WO1989003977A1

WO1989003977A1 - Method and arrangement for measuring gas flow parameters

Info

Publication number: WO1989003977A1
Application number: PCT/SE1988/000548
Authority: WO
Inventors: Bertil Johnsson
Original assignee: Fläkt Ab
Priority date: 1987-10-23
Filing date: 1988-10-20
Publication date: 1989-05-05
Also published as: SE8704134D0; DK89690D0; FI902012A0; SE8704134L; DK89690A; AU2623788A; EP0419469A1

Abstract

The present invention relates to a method and to apparatus for measuring the velocity and/or flow rate of a gas stream in a central assembly (1), in which the gas is caused to pass through at least one velocity-increasing constriction opening (26) between baffles (24) positioned in a plane at right angles to a duct section (15). A first total pressure in the assembly (1) is measured in a region upstream of the at least one constriction opening, preferably in a stagnation zone centrally in front of one of the baffles (24). A second pressure is measured at a location within or immediately downstream of the at least one constriction opening (26) with the aid of at least one measuring probe in the form of a circular-cylindrical measuring tube (32) which has at least one measuring orifice (34) on the downstream side of the tube (32) so as to obtain an amplified pressure difference value, this value being used to calculate the gas velocity and/or the gas flow rate.

Description

Method and arrangement for measuring gas flow parameters

The present invention relates to a method for measuring the velocity and/or the flow rate of a gas stream, particularly in a central unit or assembly, in accordance with the preamble of Claim 1. The invention also relates to an arrangement for carrying out the method.

At the present time there is no unitary and accepted method of measuring continuously or intermittently the flow rate in a ventilation system with a central assembly. The rate of air flow is often determined by measuring and summating the flow rate in several branched supply and exhaust air channels, e.g. by traversing with a pitot tube. The measurement of gas velocity and/or gas flow in passageways, e.g. ventilation conduits, is encumbered with many problems and those methods used hitherto to this end have many drawbacks. Furthermore, an uneven velocity distribution in such passageways will often create measuring problems.

One instrument often used to measure air speed is the pitot tube. This instrument comprises a double, angled tube which is introduced into the passageway with the tip oriented parallel with the gas stream. The tube includes a first opening for measuring a first pressure at its tip and second openings in the sides of the tube for measuring a second pressure. The total pressure, i.e. the sum of the static pressure and the dynamic pressure, is obtained in the first opening, whereas in the second openings only the static pressure is obtained, wherewith the difference between the two pressures constitutes the dynamic pressure, which corresponds to the velocity of the gas. One drawback with the pitot-tube, however, is that it must be placed precisely parallel with the direction of the gas stream in order to give a correct value. An alignment error of only some few degrees will mean that the measured' value will deviate significantly from the true value. In order to obtain a positive measuring result, the gas velocity should exceed 3 m/s. Another drawback with the pitot tube is that it will only produce a local value, which need not necessarily be representative of the gas flow rate or gas velocity in the whole of the passageway.

Flow rate can be more directly measured by inserting in the passageway or like flow line a calibrated restriction, such as a Venturi nozzle or tube. However, although this alternative method will eliminate error sources caused by irregular velocity distribution in the flow line, it results in a considerable loss in pressure, e.g. a loss in the order of 300-400 Pa (30-40 mm water column) . Naturally, such pressure losses will require a higher output from a fan or blower arranged in the flow line and therewith increase the running costs of, for instance, a ventilation system in which such flow measuring devices are installed.

In our earlier patent application SE-A-8701663-0 we have proposed the provision of a measuring device on the suction side of a fan, this device incorporating a throttle arrange- ment. During the actual measuring process, the throttle is set to a measuring position and the static pressure across the throttle is sensed. This static pressure provides a measurement of the gas flow past the measuring device in a normal operating state, in which the throttle is totally inactive, or almost so. With this method practically no pressure losses occur across the measuring device in its normal operational state. However, a measuring device of this kind necessitates complicated calibrations and calculations to be carried out in order to establish which gas streams correspond to the various pressure-drop values. Furthermore, the device cannot be used for continuous monitoring purposes, since the throttle is not set to a measuring position during normal operating conditions. US A 3 759 098 discloses an apparatus for determining fluid flow in a conduit by measuring flow resistance at an annular plate means within said conduit, the nominal diameter of which is said to be in the region of 100-200 mm, which means a very limited size. Particularly in a central assembly, the avarage velocity through the cross-sectional area is low. Applying the teaching of this US patent to a central assembly would result in a very low pressure drop and thus a low measuring signal. The cross-sectional area of a central assembly is considerably larger than the above metioned diameter of said conduit and the method according to this publication does not take into account variations of speed of gas flow across the cross-sectional area. Said speed is determined for a relatively small part of the flow of air only.

