# Other Flow Obstruction Meters

Any obstruction inserted into a duct or pipe that creates a measurable pressure difference can be used as a flow meter. The three basic standardized flow measurement devices presented above are perhaps more suitable for lab­oratory work than installation as permanent ductwork instruments in ventila­tion applications. They are sensitive to flow disturbances, relatively expensive, require considerable space, and have a narrow measurement range and a high permanent pressure loss. For these reasons, numerous attempts have been made to develop instruments without these drawbacks. Some of them, like the

TABLE 12.6 Some Required Straight Lengths {LID) for Orifice Plates and Nozzles38

 Upstream side of the primary device Downstream side P Single 90° bend or tee Two or more 90° bends in different planes Expander (0.5D to D over a length of ID to 2D) All fittings <0.2 10 (6) 34 (17) 16 (8) 4 (2) 0.4 14 (7) 36 (18) 16 (8) 6 (3) 0.6 18(9) 48 (24) 22 (11) 7(3.5) 0.8 46 (2.3) 80 (40) 54 (27) 8 (4)

Dali tube,47 which is a modification of the venturi, have even been standard instruments. Several other solutions based on plates, rings, or wing-type ob­structions are commercially available. This wide variety of devices is not cov­ered here. For further information, the reader should contact the manufacturers of such instruments.

The principle of the traversing method is to measure the local velocity at one or several points of the flow cross-section and then calculate the flow rate based on this information. Generally speaking, an integration of the local ve­locity over the flow cross-section is made. Mathematically, this is expressed as

(12.35)

Where Qv is the volume flow rate, V is the local velocity, and DA is a differential area of the flow cross-section. In practice the number of measured local veloci­ties is finite, and the integration is carried out using different graphical or nu­merical methods. For duct flow, a standard is available describing the traversing methods where a Pitot-static tube for velocity measurement is used.4* This doc­ument divides the determination of the flow rate into three categories: graphical integration, numerical integration, and arithmetical methods.

The graphical integration method is based on graphical presentation of the average flow profile. For a circular duct, the cross-section is virtually di­vided into several concentric ring elements. The spatial mean velocity Vm of such an element is determined as an arithmetical mean of local velocities along the circumference of the corresponding radius. For a circular cross-section the flow rate can be expressed as

 (12.36)

Qv = TtR-

Where R is the radius of the duct and R is the radial distance from the duct cen­ter point. For graphical integration the spatial mean velocities Vm are plotted against (r/R)2. The area under this curve is then the integral term in Eq.

(12.35) And has only to be multiplied by the duct cross-section area. For this method the measuring points may be located at any position in order to ob­tain satisfactory knowledge of the velocity profile.

In the numerical integration method, the graphical velocity profile is re­placed by an algebraic curve, and the integration is carried out numerically. A procedure has been described48 where the velocity profile is approximated using a third-degree curve between the successive pairs of mean velocity values. A sim­pler approach, though not included in standards, is the use of the general for­mulas for numerical integration. For example, Simpson’s rule49 for an even (2N) Number of equal subintervals between the velocity points along the radius gives

 _t>

 4r

, A ..

Where the number of velocity points is 2N1 (the center point and the point at the duct wrall cancel out of the sum) and the distance between successive points along the radius is 1 /(2k). For a rectangular cross-section similar methods are available.

Sn the arithmetical methods50,51 a circular flow cross-section is divided into concentric rings and a central element. The areas of the elements are equal except for the outermost ring, which has only half of that area. A hy­pothesis is made for the velocity profile for each element. For example the Log­linear rule assumes a velocity profile of

V = A log Y + By + C , (12.38)

Where Y is the distance from the duct wall and A, B, and C are constants. Based on the velocity profile assumption, measurement points for each ele­ment are located in places where the (measured) local velocity is equal to the mean velocity of the element. This approach allows certain measurement point locations, dependent on the number of the points and the assumed ve­locity profile, to be determined. Table 12.7 gives measuring points for the iog — linear rule in a round duct.

The volume flow rate is calculated as the arithmetical mean of the mea­sured velocities multiplied by the duct cross-sectional area. The number of di­ameters along which the traversing occurs is not defined. If a near-symmetrical velocity profile is expected, an even traverse along one diameter may be suffi­cient. In case of a more disturbed profile, traversing along two or more diame­ters is recommended.

In the case of a rectangular cross-section, a variety of methods and corre­sponding measurement point locations exist.48’52 Table 12.8 shows the re­quired measuring points for the log-Tchebycheff rule, where the velocity distribution in the wall-connected elements is logarithmic and in the central el­ements polynomial.

As an example, for the 5×6 = 30 points case, the principle for placing the measurement points is shown in Fig. 12.23.

