5.4.1 Principle
Laser Doppler Velocimetry (LDV) or Laser Doppler Anemometry (LDA) is a non intrusive optical method for measuring velocity of gases. It is a point measurement technique i.e. no spatial resolution is obtained, but a high temporal resolution is possible making it feasible to also do turbulence estimations.
The working principle of LDV can be explained by the fringe model. When two coherent laser beams intersect, they will interfere in the volume of the intersecting beam waists. This will produce approximately plane wave fronts or interference fringes as shown in Figure 23.
Figure 23. Laser beam crossing with interference fringes [39]
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The distance between the fringes is decided by the laser wavelength and the angle between the incident beams according to (5.6) whereț is half the angle between the laser beams. As a particle passes through the measuring volume the intensity of light reflected from the particle will vary with a frequency vDproportional to the particle velocity u normal to the fringes. Knowing the laser wavelength and the angle between the incident beams, the velocity component can be calculated from (5.7).
κ λ sin
=2
df (5.6)
λ κ sin 2u d v u
f
D = = (5.7)
To determine the direction of the velocity component a 40 MHz frequency shift is introduced to one of the two joined beams. The frequency shift causes the fringes in the measurement volume to move, thus the velocity and direction of a particle can be obtained by comparing to the known 40MHz frequency shift.
5.4.2 Seeding
To follow the fluid flow some kind of seeding particles have to be used. These must be small enough in size to ensure that they correctly follow and reflect the flow motion. At the same time they should scatter enough light to be detected. Further, it must be possible to add enough particle density to the working fluid without agglomeration of the seeding or sticking to the optical access surfaces. Lower particle density will directly lower the sampling rate and thus the data quality. Previous research by Johansson [40] with different seeding compounds has shown good results using a polystyrene-latex dispersion, which is also used here. The polystyrene-latex dispersion endures the elevated pressure and temperature during compression, but is rapidly consumed by the combustion. The downside of the extinction of the seeding is naturally that no measurements can be performed once combustion is started. On the other hand the optical access is kept clean enabling long measurements with stable conditions. Lastly, the usage of the polystyrene-latex dispersion posed no risk of excessive engine wear like some dry powder seeding as TiO2and SiO2.
5.4.3 Practise
The particle dispersion had a mean size of 0.46ȝm and was added upstream of the intake manifold by a set of 24 Hudson Up-Draft nebulizers. To minimize soiling of the optics, the seeding equipment was only activated when the engine was fired.
The fluid flow was measured by a 2-component Dantec-fibre flow LDV system. The system features a model 2040 5 W Ar-ion laser from Spectra-Physics. The laser beam is led into a transmitter, through a bragg-cell that splits the beam into two. One of the beams is frequency shifted by 40 MHz. The two beams pass a colour separator to enable three pairs of laser beams, 512, 488 and 476 nm. With the three pairs it is possible to extract three individual velocity components. Here only two are used:
488 nm (blue) and 512 nm (green), thus giving possibility of two dimensional velocity information when measuring in the same volume. The laser beams are transferred with fibre optics to the measurement probe mounted on the engine. The probe is equipped with a beam expander and a beam translator. With the beam translator the beam separation can be moderated, changing the angle of the incident beams after the focusing lens and thus the fringe spacing. An f 310 lens is used to focus the beams to
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a measurement volume near the spark plug through the optical access to the combustion chamber pent-roof. The size of the measurement volume diameter was approximately 50ȝm in diameter and the length 700 ȝm. The backscattered light from the seeding particles is collected through the f 310 lens and transferred back through a fibre. The signal is separated into the blue and green and converted into an electric signal by two Photo Multiplier (PM) tubes. This signal is digitized and analysed with Fast Fourier Transformation (FFT) by Burst Spectrum Analysers (BSA) to obtain valid velocity data. The BSAs are run with an external frequency generator giving a fixed mean data rate of close to 150 kHz.
The LDV measurements are run synchronised with both Schlieren image acquisition and in-cylinder pressure recording. The LDV-Schlieren setup is schematically shown in Figure 22. The two component laser beams was reflected on a semi transparent mirror before entering the combustion chamber. The mirror was coated to reflect the green and blue laser light while still transmitting the broadband light from the mercury lamp for the Schlieren measurements.
5.4.4 Velocity and turbulence
Stationary flow velocities can be separated by Reynolds decomposition into the mean velocity (Nj) and the instant fluctuations, u(t), as shown in (5.8).
) ( )
(t U ut
U = + (5.8)
The turbulence (u´) is defined by the Root Mean Square (RMS) of the instant velocity fluctuations according to (5.9). For steady flows the turbulence intensity is usually derived by dividing the RMS value with the mean velocity. In engine research the RMS value is used without the mean velocity and turbulence is discussed with the unit [m/s] since the mean flow in a reciprocating engine is not constant.
(
2 2)
1/22 / 1
2 1 ()
lim )
1 ( lim
' ¸
¹
¨ ·
©
§ −
¸ =
¹
¨ ·
©
= §
³
→∞³
++
∞
→
τ τ
τ
τ τ τ
t t t
t u t dt U t U dt
u (5.9)
In the definition in (5.8) above the mean velocity is time independent which is hardly appropriate in an internal combustion engine. Instead a slowly fluctuating mean velocity can be used defined the same way as the stationary mean velocity except that the time interval (IJ) is not infinite. This allows low frequency changes of the mean velocity, following the gas flow pattern (5.10).
dt t U t
U t
³
t+= τ
τ1 ( ) )
( (5.10)
The ensemble average velocity and turbulence can be obtained if calculating the mean and the fluctuating velocities from different engine cycles, but at the same crank angle, thus compensating for the engine flow pattern. Better yet is if the amount of velocity measurement per cycle are high enough for within cycle evaluation. Then the mean velocity,Nj(ș,i), can be calculated using a moving average as shown in (5.11). ș is the current CAD,Į the window width and i the cycle number. (5.12) describes the corresponding turbulence definition.
¦
+Δ
=
−Δ
=
= 2
2
) , 1 (
) , (
θ θ α
θ θ α
α
θ U i
i N
U (5.11)
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( )
2 / 1 2
2
2
2 ( , )
) , 1 (
) ,
´(
»»
»
¼ º
««
«
¬ ª
−
=
¦
+Δ
=
−Δ
= θ θ β
θ θ β
β β
θ U i U i
i N
u (5.12)
The differences between the ensemble average mean velocity and the in cycle mean velocity is illustrated for four consecutive cycles in Figure 24. As can be seen the usage of ensemble average does not take into account the single cycle deviations in the mean flow for the turbulence calculations. In this work the method of using a moving window for cycle resolved measurements has been applied.
−40 −20 0 20 40
−15
−10
−5 0 5 10 15 20
Crank angle [CAD]
Velocity [m/s]
Cycle 1
−40 −20 0 20 40
−15
−10
−5 0 5 10 15 20
Crank angle [CAD]
Velocity [m/s]
Cycle 2
−40 −20 0 20 40
−15
−10
−5 0 5 10 15 20
Crank angle [CAD]
Velocity [m/s]
Cycle 3
−40 −20 0 20 40
−15
−10
−5 0 5 10 15 20
Crank angle [CAD]
Velocity [m/s]
Cycle 4
Sample U for cycle u’ for cycle U mean
Figure 24. Sample velocities, cycle resolved mean velocity (U for cycle), ensemble averaged mean velocity(U mean) and cycle resolved turbulence(u´ for cycle) [41].