US A 3 129 587 and GB A 221 183/1910 relate to methods and devices for determination of the flow of gas by measuring the pressure drop via throttling means provided in a conduit.

DE A 2 330 746 concerns an apparatus, wherein gas flow is deter mined by measuring pressure drop across a plurality of minor orifices.

SE B 441 704 is similar to US A 3 759 098 and concerns an apparatus for measuring pressure difference due to flow resistance caused by an annular plate, page 4, lines 33-35. Particularly in a central assembly, the avarage speed across the cross-sectional area is low. Applying this latter previously known teaching would bring about a very low flow resistance and thus a low measuring signal and make this measurement less exact. This measuring method does not take into account variations of the speed of air flow across the cross-sectional area. The speed of air flow is determined for a relatively small part of the air flow only.

The object of the present invention is to provide a method of the aforesaid kind which is not encumbered with the drawbacks of the earlier known methods and to provide a method for measuring gas velocity and/or the rate of gas flow which will result in only small pressure losses, which will enable the gas stream to be measured continuously, which will engender a powerful measuring signal, and which places but a moderate demand on a precise angular setting and installation position of the measuring openings on the device. Another object of the invention is to provide a device for carrying out the method.

According to the invention this object is achieved with a method of the aforesaid kind by carrying out the measuring procedure in accordane with the procedural steps set forth in the characterizing clause of the main claim. A device for carrying out the method is characterized primarily by the features set forth in the characterizing clause of the first apparatus claim.

Thanks to the present invention, it is possible to determine very exactly in a central assembly the flow of gas by means of pressures provided by the flow of gas around a cylinder. The arrangements of baffles makes, that there may be any desired size of area of mea- surement. The connection between pressure drop across the plane measurement and the flow of air is not used for determining the flow of air. The air speed is measured at a plurality of places the total flow of air. When the air or gas passes the measuring device, the speed of air is substantially constant across the plane of measurement. Possible variations of the speed of air across the cross-sectional area are reduced within the area of measurement.

When practising the inventive method, there is obtained a sensed pressure differential which is slightly more than twice the dynamic pressure in the constriction orifice and about three times as large as the pressure drop across the measuring instrument. This- enables a measurement to be taken with a sufficiently large output measuring signal and, at the same time, obtain only a very small drop in pressure across the measuring instrument. Consequently, the instrument, or device, can be coupled to the system continuously without creating excessively large pressure losses in, e.g., a control assembly and therewith without needing to increase the power requirement of an associated fan. The invention is based on the application of a particu ar flow-technical phenomenon occurring when a gas flows around a cylinder. An explanation of this phenomenon is given below in conjunction with the description of Figure 5.

This phenomenon is utilized in accordance with the present invention, by placing a cylindrical measuring probe in at least one of the constriction orifices of the measuring device. In this way, it is possible to measure on the forward or upstream side of the probe a total pressure which is the sum of the static and dynamic pressures and which, if the losses in pressure are ignored, is equal to the total pressure measurable in the passageway or flow-line forward or upstream of the constriction orifice in question. However, a subpressure prevails on the rearward or downstream side of the cylindrical probe, due to the aforesaid=£low technical phenomenon. This is utilized in accordance with the invention, by providing measuring openings or orifices on the downstream side of a cylindrical measuring probe, thereby to obtain an amplified measuring signal.

Theoretic background of the invention

The invention is based on those pressure conditions, which prevail when air flows around a cylinder at certain flow velocities.

Assume first an ideal flow, i.e. the flow is free from friction and is stationary. When the velocity and pressure of the undisturbed unidimensional air stream upstream of the cylinder are C_i and p_i respectively, the velocity C and the pressure p at the cylinder surface are given by the following relationship: (of Figure 5)

C = 2 * C_i * sin

where α is the angle from the forward stagnation point to the measuring point.

