Multi-Schlieren CT Measurements of Supersonic Microjets from Circular and Square Micro Nozzles

Instantaneous three-dimensional (3D) density distributions of a shock-cell structure of perfectly and imperfectly expanded supersonic microjets escaping into an ambient space are measured. For the 3D observation of supersonic microjets, non-scanning 3D computerized tomography (CT) technique using a 20-directional quantitative schlieren optical system with flashlight source is employed for simultaneous schlieren photography. The 3D density distributions data of the microjets are obtained by 3D-CT reconstruction of the projection’s images using maximum likelihood-expectation maximization. Axisymmetric convergent-divergent (Laval) circular and square micro nozzles with operating nozzle pressure ratio 5.0, 4.5, 4.0, 3.67, and 3.5 have been studied. This study examines perfectly expanded, overexpanded, and underexpanded supersonic microjets issued from micro nozzles with fully expanded jet Mach numbers Mj ranging from 1.47 1.71, where the design Mach number is Md = 1.5. A complex phenomenon for free square microjets called axis switching is clearly observed with two types “upright” and “diagonal” of “cross-shaped”. The initial axis-switching is 45 ̊ within the first shock-cell range. In addition, from the symmetry and diagonal views of square microjets for the first shock-cells, two different patterns of shock waves are viewed. The shock-cell spacing and supersonic core length for all nozzle pressure ratios are investigated and reported.


Introduction
Visual observation and investigation of fluid flow provide useful and comprehensive insight into a flow field under inspection and help derive quantitative data from the observed flow patterns. Fluids are mostly transparent, and therefore, invisible; there are some good techniques that can visualize flowing fluids with non-uniform density. A Schlieren technique is very sensitive to density changes and it can visualize invisible flows in transparent media. This technique has been widely implemented in fluids and combustion. In fluid dynamics, the schlieren imaging technique is a common tool to illustrate detailed descriptions of air flows, shock waves, compressions, and expansion fans in supersonic jet flows for use in aerodynamical studies [1]. In previous works, a non-scanning three-dimensional computerized tomography (3D-CT) technique using a delicate multi-directional quantitative schlieren optical system with a flashlight source was developed and employed to measure instantaneous density distributions of several types of flames in laminar and turbulent flows [2] [3] [4] [5] [6]; in addition, some new techniques have been introduced [7] [8].
It is very difficult and unsatisfactory to investigate microjets when using measurement devices because of the very small dimensions of the micro nozzles, especially those close to the micro nozzle exit. In the present study, to provide a suitable technique for the 3D observation of a supersonic microjet (non-uniform density flow), a non-scanning 3D-CT technique using a multi-directional quantitative schlieren technique was employed [2] [3] [4] [5] [6]. This is the first study wherein the mentioned technique with a non-deviation treatment for projection images (density thickness images) is used to measure instantaneous density distributions on the shock-cell structure of perfectly and imperfectly expanded (overexpanded and underexpanded) supersonic microjets issued from circular and square micro nozzles.
Air microjets are employed to deliver pressure to a workpiece in many industrial activities using simple sonic nozzles [9]. Scroggs and Settles [9] explained that the selection of such sonic nozzles leads to restrictions and undesirable points.
They suggested an alternative method: the application of converging-diverging (Laval) supersonic micro nozzles that have highly uniform and stable properties.
A supersonic microjet is a more effective small-scale high-pressure gas delivery device compared to sonic nozzles of comparable scale at equivalent mass flow rates. The main advantage of microjets is their ability to create high-density arrays of microjets without increasing flow rate. To the best of our knowledge, Scroggs and Settles [9] were the first authors to study micro nozzle flow and obtain schlieren images of a shock-cell structure of flow and axial and transverse pitot-pressure distributions. Further, they fabricated converging-diverging micro nozzles by heating and stretching glass capillaries; in these experiments, air was used as the working gas in the experiments. The nozzle exit diameters were 600 μm and 1200 μm with exit Mach numbers ranging from 1.0 -2.8 and Reynolds numbers ranging 20,000 -45,000. Aniskin et al. [10] reported a detailed study on the structure of underexpanded mini and microjets with a wide range of diameters ranging from 341 -10.4 μm. The working gas in the experiments was nitrogen. The main parameters of supersonic underexpanded microjets are identified, including the size of shock-cells and the supersonic core length of the microjet. Phalnikar et al. [11] studied supersonic microjets escaping micro nozzles with diameters ranging between 100 -1000 μm and presented the results of only 200 and 400 μm microjets, which include most features of interest; the working gas in their experiment was nitrogen. In addition, Phalnikar et al. [11] proposed a correlation for the size of shock-cells in the jet and for the relative supersonic core length. They obtained axial and transverse pressure distributions from a pitot pressure survey.
Supersonic microjets have diverse applications in various fields of engineering and industries; for example, in the cooling of micro-electro mechanical systems (MEMS) components, fine particle deposition and removal, and as actuators to control the ground effect in short take-off and vertical landing (STOVL) aircraft when hovering [11]. Further, microjets have been used in the removal of fine particles from a surface by impinging shock waves [12], microjet engines [13], in active control of gas-dynamic flows, and for significant reduction in the overall sound pressure levels of the aircraft [14] [15] [16], and for jet noise control [17].
Supersonic free jets issued from circular, square, rectangular with different aspect ratios, and regular triangular nozzles are visualized using a laser-induced fluorescence method proposed by Teshima [18]; it is found that these jets expand most prominently in the major and minor axial directions, which results in a cross-shaped cross-section. Tsutsumi et al. [19] investigated the structure of underexpanded jets for square nozzles and explained that these types of nozzle are of interest because of their use in clustered combustors of linear aerospike engines. These combustors are designed to minimize intercell gaps using a rectangular exit; the nozzle studied in the report of Tsutsumi et al. has a circular throat and a square exit, with the D throat of 6 mm and a nozzle wall thickness of 1.5 mm. Noncircular jets were identified as an efficient technique for passive flow control [20]. Cabaleiro and Aider [21] reported the observation of the axis-switching of a microjet for the first time for free noncircular microjets.
There are very few experimental studies on supersonic microjets, especially for the square cross-section, in the literature. However, with a few exceptions (e.g. [22] [23]), most studies used the schlieren technique from a qualitative point of view and not for quantitative measurements. In most studies, quantitative measurements of the jets spreading as well as shock-cell spacing were obtained using micro-pitot probe surveys.
In the present study, quantitative measurements and qualitative investigations are combined, and supersonic microjets from circular and square micro nozzles have been successfully CT-reconstructed with a custom-made 20-directional

