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The jet from a round Laval nozzle followed by a cylindrical duct with an inner diameter of 10 mm and a length of 50 mm is investigated experimentally. The Laval nozzle has a design Mach number of 1.5. Quantitative flow visualization of the jet issued from the duct exit is performed over a range of nozzle pressure ratios from 2.0 to 4.5 using the rainbow schlieren deflectometry combined with the computed tomography to investigate the jet three-dimensional structure. The flow features of the near-field shock systems in the jets are displayed with the density contour plot at the cross-section including the jet centerline. Effects of the nozzle pressure ratio on the density profile along the jet centerline are clarified quantitatively. In addition, a comparison between the present experiment and the previous one with a conventional Laval nozzle for jet centerline density profiles is carried out to examine the effect of the cylindrical duct. Furthermore, the three-dimensional structures of overexpanded and underexpanded jets are demonstrated with the isopycnic surfaces to visualize the internal flow features.

The Mach–Zehnder interferometer with the finite fringe setting is applied for a shock-containing microjet issued from an axisymmetric convergent nozzle with an inner diameter of 1.0 mm at the exit. Experiments are performed at a nozzle pressure ratio of 3.0 to produce a slightly underexpanded sonic jet where the Reynolds number, based upon the diameter and flow properties at the nozzle exit, is $$4.45 \times 10^4$$ 4.45 × 10 4 . The reconstruction of the jet density field is performed using the Abel inversion method under the assumption of an axisymmetric flow as well as the Fourier transform method for the phase shift analyses of interferograms. The three-dimensional density field of a shock-containing microjet can be captured with a spatial resolution of 4 $$\upmu$$ μ m, and the near-field shock structure inside the jet plume is shown in the density contour plot at the cross-section including the jet centerline. In addition, the density field of the microjet is illustrated with various techniques, including representation such as the vertical-knife-edge schlieren, the horizontal-knife-edge schlieren, the bright-field schlieren, and the shadowgraphy. In addition to experiments, the Reynolds averaged Navier–Stokes (RANS) simulation with the SST k–$$\omega$$ ω turbulence model is carried out to model the microjets, and a quantitative comparison with the experiments is performed. The jet centerline density profile obtained by the present experiment is quantitatively compared with those from the previous Mach–Zehnder interferometer, the background oriented schlieren, as well as the RANS simulation.

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.

This report deals with introducing two new techniques based on a novel concept of complex brightness gradient in quantitative schlieren images, “inverse process” and “multi-path integration” for image-noise reduction. Noise in schlieren images affects the projections (density thickness) images of computerized tomography (CT). One spot noise in the schlieren image appears in a line shape in the density thickness image. Noise effect like an infectious disease spreads from a noisy pixel to the next pixel in the direction of single-path integration. On the one hand, the noise in the schlieren image reduces the quality of the image and quantitative analysis and is undesirable; on the other it is unavoidable. Therefore, the importance of proper noise reduction techniques seems essential and tangible. In the present report, a novel technique “multi-path integration” is proposed for noise reduction in projections images of CT. Multi-path integration is required the schlieren brightness gradient in two orthogonal directions. The 20-directional quantitative schlieren optical system presents only images of schlieren brightness in the horizontal gradient and another 20-directional optical system seems necessary to obtain vertical schlieren brightness gradient, simultaneously. Using the “inverse process”, a new technique enables us to obtain vertical schlieren brightness gradient from horizontal experimental data without the necessity of a new optical system and can be used for obtaining any optional directions of schlieren brightness gradient.

To optimize the leek peeling performance, a new nozzle has been developed in which the nozzle has a design Mach number of 1.68, an inner diameter of 2.0 mm at the throat, and an inner diameter of 2.3 mm at the exit. Experiments have been conducted over a range of nozzle pressure ratios from 3.0 to 6.0. Flow field issued from the new nozzle is quantitatively visualized by the rainbow schlieren deflectometry and compared with that from a conventional nozzle. Density fields in the free jets are reconstructed by the Abel inversion method for the schlieren images with the horizontal rainbow filter. The density values at the exit of the conventional nozzle obtained by the rainbow schlieren are compared with the analytical results by the flow model proposed in the past. In addition, Pitot probe surveys along the jet centerline were made to obtain the impact pressure distributions. The Mach number and velocity distributions along the jet centerline are obtained from a combination of the density and Pitot pressure data to clarify the fundamental flow structure of leek peeler nozzle jets.

