Particle Image Velocimetry on a Turbulent Jet

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Particle Image Velocimetry on a Turbulent Jet

by

Arash Sonei

Master Thesis in Aerospace University of Bologna, Forli, Italy

Master Thesis in Fluid Mechanics Royal Institute of Technology, Stockholm, Sweden

August 2016

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Abstract

The goal of the present paper is to set up, test and validate a home-made high-speed imaging system for investigating low-speed aerodynamic flows. The imaging setup includes a high-speed digital camera, a continuous wave laser and related optics. The setup has been optimized for:

a) Flow visualization

b) Particle Image Velocimetry based on an open-source code

After optimizing the experimental setup, tests were performed on an axisymmetric jet. Based on the results obtained, the limits and potential of the present setup are discussed, and suggestions for possible improvements are given.

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Chapter 1. Introduction

The application of jet engines is widely common in modern industries. The flow produced by these engines are usually very complex, three-dimensional and highly turbulent. Hence, it is very difficult to measure and characterize these types of flows. One possibility to simplify the study is to consider the whole flow as a superposition of several more basic configurations, called “canonical” flows, like for instance boundary layers, wakes or jets. As far as engines are concerned, some of the most important regions of the flow can be approximated by coaxial jets. Figures 1.1 and 1.2 display the flow produced by a jet engine as well as the one from a coaxial jet.

Figure 1.1. The flow produced by a jet engine.

Figure 1.2. Sketch of a typical coaxial jet.

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A long-term research program has been performed at the University of Bologna to study this type of

“canonical” configuration. To perform this task, the Coaxial Aerodynamic Tunnel (CAT) has been designed and manufactured. Several experimental campaigns have been accomplished and many results have been published such as Segalini and Talamelli [13]. In most of these experimental campaigns standard measurement techniques, like Pressure Probes or Hot-Wire anemometry (HWA) have been used.

Standard measurements are performed by placing a probe into the flow. However, these probes are only able to measure the flow at one point at a time and depending on the kind of probe, one may only be able to measure a single velocity component. The standard measurement techniques used such as hot- wire anemometry also have other severe limitations. For instance, they are sensitive to temperature fluctuations, not so accurate at low speeds and unable to detect the presence of backflow, all characteristics which are present in the case of jet flows.

Hence, there is a need for a more reliable measurement technique, one that is able to accurately measure the characteristics of the flow at thousands of points at once. One adequate method is particle image velocimetry (PIV). PIV is an optical measuring technique which estimates the displacement of the flow through analysing images taken of particles suspended in the flow medium. Through this, the velocity and other characteristics of the flow can be calculated.

PIV has many advantages compared to other standard velocimetry techniques such as hot-wire anemometry. Some of these advantages being:

 Insensitivity to temperature

 Able to acquire the direction of the flow, i.e. measure backflow

 Able to measure the spatial flow field in one measurement, rather than just the velocity at a single point

 Able to reconstruct streamline movements and observe vortex formation and evolution

 Able to measure a minimum of two velocity components, depending on the type of PIV

 Sub pixel displacement yields a high degree of accuracy

The goal of this paper is to set up a home-made PIV system capable of analysing both qualitatively (flow visualizations) and quantitatively through PIV (kinematic of the flow produced by the CAT). Tests were performed to check the limitations of this setup by comparing the data obtained to Pitot tube data acquired at the centreline.

The structure of this paper is as follows: chapter 2 presents a more detailed explanation for PIV, giving one insight to the method and what problems might occur as well as how they can be overcome, while in chapter 3 the experimental set-up and the components involved are described. This is followed by the qualitative imaging in chapter 4 and the results from the quantitatively analysis in chapter 5 where the results are discussed ad verified. Lastly an overview, conclusions as well as potential improvements to the setup are given in chapter 6.

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Chapter 2. Quantitative Imaging - Particle Image Velocimetry

2.1 Generalities

PIV is not a recent method, on the contrary it has been around for several decades. The first measurements using PIV techniques were used in the late 70s. In this early period, it would take one nearly a week just to set up the system, capture a few frames and evaluate the data. Whereas with today’s technology one is able to capture up to several hundred recordings per minute, and evaluate a digital recording within a few seconds.

Throughout the years’ different kinds of PIV techniques have been developed and some are still in the development phase. The main different PIV techniques are:

 Two-dimensional PIV

 Stereoscopic PIV

 Volumetric PIV

The first kind, two-dimensional PIV, is the simplest of its kind and only requires one camera whereas the other two require more than one. However, with simplicity comes limitations, as only one camera is used, only two components of the velocity can be measured. Thus leaving the last velocity component unknown. Hence the name two-dimensional PIV. Stereoscopic PIV makes use of two cameras recording simultaneously at separate viewing angles, allowing one to estimate the third component. Both 2D and stereoscopic PIV measure the (two or three) velocity components in a single plane. If one desires more accurate knowledge of the velocity field in a specific region of the measurement domain, then one can achieve this through volumetric PIV.

2.2 Two-dimensional PIV

As stated, in two-dimensional PIV, only one camera is required. The objective of the camera is to capture the motion of the flow. In order to visualize the flow, a tracer must be introduced into it, which should be distributed homogeneously in the flow. The seeding density will be linked to the final spatial resolution.

