Velocity Measurement i Introduction
In industrial ventilation the majority of air velocity measurements are related to different means of controlling indoor conditions, like prediction of thermal comfort; contaminant dispersion analysis; adjustment of supply airflow patterns, and testing of local exhausts, air curtains, and other devices. In all these applications the nature of the flow is highly turbulent and the velocity has a wide range, from 0.1 m s“1 in the occupied zone to 5-15 m s“1 in supply jets and up to 30-40 m s_1 in air curtain devices. Furthermore, the flow velocity and direction as well as air temperature often have significant variations in time, which make measurement difficult.
In air ducts, the measurement of the local air velocity is used to determine the flow rate in the duct. The duct flow is usually more stable and the flow direction under better control than in the room space. Different types of disturbances in the ductwork, such as bends, tees, or dampers, will influence the nature of the flow and cause swirl and other problems in velocity measurement.
Thermal anemometers are a group of velocity measurement instruments that depend on the principle of electrically heating the sensor and measuring the velocity based on the cooling of the sensor: The higher the flow velocity is, the greater the cooling rate. Thermal anemometers are typically used for measuring in the low velocity range from 0.1 m s_1, but many types are capable of measuring high velocities as well.
The hot-wire anemometer sensor is a very fine wire with a diameter of few micrometers and length of few millimeters. This wire is connected to a measurement bridge and an electrical current is fed through the wire. The wire is heated to a temperature above the air temperature and the air velocity is determined by the cooling effect of the wire. The voltage over the wire, Uw, is a function not only of the velocity but also of the excess temperature and the fluid properties in the following way:33
Ul=Rw(A + Bvn)(Tw-Ta), (12.26)
Where Rw is the wire resistance, A and B are coefficients dependent on the physical dimensions of the wire and properties of the fluid (air), V is the flow velocity, N is a constant (close to 0.5), Tw is the wire temperature, and Ta is the ambient air temperature.
The wire-type sensor (probe) can be a single-wire construction, or it may have two or three separate wires. With a three-wire sensor, all three velocity components can be determined. As well as wire-type sensors, there are hot —
Film sensors, which are more robust but, due to a larger thermal inertia, are not as fast-responding as wires.
Modern hot-wire anemometers are normally used in the constant temperature (CT) mode, where the wire resistance and wire temperature are kept virtually constant. In the CT-mode the wire is one part of a Wheatstone bridge circuit, which has a feedback from the bridge offset voltage to the top of the bridge (see Fig. 12.18).
A hot-wire anemometer, working in the CT mode, is capable of measuring rapid velocity fluctuations. This is an advantage in the measurement of flow turbulence and is also the main area of application for the hot-wire anemometer. It is an instrument mainly for scientific purposes.
For various reasons, this type of anemometer is not a suitable instrument for practical measurements in the industrial environment. The thin wire probe is fragile and sensitive to contamination and is unsuited to rough industrial environments. The wire temperature is often too high for low-velocity measurements because a strong natural convection from the wire causes errors. Temperature compensation, to correct for ambient air temperature fluctuations may not be available or may not cover the desired operating range.
For measuring mean velocities in the low and moderate velocity range, there are other types of thermal anemometers, that are more robust, easier to use, and not as expensive as the “real” hot-wire anemometers. These anemometers use larger sensors, thermistors, and spherical and cylindrical sensors. The working mode often differs slightly from the hot-wire anemometer. Instead of keeping the sensor resistance/temperature constant as in th..- CT mode, the system tries to keep the excess sensor temperature constant. According to Eq. (12.26), this eliminates the main effect of ambient air temperature fluctuations and gives temperature compensation. The excess temperature is kept low to prevent the effect of natural convection at low velocities.
