# Partial optimisation

The two major costs for many fan plants are the costs of ducting on the investment side and the energy costs on the operational side. The investment costs increase with increased duct diam­eter whilst at the same time operational costs decrease, see Figure 19.7.

The total costs curve represents a minimum for a certain duct diameter. As indicated, the shape of the total costs curve is

 F. 2 Aqv
 Ef =
 1 + 3
 Pfm-t
 3fLp 2 Pl _ _5j5 — clv ®
 32ti d
 And

 This should be compared with the result for circular ducting where: 8 fLpqv2 * Tr2d5 = xqv2 x0.8106 I. e. the pressure loss and power absorbed in 2:1 rectangular ducting of the same metal content and the same flowrate will be 2.94 times as high. This emphasises the need for ensuring the maximum diameter of ducting consistent with space and money available, and the desirability of using circular cross-sections at all times. Duct pressure losses are not only due to the friction in straight ducting, but also due to the effects of bends, transitions, Take-offs, diffusers, etc. For further information see Chapter 3. It should especially noted that the quality of manufacture has an important effect on pressure losses due to gross turbulence at poorly aligned connections. Many German researchers have noted a Reynolds number de­pendence on the factor k where pressure loss

 Figure 19.6 Three special cases of demand/supply variations

 I, 1 2 Pl fitting =k—pv

 Square

 Equ 19.19

 Thus, despite the assumed constancy in many textbooks k may be expected to rise at low velocities. Nevertheless, it is safe to say that: Constant Pl fitting = ^ Equ 19.20 Where there are large flow variations down almost to zero, we will inevitably enter a laminar flow region when PL straight varies as d 4 and PL • fitting varies as d-3 For fan installations we can say that Pfan = constant x qv3 The installed air power, which is required in a system with mean flow qvm and demand/production variation of ± Aqvm is: 3

 Ef =

 Saw tooth

 + 5 *9v 2 I qvm

 Sinusoidal Equ 19.22

 Ef

 Pfm’t

 Or

 Figure 19.8 Annual costs for ventilation plant using various duct diameters

 Figure 19.7 Effects on costs of duct diameter

 Equ 19.23
 Q»i = Where Qvi K D TlO 3f P F T Ke
 Such that it rises more rapidly with reduced diameter, to the left of the economic diameter, than in cases of increased diameter, to the right of the optimum value. In cases of doubt choose the one having the largest duct diameter from the feasible alterna­tives. By calculating the total costs for a number of different duct di­ameters it is possible to establish the most economic duct di­ameter. The economic diameter varies for different situations. Short operating periods and costly duct sections, for example, stainless steel, tend to reduce the economic duct diameter and to increase the economic flow velocity. By carrying out a partial optimisation, i. e. if it is assumed that all costs are independent of the duct diameter except for the costs of the ducting and energy, the following relationship is obtained:
 The mean flow for which duct diameters d, and d2 give the same annual cost (m3/s) Cost/m of ducting (currency/m) Duct diameter (m) Fan system overall efficiency factor (decimal) Annuity factor (decimal) Liquid density (kg/m3) Pipeline loss coefficient Operating time per year(hour/annum) Cost of energy (currency/kWh)
 K2 — k, ri0-7t ■ aF — 10 1 d? 1 d”’32 • p • f • t • ke
 Pim Where
 T-k. F+K,,
 «P2mtkeF+Kl2
 Component efficiency When purchasing new equipment, it is often possible to choose between a cheap fan having low efficiency and an expensive one with high efficiency. The comparative costs for the two al­ternatives are:

 Equ 19.25

 Pm = consumed mean electrical power (kW) T = operating hours per year (hours/annum) Ke = energy cost (currency/kWh) F = present capitalised value factor K| = investment cost (currency) It is important to remember that the energy costs are debited according to readings taken from the electricity meter and not from the fan shaft. Because of cable losses, the electric power used is always greater than the fan shaft power. The capital­ised value of 1 kW mean electric power is t ■ ke • F. (See Figure 19.9.)

 Figure 19.9 Capitalised value in Јs sterling/kWh for a reduction of the mean annual electric power used

 For this qv1 value the total energy costs are the same. If the mean annual flow for the plant is greater than q„ then it is eco­nomically feasible to choose duct diameter d2. If qvi is much greater than qv then the procedure must be repeated using di­ameters d2 and d3. The procedure for dampers and other fittings is carried out in a similar manner.

 R|0-7i2- aF — 103

 K2 k,

 Equ 19.24

 Q»i =

 L/dt-l/dt 32-p- Pm-1- ke

Where

K = damper cost including connectors for duct diameter d.

It should be noted that an improved fan efficiency factor tends to reduce the economic duct diameter. (See Figure 19.8.)

The efficiency of other components can be tested in the same way. Conversion to electrical power used must always be made, however. The closer the power consumption lies to the useful air power in the conversion chain, the greater the energy saving and the greater the motivation for additional investment. This is illustrated typically in Figure 19.10.

 E P* >i O C O O E © W S O S

 Energy el Ficient Standard ————————- V 4′
 80

 60

 40

 20

 0.9

 0.8

 0.7

 1/4L 1/2L 3/4L Fraction of full load

 FL

Figure 19.10 Typical efficiency and power factor values for a 37 kW 4 pole motor

Existing plant

In the case of existing plant there are certain limitations to en­ergy saving possibilities. Changes to the layout and ducts are often difficult to make. Possible improvements are replace­ments or the addition of supplementary components which do not require too great a disturbance to the plant.

All reductions of the air power, by means of improvements which reduce the system resistance in the case of a regulated plant, only result in a greater pressure loss across the damper and are thus worthless from an energy conservation point of view. To realise a saving of energy some form of improvement must also be carried out on the fan side For speed-regulated plant all pressure reductions are automatically used.

When planning a project at the time of determining fan specifi­cations, it is often the case that not all of the plant details are known. It is not therefore unnatural to choose fan sizes with a certain safety margin “to be on the safe side”. For this reason many fans are oversized and result, if adjustments are not made, in unnecessarily high energy costs.

In the case of basic oversizing, the following alterations to the fan may be considered:

For centrifugal fans:

• a new impeller with reduced diameter

• a new impeller with reduced width

• a new impeller with reduce blade angles For axial flow fans:

• a new or existing impeller with reduced pitch angle

• a newor existing impellerwith a reduced number of blades

• fitting a slower running motor For indirect drive fans:

• fitting a smaller motor

• fitting a slower vee rope drive

• changing the gear ratio of a gearbox

It may also be advantageous to review the reasons for the venti­lation system and what it is supposed to do. In a drying plant, for example, it may be possible to change operating procedures to reduce the demand for flow variation.

Attention should always be given to energy efficient methods of control such as speed regulation for all types of fan, variable pitch in motion for axial flow fans and radial inlet vane control for centrifugal fans. The advantages and disadvantages of each are given in Chapter 6.

Posted in Fans Ventilation A Practical Guide