There is also a standardized method based on the estimation of the flow rate on one measurement point only.53 In this method the velocity probe is placed in the duct so that the measured local velocity is equal to the mean ax­ial velocity. In fully developed turbulent duct flow, this distance from the wall

TABLE 12.7 Measuring Point Distances for the Log-linear Rule Circular Cross-Section50

Number of measurement points per

Diameter Distance from wall in duct diameters

 4 0.043 0.29 0.71 0.957 6 0.032 0.135 0.321 0.679 0.865 0.968 8 0.021 0.117 0.234 0.345 0.655 0.816 0.883 0.979 10 0.019 0.076 0.153 0.217 0.361 0.639 0.783 0.847 0.924 0.981

TABLE 12.8 Measuring Point Distances for the Log-Tchebycheff Rule, Rectangular Cross-Section48’52

Number of measurement points per

Traversing line Distance from wall (l/L or H/H)

 5 0.074 0.288 0.500 0.712 0.926 6 0.061 0.235 0.437 0.56.3 0.765 0.939 8 0.046 0.175 0.342 0.400 0.6 0.658 0.825 0.954 10 0.037 0.141 0.26.3 0.338 0.456 0.544 0.662 0.737 0.859 C >. 963

Is Y = 0.242R. This approach has severe restrictions, as the velocity profile in the measurement cross-section has to be very close to the fully developed pro­file, requiring minimum upstream straight lengths of about 30 to 80 duct di­ameters depending on the type of the nearest flow disturbance.

Apart from ducts, the traversing principle can be utilized in any cross-section where the flow rate has to be determined, such as supply or exhaust grills, the

L

 0.939 L 0.765 L 0.563 L 0.437 L 0.235 L 0.0 51 L ‘ Rj A I. , a; K O 1, 0.50 H w Ј Oo Oo FN O 1 1 •* 1 4 1 | L G 1 4 Fc 4 R — O O — 9 1 9 ……….. W 1 R 9 ‘ ……………………… f | G R…… —1 9………………………… 1 * ………………….. % W ‘ ‘ . G 1 I Ґ…………………… ……………………. % ………………… G R-………… -.. % |…………….. 4 9………………………… ^ 1 ■ ■ 1 W………………….. 1 | 4 L__ ____ 4 9 ! 1 4 Ґ % K 4 9 1 | 4 F % | 4 9 f | 4 9 1__ F 9 1 P" T Ґ 1 Ґ

Surface of a large heating/cooling coil, or the intake opening of a fan. If the veloc­ity is high enough, the Pitot-static tube may be used. On the other hand, the vane anemometer is a convenient instrument for traversing larger surfaces, as it Has an Integrating character due to its larger dimensions.

12.3.9.5 Tracer Method

The use of tracers for airflow measurement in ventilation ducts is not very common. There are several reasons for this. Compared to other flow measure­ment methods, tracers require more complicated equipment, skilled personnel, and are more expensive. There are, however, situations when conventional measurement methods are not applicable. For instance, if the space available Is Small, and hence the flow meter cannot be installed, or if no space is free to carry out traversing measurements, the use of a tracer might be an alternative.

Tracer methods are not as well standardized as some of the conventional methods. One standard54 is available, but it comprises radioactive tracers only, which are perhaps not the best alternative for measurements in buildings. In principle, at least three different measurement methods are available:5j the constant injection method, the pulse injection method, and the concentration decay method. Of these three, the first is the best approach for normal ventila­tion measurements. The other methods require special instrumentation and do not produce as reliable results.

Constant Injection Method

The tracer is injected into the duct at a constant rate and mixed with the flowing air. The concentration of the air-tracer mixture is measured further downstream. Assuming perfect mixing and that the air entering the test sec­tion has a zero concentration, the air volume flow rate Qm can be calculated based on the mass balance of the tracer

QVa = p1rfpL, (12.39)

Pa 1 t‘-‘!/(

Where Pt and Tt are the pressure and (Kelvin) temperature of the injected tracer, Pa and Ta are the corresponding quantities for the air, Qvt is the volume flow rate of the injected tracer and Cvt is the downstream measured tracer (volume) concentration. Good mixing of the tracer and air between the injec­tion point and the measurement cross-section is essential. Failure to achieve this will result in errors. The injection and the sampling should be carried out by a multipoint approach. A ring, cross, or rectangle formed tube with many small holes is a good injection device that will spread the tracer effectively. Similar solutions can be used for sampling. A fan is an ideal mixing device be­tween the injection and the sampling sections. The error due to incomplete mixing using a fan has been shown to be only few percentage points,56 In the case of a straight empty duct between the injection and sampling sections and a one-point injection/sampling, a distance of at least 80 duct diameters is re­quired to keep the incomplete mixing error less than 5%. Adding a multipoint injection/sampling and some mixing elements can reduce the corresponding distance to 10-20 duct diameters;57 see Table 12.9.

