188
5 Performance Measurement
5.7.4 Calculations
• Calculate for each operating point:
m, Δp 0 /ρ and shaft power.
• Calculate for each operating point the overall efficiency of the fan, with the shaft
power as input power.
• Transform by similitude (see Chap. 7) the results for each operating point to the
idling rotational speed. Apply purely kinematic similitude, so no correction for
the small change of the Reynolds number. The overall efficiency is assumed
constant in the conversion.
• Determine the work coefficient
/
2
2
W u
y D
=
for the operating point with maximum efficiency (interpolate between the results found, if necessary) and the specific speed. Determine the rotor work from the shaft power and the flow rate,
assuming that the mechanical and volumetric efficiencies equal unity. With a
radial fan, mechanical efficiency is very near to unity (bearing friction and wheel
friction being very low), but the volumetric efficiency may be significantly lower than unity (the gap between the volute and the rotor in the suction eye being
rather large). This way, we overestimate the work coefficient (by about 10 %).
Evaluate the values found for the work coefficient and the specific speed.
5.7.5 Measurement Example
• Rotational speed 2750 rpm (idling value).
• Atmospheric conditions: p a = 100.4 kPa, T a = 21.0 ºC (Table 5.3)
Answer: at 2750 rpm, the maximum energy rise (mechanical energy rise) is 2870 J/
kg at mass flow rate 0.550 kg/s (weak maximum); the optimum efficiency is 0.74 at
mass flow rate 0.825 kg/s (weak optimum). The energy rise at optimum efficiency is
2690 J/kg. At optimum efficiency, the energy rise coefficient is 0.64, the calculated
work coefficient 0.865 (the real value presumably being about 10 % lower, about
0.78). Specific speed is 0.65. Specific diameter is 3.90. These values form approximately a couple on the Cordier diagram (Chap. 7, Fig. 7.7)
Table 5.3 Test results for the fan
Operating
point
1
2
3
4
5
6
7
8
T (ºC)
22.5
23.2
23.6
23.7
24.0
24.6
25.7
27.4
p (kPa)
2.23
2.60
2.92
3.08
3.13
3.13
3.06
2.92
p 1 (kPa)
1.95
2.38
2.76
2.96
3.06
3.09
3.04
2.92
p
D (kPa)
3.25
2.38
1.60
1.05
0.60
0.27
0.07
0.00
P input (W) 3760
3400
3000
2640
2240
1840
1480
1200
5 Performance Measurement
5.7.4 Calculations
• Calculate for each operating point:
m, Δp 0 /ρ and shaft power.
• Calculate for each operating point the overall efficiency of the fan, with the shaft
power as input power.
• Transform by similitude (see Chap. 7) the results for each operating point to the
idling rotational speed. Apply purely kinematic similitude, so no correction for
the small change of the Reynolds number. The overall efficiency is assumed
constant in the conversion.
• Determine the work coefficient
/
2
2
W u
y D
=
for the operating point with maximum efficiency (interpolate between the results found, if necessary) and the specific speed. Determine the rotor work from the shaft power and the flow rate,
assuming that the mechanical and volumetric efficiencies equal unity. With a
radial fan, mechanical efficiency is very near to unity (bearing friction and wheel
friction being very low), but the volumetric efficiency may be significantly lower than unity (the gap between the volute and the rotor in the suction eye being
rather large). This way, we overestimate the work coefficient (by about 10 %).
Evaluate the values found for the work coefficient and the specific speed.
5.7.5 Measurement Example
• Rotational speed 2750 rpm (idling value).
• Atmospheric conditions: p a = 100.4 kPa, T a = 21.0 ºC (Table 5.3)
Answer: at 2750 rpm, the maximum energy rise (mechanical energy rise) is 2870 J/
kg at mass flow rate 0.550 kg/s (weak maximum); the optimum efficiency is 0.74 at
mass flow rate 0.825 kg/s (weak optimum). The energy rise at optimum efficiency is
2690 J/kg. At optimum efficiency, the energy rise coefficient is 0.64, the calculated
work coefficient 0.865 (the real value presumably being about 10 % lower, about
0.78). Specific speed is 0.65. Specific diameter is 3.90. These values form approximately a couple on the Cordier diagram (Chap. 7, Fig. 7.7)
Table 5.3 Test results for the fan
Operating
point
1
2
3
4
5
6
7
8
T (ºC)
22.5
23.2
23.6
23.7
24.0
24.6
25.7
27.4
p (kPa)
2.23
2.60
2.92
3.08
3.13
3.13
3.06
2.92
p 1 (kPa)
1.95
2.38
2.76
2.96
3.06
3.09
3.04
2.92
p
D (kPa)
3.25
2.38
1.60
1.05
0.60
0.27
0.07
0.00
P input (W) 3760
3400
3000
2640
2240
1840
1480
1200