The pressure coefficient C_p is defined as:

The velocity along the surface of the cylinder thus increases from zero at the forward stagnation point to a maximum of 2 x C_i at the point of largest cylinder width. The pressure is changed analogously from a maximum at the forward stagnation point to a minimum value at the angles α = 90 and 270º. Full pressure recovery is at the rearward stagnation point. Cf Figure 6.

An incompressible f low of air around a cylindrical surface coincides well on the forward side of the cylinder with that of an ideal fluid. Separation takes place at a given angle α and the agreement becomes poor. In the relieved region on the downstream side of the cylinder, only limited pressure recovery is obtained and the pressure remains relatively constant. This is influenced, however, by Reynolds number.

The value of the pressure coefficient C_p has been determined empirically for different values of Reynolds number Re and at various large angles α. Examples in this respect are shown in the diagram of Figure 6.

In Figure 6, the pressure distribution is given as a function of the angle α in the case of an ideal flow around a cylinder and a flow which is not ideal. The Figure 6 diagram also includes those values of the pressure coefficient C_p which were obtained when carrying out tests on one of the measuring tubes in the measuring device. The pressure in the rearward stagnation point is used as a measuring pressure on the downstream side of the measuring device.

In the case of fluid flow around a cylindrical surface, Reynolds number is defined as

d = cylinder diameter, [M] C₁ = air speed [M/S] p = air density [KG/M ] μ = the dynamic viscosity of the air, JJKG/SM]

Those values of the pressure coefficient C_p plotted in the Figure 6 diagram have been measured at Reynolds numbers within the range

C * 10³ < Re < 12 * 10³

As will be seen from Figure 6, the pressure-coefficient

C curve is essentially flat in the area around α = 180º. This is a very valuable factor in the case of the present invention, since it means that a less than precise setting of the measuring orifices or openings in the probe will not cause a change in the measured pressure value, i.e. the true value is registered.

Brief description of the invention The present invention will now be described in more detail with reference to an exemplifying, non-limiting embodiment thereof and with reference to the accompanying drawings, in which:

Figure 1 is a perspective view of an inventive measuring device located continguous with an assembly part; Figure 2 illustrates two baffles and measuring probes forming part of the device of Figure 1; Figure 3 is a diagram which shows the relationship between pressure difference and flow rate value measured by the inventive device;

Figure 4 is a diagram which shows the relationship between the gas velocity and differential pressure measured by the inventive device and the pressure drop across the device; Figure 5 illustrates a circular-cylindrical body placed in a gas flow; Figure 6 illustrates a diagram which shows variations in the pressure coefficient at different angular positions during flow around the cylinder in Figure 5; and Figure 7 is a schematic view of a central assembly in a flow passageway.

The present invention is intended particularly for use in combination with a central assembly (Figure 7) for a ventilation or air conditioning system. The central assembly 1 is connected to an inlet duct 2 and an outlet duct 3. In conventional cases, the assembly comprises a filter 4, a cooling unit 5 and a heating unit 6.

The illustrated assembly 1 also includes an outer casing 12 for a fan 7. For reasons of a process-technical nature, the speed in the heating unit 6 is maximized to 5 m/sec. and in the cooling or refrigerating unit 5 to 4 m/sec. The inlet duct 2 and the outlet duct 3 are most often branched at a location closely adjacent to the central assembly. This makes it difficult to measure the whole of the flow at a single pointin these ducts. Furthermore, the majority of the earlier known measuring apparatus require an undisturbed, stable flow in a straight duct section whose length corresponds to twice the hydraulic diameter. Consequently, when the duct sections are branched in the close proximity of the central assembly, as is often the case, it is not possible to place such measuring devices in the ducts 2 and 3 for the entire flow.