One crucial component is the illumination. The light source illuminates the tracer particles on a plane (i.e. light sheet within the flow). The light, scattered by the tracer particles is recorded onto frames, which captures the motion of the particles. For the illumination a laser is typically used. There exist two main methods for illuminating the region of interest with lasers in PIV. One is through the usage of continuous wave (CW), i.e. having a continuous laser beam on while the camera captures the image pairs used for determining velocity components by the means of a PIV algorithm later on. The CW illumination time is regulated by the camera’s shutter speed. A second method is based on a pulse laser (PL).

With a pulsating laser, the region of interest is illuminated for a very brief moment (order of nano- seconds) while capturing each frame. In this case, massive amount of energy is released at one instance, freezing the particles in place while generating desired illumination which results into clear frames captured by the camera. Note that, PL requires synchronization with the camera in order to yield a single pulse at each frame. The principle of PIV can be seen in figure 2.1; a digital image sensor is positioned parallel to the illuminated sheet, capturing the movement of the particles.

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Figure 2.1. Principle of PIV: A laser sheet illuminates the particles contained in the fluid. A camera records the displacement of the particle pattern [7].

As can been seen in figure 2.1, the camera captures the particles position at each instance of time in the image plane.

In order to obtain the actual measure of the speed a calibration must be performed, i.e. convert pixel length of the frames captured into real world measurements such as meter. In two-dimensional PIV this is a simple task, as one can relate the pixel length to real world measurements simply by a calibration factor also called magnification factor, 𝑀. In other words, one must first measure the object or model which is to be filmed, a diameter for instance or simply a ruler placed in the image plane, and then see how many pixels that object corresponds to on the frame and calculate the calibration factor.

Finally, a suitable method for measuring the particles displacement must be applied. This can be achieved by dividing the image into multiple smaller images which are referred to as interrogation areas. It is assumed that all particles within one interrogation area have moved homogeneously between the two illuminations. As a rule of thumb the time between the frames, ∆𝑡 also known as the burst time, should be chosen in such a way that the particle displacement is smaller than a third of the size of the interrogation area [4, §2.1.3]. In most cases this corresponds to that the tracer particles to move around 4 − 5 pixels between the frames of the image pair. These interrogation areas are then cross-correlated and the information is stored in the cross-correlation matrix 𝐶. It may be the case that some particles move outside the interrogation area from one frame to the other. This will reduce the Signal-to-Noise (SNR) ratio of the correlation peak, in the cross-correlation matrix 𝐶 One way to reduce this is by introducing overlapping between the interrogation areas.

The average displacement of particle from one frame to the other can be determined by making use of the intensity peaks in the cross-correlation matrix 𝐶. The particle displacements are then used to calculate the velocity of the particles and therefore the velocity field of the flow. The relationship between the velocity vector 𝑽 and the particle displacement vector 𝒅 is given by:

𝑽 = 𝒅

𝑀∆𝑡

(2.1)

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There are 2 common methods which one can use in order to solve the discrete cross-correlation function;

these methods are:

1. Direct cross-correlation (DCC) 2. Discrete Fourier transform (DFT)

In DCC, the correlation matrix 𝐶 is computed in the spatial domain. The method of DCC also allows the interrogation areas to be different in size. By allowing one interrogation area being greater than the other, one can reduce the loss of information in case the particles move outside the first interrogation area in between the frames, as the second interrogation area might cover that section as well. This will provide a cross-correlation matrix with low background noise. Both systematic error and random error of calculations reduce substantially by using DCC [9].

DFT on the other hand, computes the cross-correlation matrix in the frequency domain. This method requires that the interrogation areas are of identical size. Normally DFT would give rise to more systematic and random errors compared to DCC. However, with a modified version, it can be implemented in such way that it yields greater spatial resolution as well as accuracy than DCC. This modification also takes real life effects into account, such as shear and rotation of the particles rather than simply assuming uniform motion. This modified version is known as DFT window deformation.

This modification is done by introducing various passes or “repair routines”. Additionally, in between these passes, the velocity information acquired is smoothed and validated, as well as interpolation of missing information is done. A general comparison of DCC and DFT window deformation is shown in figure 2.2.

Figure 2.2. Comparison between DCC and DFT with window deforming based on [9, §2].

The peaks yielded by the cross-correlation may be untrue as by default only integer values are taken into consideration. Applying appropriate subpixel interpolation will increase the dynamic range and hence the accuracy. This is commonly done by fitting a Gaussian curve to the data which results to more accurate results. Some subpixel interpolation can also take real life effects into account such as particle displacements being subjected to shear or rotation within the interrogation area. Figure 2.3 displays the typical principle of subpixel interpolation.

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Figure 2.3. Principle of a typical Gaussian fit: Subpixel precision is achieved by fitting a one- dimensional Gaussian function (solid line) to the integer intensity distribution of the correlation matrix

(dots) [7].

As with any other measuring techniques there are errors. These errors can rise from, bad illumination, strong in/out plane movement and other sources. Hence one must validate the data and identify outliers to exclude them from the calculations. One way to filter out outliers is by choosing acceptable velocity thresholds, which can be done graphically through analysing the scatter plot of the longitudinal velocity, 𝑢, and radial velocity, 𝑣, yielded from the PIV analysis. Another method of data validation is by introducing limitation thresholds to the velocity.