Micro Nozzles and Coordinate System
A circular and square cross-section convergent-divergent (Laval) micro nozzle, with a design Mach number M d = 1.5, is studied ( [24] [25], Figure 1). The circular nozzle has a throat diameter of 922 μm, an exit diameter of 1000 μm, and an area ratio A e / A th = 1.18; the square nozzle has a throat size of 850 × 850 μm 2 , an exit size of 1000 × 1000 μm 2 , an area ratio A e / A th = 1.38. The convergent and divergent section lengths are 6000 μm and 1300 μm, respectively. The center of the nozzle exit is selected as the origin of the xyz-coordinate system; the nozzle exits are then located downward in the negative z-axis. The x-axis is located (a) Circular nozzle [24]; (b) Square nozzle [25].
A. Z. Nazari et al.
between camera No. 10 (θ = −4.5˚) and camera No. 11 (θ = +4.5˚); the details of the camera system are described in the next section. Detailed descriptions of micro nozzles are reported in [24] [25]. The micro nozzle was designed using a sinusoidal curve and the axisymmetric method of characteristics [26] to provide uniform and parallel flow. horizontal angle from the x-axis. For pre-investigation and for time-series observation (high-speed schlieren movies) of the target flow, a high-speed camera (HSC) is used simultaneously with the 20-direction schlieren photographing apparatus (between cameras No. 13 and No. 14, Figure 2(c)). The diagram of a single instance of a multi-directional quantitative schlieren camera system is provided in Figure 2(d). This system is composed of two convex achromatic lenses with a 50 mm diameter and a 300 mm focal length, flashlight source unit, vertical knife-edge (for obtaining horizontal schlieren brightness gradient images), and digital camera. The neutral density (ND) filter (Fuji 1.5, exposure adjustment multiple 3.16) and stepped ND filter is used for calibrating the cameras. The light unit is a xenon flashtube that emits full-spectrum white light with a uniform luminance rectangular area of 1 mm × 2 mm and a 35 μs duration. From a technological point of view, this experimental method (CT non-scanning, Figure 2(e)) is similar to a CT-scanner used in medical engineering for medical diagnostics (Figure 2(f)). The CT-scan combines a series of X-ray images obtained from different angles to produce cross-sectional (tomographic) images of specific areas of a scanned object (human body). The schlieren 3D-CT measurement technique employs schlieren photography (instead of X-ray images) from 20-directions to reconstruct 3D-density distributions data (cross-sectional density distributions) of a target flow. Density, deviation density, and density thickness values with an asterisk sign (*) express actual values, and those without the sign represent derived values from the CT-reconstruction process. Figure 3(a) depicts density distribution ρ*(x, y) of target flow with an ambient gas (air) region of constant density ρ a *(= 1.2 kg/m 3 ) on the periphery of the observed range of radius R. Figures 3

