Master's Thesis

MASTER'S THESIS

An Assessment of Colour Schlieren Photography for Supersonic Flows

Jens Kanje Nordberg 2015

Master of Science in Engineering Technology Space Engineering

Luleå University of Technology Department of Computer Science, Electrical and Space Engineering An Assessment of Colour Schlieren Photography for Supersonic Flow Visualization

Jens Kanje Nordberg [email protected] 2015-10-12

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Abstract

Research in aerodynamics and flow physics often require visual experiments in order to understand the phenomenon at work. These experiments can be very sensitive, and in order to capture and image these events a non-intrusive imaging technique is very useful. Schlieren photography is such a technique, able to capture changes in density in a fluid, by recording light waves refracted along the light ray path through the medium. This is all done without injecting anything into the flow field, such as dye or small objects, which is common in other techniques. For supersonic research purposes schlieren has been used for a long time, however colour schlieren may be able to capture additional information about the flow in the experiment. Colour schlieren can be achieved in many different ways, however this thesis focuses on the use of two main techniques. For supersonic flow imaging, a density gradient directiona detection schlieren system and a density gradient magnitude detection system. The magnitude indicating system has been designed, however not tested (due to practical complications). The gradient direction system was tested and analysed in order to assess the use of this technique in supersonic flow research. This thesis concludes that this is indeed a very good method, capable of distinguishing different directions in the density gradient (coded by colour) as well as providing a clear image of the flow in the medium. These results may also be used quantitatively in order to calculate more precise gradient directions.

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Preface

The aim of this thesis is to investigate and assess the use of colour schlieren photography for supersonic flows, using techniques in this area to produce colour schlieren images. Schlieren photography is an old, non-intrusive technique used to look at changes in density in a fluid, mainly for scientific experiments in aerodynamics and flow physics. The use of colour as an additional way to convey information in schlieren images has been around since the middle of the 20th century, and many different techniques has been tried before. This can be an important technique in flow studies, since it is inherently non-intrusive, and doesn’t disturb the flow in any way, which other methods can not always guarantee. Implementation of this can be done in several ways, which is also investigated in this thesis report.

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Contents

1 Introduction 7

2 Schlieren Photography 8 2.1 History ...... 8 2.2 DiﬀerenttypesofSchlierensystems...... 9 2.2.1 LensSchlierenSystems ...... 9 2.2.2 MirrorSchlierenSystems ...... 9 2.3 Schlierenproblems ...... 11 2.3.1 Coma ...... 11 2.3.2 Astigmatism ...... 11 2.3.3 Chromatic aberration ...... 13

3 Schlieren Theory 14 3.1 SchlierenObject ...... 16 3.2 LightSource ...... 17 3.3 Introducingcolourintoaschlierensystem ...... 18 3.3.1 Directionindicatingsystem ...... 18 3.3.2 Magnitude indicating system ...... 18 3.4 Design of colour masks ...... 19 3.4.1 Design of round source mask ...... 19 3.4.2 Design of Bulls Eye Mask ...... 20

4 Objectives 22

5 Experiment setup and equipment 23 5.1 Software programs ...... 23 5.2 MirrorsandLenses...... 23 5.2.1 Cylindricallens...... 23 5.2.2 Achromatic doublet ...... 23 5.3 Camera ...... 24 5.3.1 Camera software ...... 24 5.4 Irisdiaphragm ...... 24 5.5 LightSource ...... 24 5.6 JetRig...... 24 5.6.1 JetNozzles ...... 26 5.7 Colour Calibration ...... 27

6 Procedures 28 6.1 EquipmentSetupAlignment...... 28 6.2 SourceMaskProduction...... 29 6.2.1 Source Mask Layering ...... 29 6.3 Astigmatism Correction ...... 30 6.3.1 Measuring the Astigmatic Diﬀerence ...... 30 6.4 Taking a Colour Schlieren Image ...... 30 6.4.1 Camera Software Settings ...... 30

7 Results 32 7.1 Astigmatism Correction ...... 32 7.2 NozzleEﬀects...... 33 7.3 Monochromatic Schlieren Comparisons ...... 33 7.4 CameraEﬀects ...... 35 7.5 FinalImages ...... 36

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8 Conclusion 38

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Nomenclature

Symbol Units Description L m Length

Ma − Mach number

p Pa Pressure

ρ kg/m3 Density

n − Refraction index

T K Temperature

ε ◦ Refraction angle

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1 Introduction

In many areas of fluid flow research, visualization of the flows that are studied are important, and can be achieved in a number of ways, most of which involves adding small particles into the fluid, which then can be observed. Many of these methods are quite intrusive, and the particles introduced into the flow have a direct effect on the flow phenomenon that are studied within the fluid flow field. Pure optical methods does not introduce any particles or tracers into the fluid, and is often the only means to study the inner processes of flow fields and phenomenon occurring in fluids. For shockwave and Mach-number flow studies, relies mostly on optical methods, since the addition of particles or tracers in the fluid might both disturb the fluid flow, and not follow the flow characteristics, thereby giving a false representation of the flow. Schlieren photography is a collective term used for many different (but similar) optical flow visualization techniques, where the common factor is the detection of changes in density in the fluid flow. These changes in the transparent media can be visualized in several ways, but relies on the principle that light rays are refracted at an angle when passing through a region of changing fluid density. Ever since the days of Robert Hooke[2] in 1665 and later August Toepler[3] in the 1860s, schlieren photography has been under investigation, development and practice, being used in many different fields, but primarily in fluid flow research and aerodynamics. One of the true pioneers in schlieren photography in the early 1900s was Hurbert Schardin, who further developed and improved the state of flow visualization with his illustratrative techniques, for example in his work with spherical shock wave research using various schlieren techniques [12] in 1954. Schlieren photography can with modern computer techniques and numerical methods give quantitative results, and not only qualitative, which has been the limitation with many optical techniques for a long time. With image processing and computer algorithms these techniques can give more complex and useful information about the flow fields and fluid phenomenon that are studied. Colour schlieren has been in use for some time, with one of the first uses often credited to Paul Chords in 1967[8]. The same method (dissection method) has then been improved and used for a variety of purposes, for example in 1991 by Harald Kleine [4] in shock wave research. Various other forms of colour schlieren has also been used earlier, such as rainbow schlieren, a quantitative method used to measure the magnitude of a density gradient in the flow, notably in 3D - schlieren tomography by Agrawal, Butuk, Gollahalli and Griffin [11] in 1998, and with jet research by Nakajima, Oka, Konishi, Ono and Miyazato Y [5] in 2014. The Laboratory for Turbulence Research in Aerospace and Combustion (LTRAC) at Monash University has used monochromatic high-speed schlieren photography very successfully in visualizing various flows, for example impinging jets (Mitchell, Honnery and Soria [9]) and high-velocity jet for research in jet screech and noise (see Mitchell, Oberleithner, Honnery and Soria [10]). A colour schlieren setup has not been done, however, which is then a suitable task for this thesis project. The existing monochromatic schlieren system is to be configured into a setup capable of producing high-quality colour schlieren images, with the intention to use two-dimensional schlieren images to represent flow field density gradients. This system offers several advantages to a monochromatic system, such as the ability to detect gradients in all directions with a single image.

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2 Schlieren Photography

The following sections gives a brief introduction to schlieren photography, its history, use and development, as well as its theoretical background and some of its problems.