{𝑡_{𝑙𝑜𝑤𝑒𝑟} = 𝑢̅ − 𝑛𝜎_𝑢 𝑡_{𝑢𝑝𝑝𝑒𝑟} = 𝑢̅ + 𝑛𝜎_𝑢

(2.2) Here 𝑢̅ is the mean velocity, 𝜎_𝑢 the standard deviation of the mean velocity and 𝑛 a parameter determining the strictness of the filter. As a result, any velocities outside these thresholds are considered outliers and are filtered out.

One might also observe a discretization error which is present when particle images are too small for the peak estimators. This introduces the peak-lock phenomena, which can be detected by plotting a displacement histogram, as shown in figure 2.4, leading to false results. This phenomenon can be removed by means of different methods, for example by simply choosing a different peak estimator which is better adapted for smaller particle images. Alternatively, one could pre-condition the images using filters which optimize the particle image diameter with respect to the peak estimators [1, §5.5.2].

Once the outliers have been removed, one might be left with a significant amount of missing data. Hence there is a need for interpolating of the data to fill in the gaps. There are numerous interpolators, one of them being the boundary-value solver. The approach provides an interpolation that is generally fairly smooth, and covers larger regions with missing data, as it will tend towards the average of the boundary velocities, which prevents overshooting [9, §2]. An example of this interpolator is seen in figure 2.5.

The data interpolated by this method also deviates the least from the original one when compared to other interpolators such as spline or 2D interpolation among others.

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Figure 2.4. Histograms of actual PIV displacement data obtained from a 10-image sequence of a turbulent boundary layer illustrating the "peak locking" associated with insufficient particle image size

(left). Image preconditioning can reduce this effect (right) [1, §5.2.2].

Figure 2.5. Testing boundary value solver. Left: Original velocity data. Middle: Data is removed at random positions. Right: Gaps are filled with interpolation and compared to the original velocity data.

[9, §2].

The analysis process for PIV which the data undergoes can hence be summarized by figure 2.6.

2.3 Resolution

Earlier it was stated that the tracer particles are linked to the spatial resolution. The concentration of tracer particles more commonly referred to as image density or seeding, making out a lower limit for the spatial resolution. Generally, there are 3 cases of seeding, these cases can be seen in figure 2.7.

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10 Figure 2.7 displays 3 different seeding cases:

a) Too low

In this particles case, each particle can be tracked individually and requires Lagrangian tracking (follow particle through time) approaches like Particle Tracking Velocimetry (PTV). Similar method was used by Da Vinci who would place grass seeds on a flow and sketch the resulting trajectories. However as stated seeding determines a lower limit for the spatial resolution. Hence as high spatial resolution is desired, this approach is not adequate. Having a low seeding density will also cause a great number of outliers and bias in the PIV analysis.

b) Medium

In this case, one can still identify individual particles However, it is no longer possible to identify image pairs by visual inspection of the recording. Medium image density is required to apply the standard statistical PIV evaluation techniques and is what one should aim for. Maintaining adequate medium seeding throughout the recording can prove to be a challenging task though.

c) Too high

In this last case, one can achieve the maximal spatial resolution as possible through the aid of seeding. However due to the high density of the tracer particles, it may not be possible to detect individual images as they overlap in most cases and form speckles. This situation is called laser speckle velocimetry (LSV).

Figure 2.6. Illustration of how velocity information is extracted from an image pair.

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Figure 2.7. The three modes of particle image density: (a) low (PTV), (b) medium (PIV), and (c) high image density (LSV) [1, §1.2].

As the seeding is directly linked to the spatial resolution and defines a lower limit for it, one would desire the highest value possible for. As it cannot be too high, it is medium seeding which one should aim for, to yield an accurate analysis.

So far only the lower limit of the spatial resolution has been discussed. The upper limit is determined by the size of the interrogation area as it determines the number of independent velocity vectors.

As for the temporal resolution; this is determined by how many frames the camera is able to capture in one second. For a high speed camera this value can be quite high, however there is a trade-off, if one desired a higher frame per seconds setting then one must be willing to reduce resolution of the image (i.e. length and width of the image in terms of pixels).

2.4 Image Processing

Each image captured can, in the case of grey-scale images, be converted into a two-dimensional array 𝐼(𝑥, 𝑦), where 𝐼 defines the light intensity level. In the case of colour images one would have a three-dimensional array. The continuous space defined by the coordinates (𝑥, 𝑦) is discretised and divided into 𝑛 rows and 𝑚 columns. I.e. one has now a matrix defining the image captured. The intersection of the rows and columns (each element in the matrix), corresponds to a pixel. Hence the size of the matrix corresponds to the image’s resolution. Dividing the image into interrogation areas is now a simple task, as one only needs to split the matrix into lesser ones.

Additionally, it may be the case that that the image captured is not clear or bright enough. Which can be the case when capturing images. The image can then be enhanced by simply manipulating the matrix until one yields a desired image, which can be done by subtracting the background for instance. In some cases, it may be desirable to apply a filter to the image, this could significantly improve the number of successful correlation during the PIV analysis, as it is highly dependent on the image processing.