Usually this type of anemometer does not provide information on the flow direction. Vice versa, the sensors are made as independent of the flow direction as possible—omnidirectional. This is an advantage for free-space ventilation measurements, as the flow direction varies constantly and a direction-sensitive anemometer would be difficult to use. Naturally, no sensor is fully omnidirectional, but satisfactory constructions are available. Due to the high sensor thermal inertia, this type of anemometer is unsuitable for high-frequency flow fluctuation measurement. They can be used to monitor low-frequency turbulence up to a given cut-off frequency, which depends on the dynamic properties of the instrument.
The precision of a thermal anemometer is dependent on the instrument quality and the conditions of use. A general rule is, the lower the measured velocity, the higher the inaccuracy and vice versa. When measuring very low indoor velocities, around 0.1 m s-1, the relative error can be as high as 100% and not much lower than 30%. Low velocities are extremely difficult to measure with accuracy.
The Pitof-static tube is a basic instrument that predicts flow velocity based on Bernoulli’s equation:
pv2 + ps = pt ■ (12.27)
This states that the sum of the velocity pressure 0.5Pv1 plus the static pressure Ps, the total pressure, is constant along a streamline. In the case of standard air density (1.2 kg m-3), 0,5pv2 becomes 0.6v2. When a Pitot-static tube is immersed into the flow, as in Fig. 12.19, the velocity at the stagnation point at the tube nose is V = 0 and the local static pressure equals the total pressure P,. The flow static pressure Ps is measured a short distance downstream from the surface of the tube. The flow velocity is obtained by applying Eq. (12.27):
V = K №, (12.28)
N P ‘
Where a constant K is added to take into account the deviations from the ideal
(Bernoulli) case, AP —pt — ps is the pressure difference between the total (stagna
Tion) pressure and the static pressure, and p is the fluid density. The factor K is dependent mainly on the tube construction and is close to ideal (K = 1) for properly
Constructed Pitot-static tubes. There are several standardized constructions,34 which have different shapes of the tube nose (spherical, ellipsoidal, conical) and slightly different static pressure hole arrangements. A factor K = 1.00 for all these tubes can be applied in all practical ventilation measurements. In scientific work additional corrections for Reynolds number, fluid compressibility, turbulence, viscosity, and velocity gradient,2’34 can be applied.
By connecting manometer hoses to both output pressures given by the tube, the pressure difference AP can be measured directly. The barometric pressure and the fluid temperature are required for the determination of the fluid density. The Pitot-static tube is not a suitable instrument for measuring low velocities. It can be applied in cases where the flow velocity is high
Enough for the manometer to provide a reliable pressure difference reading. To have, for example, a pressure difference of 10 Pa in measuring airflow, the velocity has to be in the 4 m s_1 range. In practice this means measurements in air ducts, supply openings, jets, and similar cases where the velocity is sufficient.
When the axis of the Pitot-static tube is not aligned to the main flow direction, an error of inclination occurs known as yaw. It is not more than 1 % for the measured pressure difference if standard tubes are used and the deviation from the flow direction is less than 11-13° .32,34 When the yaw is further increasing, the error increases rapidly. Hence it is of prime importance to place and align the Pitot-static tube carefully in the direction of flow.
The vane anemometer is an old invention. It can be likened to a small wind turbine with 4-10 rotating blades and a handle, as in Fig. 12.20. Earlier constructions were fully mechanical, where the spindle rotation was transmitted to a pointer through a series of gears. In modern vane anemometers, an electrical sensor records the spindle rotation and the signal is processed, giving the velocity on a digital display. Such an instrument usually is able to integrate the mean velocity over a time interval.
The vane anemometer’s physical dimensions are often quite large (compared with other local velocity measurement instruments). It does not strictly measure a local velocity at all, but rather provides a spatially integrated mean value. This is an advantage in many cases where the air volume flow rate has to be predicted using “local” velocities and an integration principle.
The measurement range of a vane anemometer is typically between 0.3 and 30 m s_1. It may start rotating with slightly lower velocities, but due to the characteristic curve having a small nonlinear part in the low-speed end, the useful range is narrower. The actual precision depends on the quality of the instrument; however, the inaccuracy may vary between 1% and 5% of the scale. The larger the vane, the higher the accuracy.