2.1 History The schlieren method were first experimented with by Robert Hooke (1635-1703)[1], when he was working with microscopy, telescopy, glass and optical testing, which are all related to the schlieren method. His research in these areas, along with his fascination with refraction in the atmosphere, led to his establishment of the scientific field of optics in inhomogeneous mediums. Hooke’s primary schlieren system consisted of a candle, a lens, and his eye. With the candle as a light source, the lens projected the image of the candle onto the pupil of his eye, and he was able to see refraction effects in the test area, located ahead of the lens. Shortly after the work of Hooke, Christian Huygens (1629-1695)[1] also did some work with these sorts of techniques, reinventing Hooke’s simple schlieren setup.

Figure 1: Robert Hooke’s simple schlieren system, using only candles and a lens.

After the work of Hooke and Huygens, the study of optics of inhomogeneous media is almost forgotten for nearly 200 years, only one person makes a contribution during this time; Jean Paul Marat (1743-1793)[1], a French scientist, physician, and politician during the French Revolution. His work with flow visualization includes the first ever printed, a collection of shadowgrams, which is a method of visualizing flow by simply shining a bright light (Marat used the Sun) on the object of study, and then look at the shadows projected onto the surface behind the object. The light rays are refracted in the flow field, which then can be seen as shadows on the surface. The next big contribution to this field of study was made in 1859 by Leon Foucault (1819-1868)[1], with the introduction of the knife-edge cutoff to the schlieren technique. His knife-edge tests of astronomical telescope mirrors was instrumental in perfecting telescopes, as well as being the first use of an explicit cutoff, as all previous schlieren systems had been using the eye itself (where the most refracted rays where “missing” the eye). The cutoff introduced by Foucault is now regarded as the distinguishing feature between schlieren techniques and other related approaches to this area. Around the same time as Foucault did his experiments, August Toepler (1836-1912)[1] re-invented the schlieren technique between 1859 and 1864 (since earlier work by Hooke and Huygens had been forgotten). Toepler is in a sense the father of schlieren, since he gave the technique its name, after the German word for optical inhomogenities in glass, “schlieren”, meaning “streaks”. Toepler suffered accusations for stealing and rebranding Foucaults work, to which he responded that his own work was to use the method for scientific study, while Foucault was merely interested in testing and creating better mirrors. Toepler worked with and refined his schlieren technique for the next 15 years, with which he studied many different phenomena for the first time. Toepler still stands as the true first developer and proponent of the schlieren technique. After Toepler, many scientists used his technique for study of flow phenomenon, most notably Ernst Mach (1838-1916)[1], who did many experiments with acoustics and high-speed projectiles using schlieren photography, with the introduction of circuits for capturing photographs of astounding quality. An amateur microscopist, Julius Rheinberg (1871-1943), introduced colour to the schlieren system, as he saw the value

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Figure 2: August Toepler’s classic schlieren system, after the introduction of the knife-edge. in colour contrast to enhance microscopy, and also to code density magnitude and direction in a schlieren system. During the first half of the 20th century, the Toepler’s schlieren technique was used in laboratories around the world, but it was Hubert Schardin who pioneered the technique far into the century. Schardin developed several new schlieren techniques, and in his paper in 1942, described a dozen new techniques, of which three gave colour images; the lattice-filter, prism and colour-background techniques. After the Second World War, many improvements to different schlieren methods have been made by various scientists, engineers and amateours. Colour schlieren, as well as monochromatic methods remain an important tool today in understand flow phenomenon.

2.2 Different types of Schlieren systems Many different schlieren systems have been developed over the years since Toepler first pioneered the method, and although there are many variations, all of these methods can be derived from Toeplers technique. His method used three major parts, “the illuminator”, the “schlieren head” (the main field lens) , and “the analyser”. Today there are usually two main lenses or mirrors instead of only one, as in Toeplers days, but the method is still the same. The two main different setups are the ones using lenses, and those using mirrors. Both of these have difficulties and advantages, which will be discussed briefly.

2.2.1 Lens Schlieren Systems Lens type systems were the first used, and are often the easiest to set up, since they can be in-line and relatively simple to align, but they suffer more from chromatic aberrations than a mirror system. The lenses used need to be of exceptional quality, since the schlieren objects that are studied are usually weak, and imperfections in the lens might mask these effects. Usually a surface with deviations less than half of a wavelength of light over the diameter of the lens is required. The system used by Toepler uses only one large lens, which leads to the schlieren object not being traversed by parallell light, which can be a problem, specially when studying 2-dimensional schlieren objects, since the light will be distorted and not give an accurate representation of the schlieren object [1]. An improved setup uses two large field lenses, that gives parallel light in between the two lenses, as is required for most 2-dimensional schlieren objects.

2.2.2 Mirror Schlieren Systems Mirror schlieren setups came into being not long after Toeplers first lens-based systems, based on the strength of the Foucault test. The mirror based systems are usually more difficult to setup, as they require precise alignment, since they are usually folded, instead of in-line, as most lens systems[1]. A mirror system is also usually cheaper, since high quality lenses are more expensive than a high quality mirror, and offers improvements in field-of-view over lens-based systems as well. Larger mirrors can usually be acquired easier

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Figure 3: Improved schlieren system using two large ﬁeld lenses to collimate and refocus the light.

than large lenses, and the largest lenses in lens-based setups are in the 20cm diameter range, mirror setups can be made signiﬁcantly larger. The most common mirror based setup is the so- called Z-type mirror system, using two parabolic mirrors, based on the Herschellian method of tilting the mirror oﬀ-axis, to gain access to the image[1]. Seen from above in Figure 4 it is clear why the setup received its name.

Figure 4: Simple z-type schlieren system, with two counter-rotated parabolic mirrors instead of lenses.

This system gives a parallel beam of light that traverses the test section, illuminating the schlieren object properly, as well as eliminates some of the problems associated with mirrors, such as coma.

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2.3 Schlieren problems The careful alignment and quality of equipment used in schlieren techniques gives rise to quite a few problems, mostly regarding imperfections in illumination, mirror surfaces and alignment, which can negatively aﬀect the quality of the images produced. Most of these can be minimized by precise alignment, cleaning of mirrors and lenses, and good quality equipment. This chapter discusses two other problems that require more speciﬁc techniques to minimize.

2.3.1 Coma One of the major optical aberrations resulting from mirrors is called coma, which occurs when the direction of light reflected by a mirror is dependent on the position of the point of reflection, which is a result of tilting the schlieren field mirrors off their optical axes[1]. The result of this aberration is that a point source of light is smeared into a line, like the tail of a comet, hence the name coma.

Figure 5: A z-type schlieren system, seen from above. Mirrors are counter-rotated with the same angle, cancelling out the coma eﬀect.

Coma becomes a larger problem with larger mirror offset angles, as well as being amplified with smaller mirror f/no. By keeping the offset angle small, and using long focal length mirrors, coma can be decreased[1]. However, since coma is a problem at both of the mirrors, it can be cancelled out by tilting the mirrors in equal angles in opposite directions from the central axis, hence the z –layout of the system.

2.3.2 Astigmatism Astigmatism is a bigger problem, however, and cannot simply be eliminated in a z-type setup (or any other off-axis setup). The word astigmatism is a combination of Greek words meaning “without” and “mark” or “spot”, essentially meaning “non-point-like”, or failure to focus a point to a point[1]. This is the consequence of the off-axis rotation of the two mirrors, giving a difference in path length along the optical centreline and mirror periphery. A beam of parallel light moving along the optical axis, then being reflected off the rotated parabolic mirror, the light rays will not coincide in a common focal point, but instead the light will have two focal points; the tangential and the sagittal focal points, separated by the astigmatic difference. The astigmatic difference is dependent on the mirror offset angle and the focus length of the mirrors, and is given by the formula[1]:

2 f sin θ α = (1) cos θ where θ is the offset angle. With the offset angle small, this is simplified to:

d2 α = (2) 4f Where d is the mirror diameter, and f the mirror focus length[1]. By using a small oﬀset angle and long focal length mirrors, the astigmatic diﬀerence can be greatly reduced, but not entirely negated.