Furthermore, when recording in higher frames per seconds one may notice a flickering effect in the images captured. This phenomenon normally occurs capturing the frames in the presence of a tungsten lamp, hence it is of great importance to conduct the measurements away from these sources of light which can introduce disturbances.

Figure 2.8 displays one example of how can image can be enhanced. In this case a portion of a jet flow at 5 diameters from the nozzle has been captured.

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Figure 2.8. Comparison between Image before image processing (left) and the image post image processing (right).

A notable detail on figure 2.8 is that although the seeding density is desirable throughout most of the frame, it does not cover all of it. This will result into bias of the analysis, specifically in the unseeded portions which then in return affects the overall results when one averages the data from all the image pairs analysed.

Hence one can summarize the procedure of PIV discussed in this chapter into 6 steps:

1. Select appropriate flow tracers

2. Illuminate particles in the region of interest and capture images 3. Image-processing and measure displacement between frames 4. Compute velocity from the displacement

5. Data validation and post-processing 6. Extract quantities of interest

There are numerous algorithms which have been written to solve these kinds of problems. One of them being PIVlab [7], a free PIV toolbox designed for the commercial program MATLAB. This toolbox implements all the methods mentioned in this chapter.

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Chapter 3. Experimental Set up

The experiments have been carried out in the Coaxial Aerodynamic Tunnel (CAT) facility in the laboratory of the Second Faculty of Engineering in Forli. The general setup for PIV can be seen in figure 3.1.

Figure 3.1. The PIV setup from the point of view of the camera (right) and seen from the side (left).

3.1 The Coaxial Aerodynamic Tunnel (CAT)

The coaxial jet is a combination of two jets where the inner and outer diameters are 𝐷_𝑖= 50 mm and 𝐷_𝑜= 100 mm respectively. Both jets end with two straight pipes of 100 mm. However, rather than making use of the two jet flows of the Coaxial Aerodynamic Tunnel, only the inner jet is used here.

Hence it can be seen as a single circular jet. Figure 3.2 displays a sketch of the facility and its components.

Figure 3.2. Schematic view of the facility: (A), outer jet blower; (B), inner jet blower; (C), outer jet pre-settling chamber; (D), inner jet pre-settling chamber; (E), inner jet diﬀuser; (F), inner jet settling

chamber; (G), outer jet settling chamber; (K), electrical resistors; (H), screen and honeycombs; (L), outer jet hoses; (M), axial traversing; (N), radial traversing; (P), calibration device.

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The Jet stream, has a so called potential core as seen in figure 3.3. In this conical shaped region, the velocity is nearly uniform. The potential core is in most cases about 5 − 6 diameters long. The flow field around the potential core, is called the shear layer. In this region vortices are formed as a result of shear layer instability. This is the region in which the jet mixes with the surrounding fluid.

Figure 3.3. Sketch of the jet flow.

The mass flow increases with increasing distance from the exit. This is because of the entrainment phenomenon; as surrounding air gets dragged into the jet flow. The momentum on the other hand is constant throughout the entire flow, as there are no external forces applied to the fluid.

Flow conditioning is performed by means of screens and honeycombs in both the inner and the outer circuits. The fog produced by the ROSCO 1600, is injected into inner jet blower, denoted B in figure 3.2. The velocity of the jet flow is not a known parameter when handling the jet, hence the need of a suitable measuring technique such as PIV in this case. The parameter which one does have control over is the rotational speed of the jet’s motor. A higher frequency results into a higher velocity output.

The calibration device, P, for the PIV measurements is a simple ruler, as described in chapter 2 and is placed in the image plane.

As the traversing is movable and is place in the middle of the flow, the calibration device can be used for various things such as:

1) Focusing the camera for a sharp image, as it is in the plane of interest.

2) Acquire a calibration snapshot

3) Aligning the laser sheet in the plane of interest.

4) Act as a precise tool to measure how many diameters away from the jet exit one is measuring.

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3.2 Hot-wire Probe

In order to test the PIV system, hot-wire measurements are conducted at different flow scenarios to measure the velocity at the jet’s nozzle. Note that the hot-wire measurement can only be considered accurate for higher velocities, as this measuring technique has a accuracy which increases with increasing speed. For the hot-wire measurements a Dantec 55P11 single wire probe was used. The characteristics of the sensor is shown in figure 3.4. This single wire probe is unfortunately only able to measure flows in one dimension, hence only the longitudinal velocity component can be used as a comparison to the results yielded from a PIV analysis. Moreover, the HWA is not able to detect the presence of backflow, which might occur in a jet due to the presence of strong vortices. This might also cause scattering among the measured points.

Figure 3.4. Dantec 55P11 single wire probe, all measurements are given in millimetres [17].

To simplify the calibration procedure a direct relation between the driving frequency of the motor and the actual jet velocity at the exit was found and reported in Figure 3.5

Figure 3.5. Relationship between the jet-motor’s rotational speed and its exit velocity.

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For the measurements a Dantec Streamline anemometric system was used. The output signal was recorded with a sampling frequency of 2000 Hz along with a sampling time of 10 sec.