The vane anemometer is not seriously affected by small deviations in alignment in the main flow direction. However, care is necessary since over 20° misalignment causes significant errors. With regard to providing a correction for fluid density, slightly different opinions exist.32’35 Based on measurements, it is recommended35 that the following density correction procedure be applied:
Where V is velocity, p is density, and indices C and m refer to calibration conditions and actual measurement conditions, respectively.
Errors related to velocity measurement instruments have different origins depending on the measurement principle. The most important of these have been covered in previous sections. One common source of error for all instruments is the disturbance of the flow field by the sensor/meter or the person carrying out the measuring. The influence of the sensor in an open space is usually
Not critical. The effect of the measuring person, however, can be — In the case of hand-held instruments, the person carrying out the measurements must take care not to influence the flow at die measurement point with his or her body.
In measuring the local velocity in ducts, the sensor will obstruct a part of the duct cross-section. This results in accelerated flow by the sensor and an error occurs. In a Pitot-static tube, this is called stem blockage. If the ratio of the tube diameter to the duct diameter is smaller than 0.02, stem blockage can be neglected. Otherwise a correction has to be applied.34
The blocking effect does not apply to the Pitot-static tube alone. Any sensor/instrument immersed into a duct has a similar effect; the larger the sensor is, the greater the problem. For other types of instruments an anah^is must be made, so as not to block large proportion of the duct cross-section with the meter. A good rule of thumb to avoid corrections is to keep the cross-section of the meter less than 5% of the duct cross-section.
Constant calibration of most velocity instruments is necessary. Hot-wire or other thermal anemometers require frequent calibration due to their complex and sensitive nature. They usually have a significant time change in their metrological characteristics, a drift. Vane anemometers are not that sensitive but require checking at set intervals. The Pitot-static tube is the only exception. Due to its fundamental nature, it does not require calibrating. It also can be used as a reference for other meters. This applies to the tube itself, provided it maintains its original geometry unchanged. However, the manometer used in conjunction with the Pitot-static tube requires calibration.
A calibration facility must produce the desired velocity range for the meter to be calibrated. The air temperature should be kept constant over the test to ensure constant density. For thermal anemometers, velocity calibration only is not sufficient. They should also be checked for temperature compensation. In the case of omnidirectional probes, sensitivity to flow direction should be tested. In the case of low-speed (thermal) anemometers, their self-convection error should be measured, and, for instruments measuring flow fluctuation (turbulence), dynamic characteristics testing should be carried out as well.36
Manufacturers of thermal anemometers provide small rigs for their calibration. They typically consist of a nozzle, an air supply unit, and a regulating valve. The probe is placed into the nozzle jet. The reference velocity is calculated from the nozzle upstream pressure and nozzle characteristics. Due to its small size, this type of rig can be used only for hot-wire or other thermal anemometers.’3
A good method for a simple calibration facility is a system where a constant airflow is produced by using two water containers and an arrangement of a virtually constant pressure head,37 The constant water flow into the second container displaces an equal airflow out of the container (Fig. 12.21). With this arrangement the difficult measurement of a small airflow is changed into a much easier and accurate measurement of a smalt water flow.
The calibration air flows through a thin tube. The probe is placed at the exit of the tube. When the tube is long enough and the tube flow is laminar, the reference velocity for calibration can be calculated from the theoretical, fully developed laminar velocity’ profile.
To calibrate larger sensors/instruments such as vane anemometers, a wind tunnel is required. A calibration wind tunnel consists of an open or closed tunnel, a fan to deliver the air, a nozzle to shape the velocity profile, and a mesh arrangement to uniform and reduce the flow turbulence. It may be necessary to control the air temperature in the tunnel by means of a heating/cooling sys —
12. ) MEASUREMENT TECHNIQUES Air in
Ail parties to have a sound foundation for the necessary measurements. Because of the importance of the measurement of flow rate in ventilation and many other fields, a comprehensive selection of standards covering different measurement methods and instruments is available.