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Figure 6: An illustration of astigmatism due to a rotated mirror.

In order to reduce the astigmatic difference, a plano-concave cylindrical lens can be placed after the source mask, in order to move the sagittal (or tangential) focus point backward (or forward). Such a lens would alter the light rays of only one plane, and can be placed in such a way that it would bring back the focus of the primary schlieren mirror to a single point, thereby reducing the astigmatic difference greatly. For this purpose, the cylindrical lens must be placed at a specific point. Using the thin lens equation, a formula for the position of the cylindrical lens can be constructed; 1 1 1 + = (3) do di fcyl

where do is the object distance, di the image distance, and fcyl the focal length of the lens. Rewritten, this gives the image distance;

dofcyl di = (4) do − fcyl

Using the formula for the astigmatic diﬀerence (equation 1), along with expressions for di and do;

di + do = α (5)

dofcyl do = α − (6) do − fcyl

2 α ± α − 4αfcyl d = (7) o p 2

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Figure 7: Ray trace diagram for a plano-concave cylindrical lens.

From this formula, two values are produced; the negative value should be used as the distance from the source mask to the cylindrical lens. Since the cylindrical lens only aﬀects one plane, the source mask needs to be adjusted. The magniﬁcation produced by the cylindrical lens is written as;

d − m = − o (8) di

Where do− denotes the negative value of do. The value of m is used in the design of the source masks, to distort (extend the width) them so that the image after the cylindrical lens will be circular.

2.3.3 Chromatic aberration Chromatic aberration is a type of distortion which occurs when light of different wavelengths are focused by a lens. Due to the lens having different refractive indices for different wavelengths (n decreases with increasing wavelength), the lens will fail to focus all colours to a single convergence point, as illustrated in the figure below.

Figure 8: On the left; illustration of chromatic aberration with a normal (double-convex) lens. On the right; a chromatically corrected lens.

Chromatic aberration is visible in the final picture as coloured fringes around objects, and also contributes to an overall defocusing in the image. Using a chromatically corrected lens, constructed from two pieces of glass (called the crown and the flint ), both made to fit together and neutralize the effect. Such a lens is designed to focus certain wavelengths (the design wavelengths) to the same point. Usually these wavelengths are chosen from different points in the colour spectrum. The lens used in this project have the design wavelengths 486.1 nm, 589 nm and 656.3 nm.

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3 Schlieren Theory

In a homogenous media light propagates uniformly and undisturbed. For example, the light rays from distant stars have travelled through empty space, undisturbed for a very long time, and are parallel rays when they reach the Earth, and stars would as such appear as a near-perfect point. Since the Earths atmosphere is not as uniform and homogenous as outer space, however, the light rays are disturbed and bent by all the small (and large) inhomogenities, such as winds, thermal convection, turbulence and many other atmospheric phenomenon and effects. These effects all affect the starlight as it travels through the atmosphere, and the star appears no longer as a point, and it twinkles based on the timescale of these fluctuations. As the light travels through a medium and interacts with matter, it slows down. This change is given by the refractive index of light n = c0/c, where c is the speed of light in the medium, and c0 is the speed of light in a vacuum, approximately 3 × 108 m/s. For gases such as air, there is a simple relationship between the refractive index and the density;

n − 1= kρ (9) where n is the refractive index of the medium, ρ is the density of the medium, and k is the Gladstone- Dale coeﬃcient, which has a value of ≈ 0.23cm3/g for air at standard conditions. The refractive index n requires only a small change in order to give a visible eﬀect, but is only weakly dependent on the density ρ, as seen in equation 9 . The refractivity (n − 1) depends on the gas composition, temperature, density and the wavelength of the light that is illuminating the gas[1]. In most cases the ideal-gas equation can be used:

p = ρRT (10) where p is the pressure, R the specific gas constant, and T is the temperature of the gas. If the flowing gas has a variation in density, it is a compressible flow. Such flows can arise from temperature differences or high gas flow speeds, all of which gives rise to disturbances that can be seen utilizing these refraction effects.

Figure 9: Diagram of elemental light ray refraction by a gradient in refractive index δn / δy . The light ray propagation direction is along the z-axis, with ∆z representing the schlieren object thickness.

From deﬁnition n=c0/c, so that the local value of the speed of light c is equal to c0/n. From the ﬁgure we can formulate:

( c0 − c0 ) ∆ε = n2 n1 ∆t (11) ∆y

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The diﬀerence in time ∆ t can be expressed as: n ∆t =∆z (12) c0 Combining these expressions,

c0 c0 n ( − ) ∆ε = n2 n1 ∆z (13) c0 ∆y and simplifying,

n (n1 − n2) ∆ε = ∆z (14) n1n2 ∆y Letting all the ﬁnite diﬀerences approach zero and simplifying further, dε 1 dn = (15) dz n dy Since ε is a very small angle, it can be approximated to dy/dz, the slope of the refracted light ray. Implementing this and writing the derivatives as partials (to account for the general case), the following is obtained;

δ2y 1 δn δ2x 1 δn = = (16) δz2 n δy δz2 n δx which relates the curvature of the refracted light ray to the magnitude of the gradient of refractive index, here for both x and y. Integrating gives the angle components; 1 δn 1 δn ε = δz ε = δz (17) y n Z δy x n Z δx using L as the length of the refractive disturbance (length of the schlieren object along z-axis); L δn L δn εy = εx = (18) n0 δy n0 δx

where n0 is the refractive index of the surrounding medium. These formulas provide the basis for schlieren ∆n and shadowgraph flow visualization techniques[1]. These techniques show the gradients of refractivity, ∆x ∆n and ∆y , and not the difference in n directly, which is relatively uninteresting. These equations also shows that the angle of refraction is always toward the area of higher n (higher density). If one point in the test area is subjected to a refractive disturbance by a schlieren object, a group of rays from all the points in the light source is refracted with angle ε. This group of rays is deflected form its initial path, and forms an image at the cutoff plane, separate from the undisturbed composite source image. This group of rays is then subject to a different amount of cutoff in the plane, allowing only part of the light (or none of it) to pass through the cutoff plane. The rays are then recombined in the imaging plane, creating illuminance variations in the image. The whole of the image at the imaging plane is built up by many such points of different illuminance, corresponding to the magnitude and location of the refractive disturbances (the schlieren object)[1]. This continuous variation of illuminance in the image (as caused by different groups of rays having different amount of cutoff) makes the image a greyscale image, instead of just black and white, as a true point source would make. If the whole of the weak source image has been moved completely onto the cutoff (very strong refractions), or off of the cutoff, the measuring range of the system has been reached, since an increase in refraction will no longer make any difference in the illumination of the image. Since the illuminance level E is linearly proportional to the amount of cutoff, and that

∆a = f2ε (19)

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Figure 10: Diagram of the knife- edge plane. A rectangular composite source image is shown, with about half cutoﬀ, with height a remaining unobstructed. Due to refraction in the test area, a weaker displaced source image is shifted upwards and to the right. Its unobstructed height a+∆ a allows for extra light to a corresponding point in the schlieren image.