3.3 Camera and Tracer Particles

One of the goals of this paper is to set up a home-made PIV system. As high-speed cameras decrease in price with each year; it has become possible to set up a self-made PIV system making use of such cameras along with a continuous wave laser rather than a commercial system which typically makes use of pulse lasers and not necessarily a high-speed camera.

In the present system a Phantom camera model Miro 340 from Vision Research [6] has been used, along with a Sigma 180 mm F/3.5 D APO Macro HSM lens. The Phantom camera is a grayscale high speed camera equipped with a 4 Mpx sensor capable of a maximum resolution of 2560 x 1600 pixels. The quality of the images captured by the camera depends mainly on 3 settings, namely:

 Resolution

 Frames per second

 Exposure time

The resolution of the image describes the length and width of the image in terms of pixels. Decreasing the resolution will result into an increase of the maximum frame per seconds, i.e. the number of images the camera captures per second. In other words, it is a trade-off between the spatial and temporal resolution. The exposure time sometimes also called the shutter speed, is the time when the digital sensor inside the camera is exposed to light when capturing images. Hence the longer the exposure time the more light is acquired by the sensor resulting in a brighter image. The maximum exposure time is a function of the frame rate, the lower the frame rate the higher the limit for the maximum exposure time is.

Due to restrictions in the cameras control program and limitations on the cameras internal memory, a resolution of 1024 x 1024 pixels is used along with a burst time ∆𝑡 = 500 𝜇s between the image pairs captured for the PIV analysis of relative low velocity flows. Due to the lens being unable to zoom, the camera is placed at a distance such that the 1024 x 1024 pixels corresponds approximately to 64 x 64 mm. This relationship is then defined as the calibration factor.

As for the tracer particles, fog generated from a ROSCO 1600, a fog machine from Rosco Laboratories Inc. is used. The fog machine generates its smoke through heating an aqueous glycol solution. These tracer particles do not travel at the exact same velocity as the flow. The particles have a certain response time also known as velocity lag defined by:

𝜏_𝑝=𝜌_𝑝𝑑_𝑝 18𝜇

(3.1) where 𝜇 is the viscosity of the fluid (air in this case), 𝜌_𝑝 and 𝑑_𝑝 are the particle density and diameter respectively. [5, §5.3.1] suggests that for a Glycol–water solution 𝜌_𝑝= 10³ kg m⁄ ³ and 𝑑_𝑝= 1-3 𝜇m.

Tracer particles with greater diameters will have a better light scattering property but also have a greater velocity lag which is undesired. Hence it is of great importance to have sufficient concentration of tracer particles in the region of interest while capturing the frames. Not doing so could lead to bias in the PIV analysis. These biases could lead to untrue results, yielding that the velocity calculated from the average of the statistical samples acquired could be lower than their true value. As low seeded sections might give rise to very small velocities and when one takes the average result throughout all image pairs, then the portions with untrue low velocities will decrease the total result as well.

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3.4 Laser Illumination

As for the illumination, a Stabilite 2017 from Spectra-Physics is used. This model uses Argon as an excitation medium to produce a continuous laser beam, figure 3.6 displays the different components of the laser head.

The laser beam consists of photons emitted from the medium, this case Argon, as it gets hit by an energy source. The exact procedure on how the beam is obtained is as follows:

A resonant cavity defined by two mirrors provides feedback to the active medium. Photons emitted parallel to the cavity axis are reflected, returning to interact with other excited ions. Stimulated emission produces two photons of equal energy, phase and direction from each interaction. The two become four, four become eight, and the numbers continue to increase geometrically until an equilibrium between excitation and emission is reached. Both mirrors are coated to reflect the wavelength, or wavelengths, of interest while transmitting all others. One of the mirrors, the output coupler, transmits a fraction of the energy stored within the cavity, and the escaping radiation becomes the output beam of the laser [14,

§3-5].

The emitted laser beam then travels through an optical fibre until it reaches a cylindrical lens, where the beam is transformed into a relative thick laser sheet, and is positioned to coincide with the centreline of the jet flow. For the conducted experiments the laser power is set to 32 ampere, which is 91.43 % of its maximum operational setting rather than at 100% , due to safety reasons.

Normally for a PIV set up, all the images would be acquired during the evening where no or little interference from ambient light is present. However, in this case all the images were captured during the day, hence making image processing an even more crucial process as the ambient light strongly affects the frames captured, and no analysis can be performed in the condition the frames are pre-image processed.

As a continuous laser is used, the exposure time must be set to a low value to avoid blurring.

Figure 3.6. Laser head of the Stabilite 2017.

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Chapter 4. Qualitative Imaging - Flow Visualization

Flow visualizations are still widely used since they allow to see how the flow behaves at different velocities, for instance, when and how the transitions from laminar flow to turbulent takes place and how it looks like. However, even if it shows the structure and behaviour of the flow, it does not give any quantitative information regarding its characteristics.