Image Processing
shows observations in the direction of θ from the x-axis in the inclined coordinates denoted by X(θ) and Y(θ).
The first goal is obtaining the density thickness of deviation density (Dt*(X(θ))), as shown in Figure 3(d) with a unit of (kg/m 3 )(m). The density thickness of deviation density Dt*(X(θ)) is obtained automatically from schlieren observation using spatial integration of deviation density Δρ*(X(θ),Y) along the line of sight. In other words, the density distribution of target flow is reconstructed using a 2D distribution (image) of "density thickness" as a projection in the CT-reconstruction process.
In the practice for obtaining the density thickness of deviation density ( Figure   3(i)), the image processing activity starts from Figure 3 where K is the Gladstone-Dale constant for air (K = 2.26 × 10 −4 m 3 /kg), Δs (= 1 mm × 2 mm (Hor. × Ver.)) is the transparent width of the light source image on schlieren stop location and f (= 300 mm) is the focal length of the convergent lens. Deviation density thickness Dt(X(θ)) is, therefore, reproduced by the Journal of Flow Control, Measurement & Visualization transverse integration of d(Dt)/dX from schlieren images, as shown in Figure   3(h). Finally, the density thickness Dt′(X(θ)) is obtained by adding the thickness of ( ) to the deviation density thickness Dt(X(θ)) on the peripheral of the observed range of radius R (Figure 3(i)), as expressed by In the present study, ρ ref = 0.8 is selected as a reference density because the minimum jet density is above this amount. Using non-deviation treatment for projections of CT by employing reference density guarantees that the CT-reconstructed deviation density non-negative and the CT-reconstruction is possible.

CT-Reconstruction
Density thickness images are used for CT-reconstruction by maximum likelihood-expectation maximization (ML-EM) [27] as an appropriate CT algorithm to obtain the 3D reconstruction of density distribution; the ML-EM method [2]- [8] is employed for CT-reconstruction. The CT procedure is carried out in each horizontal plane of the z-axis for the reconstruction of deviation density distribution Δρ(x, y) from a linear data set of density thickness Dt'(X(θ)) ( Figure 3(j)).
Finally, 2D density distribution  is obtained as follow, and ρ ref , in which one step (Figure 3(i)) was added, at this step is again subtracted and removed (Figure 3(k)).

( ) ( )
, , a x y x y ρ ρ ρ * = ∆ + The reconstruction was performed cross-section by cross-section and then the cross-sections were stacked to form a three-dimensional density distribution.

Supersonic Microjets [28]
A jet is referred to as underexpanded if jet pressure ratio (JPR), P e /P b ˃ 1, overexpanded if P e /P b < 1, and perfectly expanded or pressure matched if P e /P b = 1.
In the present work, axisymmetric convergent-divergent (Laval) circular and  Table 1 and Table 2, respectively.