The three-dimensional density field of a supersonic microjet issued from a square convergent nozzle with a cross-sectional area of 1 mm × 1 mm at the exit is measured by the Mach-Zehnder interferometer with the finite fringe setting. The experiment is performed at a nozzle pressure ratio of 4.0 to produce underexpanded free jets. Interferogram analyses for reconstructing the density field of the microjet are performed using the convolution back projection (CBP) algorithm in which the analysis of the phase shift of the deformed fringe relative to the background fringe is carried out by the Fourier-transform method. A flow topology of the microjet is clarified with various visual representations.

The Mach–Zehnder interferometer with the finite fringe method is applied for the first time to diagnose the three-dimensional density field of a shock-containing microjet issued from a convergent nozzle with an inner diameter of 1 mm at the exit. Experiments are performed at a nozzle pressure ratio of 4.0 to produce an underexpanded free jet with a Mach disk in the first shock-cell where the Reynolds number, based upon the diameter and flow properties at the nozzle exit, is turbulence model for a quantitative mutual comparison between the simulation and the experiment. The detailed variation of the density field associated with the Mach disk, the slip streams and the outer shear layers near the jet boundaries are successfully captured. Furthermore, the density profile along the jet centreline obtained by the present experiment is quantitatively compared with those from prior quantitative visualization studies, such as rainbow schlieren deflectometry, background oriented schlieren, moire schlieren and Mach–Zehnder interferometer. The three-dimensional contour map coloured by the magnitude of the density gradient vector inside the microjet reveals the flow topology of the near-field shock systems and elucidates the spatial variation of the shock strength.

Two-dimensional critical nozzle flows at low Reynolds numbers are visualized by the rainbow schlieren deflectometry. Experiments have been performed in a region of overexpanded nozzle flow. The variation of the shock structure against the back pressure ratio can be clearly visible with color gradation. Static pressure rises due to the shock-induced flow separation are compared with the previous theories. The unsteady characteristics of overexpanded critical nozzle flows at low Reynolds numbers are quantitatively and qualitatively visualized using laser schlieren and Mach-Zehnder interferometer systems combined with a high-speed digital camera. It was found that an oscillating normal shock wave appears inside the nozzle, and that the shock wave has a specified dominant frequency. Also the time-history of the oscillating shock wave is obtained from both the systems and compared with each other.

The focusing schlieren PIV technique is being done to investigate the velocity vector, and it is considered as the useful measurement technique in the compressible flow. In this study, the LED light sources of a focusing schlieren system was used to visualize the flow fields of helium jets. And the flow vector was estimated by using PIV software as the first step. The system was constructed by an extended light source, a Fresnel lens, source and cutoff grids, focusing lens, and a CCD camera. The three source grids were prepared. The light source was designed by consisting of four LEDs. This system was used to visualize free jets from the convergent nozzle. The helium gas was used as the test gas to obtain large density gradient in low-speed flows. As the result, the density gradient could be seen though the condition was low speed. And the flow field from the nozzle was visualized by the LEDs as the extended light source. The jet at the focal plane could be seen clear, and the flow vector due to the turbulence was seen by the PIV analysis.

The rainbow schlieren deflectometry has been combined with the computed tomography to obtain three-dimensional density fields of shock containing free jets and we call the method the schlieren CT. Experiments on the schlieren CT have been performed at a nozzle pressure ratio of 4.0 by using an axisymmetric convergent nozzle with an inner diameter of 10 mm at the exit where the nozzle was operated at an underexpanded condition. Multidirectional rainbow schlieren pictures of an underexpanded sonic jet can be acquired by rotating the nozzle about its longitudinal axis in equal angular intervals and the three-dimensional density fields are reconstructed by the schlieren CT. The validity of the schlieren CT is verified by a comparison with the density fields reconstructed by the Abel inversion method. As a result, it is found that excellent quantitative agreement is reached between the three-dimensional jet density fields reconstructed from both methods.

