature of the reference heating device 74 over one sinusoidal cycle of 48 seconds.

are the instantaneous values of the temperature of the reference heating device 74, 0o being the initial temperature of the reference heating device 74 at the start of the cycle, and 0" O2 being the temperature of the reference heating device 74 at one second and two seconds later respectively, and so on, and U and V are convenient labels which arise as follows from Fourier's Theorem:: f(t) = a0 + a1 sin a)tt ...... ansin nwt (17) + b, cos wt + bn cos n#t where f(t) is a periodic function of periodicity of 1/w. The coefficients a, etc and b1 etc are given by the expressions:

W is equivalent to a0 U is equivalent to a, V is equivalent to b1.

As the reference heating device 74 is being excited with a sinusoidal power variation and the system is linear, we would expect a2, b2 and all the higher values of the coefficients a, b to be zero.

The integrals in the expressions (18) and (19) may be replaced by summations as follows:

Now f(t;) = Oi, the instantaneous temperature. Therefore

At the end of the 48 second cycle, #mean (i.e. W) is calculated and the uncorrected value for the temperature amplitude of the reference heating device 74

Since the reference heating device 74 has a thermal mass, then its temperature cycle lags the variation of the power applied to it by a phase angle #.

tan I = - V/U (23) In order to calculate the ambient temperature, it is necessary to determine the amplitude of variation that would occur if there were no such lag, i.e. if the variation of the reference heating device 74 was performed very slowly. This amplitude is given by

If fouling occurs in the conduit 70, then the value of V/U, i.e. the time constant, will change.

T = -- V/U/(2#/48) (25) where T = thermal mass/composite conductivity of the fluid in the pocket 68 and of the support 76 in parallel.

The composite conductivity Su of the fluid in the pocket 68 and of the support 76 in parallel is given by the expression: Su = the amplitude of variation of the power supply to the reference heating device 74/the correct amplitude of the temperature variation of the reference heating device 74.

The thermal mass of the reference heating device 74 can thus be calculated. If this changes, then fouling of the pocket 68 and/or reference heating device 74 is indicated.

Put simply, the temperature of the fluid in the conduit 70 and in the pocket 68 is given by: P mean fluid = 0mean ' (26) S where mean is the mean power supplied to the reference heating device 74, and 0fluid is the temperature of the fluid passing through the conduit 70 and filling the pocket 68.

However, since a correction should preferably be made for the effect of the wave which is created by the thermal disturbance to the reference heating device 74 and which travels through the body of the probe 64, it is desirable to replace Su which has been obtained by the use of the above equations, by S, where S is the composite thermal conductivity through the support 76 and through the fluid passing through the conduit 70.

S is calculated as follows: Su S= (27) (1 +Fs.Su) where Fa = a + bS + cS2 + dS3, and a, b, c and d are calibration constants.

The thermal conductivity Kfluid of the fluid passing through the conduit 70 is related to the composite thermal conductivity S by the formula Kfluid = e + fS + gS2 + hS3, (28) where e, f, g and h are calibration constants.

Once the values of Kfluid and # fluid are obtained, these values and the heat loss from the main flow heating device 75 are used by the micro-computer 81 to calculate the value of the Reynolds Number R,,; from equation (4) by ignoring the natural convection term, and correcting for the radiation and conduction terms which are determined by calibration. The micro-computer 81 thus calculates the Reynolds Number of the fluid passing through the pipe 66.

#fluid should also desirably be corrected by using S in place of Su, i.e.

fluid = Demean = Pmean/S (29) One might expect from simple theory that 1 1 1 Fluid. Ksupport 4 + + ----- or 5 = S Kfluid Ksupport (Ksupport + Kfluid) Re-arranging for Kfluid:-- S Kf,Ujd ~ S(1 + ) (30) Kaupport where Support is the thermal conductivity of the support 76.

In practice, however, Kfluid can be better calculated from formula (28) above, which agrees better with experimental results. This may be explained physically as follows. In a high conductive fluid, the support 76 is better cooled and so the effective area of conduction is reduced. In a poorly conductive fluid, however, the support 76 gets hotter and so the effective area of conduction in the fluid is increased.

