11. traditional measurement of volume flow rate · 11.4. comparison between volume flow rate...
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11. TRADITIONAL MEASUREMENT OF VOLUME FLOW RATE
11.1. Volume flow rate deduced from velocity measurement data
11.1.1. Application example
11.1.2. Principle and layouts
∫='
'A
V dAvq ∫=A
dAv ∫ ⊥=A
dAv
Dr. János VAD: Flow measurements
A A
⊥
i
n
i
i Av ∆∑=
⊥≈1
∑=
⊥=n
i
ii vA1
∆
⋅= ∑
=
⊥
n
i
ii vn
An1
1∆ ⊥
= vA
DISCRETISATION:For rectangular cross-sections:•k x k•Log-lin method ISO 3966-1977
Dr. János VAD: Flow measurements
∑
∑
=
=
⊥
=⊥ n
i
i
n
i
ii
k
vk
v
1
1 weighting
Dr. János VAD: Flow measurements
For circular cross-sections:•10-point method
( )
−=
n
ii
R
rvrv 1max
Dr. János VAD: Flow measurements
Accurate integration: for 2nd order paraboloid profile only!
si /D = 0.026; 0.082; 0.146; 0.226; 0.342; 0.658; 0.774; 0.854; 0.918; 0.974
•Log-lin method ISO 3966-1977
3 partial areas
( ) iiii CyByAyv ++= lg
si /D = 0.032; 0.135; 0.321; 0,679; 0.865; 0.968
Dr. János VAD: Flow measurements
General notes
•The nose of the probe is to be adjusted parallel to the wall of the duct
•p_dyn_ref
0__0
2refdynref pv
ρ=
irefdyniref pv ___
2
ρ=
2=
Check of steadiness
Dr. János VAD: Flow measurements
idyni pv _
2
ρ=
irefdyn
refdyn
i
iref
ref
icorrip
pv
v
vvv
__
0__0==Correction:
•Obtainment of density
•Advantages and disadvantages
•Quick scanning:
Dr. János VAD: Flow measurements
STANDARDS: the recent one, being in effect, is to be used!Example: ISO 5801:2007(E): Industrial fans — Performance testing using standardized airways
Dr. János VAD: Flow measurements
Dr. János VAD: Flow measurements
Dr. János VAD: Flow measurements
Dr. János VAD: Flow measurements
Calibration of an AMCA type probe
Dr. János VAD: Flow measurements
Dr. János VAD: Flow measurements
Dr. János VAD: Flow measurements
0,00
0,20
0,40
0,60
0,80
1,00
1,20
0 1 2 3 4 5 6 7 8 9 101112131415
K[-]
v[m/s]
y = 0,9614x + 0,4445
R² = 0,9997
0
2
4
6
8
10
12
14
16
0 5 10 15
v P
ran
dtl
[m
/s]
v LDA [m/s]
Dr. János VAD: Flow measurements
•Velocity magnitude within +/- 1 % at higher velocities;•For this uncertainty: directional insensitivity within +/- 5 deg
Dr. János VAD: Flow measurements
11.2. Volume flow rate measurements using contraction elements
11.2.1. Application example
11.2.2. Principle and layouts
•Inlet orifice plate (inlet orifice meter)
Dr. János VAD: Flow measurements
2
2
0
vpp ρ+= ( ) mpppv ∆
ρρ
220 =−=
Assumption of ideal fluid: inviscid, incompressible flow
mV pd
vd
q ∆ρ
ππ 2
44
22
==
Reality: viscous, compressible flow
A/ Effect of viscosity
Dr. János VAD: Flow measurements
A/ Effect of viscosity
flow coefficient αdependence on d/d_in, Re
for the inlet orifice meter: α = 0.6
B/ Effect of compressibility
expansion coefficient εdependence on d/d_in, ∆p, p_in, κ
for the inlet orifice meter: ε = 1
mV pd
q ∆ρ
πεα
2
4
2
=
•Through-flow orifice plate (through-flow orifice meter)
Standard in effect:ISO 5167 / 2003
Dr. János VAD: Flow measurements
Standard in effect: Measurement of fluid flow by means of pressure differential devices inserted in circular cross-sections running full ISO 5167 (2003)
Dr. János VAD: Flow measurements
Dr. János VAD: Flow measurements
•Geometry•α, ε•Installation – Examples•Accuracy – Examples•Problems
mV pd
q ∆ρ
πεα
2
4
2
=
Dr. János VAD: Flow measurements
•Venturi meter ISO 5167
Dr. János VAD: Flow measurements
•Inlet cone ISO 5221-1984 (E)
νπρd
qV4Re =
( ) 55 103Re102020.0955.0 ⋅<<⋅±= ifαε
( ) 5103Re015.0960.0 ⋅>±= ifαε
Dr. János VAD: Flow measurements
11.3. Other types of traditional flowmetersExample:•Elbow meter
Dr. János VAD: Flow measurements
11.4. Comparison between volume flow rate measurement deduced from velocity data (VEL) and using contraction elements (CON)
ASPECT CON VEL
1/ Intrusiveness “ – ”
Introduces considerable
losses ⇒ the operating
state may be modified ⇔ to
be included already in the
system design state
“ + ”
Negligible intrusiveness
(wall bores)
Dr. János VAD: Flow measurements
2/ Following temporal
changes in the operational
state
“ + ”
Follows unsteady flow rate
continuously
“ – ”
Does not follow (surface
integration)
(⇔ correction..?)
3/ Requirements “ – ”
Strict (manufacturing,
installation, system is to be
stopped…)
“ + ”
Moderate (no requirements,
only recommendations,
system may run
continuously…)
4/ Expenses “ – ”
High (manufacturing,
installation, operation:
losses to be covered)
“ + ”
Moderate
5/ Accuracy “ + ”
High (limited uncertainty,
guaranteed by the standard)
Legally defensible!
“ – ”
Moderate (limits of
uncertainty are not
guaranteed)
Legally assailable!
Dr. János VAD: Flow measurements
CON: high-precision, continuous, legally defensible measurements(e.g. accounting, process control, etc.)VEL: occasional (case study) measurements, brief estimation(e.g. fault diagnostics)
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