The range of the airflow in ventilation systems is wide. The flow rate in an individual supply or exhaust terminal may only be a few liters per second, while the flow in a main duct or supply chamber of a large system may be in excess of 100 cubic meters per second. No general method to deal with the whole range exists. Each case requires individual consideration for the most suitable methods and instrumentation to be selected.
The orifice, the venturi, and the nozzle are instruments for the measurement of duct or pipe flow rate. A constriction, throttling the flow, is placed in the duct, and the resulting differential pressure developed across the constriction is measured. It is the difference in the geometric shape that characterizes the three devices; see Fig. 12.22.
The orifice plate is simple to manufacture and has a relatively low cost, It does, however, create a quite large permanent pressure loss when installed in the ductwork. The venturi is smoothly shaped with a low permanent pressure loss but requires more space and is more expensive. The nozzle is a compromise between the orifice and the venturi. All three devices are standardized flow meters with very detailed descriptions of their geometry, material, manufacturing, installation, and use.38^*2
Based on the measured pressure difference over the device, the throat diameter, and some other parameters, the flow rate can be determined. The equation for the volume flow7 rate is, in genera!,38
Qi: = CEe^- (12.30)
Where C is the coefficient of discharge, E is the velocity approach factor, e is an expansion factor, D is the diameter of the throat of the device, AP is the measured pressure differential, and p is the fluid density at the upstream pressure tapping. Correspondingly, the mass flow rate is
Qm = CEe^f-,JTKpp. (12.31)
The product of the discharge coefficient and the velocity approach factor,
A = CE, is called the flow coefficient. For the orifice, the discharge coefficient
Is given by the equation38
C = 0.5959 + 0.0312/32′ — 0.184/38 + 0.0029/325
+ 0.09L,—t — 0.0337L>/3
1-|34 ‘ ‘
Where /3 = D/D is the diameter ratio of the throat and the duct diameters, ReD is the duct Reynolds number, LJ = /j /D is the distance of upstream pressure tapping from the upstream face of the orifice plate divided by the duct diameter, and L2 = /2/D is the distance of the downstream pressure tapping
From the downstream face of the plate divided by the duct diameter. From the above it can be noticed that the calculation of the discharge coefficient is an iterative process, as the duct Reynolds number is included in the equation. The discharge coefficient for a nozzle is given by a slightly simpler equation:
C = 0.99 + 0.2262/341 + [0.000215 — 0.001125/3
The discharge coefficient of the venturi tube depends on the convergent of the venturi, but is given as a constant value for a specified device. The range is from 0.984 for a rough-cast convergent to 0.995 for a machined convergent.38
The velocity approach factor is dependent on the diameter ratio Only: R: — 1
The expansion factor e takes into account the compressibility effects of the fluid. It is close to unity in most industrial ventilation applications.
For the above equations to be valid, the measurement devices must be manufactured according to standards and also must be installed according to given specifications. There are strict requirements concerning the minimum upstream and downstream straight lengths. These lengths depend mainly on the diameter ratio of the device and the type of the nearest upstream fitting causing a disturbance in the incoming flow velocity profile. Table 12.6 provides typical values of the required straight lengths for orifice plates and nozzles.
If the lower values in the brackets are applied, an additional ±0.5 uncertainty (error on 5% risk level) has to be added arithmetically to the flow coefficient confidence limits. The use of flow straighteners is recommended in cases when a nonstandard type of upstream fitting disturbs the flow velocity profile.
Every measured quantity or component in the main equations, Eqs. (12.30) and (12.31), influence the accuracy of the final flow rate. Usually a brief description of the estimation of the confidence limits is included in each standard. The principles more or less follow those presented earlier in Treatment of Measurement Uncertainties. There are also more comprehensive error estimation procedures available.43-46 These usually include, beyond the estimation procedure itself, some basics and worked examples.
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