Typical exam “Physical measurement methods”

```Typical exam “Physical measurement methods”
Problem 1 Flow-rate measurements using orifice meters.
(a) Describe the working principle of orifice meters.
Orifice meters employ relation
s
Φ = αA
2∆p
,
(1 − m2 )ρ
for evaluation of the flow rate.
(b) Derive the above relation.
(c) What is the meaning of parameter α? How is its value determined?
Problem 2 Tracer particles are used in a wide range of experimental methods. For
example, visualisation experiments and optical velocity measurements (LDA, PIV, PTV).
What general criteria must the particles fulfill in order for the experiments to be reliable?
Problem 3 Velocity measurements using Particle-Tracking Velocimetry (PTV).
(a) Sketch the general laboratory set-up for velocity measurements using PTV. Specify
its basic components and briefly describe their function.
(b) Describe the basic steps and the working principle of the PTV data-processing.
The standard nearest-neighbour algorithm is the simplest possible matching algorithm.
However, an important limitation is that it can handle only relatively low seeding densities.
(c) Explain how the standard nearest-neighbour algorithm works. Support your explanation with mathematical expressions.
(d) Explain the cause of the limitation mentioned above.
(e) How can the algorithm be improved such that it can handle higher seeding densities?
Problem 4 Temperature measurements using Laser-Induced Fluorescence (LIF).
(a) Sketch the general laboratory set-up for temperature measurements using LIF. Specify its basic components and briefly describe their function.
(b) Explain the principle of the ratiometric intensity that underlies LIF. Support your
explanation with mathematical expressions.
(c) What is the essential advantage of the ratiometric approach over an approach in
which the temperature is evaluated directly from the measured intensity?
1
For fluctuating laser intensities, the ratiometric intensity Ir assumes the form
Ir = (1 + ∆Iex ) φref (T ) , ∆Iex (t) =
Iex (t) − Iex (tref )
,
Iex (tref )
with φref the normalised quantum yield, t the current time and tref the time at which the
original reference intensity has been recorded.
(d) Derive the given expression for ∆Iex .
(e) How does ∆Iex manifest itself in the temperature measurement? What could one do
Problem 5 Laboratory experiments have been performed for velocity measurements
using PTV. Suppose one afterwards decides to alternatively process the experimental data
with the procedure following Particle-Image Velocimetry (PIV). Would this be possible?
2
Problem 2 Particles must have:
• Low response time: Stokes drag=inertia → Up (t) = U (1−exp(−t/τ )), τ = 2R2 ρp /9η;
τ must be low so as for the particle to rapidly pick up the actual flow velocity U .
• Insignificant influence from gravitational effects: Up (t) = U∞ (1 − exp(−t/τ )), U∞ =
2(ρp − ρ)R2 g/9η, τ = 2R2 ρp /9η; U∞ = τ (1 − ρ/ρp ) must be as small as possible:
density difference must be as small as possible.
• small diameter so as to minimise lift-effect in boundary layer
• sufficiently large diameter so as have uniform scattering properties (e.g. no Miescattering), exceed pixel size of camera, enable illumination with reasonable illumination intensity
• monodisperse so as to have uniform intensities in the images
Possible further problems
Problem 4 Temperature measurements using Laser-Induced Fluorescence (LIF).
(a) Sketch the general laboratory set-up for temperature measurements using LIF. Specify its basic components and briefly describe their function.
(b) Explain the principle of the ratiometric intensity that underlies LIF. Support your
explanation with mathematical expressions.
(c) What is the essential advantage of the ratiometric approach over an approach in
which the temperature is evaluated directly from the measured intensity?
For fluctuating laser intensities, the ratiometric intensity Ir assumes the form
Ir = (1 + ∆Iex ) φref (T ) ,
with φref the normalised quantum yield.
(d) Give an expression for ∆Iex in terms of the actual reference intensity at the present
time t and the original reference intensity recorded at the reference time tref .
(e) How does ∆Iex manifest itself in the temperature measurement? What could one do
3
Problem 1 ...
Venturi-type
“classical” velocimetry ...
flow-rate meters: standard, nozzle-type,
(a) Discuss the working principle of these flow-rate meters ... use Bernouilli to determine
velocity from pressure drop
(b)
(c) Correction factor; why? departure from Bernoulli due to viscosity, rotational effects
Problem 2 ... point-measurements ...
(a) Discuss the working principle of the Pitot-tube and its limitations
(b) ... LDA ... why always 2 beams??
Problem 2 ... thermocouples ...
Problem 4 Beschouw een 2D waterstroming in een gesloten domein van 10x10 cm. De
kleinste structuren in de stroming hebben een typische grootte van 8 mm en een typische
snelheid van 1 cm/s; voor de grootste structuren is dit respectievelijk 30 mm en 2 cm/s.
Het snelheidsveld wordt bepaald m.b.v. PIV. Hiertoe wordt een camera met een resolutie
van 1000x1000 pixels gebruikt die het domein volledig in beeld heeft.
(a) Schets de basisopstelling voor snelheidsmetingen m.b.v. PIV, benoem de componenten en omschrijf kort hun functie.
(b) Beschrijf de basisstappen en het werkingsprincipe van de PIV-dataverwerking.
(c) Geef een schatting voor de grootte van het kleine interrogatie-gebied benodigd voor
een duidelijke resolutie van alle stromingsfenomenen.
(d) Gegeven 16 pixels en 32 pixels als grootte van het kleine en grote interrogatie-gebied.
Geef een schatting voor de minimale en maximale opname-frequenties van de camera
om een betrouwbare data-verwerking te kunnen garanderen.
(e) Stel men zou alternatief de data voor bovengenoemde PIV-meting met PTV willen
verwerken. Zou dit kunnen? Motiveer het antwoord.
4
```