For this analysis, the camera’s maximum resolution is chosen along with its corresponding maximum frame rate and exposure. In other words, with a resolution of 2560 x 1600 pixels, frame rate of 800 fps and an exposure time of 1200 𝜇s. With this configuration the camera is able to film for 1.215 s. This may not seem long but is sufficient to see how the flow behaves and capture patterns not visible to the naked eye. Figures 4.1 -4.5 displays a sample of the instantaneous flow visualization when the jet’s exit velocity is 3.02 m/s, figures 4.6-4.10 a sample when the jet’s exit velocity is 6.24 m/s and figures 4.11- 4.15 a sample when the jet’s exit velocity is 9.61 m/s. These images were taken during the day, where ambient light strongly affects the images acquired. Hence one must first preform image processing in order to display the interesting characteristics of the flow. The Reynolds number for the instantaneous flow visualizations are based on the jet’s inner diameter and its centreline velocity at the nozzle and are measured by the means of hot-wire anemometry. Note that the flow visualization and measurement of the centreline velocity at the jet’s exit were done on two separate occasions, leading to that the calculated Reynolds number might slightly differ from the actual one.

𝒖_{𝒄𝒆𝒏𝒕𝒆𝒓}= 𝟑. 𝟎𝟐 𝐦/𝐬, 𝑹𝒆 = 𝟏𝟎𝟑𝟐𝟎:

Figure 4.1. Instantaneous flow visualization at 𝑡 = 0 ms with exit velocity of 3.02 m/s.

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Figure 4.3. Instantaneous flow visualization at 𝑡 = 21.25 ms with exit velocity of 3.02 m/s.

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21 𝒖_{𝒄𝒆𝒏𝒕𝒆𝒓}= 𝟔. 𝟐𝟒 𝐦/𝐬, 𝑹𝒆 = 𝟐𝟏𝟑𝟑𝟖:

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24 𝒖_{𝒄𝒆𝒏𝒕𝒆𝒓}= 𝟗. 𝟔𝟏 𝐦/𝐬, 𝑹𝒆 = 𝟑𝟐𝟖𝟖𝟑:

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While preforming the experiments, it was noticed that the flow is not always entirely symmetric and in some cases tends to flow slightly upwards or more frequently downwards with a significant radial movement. The downward movement of the jet flow may be explained by its temperature. It must be pointed out that, this movement was mostly present for the lower velocities than the ones presented in this chapter.

In other cases, the smoke tends to move upwards from the longitudinal axis. The reason behind this effect may lie in the facility itself. The laboratory of the Second Faculty of Engineering in Forli is located in an old airport hangar and it is not fully sealed off from the outside environment. The movement of the flow may be explained by the presence of these openings.

It has also been noticed while performing the experiments that in some cases the smoke did not follow the jet flow at all, but instead moves in an entirely different direction right after the nozzle. This if used, will of course cause bias in the PIV analysis, as this is an optical analysis which is dependent on the movement of the smoke in order to calculate the flow’s velocity. The samples selected to be analysed have been chosen amongst a greater amount of samples and have shown the least radial moment. This effect was seen more frequently among lower velocities whose instantaneous flow visualizations are not presented here. Even if the flow only moves very slightly in the radial direction, it can still cause significant relative error as the information area (image plane) is relatively small, especially if this phenomenon lessens the seeding in the upper and/or lower boundaries of the captured frames. Hence the measured longitudinal velocity component would does correspond to its true value.

For further instantaneous flow visualizations with exit velocities of 12.93, 16.23 and 19.61 m/s, please refer to appendix A.

For the evolution of the velocity profile over the distance of the flow captured for these visualizations through HWA, please refer to appendix B.

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Chapter 5. Velocity Measurements

In this chapter, the results from the PIV system are presented, verified and discussed. As previously mentioned in chapter 3, a resolution of 1024 x 1024 pixels is used along with a ∆𝑡 = 500 𝜇s between the image pairs, enabling one to gain the information of the flow field of a plane approximately corresponding to 64 x 64 mm. The centre of the image plane of the camera is positioned 5 diameters away from the jet exit.

As mentioned before there are numerous factors which can cause bias in the data, hence it is of great importance to acquire a significant amount of statistical data in order to obtain a converged statistic. For this purpose, 4 sets of videos for each analysis are captured and averaged. Each set contains 1900 image pairs with the mentioned camera settings. In other words, a total of 7600 image pairs have been averaged to yield the data presented in this chapter.

Figures 5.1-5.9 display the averaged results of these analyses yielded from PIV obtained when the jet’s exit velocity was measured to be approximately 0.90 , 1.80 and 3.02 m/s along with one image pair from each flow scenario to display the quality of the image processed images.

Since hot-wire anemometry is not reliable at low velocities, the mean centreline velocity has been measured with a Pitot tube positioned 5 diameters away from the jet exit as a comparison to PIV. This will give a more accurate indication to what the “true” velocity of the flow might be. The maximum velocity yielded from PIV analysis it displayed in table 5.1 together with the Pitot tube measurement. It must be pointed out that at 0.90 m/s, even the Pitot tube cannot be used since the velocity is too low to yield enough pressure difference.

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28 𝐄𝐱𝐢𝐭 𝐕𝐞𝐥𝐨𝐜𝐢𝐭𝐲: 𝟎. 𝟗 𝐦/𝐬

Figure 5.1. Averaged flow field at the image plane when the jet’s exit velocity corresponds to 0.90 m/s.

Figure 5.2. Averaged PIV data at 5 diameters from the jet exit.

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Figure 5.3. An image pair used for the PIV analysis with the exit velocity corresponding to 0.90 m/s.