Quantitative Schlieren and Projections (Density Thickness) Images
Owing to page limitations, only sample sets of images in some directions and some positions for some NPR (nozzle pressure ratio) are shown in the subsequent figures and sections. Figure 4 indicates the quantitative schlieren images of deviation brightness in schlieren images (as shown in Figure 3(f)) for supersonic microjet from the square nozzle for NPR = 5.0. The numbers inserted in each picture expressshooting angles θ.
The images in Figure 4 are processed by the above-mentioned conversion procedure for projection images of density thickness

CT-Reconstruction Results
Using the density thickness images (    Based on the viewing angle, two types of schlieren images (Figure 9(c)) for square supersonic microjets are observed using multi-schlieren optical system photography. Views for the square nozzle outlet, toward the "side" represent the "symmetry view" and toward the "corner" represent the "diagonal view". As depicted in Figure 9(b), the corner of the square micro nozzle outlet located toward the high-speed camera is used for pre-investigation and for time-series observation. The types of view for each camera are shown in Figure 9(b). Sample schlieren images for both types of views are shown in Figure 9(c) for the underexpanded square supersonic microjet, NPR = 5.0, and the schlieren images for all 20 directions are illustrated in Figure 4. As reported in [18] [19] [31], the first shock-cell composed of two types of shock waves, intercepting shock waves and recompression shock waves, can be classified into four categories, as marked by letters A, B, C, and D (Figure 9(c)). The jet expands almost two dimensionally on the symmetry planes, whereas shock waves recompress expansion on the diagonal planes, which results in a cross-shaped jet cross-section (Figure 10(d)).   larger till it forms a brighter square shape surrounded by a diamond-shape ( Figure 10(h)), which is located near the end of the first shock-cell.

Square Microjets Structure and Axis-Switching
By comparing cross-sections near the nozzle outlet and the near end of the first shock-cell, we can see microjet axis-switching clearly as sketched on the left side of Figure 10. Axis switching is a phenomenon in which the cross-section of an asymmetric jet develops gradually, and in such a manner that, after a certain distance from the nozzle exit, the major and the minor axes are interchanged.
Therefore, as observed, the initial axis-switching is 45˚ inside the first shock-cell Journal of Flow Control, Measurement & Visualization Recently, Cabaleiro and Aider [21] observed the axis-switching of a microjet for the first time, and probably in small-scale, in this investigation is for the second time such delicate, complex and beautiful phenomenon for square microjets is observed more clearly. The deformation of a micro-vortex ring caused by induction because of corner vortices is responsible for axis switching as it occurs in large-scale non-circular jets [21] [32] [33]. Further, Zaman [32] introduced the second mechanism caused by the induced velocities of two streamwise vortex pairs situated at the ends of the major axis. These two vortex pairs can effectively resist or enhance axis-switching, which depends on their relative distribution at the edge of the nozzle.