Figure 1 illustrates schematically and in perspective a measuring device 10 which is located in front of an assembly section 12, which in the illustrated case is an outer fan housing which connects with an outlet opening 14. Further assembly sections may be arranged forwardly of the measuring device 10. The illustrated measuring device 10 comprises a substantially rectangular section part 15, comprising sides 16 and 18, bottom 20 and top 22. Located between the bottom 20 and the top 22 are substantially parallel baffles 24 with intermediate constriction openings or orifices 26. Arranged in front of at least one of these baffles 24 is a first measuring probe 28 having at least one first measuring orifice 30 located centrally on the upstream side of the probe for measuring a first total pressure. By locating a measuring probe in a stagnation zone centrally in front of and immediately adjacent a baffle, the pressure measured will comprise almost solely static pressure. Because the dynamic pressure forms only a small part of the measured pressure, or no part at all, the pressure measurement will not be affected by any possible obliqueness in the positional setting of the probe orifices 30. In principle, however, firs probes 28 can be placed at any desired position on the upstream side of the baffles and at any desired distance there- from, say for instance one meter in front of the baffles, provided that stable flow conditions prevail at the measuring site and that no device or apparatus which is liable to cause a reduction in pressure is located between the probes 28 and the baffles 24.

Located centrally in at least one of the openings 26 is a second circular-cylindrical measuring probe 32 which has at least one second measuring orifice 34 arranged centrally on the downstream side of the probe 32. The second probe 32 is preferably located centrally in the opening 26, although this is not an absolute necessity. The probe may be positioned anywhere in the constriction opening 26, or immediately behind this opening, provided that it is located well within the extension 36' of the opening sides 36. An alternative positioning is shown at 32'. The total throughflow area has been chosen so that a turbulent flow will always prevail therewithin. The air velocity and there- with the dynamic pressure is then constant across the whole of the free throughflow area. These conditions also continue slightly on the downstream side of the constriction openings. For reasons, inter alia, of a technical manufacturing nature, it has been found particularly convenient to place the second probe 32 immediately downstream of the openings 26, suitably 15 mm therefrom. The first and second measuring probes 28 and 32 are connected to respective outlet nipples 38 and 40, by means of connector pipes not shown. When more probes 28, 32 are used at respective measuring locations, the probes are coupled together, wherewith any pressure difference which occurs will be equalized. Pipes 42 and 44 extend from the nipples to an instrument 46 for measuring pressure difference, this instrument being only schematically indicated. The instrument 46 may be any desired kind and in its simplest form will comprise a liquid-filled U-tube in which the difference in levels is a direct indication of the pressure difference. Alternatively, the instrument 46 may exhibit or be connected to an analogue or digital pressure indicator 48. The instrument 46 may also be connected to a control centre 50 constructed to transmit signals effective in changing the operating conditions of a machine incorporated in the duct system, e.g. a fan or blower, in response to the sensed difference in pressure.

Functional description

When using the inventive measuring device, the pressure difference across the nipples is measured and a pressure difference Δ p between the total pressure in front of the baffles and the pressure on the downstream side of the circular probes is obtained. As beforementioned, the total pressure before the baffles is the same as that on the front side of the second probe or probes 32. Any deviatiosn that might occur are due to friction against the sides 36 of the baffles and similar effects and cause only a negligible change in the amplifying factor of the measuring device, which has no influence on the amplifying factor.

The pressure difference which forms output signals from the measuring device is directly proportional to the dynamic pressure p_d1 in the free area between the baffles. The amplifying factor is the quotient of the pressure difference Δ p divided by the dynamic pressure:

C_F = Δ_p/P_d1 Provided that the total pressure in front of the baffles is the same as the pressure on the front side of the measuring probe, the following relationship will also apply:

C_F = 1+C_p

As will be seen from the Figure 6 diagram, there is then obtained an amplifying factor of slightly above 2.

The dynamic pressure is defined as:

where C₁ is the air velocity between the baffles, i.e. in the constriction openings 26.

The relationship between this velocity and the velocity of the air C₀ over the cross-sectional area A₀ of the duct 12 is directly proportional to the quotient between the cross-sectional areas:

C₁ - <A₀/A₁) *C₀

A₀ = cross-sectional area of the duct 12

A₁ = the free area of the measuring device i.e. the free area of the constriction openings 26.

The area ratio A ₀ /A₁ has been chosen so that turbulent flow will always be obtained. This means that velocity and dynamic pressure will be constant over the free area in the measuring device.

The mean distance C₀ over the cross-sectional area of the duct as a function of the pressure difference is obtained from the following equation:

The constant C_M is defined as :

p = the air density at 20°C, 1.2 kg/m³

When the cross-sectional area of the duct 12 is A₀ m² , the air flow rate q will be:

The installation of this measuring device in a central assembly will result. in a given small pressure loss which increases the energy consumption of the fan means of the assembly.

