11. traditional measurement of volume flow rate · 11.4. comparison between volume flow rate...

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


∑

∑

=

=

⊥

=⊥ n

i

i

n

i

ii

k

vk

v

1

1 weighting


For circular cross-sections:•10-point method

( )

−=

n

ii

R

rvrv 1max


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


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


idyni pv _

2

ρ=

irefdyn

refdyn

i

iref

ref

icorrip

pv

v

vvv

__

0__0==Correction:

•Obtainment of density

•Advantages and disadvantages

•Quick scanning:


STANDARDS: the recent one, being in effect, is to be used!Example: ISO 5801:2007(E): Industrial fans — Performance testing using standardized airways


Calibration of an AMCA type probe


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]


•Velocity magnitude within +/- 1 % at higher velocities;•For this uncertainty: directional insensitivity within +/- 5 deg

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)


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


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


Standard in effect: Measurement of fluid flow by means of pressure differential devices inserted in circular cross-sections running full ISO 5167 (2003)


•Geometry•α, ε•Installation – Examples•Accuracy – Examples•Problems

mV pd

q ∆ρ

πεα

2

4

2

=


•Venturi meter ISO 5167


•Inlet cone ISO 5221-1984 (E)

νπρd

qV4Re =

( ) 55 103Re102020.0955.0 ⋅<<⋅±= ifαε

( ) 5103Re015.0960.0 ⋅>±= ifαε


11.3. Other types of traditional flowmetersExample:•Elbow meter


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)


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!


CON: high-precision, continuous, legally defensible measurements(e.g. accounting, process control, etc.)VEL: occasional (case study) measurements, brief estimation(e.g. fault diagnostics)

11. traditional measurement of volume flow rate · 11.4. comparison between volume flow rate...

Documents