Frame 1 Frame 2

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30 𝐄𝐱𝐢𝐭 𝐕𝐞𝐥𝐨𝐜𝐢𝐭𝐲: 𝟏. 𝟖 𝐦/𝐬

Figure 5.5. Comparison between Pitot tube and averaged PIV data at 5 diameters from the jet’s exit.

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Figure 5.6. An image pair used for the PIV analysis with an exit velocity of 1.80 m/s.

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32 𝐄𝐱𝐢𝐭 𝐕𝐞𝐥𝐨𝐜𝐢𝐭𝐲: 𝟑. 𝟎𝟐 𝐦/𝐬

Figure 5.8. Comparison between Pitot tube and averaged PIV data at 5 diameters.

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In order to increase the Reynolds number to better match the applications, experiments have been performed at higher speeds. In order to do so, one must first change the settings of the camera. If one wishes to capture faster moving objects, then the burst time must be decreased. This can only be done by reducing the resolution, reducing the area of information. What one can do, is to decrease the width of the frame and keep the length constant. By doing so, it is possible to capture faster moving flows while covering the same radial distance as the previous settings. For this purpose, a resolution of 640 x 1024 pixels corresponding approximately to 40 x 64 mm, with a frame per seconds of 2000 along with an exposure time of 100 𝜇s is used. This setting enables one to reduce the burst time to ∆𝑡 = 250 𝜇s. This value is used to analyse the flow with 2 different speeds; at 6.24 and 9.61 m/s as exit velocities. By increasing the frames per seconds in this setting, it is possible to capture more frames and hence provide a better statistical comparison. For both these flow scenarios 5 sets of videos have been taken, each containing 6084 frames i.e. 3042 image pairs giving rise to a total of 15210 for each case.

Figures 5.10-5.15 display the results obtained from these analyses, along with one image pair from each flow scenario to display the typical image quality of the image processed frames.

𝐄𝐱𝐢𝐭 𝐕𝐞𝐥𝐨𝐜𝐢𝐭𝐲: 𝟔. 𝟐𝟒 𝐦/𝐬

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36 𝐄𝐱𝐢𝐭 𝐕𝐞𝐥𝐨𝐜𝐢𝐭𝐲: 𝟗. 𝟔𝟏 𝐦/𝐬

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As can be seen from the averaged flow fields, the smoke does not seem to move entirely parallel to the longitudinal axis. The largest radial movement can be seen of course at the lowest velocity. From the images it can be observed that the smoke tends downwards causing the flow to have a maximum deviation at a lower radial coordinate than that at the centreline. This effect can be related to the different temperatures of the jet. Since it is relatively cooler than the surrounding air, it may deflect downwards.

Another effect that may cause a deviation of the flow is condensation. This phenomenon was observed by noticing that the glycol used to create the smoke leaked in liquid state from the jet in various position.

The leaks were found on the inner jet blower, where the smoke was injected and at the inner jet diffuser denoted B and E respectively in figure 3.2. Residual glycol was also found in the jet’s nozzle. This could explain the slight unsymmetrical geometry of the velocity profile.

Another effect which should be further investigated is the deviation of the peak of the mean velocity profile, which appears to be slightly shifted. In most cases this shift seems to correspond to approximately 8 mm. With the camera being placed at an approximated distance of 1.2 m away from the image plane, then simple trigonometry states that the tripod which the camera was places on was not perfectly horizontal but rather tilted a with an angle of 0.38 degrees. This could be the most plausible cause for the location of the velocity profile’s peak. This problem can be easily corrected with a better positioning setup.

As can be seen on the figures and table above, the lower velocities where the Pitot tube could be used as a reference (i.e. at 1.80 and 3.02 m/s), is in good agreement to the PIV analysis and the quality of the images are as desired, suggesting that the correct settings were used. There still exists a small mismatch, but this could depend on the ambient conditions as the measurements were not conducted on the same occasions. However, for the higher velocities (6.24 and 9.61 m/s) one can observe a significant mismatch between the results from the different measuring techniques, especially at the highest velocity.

A possible reason can be deduced by looking at image pairs at these velocities. As stated previous in chapter 2, the CW illumination time is regulated by the camera’s shutter speed, which in high speed application could lead to blurring of the frames. Even though the burst time for these flow scenarios is half the burst time of the lower velocities, the blurring phenomena could not be avoided. Figure 5.12 displaying an image pair the analysis at 6.24 m/s, shows that with the settings used, the particles are on the limit to become blurred. Hence the difference between the PIV and Pitot tube results. As for the case of 9.61 m/s, figure 5.15 shows that the particles now are fully blurred, giving rise to a significant decrease in the image quality. Hence the faulty results obtained from it. Additionally, the particle movement of the flow case of 9.61 m/s appears to be too large, which is another indicator that the burst time between the frames is probably not sufficiently low.

It would appear that for these two last scenarios, the camera settings used were not adequate. If one were to reduce the burst time even further, then the resolution would have to be decreased even further, reducing the area of information even more. Additionally, as the exposure time by default must be lower

Jet’s exit velocity [m/s] PIV [m/s] Pitot Tube [m/s]

0.9 0.51 −

1.8 1.18 1.25

3.02 2.44 2.33

6.24 4.61 5.15

9.61 5.38 8.30

Table 5.1. Maximum mean longitudinal velocity obtained from PIV measurements and Pitot tube measurement, at 5 diameters away from the exit.