As a tracer, either a gas or particles can be used. In ventilation ductwork measurement, gas is recommended. Particles tend to adhere to the duct surface,

TABLE 12.9 Required Mixing Lengths (L/D) to Keep the Error due to Incomplete Mixing Smaller Than 5% or 10%57

L/D

Maximum Maximum

Type of injection, sampling, and duct section error 5 % error 10 %

Straight duct without disturbance 80 60

Injection at center, sampling at center Straight duct without disturbance

Injection through a ring whose diameter is 63% of the duct’s (four holes in ring)

TOC o "1-5" h z (a) Sampling at center 25 20

(bj Sampling at four points in duct (situated as in injection) 15 10

Duct with two 90" bends

Injection through a ring whose diameter is 63% of the duct’s (four holes in ring)

(a) Sampling at center 20 15

(b) Sampling at four points in the duct (situated as in injection) 10 5

Injection before a fan and sampling after the fan 10 5

Injection through a ring whose diameter is 63 % of the duct’s

(four holes in ring)

Which will adversely influence the measurement and also hygiene. Widely used tracer gases are nitrous oxide (N20) and sulfur hexafluoride (SF6), which are readily detectable using infrared analyzers or gas chromatographs. It is advis­able to use a diluted tracer with a density close to air density. Otherwise mixing with air in the duct is difficult, and can lead to large measurement errors. Trac­ers having strong ozone-depleting features are not recommended.

The previous methods are mainly used to measure duct flow. When measur­ing flows on supply or exhaust terminals, different methods are used. The mea­surement on exhaust terminals is simple to carry out, as the velocity field near the terminal is relatively constant, with no steep gradients or swirls. In the case of a grill, traversing across the terminal surface using a suitable velocity instrument is a good alternative. A suitable instrument for most cases is the vane anemometer.

Different nozzle-shaped tubes are available, which are pressed onto the exhaust terminal. The air passes through the tube and a one-point velocity measurement is carried out in the throat of the device. The flow rate is deter­mined from the calibration curve.

One of the best and most convenient methods of measuring the flow in the terminal is to use the terminal characteristic pressure difference. This re­quires that the manufacturer of the terminal provide calibration curves, where the flow rate is expressed as the function of the characteristic pressure differ­ence. Some devices have integrated pressure measurement tappings, and the user has only to attach a manometer to measure the pressure difference.

Flow measurement on supply terminals is difficult, as each terminal creates its own velocity pattern, and a reliable correlation between a local velocity and

The flow rate is difficult to achieve. The balometer is a hood-shaped device that is pressed onto the terminal, and the airflow is passed through the instrument’s throat. The local velocity is measured at several points in the throat using, fixed thermal sensors. In modern balometers the flow rate is computed in an elec­tronic module into which the calibration information has been fed,

The old, tedious, but quite reliable method is to measure the suppl) flow by the bag method. A tightly rolled plastic bag empty of air at the commencement of the test is pressed on the terminal with all the supply air passing into the bag. The filling time of the bag is measured and the flow rate calculated based on this information. The bag volume has to be determined in advance by a special mea­surement. Finally, the characteristic pressure difference method, mentioned above, can also be applied to supply terminals.

The measurement errors encountered in determining flow rate depend on the methods and instruments used. In conventional duct flow measurements, the greatest error-generating phenomenon is the irregularity and swirl of the duct flow itself. The duct flow velocity profile strongly influences the result of the measurement. The shape of the profile changes along the ductwork. At the end of a long straight duct (30 to 50 duct diameters) the profile is fully devel­oped. Any other components such as tees, bends, or dampers reshape the ve­locity profile, after which it begins to move again toward the fully developed profile until it hits the next disturbance.

Because all measurement methods and instruments are sensitive to the ve­locity profile, the choice of the measurement cross-section is of vital impor­tance. In most ventilation systems there is seldom enough straight duct to allow a fully developed velocity profile to develop, which is the most favorable for flow measurement. Thus, the principle in selecting the measurement cross­section is to find the place where the velocity profile is as near to the fully de­veloped profile as possible. In practice the distance from the nearest source of disturbance upstream is maximized, ensuring that the distance to the nearest downstream disturbance is at least 3 to 5 duct diameters.

Constriction measurement devices constructed to standards42 do not neces­sarily require calibration. One idea of strict standardization is to define the manu­facturing, tolerances, and other features in such a way that the instruments made according to these rules require no calibration. The properties are so well known that a certain accuracy can be guaranteed. If the accuracy specified in the standard is inadequate, additional calibration procedures are required. The same applies to Pitot-static tubes made according to standard specifications.48

The simplest calibration procedure for a gas flow-measuring device is to con­nect it in series with a reference meter and allow the same flow to pass through both instruments. This requires a reference instrument of better metrological qual­ity than the calibrated instrument. One fact to consider when applying this method is that the mass flow rate in the system containing both instruments is constant (assuming no leakage), but the volume flow rate is not. The volume flow rate depends on the fluid density and the density depends on the pressure and the temperature. The correct way to calibrate is to compare either the measured mass

Flow rares or the volume flow rates which have been converted to correspond to the identical state (pressure and temperature) of the fluid.