where f2 is the focal length of the second mirror (or lens), and ε the refraction angle in the direction δn of displacement, the illuminance can be used to quantitavely measure δy . This can also be used further by measuring the refraction angle, with for example a graded colour ﬁlter, to determine the density gradient magnitude. Combining equations 9, 18 and 19, an expression for the density gradient can be obtained;

δρ ∼ ∆a = (20) δy kLf2 where k is the Gladstone-Dale coeﬃcient, L the length of the refractive disturbance along the optical axis (z-axis), and ρ the density. Integrating in y to obtain the jet centerline density distribution ρ(y), and assuming that the ﬂow density ρref at a reference point is known;

y2 ∼ 1 ρ(y) = ∆a(y)dy + ρref (21) kLf2 Zy1 The above expression contains the essence of quantitative schlieren analysis, and can be used to calculate the density values for positions in the schlieren object, by correlating illuminance values in the schlieren image with source image displacement values ∆a (see 3). These derivations illustrate how a simple monochromatic schlieren system operates, using a knife-edge cutoff (such as a razorblade). In this project however, an iris diaphragm is used as a cutoff, allowing for omnidirectional sensitivity, but it works according to the same principles[1]. The circular cutoff also means another definition of the cutoff value is needed. This definition is based on the definition of cutoff for a one-dimensional knife-edge schlieren system, and adjusted for a circular cutoff.

2 − Ac − a C = 1 = 1 2 (22) Ai r

where Ac is the area of the iris aperture (with radius a), and Ai is the area of the source mask image in the cutoﬀ plane, with radius r.

3.1 Schlieren Object The schlieren object itself is deﬁned as a small diﬀerence in refractive index within the overall background, which bend light rays in any direction other than the normal direction (light ray travel direction, here along positive z-axis)[1]. Schlieren objects can have refractive index gradients in one, two or three dimensions, and should be positioned and oriented such that the z-axis is aligned along the path of visualization. Schlieren objects can be found in solids, liquids and gases, and may result from a variety of causes, such as changes in

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temperature, high-speed ﬂows and material mixing (of not too similar materials). In solids such as glass or plastic, they can be causes by diﬀerences in thickness or variable densities in the material.

3.2 Light Source For a simple schlieren system, a point source, two large lenses, and a knife edge is used. The beam of light from the point light source is collimated by the first lens, and the second lens refocuses the beam to an image of the point light source, and finally hits the viewing screen (a distance behind the focus point). When a schlieren object is placed between the two lenses (in the test section of the system), this will refract light rays away from their original paths, so that the bent rays miss the focus point, and illuminates the viewing screen. Until a cutoff, or knife-edge is introduced, no transparent schlieren object will be visible on the viewing screen.

Figure 11: A simple schlieren system with a point light source, using two lenses to collimate and then refocus the light, and a knife-edge at the focus point of the second lens.

When a knife-edge (usually an ordinary razor blade is used) is placed in the focal point of the second mirror (where the image of the point light source is), this obstacle cuts off the bent light rays, and their corresponding positions on the viewing screen will be darker. Using an ordinary razor blade, only light rays refracted in one direction can be cut off, which makes such a system only being able to detect changes in one direction of the density gradients of the schlieren object. For example, a schlieren object with only horizontal gradients will be invisible in a system with a horizontal knife edge. In order to detect gradients in all directions (in the x,y-plane), a circular cutoff is required, such as an iris diaphragm. However, a point light source is not practical, and extended light sources are the default option.

Figure 12: Schlieren system with an extended light source, with the grey arrow representing the image of the black arrow.

With the more realistic case of an extended light source, the light ray beam that is collimated by the mirrors, will no longer be exactly parallell[1]. Imagine the extended light source as an array of many small point sources, each of these sources sending out a beam that focuses to a corresponding point in the light source image at the focus point of the second mirror, the cutoff plane. Since the light source is now of a finite size, every point in the test section will be illuminated by many rays, within a cone with limits at the extreme (edges) of the light source, and each point in the light source illuminates every test area point. This effect gives the schlieren system its depth of focus, which it did not possess with only a point source.

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Another, more important effect from this is the creation of a composite light source image at the cutoff plane[1]. The composite light source image is made up of many superpositioned elemental source images, from all points in the test section. This gives the effect that if a sheet of paper with a small hole is put into the test section, the image at the cutoff plane will still be a complete image of the light source, only weaker in intensity.

3.3 Introducing colour into a schlieren system In order to produce images capable of giving additional information about the flow studied in schlieren photography, colour can be added to the system. Colour can be used to code different features of the flow, such as density gradient direction or magnitude. Adding colour to the schlieren technique also allows for easier distinction between different features of the flow field from each other, as well as from the opaque silhouettes of objects in the test section (such as nozzles or models). Using colour contrast, hue, intensity or saturation, different sorts of colour techniques can give quantitative information about a given flow field, that a monochrome schlieren system cannot do[4]. The addition of colour often gives the images produced a more aesthetically pleasing look, and can be quite useful for visualizing different effects as well, such as in the case of teaching and demonstration[7]. To be able to produce colour schlieren images, colour needs to be introduced into the system, in one of several ways. Either colour is added to the light at the light source, or at the cutoff plane, by adding a coloured mask, or filter, to the system.

3.3.1 Direction indicating system To be able to visualize the direction of density gradients in the flow field, each direction of possible refraction angles (in the x,y- plane) must be assigned a colour; this is done by placing a colour coded mask at the light source, effectively making a coloured extended light source[4],[8]. An image of this source mask appears at the cutoff plane, where the iris diaphragm is placed, such as that the source mask image is at the centre of the iris, to get an even cutoff in all directions. Light rays deflected inwards (toward the center of the image) is allowed to pass through the iris, while outward deflected rays will be blocked. Since the source mask consists of colour sections, each point on the circle will have a different colour associated with it.

3.3.2 Magnitude indicating system In order to detect the magnitude of a density gradient, several methods are possible. In monochrome schlieren, a larger gradient magnitude will cause a greater refraction effect, proportional to the change in density, which will give that part of the image a higher contrast compared to the background (with brighter and darker representing opposite directions). In such a system, by measuring the image illuminance, one can integrate and calculate the changes in refractive index, which also gives the density. Another method is to place a colour coded filter at the cutoff plane[6]. When refracted light hits certain portions of this filter, colour is added to the light. By determining the colour on the final image, this method can provide measurements of the refraction angle, and thus the density gradient magnitude, can be calculated. Called a rainbow filter, these filters effectively code a certain ray displacement to a certain colour[5].

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3.4 Design of colour masks For this project, two types of colour schlieren masks have been designed; a bulls-eye mask and a round source mask. The bulls-eye mask is designed to allow for detection and diﬀerent colourization depending on the magnitude of the refractive-index gradient, while the round source mask is designed to detect and colourize diﬀerent directions of refractive-index gradient.