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than the burst time, it may not be possible to acquire good quality frames. As the experiments were carried out in daylight and with the usage of a continuous laser, it is uncertain if one would yield frames clear enough, even by means of image processing to then use the PIV algorithms on.

Another interesting feature of a PIV analysis is that, as one measures the distance individual tracer particles, one is able to recreate the path they travel. In other words, one is able reconstruct the streamlines of the flow. This can be particularly interesting when one is analysing the movement of a vortex for instance. Figure 5.16 shows the movement of a vortex, from left to right, seen at the bottom of the frame in a duration of 75 ms apart, with jet’s exit velocity being 0.90 m/s.

Figure 5.16. Instantaneous velocity field at the image plane when the exit velocity corresponds to 0.90 m/s. The black lines represent streamlines.

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Chapter 6. Conclusion and Overviews

The results obtained from the PIV analysis agree well with the Pitot tube measurement when using the setup within its limitations. However, the current setup has shown limitations in what flow scenarios one is able to measure with enough accuracy. The most important limitation is mainly due to the blurring of the frames when the camera is used at higher speeds. Lowering the resolution would enable one to capture faster moving flows but would yield a much lower information area. This would also decrease the exposure time of the camera, giving less illumination to the frames captured which is not also desirable.

During the analysis it has been also assessed that the number of successful correlation from the PIV highly depends on how well the images are processed. Even a minimum change yields a significant difference in the outcome. This is seen commonly for the blurred frames. The same can be noted for the seeding density.

For further experiments it could be wise to conduct the tests in a more appropriate laboratory, i.e. fully sealed off from the outside environment, especially when measuring flows at very low speeds. Another suggestion which can be deduced from the results is that the experiments should be performed during the evening to reduce the influence of ambient light.

Of course, one might also consider to use a different type of high-speed camera, which has sufficient internal memory enabling one to explore lower burst times without having to decrease the resolution significantly.

Finally, as the limitation of the analysis in the paper is linked the blurring of the frames, an alternative illumination source should be considered. Preferably a pulsed laser. With this type of light source, one could analyse flows at much higher speed, improving the accuracy.

In conclusion the analysis has shown that under optimal settings the home-made developed setup has the potential to get similar accuracy than standard measuring techniques such as HWA which, on the other hand, do not take the direction of the flow into account and in this particular application can be considered inaccurate at the edge of the jet where low velocities, high turbulence level and strong flow recirculation is present.

Further experiments at higher speeds need to be performed to gain a better insight of more interesting flow scenarios.

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Appendix A. Instantaneous Flow Visualization at Higher Velocities

For the flow visualizations below, the same camera settings as mentioned in chapter 4 were used. The velocity and Reynolds number as based on the mean centreline velocity at the jet exit.

𝒖_{𝒄𝒆𝒏𝒕𝒆𝒓}= 𝟏𝟐. 𝟗𝟑 𝐦/𝐬, 𝑹𝒆 = 𝟒𝟒𝟐𝟒𝟒:

Figure A.1. Instantaneous flow visualization at 𝑡 = 0 ms with 𝑢_{𝑐𝑒𝑛𝑡𝑒𝑟}= 12.93 m/s.

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Figure A.3. Instantaneous flow visualization at 𝑡 = 21.25 ms with 𝑢_{𝑐𝑒𝑛𝑡𝑒𝑟}= 12.93 m/s.

Figure A.5. Instantaneous flow visualization at 𝑡 = 63.75 ms with 𝑢_{𝑐𝑒𝑛𝑡𝑒𝑟} = 12.93 m/s.

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43 𝒖_{𝒄𝒆𝒏𝒕𝒆𝒓}= 𝟏𝟔. 𝟐𝟑 𝐦/𝐬, 𝑹𝒆 = 𝟓𝟓𝟓𝟐𝟗:

Figure A.8. Instantaneous flow visualization at 𝑡 = 21.25 ms with 𝑢𝑐𝑒𝑛𝑡𝑒𝑟= 16.23 m/s.

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45 𝒖_{𝒄𝒆𝒏𝒕𝒆𝒓}= 𝟏𝟗. 𝟔𝟏 𝐦/𝐬, 𝑹𝒆 = 𝟔𝟕𝟏𝟎𝟏:

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Appendix B. Evolution of the Velocity Profile

In this section the evolution of the velocity profile at various distances for the flow visualizations presented in chapter 4 are given in form of HWA data:

𝐄𝐱𝐢𝐭 𝐕𝐞𝐥𝐨𝐜𝐢𝐭𝐲: 𝟑. 𝟎𝟐 𝐦/𝐬

Figure B.1. 3 diameters from the nozzle.

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49 𝐄𝐱𝐢𝐭 𝐕𝐞𝐥𝐨𝐜𝐢𝐭𝐲: 𝟔. 𝟐𝟒 𝐦/𝐬

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51 𝐄𝐱𝐢𝐭 𝐕𝐞𝐥𝐨𝐜𝐢𝐭𝐲: 𝟗. 𝟔𝟏 𝐦/𝐬

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Particle Image Velocimetry on a Turbulent Jet