The quotient between the pressure loss p_L as a function of the dynamic pressure- in the assembly defines the. loss factor CL - ΔPL/Pdl

With the given area ratio A₁/A₀, the pressure loss ΔP_L can be calculated as a dynamic function of the pressure in the assembly.

The pressure loss ΔP_L is a function of the area ratio A₁/A₀ and the dynamic pressure in the measuring device. Consequently, a loss factor C_L= 0.6 is obtained at the preferred air velocities and constriction or throttling conditions.

The gas flow q can now be calculated with the aid of the measured pressure difference Δp. This can be accomplished for instance, with the aid of the diagram shown in Figure 3. At the bottom of this diagram there are shown various different. scales which disclose the magnitude of the flow in respect of mutually different cross-sectional areas, in the present case fan housings of mutually different sizes The measuring device can be adapted directly to the area concerned and register the sensed pressure difference as a gas flow rate on an instrument board 48 or by means of a control centre 50. Figure 4 shows a corresponding diagram for a single duct or assembly size. Figure 4 also shows the pressure drop Δ p_L over the measuring device. In a corres-ponding manner, the inventive measuring device can also be used to register the linear speed or velocity of a gas stream.

As will be seen from Figures 3 and 4, the relationship between the pressure difference and the gas flow rate and the gas velocity respectively is a straight line in a double logarithmic diagram. This will apply provided that Reynolds number is not changed to such an extent that the pressure coefficient C_p is also changed, which corresponds to a very pronounced velocity deviation from the normal measuring range. In the case of a preferred application, in connection with a fan mounted in a ventilation system, the flow velocit and flow rate varies normally between 40 and 90% of the maximum flow rate and consequently no such problems will occur. It lies within the scope of the invention, however, to use the measuring device for measurements which lie outside the linear range. This can be effected readily by changing the scales in the outer parts in the lower part of Figure 3 or on an instrument board, or alternatively throug a separate program in a control centre.

Example

The following data applies in respect of a ventilation assembly:

Cross-sectional area of the assembly A = 1.165 M²

Cross-sectional area of the measuring device A₁ = 0.318 M²

Quotient A₀/A₁ = 0.273 Amplification factor C _F = 2.16

The constant C_M = 0.24 The flow rate q is calculated as the function of the pressure difference with the following formula

With the loss factor C_L= 0.6 and the area ratio A₀/A₁ = 3.66 the pressure loss can be calculated from:

Figure 6 illustrates the relationship between the measured pressure difference Δp and the rate of air flow q and the pressure drop ΔP_L respectively.

In the preferred working range of C_L = 5.5 m/s - 12.5 m/s in the constriction openings 26, there has been established measuring accuracy of - 21.

Construction When constructing a measuring device according to the invent the gaps between respective baffles are selected so that the velocity of the gas within the gaps lies from 5 to 15 m/s, preferably from 5.5 to 12.5 m/s. The lower value is contingent on the desire for a sufficiently strong measuring signal and the upper value is contingent on the desire to avoid unnecessary pressure losses. Lower values, e.g. 3 m/s, and higher values are conceivable, however, when circumstances so demand.

An advantage is gained when the gas velocity in the associated duct section 12 is chosen at 1.5 - 3.5 m/s. This will result in low pressure losses in the duct section and also in a suitable value of A₀/A₁.

The baffles are preferably in the form of flat slats or the like having rounded corners on the upstream side and extending in parallel relationship with one another and with one of the defining walls of the section 15.

The measuring device can advantageously be positioned immediately before a fan component 12 in a central assembly for controlling the rate of air flow through an associated ventilation system, e.g. as described in our patent application SE-S701663-0.

The measuring probes 28 and 32 will conveniently have mutually the same form. This will reduce the number of different components in the measuring device. There is no danger of wrong assembly.

Although it is possible, in principle, to position a first measuring device at any desired location before the baffles, it is preferred to place the device immediately before the baffles. This will enable the measuring device to be configured as a short assembly section part which can be readily mounted in a central assembly, even in a confined space.

The second measuring device is positioned advantageously, slightly downstream of the constriction opening. This will prevent the device from forming a further constriction and the construction will be simple.

The pressure difference measuring instrument 46 may include a line which passes to a system computer or like device for monitoring and controlling the gas circulation system.