3.4.1 Design of round source mask The round source masks in this project are designed bases on the round annular source filter created by Gary Settles, as mentioned in his book[1]. Similar methods have also been used in other works (example [4]). This is used together with a round iris diaphragm in the cutoff plane, to allow for omnidirectional sensitivity. In his project, Settles used only three primary colours in the masks, but it was deemed to be enough. Previously such masks have been produced by hand, using colour gelatin filters for the colour sections, however in this project the source masks are produced digitally, allowing for further precision and easier design. A MATLAB computer code creates the digital images, allowing for easy changes to be made in regards to size, number of colour segments, and astigmatism correction. The final images used are made up of 1200 colour segments, arranged in a colour wheel configuration. The different source masks in Figure 13 are examples of source mask design. In(a) and (b) three colour segments are used, with red, green and blue colours. Images (c) and (d) contain ten colour segments, divided into a colour wheel. Images (e) to (j) have 1200 colour segments. Different thicknesses of masks were also produced and tested, ultimately using the mask example in image (f). For the astigmatism correction, the cylindrical lens will distort the image of the source mask, depending on the position of the lens. Using equations 7 , 4 and 8 , the distortion factor m can be calculated. For this project, the values calculated are do = −55.1 mm, di = 76.1 mm and thus m = 0.724, which means that the width of the image will be 1 multiplied by a factor of m = 1.38. Source masks corrected for astigmatism are shown on the right side in Figure 13. These digital images must then be transfered to a transparent medium. For this, several alternatives was considered, with the colour saturation and transparency requirements as primary factors. Printing the digital images on transparent sheets with a colour printer, and combining in layers of four, was found to be very effective, as well as simple and quick to produce.

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(a) (b)

(e) (f)

(g) (h)

(i) (j)

Figure 13: Examples of source masks, with a varying number of colour segments.

3.4.2 Design of Bulls Eye Mask The round bulls eye mask discussed previously in this text is designed to be able to code diﬀerent light refraction angles into diﬀerent colour segments, in order to be able to make quantitative measurements in a

20 October 12, 2015 Jens Kanje Nordberg colour schlieren system. This mask is placed in the cutoﬀ plane, replacing the iris diaphragm (knife-edge), in order for light to hit colour segments instead of being cutoﬀ completely (with an opaque edge around the mask).

(a) Example of bulls eye mask, 12 colour seg-(b) Example of bulls eye mask, 1200 colour segments. ments.

As seen in the ﬁgure above the number of colour segments in the bulls eye mask can be varied greatly, as well as changes in colour are possible. These are just examples, and have not been manufactured, since a method of creating such masks to a satisfactory level of colour quality and resolution in the correct size (since the refraction angles are so small, the ﬁlter should only be a few mm in diameter) have not been available. If production of these masks with satisfactory results are possible, the installation of these is rather simple, however, some calibration is needed in order to correctly code a colour RGB value to a certain refraction angle.

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4 Objectives

The objectives for this project are:

• To design and construct a colour schlieren system in the LTRAC (Laboratory for Turbulence Research in Aerospace and Combustion) lab, replacing the monochrome schlieren system in place. This system should be able to produce repeatable results suitable for quantitative analysis. • To analyze and assess the use of colour schlieren photography for use in supersonic ﬂow research, to investigate if this tool is suitable for this type of testing. • Test diﬀerent experiment setups, nozzles and conditions to investigate the performance of the system.

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5 Experiment setup and equipment

This section describes the equipment used in the experiment setup, as well as the software used in both testing, design and production of source masks as well as post-editing for certain experiment tests.

Figure 15: Figure of experiment setup.

Figure 15 shows the experiment setup conﬁguration. A standard z-type schlieren system, with the additional components marked out as following; a denotes the cylindrical lens, b the colour masks, c the small plate covering the light source marked as d. The iris diaphragm is marked as e, and the achromaric doublet as f. The nozzle and jet rig is placed in the test area.

5.1 Software programs For the design and production of source masks used in the experiment setup, MATLAB 2014a and Adobe Photoshop CC 2014. The code to produce the images was written in MATLAB, and the images were saved in a .tiﬀ format, for high image quality. Images were then imported to Photoshop, resized and adjusted for printing on transparent sheets. Images were printed with 300 dpi, in full colour. For the post-editing work, GIMP 2.8 (The GNU Image Manipulation Program, available for free on the Internet) was used.

5.2 Mirrors and Lenses The two large Schlieren parabolic ﬁeld mirrors used in the setup were 200mm in diameter, with a focal length of 2032mm (which gives an f-number of approximately f/10), mounted on adjustable heavy base stands, which makes for easy adjustments on position and alignment of the mirrors.

5.2.1 Cylindrical lens The cylindrical lens is used for astigmatism correction, where the primary design characteristic is the focal length of the lens, which in this setup is -200 mm. The lens is rectangular with dimensions 55x70mm and made of crown glass (BK-7).

5.2.2 Achromatic doublet The achromatic doublet lens are really two lenses put together, cut of different glass to achieve a uniform focus point for all wavelengths of light. The two pieces are of crown glass and flint glass, made to fit together perfectly. When put together, the doublet behaves as a single lens. The primary design wavelengths for the doublet are 486.1 nm, 589 nm and 656.3 nm. The diameter of the doublet is 50mm and a focus length of 300mm, with thickness at edge and center of 12.5 mm and 14.7 mm, respectively.

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5.3 Camera The camera used in this experiment setup is a Hitachi KP FD140F colour camera, capable of taking high- 1 quality colour images at shutter speeds up to 100,000 s, using an array consisting of approximately 1.5 million square pixels (pixels are 4.65 µ m x 4.65 µ m ). This camera is attached to a small plate, mounted such that camera position can be adjusted.

5.3.1 Camera software The Hitachi KP FD140F camera is connected to a PC by ﬁrewire IEEE 1394.b interface, giving a high-speed connection of 800 Mbps. The camera software HiKE 1394 CamView is installed on the PC, which controls the camera and shows the captured images instantly. Using this software, numerous settings and advanced features for the camera and post-processing can be enabled and adjusted.

Figure 16: Image of the iris diaphragm with and adjustable (by the small lever) iris, from Edmund Optics.

5.4 Iris diaphragm For this Schlieren setup, the iris diaphragm used as cutoﬀ is an adjustable 50.8 mm outer diameter iris. The minimum and maximum aperture sizes are 0.8 mm and 25.0 mm, respectively. The aperture size can be easily adjusted, and the iris diaphragm itself is mounted on an optical stand, which allows for easy adjustments in position as well.

5.5 Light Source For colour Schlieren a powerful light source is required, even more powerful than in monochromatic Schlieren. In this setup a flash is used, the Mecablitz 52 AF-1 Nikon digital from Metz, that produces a powerful flash with a colour temperature of 5600 K. To achieve a small aperture (to approximate a point light source), a metal plate with a small hole is put in front of the flash. This plate is shown in the figure below. The flash unit is connected to a trigger, that also connects to the camera. With this trigger, the flash and camera are coordinated, and the image is taken at the same time as the flash. This small hole effectively reduces the light source to an approximated point source, as the ratio of hole 5 diameter and distance is small ( 2032 mm). This is counteracted by the size of the colour filter, however, that size can be adjusted as well as using different sized filters.

5.6 Jet Rig To produce a stable, high-speed air a plenum chamber is used, fed with compressed air. A nozzle is attached to the top of the chamber to produce the jet. A valve at the bottom of the plenum chamber is used to regulate the pressure and air speed. A pressure sensor is also connected into the chamber and a voltmeter,

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Figure 17: Figure of the small metal plate, 60 mm x 30 mm with a 5 mm in diameter hole. allowing for readouts of the chamber pressure (in terms of voltage). This voltage is converted into Nozzle Pressure Ratio and Ideal Mach Number from a table.

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5.6.1 Jet Nozzles For the jet rig, several nozzles were available, made to be easy to switch between. For different experiments and test, different nozzles can be used. For this project, the changing about of nozzles is primarily to see some different flow effects and artifacts, to get a better sense of the colourization and over-all quality of the images and schlieren system. Figure 18 below shows the varying nozzles used.