Although the above description of the said third embodiment is based on the taking of 48 measurements of the instantaneous temperature of the reference heating device 74, it will be readily appreciated that this number of measurements is purely exemplary. However, the accuracy of the result obtained is obviously related to the number of temperature measurements taken and improves approximately as , so that the use of 48 measurements is about 7 times better than a single point evaluation.

It will also be appreciated that the manner in which Kfluid and of lurid are calculated in the third embodiment may be used also in calculating the values of K fluid and 0fluid in the first and second embodiments.

It will further be appreciated that although a sinusoidal variation of the power supply to the reference heating device 74 is described above, any cyclical variation of this power supply can theoretically be employed.

Referring now to Figure 7, the data base 80 of the micro-computer 81 comprises a CPU (central processing unit) section 82, a RAM (random access memory) section 83, a ROM (read only memory) section 84, an EA ROM/EE PROM (eiectrically alterable read only memory/electrically erasable programmable read only memory) section 85 and a D to A (digital to analog) and A to D (analog to digital) section 86.

The D to A and A to D section 86 is supplied with auxiliary analog inputs 87 (e.g. of 4-20 mA or 1 -5V) and with inputs from the heating devices 74, 75. These inputs may, for instance, comprise inputs from the heating devices 74, 75, and/or from a platinum resistance thermometer (not shown) or other temperature sensor disposed in the pipe 66, and/or from a pressure sensor disposed in the pipe 66. The auxiliary analog inputs 87 may also comprise an input from another micro-computer and respective probe (not shown) which are similar to the parts 64, 81 but are arranged to measure a higher or lower range of flows so as to extend the scope of the instrument from a range of flows of, say, 8 to 1 to a range of flows of, say, 70 to 1.Such an arrangement is, for example, very useful in measuring gas consumption which varies considerably during any period of 24 hours.

All the above-mentioned inputs are analog inputs but these are converted to digital form in the section 86 so that they may be processed. After such processing they are re-converted to analog form in the section 86 so as to be transmitted as an analog output 90, e.g. of 4-20 mA. This output may be transmitted to a chart recorder or other instrument (not shown), e.g. to indicate how the mass flow varies in a 24 hour period.

The main program is held in the ROM section 84 which control the operation of the CPU section 82, the RAM section 83 acting as a temporary store of information from the CPU section 82. The EA ROM/EE PROM section 85 contains non volatile computer constants and programme links which can be readily but infrequently changed. Information from and to the RAM section 83 is transmitted by way of a database access and monitor 91 to and from a keyboard/display 92 and a communications interface 93.

The latter enables information from the RAM section 93 to be transmitted over a telephone, radio, satellite or other communications link to a distant location.

The database access and monitor 91 comprises a Peripheral Interface Adapter (PIA) and an Asynchronous Communication Interface Adapter (ACIA), the latter permitting information to be transmitted to and from the RAM section 83 at any time.

The database access and monitor 91 is connected to an alarm operating device 94 which may be arranged to operate the contact closures of a relay (not shown) so that an audible or visual alarm may be produced. Such an alarm could, for instance, be produced if the mass flow being measured was outside a given range.

The database 80 can also be arranged as shown to produce a pulse totaliser output 95 so as to indicate the weight flow or the volume flow or the energy flow per unit time. For example, if a flow of gas is being measured, a relay contact could be closed whenever a given cubic flow of gas had passed a certain point. If this contact closed X times in an hour, the pulse totaliser output 95 would indicate the cubic flow per hour as X units per hour.

Claims

1. A method of measuring the Reynolds Number of a fluid or of measuring a parameter of the fluid whose value is dependent on the said Reynolds Number, the said method comprising passing the fluid through a conduit, arranging at least one electrical heating device in heat transfer relationship with the fluid in a respective portion of said conduit, supplying the or each heating device with electrical power, effecting a variation in the amount of electrical power to the heating device, or to at least one of the heating devices, so as to vary its temperature differential with respect to that of the fluid while ensuring that the temperature of the heating device is always above that of the fluid, sensing the temperature of the or each heating device at different times during the said variation, determining therefrom the power loss of the or at least one of the heating devices per unit temperature, and employing the said power loss per unit temperature to effect a calculation of the said Reynolds Number or the said parameter.

