Smooth intake Air flow
Centre line of duct
Maximum velocity
Undeveloped flow close to intake
Fully developed flow, >30 diameters from intake
Partially developed flow 5-10 diameters from intake
Figure 3: Development of air flow regimes in a ducted air system with conical inlet. The length of arrow is proportional to the average velocity at that point (Source: Legg2
)
Figure 2: Example of poor performance of outdoor air regulation. The ‘required outdoor air fraction’ should be matched by the ‘actual outdoor air fraction’, but the actual airflow is significantly higher – possibly due to a faulty damper assembly (Based on material from PNNL training document1
)
The streamlines of ducted airflow When air passes through a duct – whether it is rectangular or circular in section – it does not have a uniform velocity over the cross-section of the flowing air, but will have a ‘velocity profile’. The profile will depend on the upstream and downstream ductwork, its roughness and shape, and the qualities of the air. For example, as discussed by Legg2
, if an airstream enters
the duct through a smooth intake – as in Figure 3 – the velocity profile will develop as the air flows through the duct (the length of the arrows is proportional to the average velocity at that point). It is not until some distance down the duct – possibly greater than 30 times the diameter of the duct with a smooth intake, somewhat less if the intake is more abrupt – that the flow will be ‘fully developed’. Although air is often shown schematically
as flowing in a set of parallel streamlines (as in Figure 3) that may infer to some that it is ‘laminar flow’, the typical velocity of the air in an air distribution network will determine that the flow will be ‘fully turbulent’. This means that although the bulk of air is moving forward at an average velocity, there is a continuous eddying and mixing within the airflow. Reynolds number (Re) is used to characterise the flow regime. Reynolds number is a ratio of the inertia of a fluid to its viscosity – as the ratio increases, the viscous forces will be overcome by inertia and the air will be able to more readily move around, independent of the adjacent air molecules. A Reynolds number value in excess of 4,000 would typically confirm that the flow is turbulent, and this is the normal situation in HVAC ductwork (see example calculation in box, above right). Such a turbulent regime will have a ‘flatter’
velocity profile than that of a laminar flow, since the air is moving in all directions – while
66 CIBSE Journal February 2014 Venturi D p1 Orifice D p1 d p2
Figure 4: Simplified sketches of orifice plate and venturi measuring devices
generally moving forward – so reducing the variations in streamline velocities across the duct. Due to the shear stresses of the air at the wall of the duct (where at its closest the air is practically static) there will be a steep increase in velocity between the turbulent air moving down the duct and the duct wall.
Methods of measurement The principal measurement techniques for permanent devices are based on basic principles that relate the cross-sectional area, A (m2 duct and the velocity, c (m·s-1
), of the ), of the travelling air to determine the volume flow rate, q (m3 ·s-1 ),
simply from q = A x c. The actual measurement of the air velocity will be achieved either by using a measurement of pressure drop across a device, or determining another secondary parameter that enables the velocity to be determined.
Pressure drop method of determining air volume flow rate Any obstruction in an air stream will cause a pressure drop in the flowing air, due to the
Figure 5: A commercial venturi for ducted air flow measurement close-coupled to a control damper (Source: CMR Controls)
www.cibsejournal.com Flow d p2 Flow
frictional resistance and turbulence. By characterising the obstruction and calibrating the pressure drop against known flow rates, the value of pressure difference may be used to determine the air volume flow rate. For ducted air systems, such measuring devices include venturis and orifice plates – as shown in Figure 4. Considering the example of the orifice plate,
as shown in Figure 4, the volume flow rate of the air may be readily obtained from the differential pressures measured across the two tappings, by combining the continuity equation A·c = constant
and Bernoulli’s equation p/ρg +c2
) /2g = constant (assuming the
ductwork is level) where p is pressure (Pa), ρ is density (kg·m3 g is gravity (9.81m·s-2
),
This is used with a flow (or discharge) coefficient, Cd, that relates to the energy lost as the air passes through the constriction (that is dependent on the Reynolds number and design of orifice), and the expansibility of air, ε, (that is practically 1 for ventilation air ductwork applications). So for an orifice plate of diameter d (m) that is installed in a duct diameter D (m) (and the ratio β = d/D) with pressure measurements p1 p2 (Pa), the volume flow rate, Q (m3
and ·s-1
obtained from Q = Cd ·ε ·π·d2
/4 · 1/√ (1-β4 ), can be ) ·√[2(p1 - p2)/ρ]
Wed, 4/5 12:00 AM Wed, 4/5 6:00 AM Wed, 4/5 12:00 PM Wed, 4/5 6:00 PM Thu, 5/5 12:00 AM Thu, 5/5 6:00 AM Thu, 5/5 12:00 AM Thu, 5/5 6:00 PM Fri, 6/5 12:00 AM Fri, 6/5 6:00 AM Occupancy
Required outdoor air fraction Actual outdoor air fraction
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