(a) Circular nozzle. (b) An elliptical nozzle.

(e) Nozzle with two chevrons. (f) Nozzle with four chevrons.

Figure 18: Nozzles used in schlieren tests. Resulting images can be found in 7.2 .

The first nozzle (figure (a)) is the simplest of the nozzles, with a circular opening, 15 mm in diameter. This was the first nozzle used in the schlieren system in this project. Figure (b) shows an elliptical nozzle, quite similar to the circular one, this simply has an elliptical opening instead of a completely circular one. The difference in plate and fastening methods can be seen, since the elliptical (and the aerospike nozzle) has larger plates which are fastened directly on top of the plenum chamber, while the other nozzles are attached to a separate plate, which is in turn fastened on top of the plenum chamber, which makes for easier swapping between different nozzles. The aerospike nozzle (figure (c)) has a spike extending 20 mm above the opening, which is 20 mm in diameter. The spike itself is at the opening 10 mm in diameter. Nozzles (d), (e) and (f) are designed to reduce jet screech (a set of particularily nasty frequencies in jet noise). These nozzles makes for a much more comfortable test environment, since the noise is significantly reduced while operating the jet rig using these nozzles. All nozzles used here were already in the LTRAC laboratory when this project started, for use in various other projects and research ventures (mostly concerning jet noise).

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5.7 Colour Calibration This chapter details the image colour calibration, in which a circular plano- convex lens is used as a calibration lens, the lens creates uniform ray deﬂections in all directions, to help understand what colour represent which direction of a density gradient changes. The lens is mounted in a lens holder, placed in the center of the test section and an image is taken. The iris diaphragm is put to 60% cutoﬀ, as in many of the other test images of the jet in operation.

Figure 19: Schlieren image of a calibration lens, with colours enhanced in post-editing software (using GIMP).

In the image above (ﬁgure 5.7) the lens is seen to distribute the colours, which have been enhanced in post-editing to improve the colour saturation in the image. In order to distinguish the colour hue depending on direction, the image is cropped and edited using GIMP image editing software. A cropped section from the center of the lens is shown in Figure 20, with an axis inlaid to display the orientation of the image. The Z direction in the image is towards the camera, along the path of the light rays (as discussed in Chapter 3). This image shows that for example a red colour in the schlieren image indicates a density increase in the negative x-direction, and a purple colour a positive y-direction gradient. This gives important information for analysis of the images in a simple enough way. The light rays refracted by the schlieren object in the test section are refracted in angles of x and y, εx and εy, respectively, dependent upon the expressensions in equation 23 below. The equations describes the relationship between the refraction angle and the refractivity gradient, which is integrated along the light ray path inside the schlieren object (the refraction angle changes along the whole path inside the density variations). Figure 20: Arrows mark the pos- 1 δn 1 δn ε = δz, ε = δz (23) itive direction of the density gra- x n Z δx y n Z δy dient indicated by the colours in The combined angle ε, which is the combination of ε and ε is the the image. x y true angle in the 2D XY-plane of the light ray, and corresponds to a colour in the calibration image. Determining the relative values of these angles can give information about the density gradient direction, using the same expressions as in equation 23 along with other equations discussed in Chapter 3.

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6 Procedures

In this section the various procedures and methods of this project will be presented.

6.1 Equipment Setup Alignment In order to achieve a clear image in the cutoff plane and on the camera CCD-array, the schlieren system needs to be aligned properly. First the large field mirrors are placed on oppisite sides of the test section (for this setup, the distance between the mirrors is approximately 4800 mm) and aligned with each other, so as much of the collimated light beam is reflected as much as possible. With the mirrors properly aligned, positioning the light source and source mask (with the mask at the focal point of the first mirror) is quite simple. Between the two schlieren field mirrors the test section is located, which the light should pass through on the way to the second field mirror. Careful alignment is needed to make sure that the test section is illuminated by the light collimated and reflected by the first mirror. The source mask is placed in an optical stand approximately 50 mm from the light source, placed in the focus point of the first schlieren field mirror (2032 mm from the mirror). Using a piece of paper as screen and activating the light source, the focal point of the second schlieren mirror can be found, located 2032 mm from the mirror. The image should be sharp at this location, and the iris diaphragm is then set up at the focal point. It is crucial that the image of the source mask in the cutoff plane is located in the exact middle of the iris diaphragm. If the image is off-center, the final schlieren image will be shifted toward one side of the colour wheel on the source mask, since extra light from that region will pass through the iris. Behind the iris, a lens is placed, to focus the light onto the camera CCD. This lens is an achromatic doublet lens, to accomodate for refractive difference in colours. This lens is placed in a lens holder approximately 50 mm from the iris. Since the lens has a focal length of 300 mm, the camera needs to be placed at this distance from the lens. The camera is mounted on a plate attached to a special contraption, allowing for easy adjustment of camera position along three axes.

(a) Blue dominated background. (b) Orange dominated background.

Figure 21: Examples of source mask image placed oﬀ-center towards the blue (Fig a) and yellow and red (Fig b) sections.

Removing all the safety covers from the mirrors, lenses and the camera, a ﬁrst test image is taken and analyzed making sure that the test area is visible and in focus in the picture, and that the background is an even colour, and adjusting the equipment until the result is satisfactory. If for example the nozzle exit is a little out of focus, the camera position is adjusted until the image is sharp, and the background colour eveness depends on the position of the iris diapghragm. With this setup, the size of the test section photographed is approximately 30x30 mm.

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(a) Uneven background (b) Even background

Figure 22: Example of uneven background, caused by misplacement of cutoﬀ.

6.2 Source Mask Production To produce the source masks a MATLAB program was written, accepting inputs on number of colour segments and the size of the colour filter. With these inputs, the program creates a source mask image, which is automatically saved as a .TIFF-file without compression. The image is then edited in photoshop, to accomodate a more precise size, and then printed on transparent OH- sheets . The transparency sheets have two different sides, one being rough and the other more smooth. The ink from printers (using InkJet printers and transparencies) stick better to the rough side, and the source mask images are printed on this rougher side. These are then cut out of the sheet, and glued together with precise alignment. This gives more colour into the light, counteracting the otherwise ”washed out” look of the images. Examples of this will be seen in the Results section. With astigmatism correction, a plano-concave cylindrical lens is placed behind the source mask, which will cause a distortion of the image of the source mask in the cutoff plane. To counteract this, the source mask is ”stretched out” along the horizontal axis (when the lens is placed vertically). This distortion is calculated with Equations 4, 7 and 8. For this setup, the distortion value calculated is m = 0.724, which 1 means that the width of the image will be multiplied by a factor of m = 1.38. Source masks corrected for astigmatism can be seen in Figure 13.

6.2.1 Source Mask Layering Determining how many layers of source masks used was done by trying out sets of two, four and six layers of masks. Images captured with these different mask configurations can be seen in the figure below.

(a) Two layer mask. (b) Four layer mask. (c) Six layer mask.

In the ﬁgures we can clearly see that more layers increases the colour saturation of the images, but the overall image will be darker (since less light gets trough the additional layers). The masks with four layers are chosen as the masks for this particular project, in order to acheive a satisfactory colour saturation as

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well as having enough light to get trough the filter, without having to use camera effects such as the input gain function (this function is demonstrated briefly in the Results section).