Shock-Cells Spacing (Ls) and Supersonic Core Length (Lc)
For better evaluation of the reconstructed density values, radial and axial density distributions diagrams are illustrated in Figure 11 and Figure 12. Amplitude increases and decreases along the jet downstream, which is higher for square microjets compared to circular microjets. Thus, it reaches a peak value near the center of the diamond-like pattern and after these points gets its minimum values periodically.
Shock-cell parameters are important to characterize supersonic jets such as "shock-cell spacing (length) L s " and "supersonic core length L c ". Note that shock-cell spacing L s for all shock-cells can be obtained from schlieren images.
The shock-cell spacing for the first five shock-cells based on our experimental data and results is depicted in Figure 13(a) and Figure 13(b) for circular and square supersonic microjets, respectively. The cross-section area of a square is larger than a circle with a diameter equal to the width of the square, and accordingly, square microjets have larger shock-cells lengths and amplitudes than circular microjets. Furthermore, the second shock-cells length is longer than the first shock-cells length for circular microjets in all nozzle pressure ratios except for NPR = 3.5 (overexpanded microjet); however, for square microjets, the second shock-cells length is shorter than the first shock-cells length. Tam and Tanna [34] and Tam [35] proposed the following relations (Equations (5) and (6)) for estimating the first shock-cell spacing (L s ) in supersonic circular [34] and square [35] jets, respectively. where M j , D j , and h j are the fully expanded jet Mach number, diameter (circular jets), and width (square jets), respectively. For the first L s , Mehta and Prasad [36] obtained a linear relation forcircular macrojets, and Phalnikar et al. [11] proposed the following correlation based on the experimental data for estimating the first shock-cell spacing L s ; no attempt was made to compute the lengths of the second and later cells for microjets.
where D is the nozzle diameter.
We compare the shock-cell spacing (L s ) determined from our experimental results and estimated using Tam, Phalnikar and Mehta's correlations, as shown in Figure 14(a) for circular microjets and Figure 14(b) for square microjets. An overall good agreement is seen between the first L s in this study and Tam's correlation. However, the measured values of the L s in our studies a little differ from those estimated by Tam's correlation. The L s in the present study, about 9% -13% for circular and 4% -8% for square microjets, are smaller than those predicted by Tam's correlation (Equations (5) and (6)). Similar comparisons were also made by Hu and McLaughlin [37]; their L s of about 10% was smaller than that predicted by Tam's correlation (Equation (5)). Further, they mentioned that the difference is attributed to a thicker boundary layer caused by the low Reynolds number for the microjets, as the boundary layer thickness would be inversely proportional to that of Reynolds number, and the Reynolds number directly proportional to the nozzle outlet size [37]. Schlichting [38] for the boundary layer thickness (δ) for turbulent flow obtained one estimated equation, 1 5 0.37 , where x is the distance downstream from the nozzle exit and Re x is the Reynolds number. For circular and rectangular microjets, NPR = 5.0, the boundary layer thickness within a distance equal to the nozzle diameter is almost one-pixel (0.04 mm) or rarely two-pixel (0.08 mm) and based on Schlichting equation [38] the boundary layer thickness is δ = 0.045 mm. This compares very well with the experimental values given the level of approximation.
Phalnikar et al. [11] conducted experiments using micro nozzles with internal diameters (200 μm and 400 μm) smaller than 1000 μm, and Mehta performed experiments using macro nozzles with internal diameters (23,000 and 30,000 μm) several times bigger than 1000 μm; accordingly, as shown in Figure 14(a), Phalnikar and Mehta's correlations results are the lowest and the highest, respectively. Since the smaller nozzle exit size and accordingly low Reynolds number resulted in smaller L s .
Further, "supersonic core length L c " is usually used to characterize supersonic jets. It is defined [11] as the distance from the nozzle exit to the axial location along the centerline, where the local flow Mach number drops below 1.0 and reaches a local sonic velocity. Scroggs and Settles [9] estimated L c as the length of the conical region surrounding shock-cells from schlieren images. Phalnikar et al. [11] proposed the following correlation (Equation (8)) for estimating L c for circular microjets.
A. Z. Nazari et al.
where D is the nozzle diameter and NPR = nozzle pressure ratio (P o /P b ). We used CT-reconstructed density data for estimating L c and compared it with Equation (8), as shown in Figure 15. As depicted in Figure 15, the L c for square microjets is less than that for circular microjets (Figure 15  spacing L s (Figure 15(b)) for square microjets, which is larger than that for circular microjets. A good agreement is seen between the Phalnikar relation and our circular microjets experimental data, and Equation (8) is proposed for the circular microjets and not for square microjets.

Conclusions
By employing the non-scanning 3D-CT technique using a 20-directional quan- A complex phenomenon for free square microjets, which is called axis switching, is clearly observed with two types "upright" and "diagonal" of "cross-shaped". In addition, for the first shock-cells from the symmetry and diagonal views of square microjets, two different patterns of shock waves were observed.
The shock-cell spacing and supersonic core length for all nozzle pressure ratios were investigated and reported. Comparisons with experimental and theoretical computations (particularly those of Tam and Tanna [34] and Tam [35]) showed an overall remarkably good agreement for the first L s and L c in this study and other correlations. As microjets have low Reynolds number, some acceptable differences exist between the compared results.