Alternatively, a system computer or microprocessor may be incorporated in the pressure difference measuring instrument itself. The measurement values may be used, e.g., for regula- ting or controlling the speed of the fan motor in dependence on the magnitude of the gas flow rate. This will reduce the energy requirements of the fan and also wear thereon. Measurement data relating to the rate of air flow can be used for controlling other equipment, for instance a heating battery, which is liable to become overheated at low volumetric flows. The measuring device can also be used to control the flow through the system, e.g. in co-action with other measuring and/or control devices.

Claims

1. A method for measuring the linear velocity and/or the rate of flow of a gas which flows within or through a central assembly (1), by measuring differences in pressure, c h a r a c t e r i z e b y causing the gas to pass through at least one velocity-increasing constriction opening (26) configured with the aid of baffles (24) disposed in a plane perpendicular to the longitudinal extension of said assembly; measuring a first total pressure in the assembly at a location upstream of said constriction opening (26); measuring a second pressure at a location within or downstream of said at least one constriction opening (26), at a location immediately behind said opening but inwardly of the extension of the opening-containing sides, using herefor at least one measuring probe (32), e.g. a circular-cylindrical measuring tube, which includes a plurality of measuring orifices (34) on the downstream side such as to obtain an amplified pressure difference value; establishing the difference between the first and the second pressures; and calculating the gas velocity and/or the rate of flow with the aid of the established pressure difference.

2. A method according to Claim 1, c h a r a c t e r i z e d b y increasing the gas velocity in said at least one constriction opening (26) to at least 5 m/s, preferably to 5.5-12.5 m/s, at least during normal or most common operating conditions.

3. A method according to Claim 1 or Claim 2, c h a r a c t e r i z e d b y increasing the gas velocity so that the Reynolds number (Re) for the measuring probe obtains a value of 6 x 10³ < Re < 12 x 10³.

4. A method according to any of Claims 1-3, c h a r a c t e r i z e d b y converting the obtained pressure difference value to a gas velocity value and/or a pressure difference value and registering this latter value analogously or digitally on, e.g., an instrument board (48) and/or converting the obtained value to an input signal and supplying said signal to a control centre or the like (50).

5. A method according to Claim 4, c h a r a c t e r i z e d b y using the input signal to control the operation of a fan or like apparatus in the central assembly (1).

6. Apparatus for carrying out the method of Claim 1 for measuring the velocity and/or the flow rate of a gas within or through a central assembly (1), said apparatus comprising a measuring device (10) for measuring pressure differences in connection with a flow constricted zone, c h a r a c t e r i z e d i n t h a t said constricted zone includes at least one velocity-increasing constriction opening (26) configured with the aid of baffle means (24) extending perpendicularly to the longitudinal extension of said assembly; in that arranged upstream of the constricted zone is a first measuring probe (28) which has a measuring orifice (30) facing in an upstream direction and which is operative in sensing a first total pressure, said first probe (28) being located in a stagnation zone centrally in front of baffles (24) or the like; in that a second measuring probe (32) operative in sensing a second pressure is located within or downstream of said at least one constriction opening (26) in a region immediately behind said opening but within the extension (36') of the openingcontaining sides (36), said second probe (32) comprising a cylindrical measuring body having a plurality of measuring orifices (34) located symmetrically on the downstream of said second probe (32) such as to obtain an amplified pressure difference; an in that the measuring probes (28, 32) are connected via connecting means (38, 40) to an instrument (46) for measuring differences in pressure and/or indicating means (48) for indicating pressure differences, gas velocity or gas flow rate.

7. Apparatus according to Claim 6, characterized in that the second probe comprises a circular-cylindrical measuring body (32) which is positioned at right angles to the direction of gas flow, and/or in that the first measuring probe (28) and the second measuring probe (32) are identically configured.

8. Apparatus according to Claim 6 or Claim 7, characterized in that it includes more than one first and second probes (28, 32), said first and said second probes respectively being connected together each per se by means of said respective connecting means (38 and 40) ; and/or in that the first and second probes (28 and 32) have more than one measuring orifice (30 and 34 respectively).

9. Apparatus according to any of Claims 6-8, characterized in that the probes (28 and 30) and the baffle means (24) are arranged in an assembly section part (15) which is intended to be mounted in a central assembly (1), preferably immediately upstream of the fan part (12) of said assembly.