6.3 Astigmatism Correction Correcting for astigmatism requires some adjustments to the experiment setup, but can be done quite easy after some calculations, mentioned in more detail in Chapter 2.3.2. To be able to counteract the astigmatism eﬀect a plano-concave cylindrical lens is added to the system, placed behind the source mask. This lens will adjust the light in either the tangential or the sagittal plane, depending on the position (vertically or horizontally placed) of the lens. The light is adjusted in such a way that the focal point is shifted either forward or backward, depending on the orientation of the lens. Placing the lens in the correct position is critical, and needs to be calculated (details in Chapter 2.3.2. For this setup, the lens is placed 55 mm behind the source mask. This may need to be adjusted, depending on the accuracy of the calculated (or measured) value of the astigmatic diﬀerence. As the plano-concave cylindrical lens is in place, it shifts the focus point, requiring a re-adjustment of the iris diaphragm. The iris is positioned at the focus point, and when correctly positioned the image of the source mask should be very clear and sharp (in-focus) on the closed iris.

6.3.1 Measuring the Astigmatic Difference The calculations shown in Chapter 2.3.2 gives apprixmate values, since the astigmatic difference is difficult to calculate, when it depends on many different factors. Measuring the difference of the two focal points in the system itself is another way of determining the difference, and then calculating the other needed values (such as do and di). This measurement is done by replacing the source mask with a crosshairs (two small wires/strands of hair), and then a paperscreen put in place where the focal points are. By looking at the focus of the horizontal and vertical ”wires” on the paper, the two focal points can be marked and the difference measured. In this project, the measured value α = 21 mm.

6.4 Taking a Colour Schlieren Image Before taking images, all the equipment needs to be in place, and the protective covers removed, and the camera connected to the computer. Adjusting the iris diaphragm inner diameter size (to approximately the inner diameter of the source mask) makes for a good starting point. As images are taken, this is adjusted as needed. First a calibration picture is taken, to check if any adjustments need to be made. In this image, the background colour is checked to be fairly ”neutral” and even. An uneven background is caused by a slightly mispositioned cutoff, requiring to move the iris diaphragm forward or backward. Images are taken through the camera software program HiKE 1394 CamView, using the trigger connected to both the camera and the flash unit. The image is taken, and then immediately appears on the PC screen. CamView allows for saving and naming of images, as well as some pre- and post-editing configurations.

6.4.1 Camera Software Settings The HiKE 1394 CamView software that accompanies the camera has several settings, which will be discussed here. For most of the experiments, the default settings in the program was used, except for the trigger timer delay function for the camera. When connecting the camera with the software, the first dialogue window appears, requesting some choices to be made regarding the image resolution and colour, as well as the framerate of the camera. Figure 24 shows options available for the camera, where resolution is chosen at 1280x960 pixels (highest standard resolution available), used for all the test in this project. Using an RGB colour format for simplicity and effectiveness. The framerate option here is not very important, since it only relates to video (which is not used in this project). Most of the Basic image settings are left to their default (neutral) settings, as seen in Figure 25a. The 1 Shutter Speed is set to the quickest possible with the camera used, which is 100,000 s. This allows for a short exposure time, but it is not entirely quick enough for some of the flows imaged in the tests, which contributes to some time-averaging in some test images.

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Figure 24: Dialogue box in Camview software, displaying options of resolution, colour and framerate.

(a) Basic image options in (b) Masking options in the (c) Trigger options menu in Camview software.Options are Camview software. All of these Camview software, set to accept left to default, except for Shutter settings were left to the default a trigger that is connected to the Speed. value. camera.

Figure 25b displays Masking options in the Parameter Settings window in the Camview software program. All of these settings are set to the default value. The final options tab (Figure 25c ) in the settings window concerns the trigger of the camera. Here the trigger delay is set to 750µs, to better time the flash from the light source. These settings are used for most of the tests done in this project, however a few images have been taken with different settings. This will be detailed in Results, alongside the relevant images.

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7 Results

In this chapter the results from the experiments in this project will be shown. These are the test images taken with the colour schlieren system inplemented, taken with different configurations and settings, as well as example images from the final setup.

Figure 26: Image showing the coordinate system directions for the schlieren images presented later.

The images in this chapter will be presented in line with this example above (Figure 26), showing the orientation of the images and test section. The imaged part of the test section is x=35mm, y=27mm in size, with the nozzle in the bottom portion, and the X and Y axes representing horizontal (with the positive direction deﬁned as to the right) and vertical (positive direction upwards) directions, respectively. This is also indicated by the coordinate axes shown in the image. The Z direction is towards the camera, along the light ray path. This is further discussed in Chapter 3.

7.1 Astigmatism Correction After implementing the astigmatism correction, as explained in Chapter 2.3.2. For most of these test images, the astigmatism correction is only a small improvement, however for quantitative testing this is more important, since quantitative testing is usually more sensitive to small eﬀects, especially with a magnitude- indicating system (which can be easily implemented into this experiment setup). These example images in Figure 27 were taken with the the Nozzle Pressure Ratio (NPR) set to 3.0, which corresponds to an approximate Mach number of 1.36 and the iris diaphragm is dialated to 11mm, which corresponds to a cutoﬀ of 70% in both of the images. In the images a jet with a Mach diamond shockwave structure is present, with the jet boundary seen very clearly (areas with strong gradients are the most visible). The Mach diamond edges are sharper in image 27b, indicating some improvement has been made.

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(a) Image taken without astigmatism correction. (b) Image taken with astigmatism correction.

Figure 27: Examples of images taken with and without astigmatism correction.

7.2 Nozzle Effects Using different nozzles (as detailed in Chapter 8.6.1) to achieve different flow fields and flow appearances, a large difference in the flows from the nozzles can be seen. With these varying types of nozzles, a change in the flow structure is expected. In Figure 28 some different nozzles are shown. The Nozzle Pressure Ratio (NPR) is set to 3.0 in the tests shown, as well as using an iris dialated to 12mm (approximately 65% cutoff). The Nozzle Pressure Ratio 3.0 corresponds to an ideal Mach number of 1.36, however with these nozzles it is possible that it is slightly higher. In all of the images in the figure shockwaves can be seen clearly, as well as the colour corresponding to the direction of the density gradient, which helps to get a sense of the flow features and symmetries. The structure of these jets imaged all have the same basic characteristics, with some variations. The flow from the aerospike nozzle is perhaps easiest to tell apart, mainly from the shockwaves more visible closer to the nozzle exit (which is barely visible at the bottom edge of figure (a)). The other nozzles produce a free stream jet containing shockwaves eminating from the nozzle edges along with a Mach diamond at roughly the same distance from the nozzle exit. The outer stucture of the flow is more different, being closely contained in figure (f) but more spread out in the figures (b) and (e). The four chevroned nozzle in figures (d) and (e) gives a quite different schlieren image depending on the rotation of the nozzle, with a sharper free jet boundary in the first image (d). In the other direction (when the nozzle is rotated 90 degrees) the flow is more spread out. The Mach diamond structure in this image looks quite different from the same phenomenon from a different angle, being wider along the second axis.

7.3 Monochromatic Schlieren Comparisons Using the same experiment setup, with the source mask removed (and instead using only the flash unit) and the camera set to black and white settings (detailed in Chapter 6.4.1. This gives monochromatic schlieren images with a circular cutoff, in order to compare the images in terms of qualitative quality and difficulty of differentiating between flow features and artifacts. For qualitative purposes it is essential to be able to differentiate between features in the flow, which often is easier with coloured than monochromatic images. This example demonstrates the important differences between monochrome and colour schlieren photography, most simply that the colour gives and extra dimension in the image, that can be used for several different purposes. Here the colour is coded to the direction of the density gradient in the air within the

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(a) Aerospike nozzle. (b) Spiked nozzle.

