Annubar Flowmeter Calculation

Case
Steam at 10.9 barA (22765.1 psiA) and 184.52 oC (364.14 oF) is flowing in a 889 mm (35 in) ID carbon steel pipe. The measured differential pressure on a Sensor Size 3 Rosemount 485 Annubar primary element is 1477 mmH2O. What is the flowrate in kg/hr?

Solution
P = 10.9 barA = 1090 kPaAbs
T = 184.52 oC = 364.14 oF
D = 889 mm = 35 in
hw = 1477 mmH2O

W = x (From Equation 3 on page 1)
= x K x D2 x x x

Where:
= 3.4751E-6 (From Table 3 on page 4)
K = (From Equation 8 on page 10)
Where:
B = 4d/(πD) = 4(48.768)/(889π) = 0.069846 (From Equation 7 on page 8)
C1¬= -1.5856 (Sensor Constant-1) (From Table 6 on page 10)
C2= 1.3318 (Sensor Constant-2)

So:
K = (1-1.3318x0.069846)/sqrt(1-(-1.5856)x(1-1.3318x0.069846)2 = 0.597482
D2 = 8892 =790321 mm2
Ya = 1-(0.011332(1-B) 2-0.00342) (From Equation 6 on page 8)

Where:
hw = 1477 mmH2O
Pf = 1090 kPaAbs
γ = 1.3 (for steam) (page 8; γ = 1.3 or 1.4)

so:
Ya = 1-(0.011332(1-0.0698) 2-0.00342). = 0.993346
= 1.004 (From Table 12 p. 15; CSteel, T=364oF)
= = 2.386003 (From ASME Steam Table, = 5.693013 kg/m3)

Hence,
= x K x D2 x x x
C` = 3.4751E-6 x 0.597582 x 790321 x 0.993346 x 1.004 x 2.386003 = 3.905810
W = 3.905810 x sqrt(1477) = 150.1071 kg/s.

From this calculation, we get information that span of element indication is design from 0 to 1477 (mmH2O) (or 0 to 144.84 mbar).

Proof :
When we input DP (pressure drop) for max flow = 124.378 mbar = 1268.3 mmH2O on two designs of span setting.
1. For current setting, max flow = 139.09 kg/s.
W = 3.905810 x sqrt(1268.3) = 139.09 kg/s.

2. For recommended setting, max flow = 150.10 kg/s.

W = 3.905810 x sqrt(1477) = 150.1071 kg/s.
Max pressure drop = 1477 mmH2O = 144,844 mbar.

Conclusion:
From the calculation, it determined why there is different REK Annubar from FUJI ventury flow indication, if the assumption FUJI ventury is the accurate flowmeter. The difference of indication may vary to +9 kg/s.
So, it recommended to reset the span setting of transmitter of Annubar.


Note :
W = mass rate of flow – gas and steam (kg/s)
C` = Annubar Flow Constant (dimensionless)
Fna = Unit Conversion Factor (dimensionless)
K = Flow Coefficient
Ya = Gas Expansion Factor
B = Blockage
D = internal pipe diameter (mm)
d = probe width (mm)
hw = differential pressure (mmH2O)
Pf = flowing line pressure (kPa abs)
γ = ratio of specific heats
Faa = thermal expansion factor