FANS


About fans W


e now turn to the term 'affinity laws' which is of essential relevance for selecting fans for a cooling or air


conditioning system.


The affinity laws for fans – also known as the 'fan laws' – are used to express the relationship between variables involved in fan performance, such as head, volumetric flow rate, shaft speed and power. Affinity laws apply both to centrifugal and axial flows. The affinity laws are useful as they allow


prediction of the head discharge characteristic of a fan from a known characteristic measured at a different speed or impeller diameter. The only requirement is that the two fans are dynamically similar, that is the ratios of the fluid forced are the same. It is also required that the two impellers' speed or diameter are running at the same efficiency. Q When the fan speed changes: The characteristic curve changes with the fan speed of rotation denoted as n (rpm) according to the following laws provided that all other parameters remain unchanged. The volume flow changes proportionally to the speed n: V̇ 1


/ V̇ 2 = n1 / n2


The pressure increase changes proportionally to the square of the speed n:


∆ptotal,1 / ∆ptotal,2 = (n1 / n2)2 = (V̇ 1 / V̇ 2 )2


The power demand of the fan and the flow power introduced into the conveyed medium change proportionally to the third power of the speed n:


Pshaft,1 / Pshaft,2 = (n1 / n2 )3 η = (∆ptotal • V̇ ) / (Mshaft


Q When the density changes: The characteristic curve changes with changing air density according to the following laws (provided that all other parameters remain unchanged). The volume flow is independent of the air density at the same speed: V̇ 1


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The coefficient of pressure ψ (psi) is defined as the ratio of the total pressure head generated by a fan to the dynamic pressure of the circumferential speed u. The coefficient is a dimensionless key figure for describing single-stage turbomachines. In connection with the flow coefficient, the


∆ptotal,1 / ∆ptotal,2 = ρ1 / ρ2


The power demand of the fan changes proportionally to the air density:


Pshaft,1 / Pshaft,2 = ρ1 / ρ2


Q When the fan diameter changes: V̇ 1


/ V̇ 2 = (n1 / n2)3 ∆ptotal,1 / ∆ptotal,2 = (d1 / d2)2 Pshaft,1 / Pshaft,2 = (d1 / d2)5 φ = V̇ / u • (π • d2


Q When fan speed n, fan diameter and density change:


V̇ 1 / V̇ 2 = n1 / n2 • (d1 / d2)3 ∆ptotal,1 / ∆ptotal,2 = (n1 / n2)2 Pshaft,1 / Pshaft,2 = (n1 / n2 )23 • ρ1 / ρ2 • (d1 / d2)2 L = ψ • φ • ρ1 / ρ2 • (d1 / d2)5


Different conditions lead to different characteristic curves, as explained above. For comparability of characteristic curves despite different conditions or between different fans, dimensionless representations can be used. Dimensionless means that such indices are just ratios and do not bear any physical dimension. This is an (incomplete) overview of such dimensionless indices: Q The efficiency (derived above) describes the ratio of the volumetric displacement to the shaft power.


The coefficient of performance λ is a measure of the required shaft power and the ratio of the power density and the efficiency.


λ = L / η = (φ • ψ) / η


Different operating conditions lead to different characteristic curves. For comparability of characteristic curves in the light of different conditions or between different fans, dimensionless representations can be used, for example: Q Instead of the volume flow rate, the flow rate number is used.


Q The pressure number is used instead of the pressure.


This representation allows the comparison of characteristic curves despite different fan speed, density or impeller diameter. In the following, the control of fans is to be understood as the control of the volume flow.


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The product of the coefficient of pressure ψ and the flow coefficient φ is called the power density L.


In this fourth and final part of our in-depth look at fans, Martin Altenbokum of 'Xprotec looks at the theory which affects fan selection and controls.


The pressure changes proportionally to the air density:


pressure coefficient is also described as a quantity of the power conversion of the stage. The parameter u is the circumferential speed of the fan in m/s.


ψ = ∆ptotal / (ρ/2 • u2 )


The flow coefficient φ (phi) is a dimensionless key figure for describing the throughput of fluid flow machines. It can be understood as the ratio of the actual delivery rate at the outlet of the impeller to a theoretically possible but imaginary volume flow, which is formed from the circular area of the outer diameter d of the impeller and its circumferential speed u.


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