(e) Four chevroned nozzle, rotated. (f) Two chevroned nozzle.

Figure 28: Images of jet with some diﬀerent nozzle types.

flow, but it can also be used to measure the strength of the density gradient, as well as simply highlighting different features of the flow.

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(a) Monochrome schlieren image. (b) Colour Schlieren image.

Figure 29: Examples of images taken with monochrome and colour schlieren methods.

7.4 Camera Effects Tests were done using some of the settings and effects discussed in 6.4.1, here the GAIN feature of the CamView software program is demonstrated. Three images taken with different GAIN values applied are shown in Figure 30 below.

(a) Image with no gain applied. (b) Image with a little gain applied. (c) Image with max gain applied.

Figure 30: A simple demonstration of the gain function.

In Figure 30, three images are shown. The first image (30a) have been taken with no settings changed, but with a higher cutoff (10mm iris aperture, approximately 75% cutoff used in all three images). The large cutoff gives a darker image, but higher sensitivity. The GAIN function of the camera artificially magnifies the light intensity on the camera CCD, and outputs an image with amplified light sensitivity. This can help in analyzing the images, since more can be seen than if the image was much darker, without using additional post-processing. The middle image 30b has been taken with a GAIN value of 8.04 dB, which helps enhancing the light in the otherwise dark image. The last image taken with the GAIN function at a maximum (18 dB), 30c, looks over-exposed, a sign that too much GAIN might have been applied. This over-exposure also obstructs some of the finer details of the imaged flow, while the middle image gives a good representation, with features more clearly visible than in the first, darker image. Using post-editing software (such as GIMP) the images can be enhanced as well, requiring no GAIN function to be used. The choice of either using GAIN or doing the enhancements in post-editing may depend on the image itself, the object photographed and the method used. Both methods can be applied to the same image as well, depending on the necessity. In figure 31 a few examples of the same (no gain version) of the image in figure 30 are shown. In the first two images, (a) and (b), the lightness (also known as value or tone in colorimetry) have been increased by 25% and 50%, respectively. This increases the overall brightness in the colour of the image, while keeping the other colour values (hue and saturation) intact. Increasing contrast as well (as in image (c), with increased lightness by 25% and contrast by 20%) gives a clearer image, if the original is too dark.

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(a) Image with colour lightness in- (b) Image with colour lightness in- (c) Image with colour lightness and creased by 25%. creased by 50%. contrast increased.

Figure 31: A simple demonstration of post-editing enhancements.

7.5 Final Images So far the images shown have been in relation to different effects or features of the experiment setup, but here a more in-depth analysis of a few of the final images taken will be made. These images was chosen to be displayed from their quite unique and interesting flow characteristics, to give a good example of how colour schlieren photography can be used for this type of imaging. Due to the fact that the camera has a shutter 1 speed of 100,000 s, some of the flow features will be time-averaged, since they are too fast to be captured properly by the camera. This is not always happening, but in some images this can be more clearly seen.

Figure 32: Flow from an aerospike nozzle.

In figure 32 the airflow out of the aerospike nozzle is about Mach 1.7 (at NPR 5.0), and the cutoff is set to 65%. In this test the standing shockwaves around the spike can be seen very clearly, together with the main jet and the vertical gradients as well. The colour in the image shows different gradient directions prominently, with a corresponding gradient strength (showing as lighter and darker areas). On the left hand side of the jet, a blue bright rim displays a density gradient in light blue, representing a gradient positive along the positive X-axis, using the correlation diagram in Chapter 5.7. On the other side of the jet, a darker rim of orange is visible, which represent a density gradient in the opposite direction, darker opposed to bright and orange, which represents the negative x direction. This is a good example of the type of schlieren image

36 October 12, 2015 Jens Kanje Nordberg

produce in these tests, with clear resolution of several important ﬂow features, and an easy to distinguish nozzle outline (opaque objects in the test section will always be black in the schlieren image). Shown below here is the spiked nozzle, one of the other nozzle setups that shows quite interesting (and beautiful) ﬂow characteristics.

Figure 33: Spiked nozzle ﬂow at NPR 4.5

Image 33 shows the flow from a spiked nozzle, with an approximate Mach number of 1.65, and cutoff at 65%. This image shows a Mack disc, with the oblique shockwaves as well, in bright colour indicating the structure of the flow. At the top of the image above the Mach disc, a sharp transition from purple and blue to green and yellow, representing a change in density gradient direction from positive to negative in the Y-direction. The free jet boundary is also visible, at the edges of the flow (indicated by the darker and brighter ridges along the edges of the jet). Small density changes in the outer parts of the flow (spreading out in the top half of the image) can be seen as much less sharp changes in hue and brightness in the image.

37 October 12, 2015 Jens Kanje Nordberg

8 Conclusion

This section is the final part of the document, and will discuss the project as a whole, with special regards to the objectives listed (in chapter 4) and the results presented. The colour schlieren system constructed have the capacity to capture colour photographs of the schlieren object in the test section in full colour. This system has been proven effective (see Chapter 7) for qualitative results, but has however not been fully tested for quantitative measurements of the kind expected (design done for both gradient direction and gradient magnitude measurements). This is because of complications with the bulls-eye type mask, described in chapter 3.4.2. Improvement of the design and production of the bulls-eye mask should make it possible to convert the in-place (gradient direction detection) colour schlieren system to a gradient magnitude detection system, with only making small adjustments. Additional work might also yield positive results in post-processing work on gradient direction detection schlieren, allowing for quantitative results in this area, without requiring any changes to the physical setup, merely utilizing post-processing and images taken with the camera. Using colour schlieren photography of this type to investigate and image advanced supersonic flow struc- tures is indeed possible, and can give very interesting results, containing more information than a simple monochromatic schlieren system, due to the extra dimension of information carried by the colour in the image. This is very helpful in both research of these flows (and other types of schlieren objects) and in teaching students in flow physics. Images in 7 show clear colour images of several supersonic flows, proving the use of this technique for this type of research. The setup in the LTRAC lab is fully functional in this area, and should be used in the future for similar experiments in supersonic flow research, requiring only small improvements to yield higher-quality results. The different flow varieties tested also show that the setup is dynamic, and can easily be modified to suit specialized experiements. The objectives of the project have been reached, however the fully quantitative features have not been implemented due to time and resource limitations. An assessment made of the different techniques reviewed and implemented in this project have been found suitable for the type of research that is being done in the LTRAC laboratory.

38 October 12, 2015 Jens Kanje Nordberg

Acknowledgements

First of all I want to express my gratitude and thanks to my supervisor at Monash University, Professor Damon Honnery, for all the guidance and advice during this project. I also would like to thank Dr Daniel Edgington-Mitchell, that also helped me and gave advice, along with the other students and scientists in the LTRAC (Laboratory for Turbulence Research in Aerospace and Combustion) lab at the Department of Mechanical and Aerospace Engineering at Monash University. Your help has been crucial to this project from the start, when I ﬁrst started learning about schlieren in practice. I also wish to thank Lars-G¨oran Westerberg, Associate Professors at Lule˚aUniversity of Technology, being my examiner and helping me start this thesis before it even began.

Jens Kanje Nordberg Lule˚a,Sweden 2015

39 October 12, 2015 Jens Kanje Nordberg

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