2. A method as claimed in claim 1 in which there are two similar heating devices in the conduit, and the said calculation is effected by determining the difference between the power losses of each of the heating devices when the heating devices are simultaneously operated at different temperatures.

3. A methods claimed in claim 2 in which each of the two similar heating devices is maintained at a temperature above that of the fluid.

4. A method as claimed in claim 3 in which each heating device is always operated at a temperature of at least 300C above that of the fluid, and the temperature at which the heating devices are operated do not differ from each other at any time by more than 50C.

5. A method as claimed in claim 2 in which one of the heating devices is allowed to cool to the temperature of the fluid.

6. A method as claimed in any preceding claim in which the conduit comprises a flow sampling tube communicating with a pipe through which there is a main flow of the fluid.

7. A method as claimed in any preceding claim in which the or each heating device has a positive, substantially linear resistance temperature characteristic.

8. A method as claimed in claim 7 in which the or each heating device is a platinum resistance thermometer.

9. A method as claimed in any preceding claim in which the or each heating device is spaced from a support or from another heating device by a space such that the Grashof number of the space does not substantially exceed 2000.

10. A method as claimed in claim 2 or in any claim appendant thereto in which each of the heating devices is alternately operated so as to be relatively hotter and cooler than the other.

11. A method as claimed in claim 6 in which the flow sampling tube has two similar heating devices therein, one of which is disposed in a first portion of the flow sampling tube, the said first portion being of substantially constant cross-sectional area, and the other of which is disposed in a section portion of the flow sampling tube, the said second portion being a tapering portion or a portion having a substantially constant cross-sectional area which differs from that of the first portion.

12. A method as claimed in claim 6 in which the flow sampling tube has two similar heating devices therein which are disposed adjacent to each other.

1 3. A method as claimed in claim 12 in which the heating devices are plate-like members which are disposed parallel to each other.

14. A method as claimed in any of claims 1-1 0 in which there is a portion of the conduit in which the fluid is substantially stagnant, a said heating device being disposed in said portion.

1 5. A method as claimed in claim 14 in which, in addition to the heating device in the said substantially stagnant portion, a heating device is also disposed in the main portion of the conduit through which the fluid flows.

16. A method as claimed in claim 1 5 in which the heatingdevice in the said substantially stagnant portion is the only heating device whose electrical power is varied so as to vary its temperature differential with respect to that of the fluid.

1 7. A method as claimed in any preceding claim in which the amount of electrical power supplied to the heating device, or to at least one of the heating devices, is varied cyclically, the temperature of the respective heating device being determined at a plurality of times during the substantially cyclical variation.

1 8. A method as claimed in claim 17 in which the determination of the said temperature is used to deduce the mean temperature of the respective heating device, the amplitude of variation of its temperature, and the phase lag between temperature and power.

19. A method as claimed in claim 18 in which the said amplitude is corrected by using the said phase lag to give an undamped amplitude, and the latter is used with the mean temperature to determine the ambient temperature.

20. A method as claimed in any of claims 1 7-1 9 in which a correction is made to compensate for the effect of the wave which is created by the thermal disturbance of the heating device whose electrical power is varied cyclically.

21. A method of measuring the mass flow of a fluid substantially as hereinbefore described with reference to the drawings.

22. Apparatus for measuring the Reynolds Number of a fluid or for measuring a parameter of the fluid whose value is dependent on the said Reynolds Number, the said apparatus comprising a conduit, at least one electrical heating device in heat transfer relationship with the fluid in a respective portion of said conduit, means for supplying electrical power to the or each heating device, means for effecting a variation in the amount of electrical power supplied to at least one of said heating devices so as to vary its temperature differential with respect to that of the fluid while ensuring that the temperature of the heating device is always above that of the fluid, means for sensing the temperature of the heating device at different times during the said variation, means for determining therefrom the power loss of the or at least one of the heating devices per unit temperature, and means for employing the said power loss per unit temperature to calculate the said Reynolds Number or the said parameter.

23. Apparatus substantially as herein before described with reference to and as shown in the accompanying drawings.

24. Any novel integer or step, or combination of integers or steps, hereinbefore described and/or shown in the accompanying drawings, irrespective of whether the present claim is within the scope of, or relates to the same or a different invention from that of, the preceding claims.