The slightly underexpanded free jet issued from a supersonic micro nozzle with a design Mach number of 1.5 and a square shape of 1 mm × 1 mm at the nozzle exit has been experimentally investigated using the rainbow schlieren deflectometry combined with the computed tomography where the nozzle operating pressure ratio is held constant at 4.0. Density fields in the free jet obtained from the rainbow schlieren deflectometry are the vortex sheet theory proposed by Tam. It is shown that there is good quantitative agreement between experiment and theory. It is shown that the rainbow schlieren deflectometry is a useful tool for studying the three-dimensional structure of shock containing free jets from micro-scale supersonic nozzles.

The rainbow schlieren deflectometry is effective in studying quantitatively the density fields in shock-containing free jets at high precision and high spatial resolution. However, there has been no practical application of rainbow schlieren deflectometry for shock trains in a confined duct. Therefore, in the present study, the rainbow schlieren deflectometry is applied to the flow field including a shock train in a constant-area duct where just upstream of the shock train the freestream Mach number is 1.34, the unit Reynolds number is 5.39 × 107 m-1, and the boundary layer displacement thickness is 0.149 mm. As a result, a two- dimensional density field of the shock train is for the first time quantitatively displayed and the fine structure of the shock train is illustrated as a color gradation representation.

We have developed new firefighting hoses and compared them to conventional hoses, measuring their pressure loss when water alone or mixed water passed through. As a result, it is found that the new hoses have lower pressure loss than conventional hoses, and fewer kinks and they are more durable.

The two dimensional unsteady structure including the interaction between a normal shock wave and turbulent boundary layer in a transonic diffuser is quantitatively and qualitatively visualized using high-speed Mach-Zehnder interferometry. Experiments have been performed at an operating pressure ratio of 1.4 where the freestream Mach number just ahead of the normal shock wave is around 1.1. The normal shock oscillatory characteristics in the diffuser are also investigated by a high-speed schlieren method. Streamwise static pressures on the diffuser side wall have been measured and the time-mean wall pressure distribution in the diffuser is compared with that from the RANS equation with the k- SST turbulent model. The dominant frequency of the normal shock oscillation obtained from the Mach-Zehnder interferometry is quantitatively identical to that from the high-speed schlieren mothod.

The numerical analysis of a turbulent sonic jet from a two-dimensional convergent nozzle has been carried out using the compressible k-ɛ turbulence model and TVD finite difference scheme. Numerical conditions have been varied over a range of operating pressure ratios from 1.893 to 6.0 which cover the jet flow conditions from correctly expanded to underexpanded. Numerical flow visualization of sonic jet structure using the computer schlieren, a relation between shock cell length in the jet with the operating pressure ratio and the pressure distribution along jet centerline are obtained. Also, a transition process of a two-dimensional sonic jet from correctly expanded to underexpanded conditions is shown in detail and a flow model of jet structure is proposed.

This paper analyzes the correctly-expanded supersonic jet from a convergent-divergent axisymmetric nozzle by using numerical simulation of turbulent flow. And the calculated density distributions in this flow are compared with the present experimental data using rainbow schlieren deflectometry. The value of the density from the experimental data agrees well with the results calculated by this simulation. Therefore, the present method of the measurement using rainbow schlieren deflectometry is useful for the measurement of the density of the correctly-expanded supersonic jet.

When sonic nozzles of significantly smaller diameter are used as standard flow meters, the critical back pressure ratio is affected by the boundary layer at the nozzle throat. However, the effect of the boundary layer on choking criteria is still controversial. Then, the choking phenomenon of a convergent nozzle flow has been experimentally investigated using four convergent nozzles with the same diameter followed by a straight pipe of a variable length. As a result, it is shown that the critical back pressure ratio is smaller than that for the steady one-dimensional isentropic flow and decreases as the boundary layer thickness increases. Moreover, the main flow Mach number at the nozzle exit is supersonic when the back pressure ratio is equivalent to the choking condition, and the Mach number increases as the boundary layer thickness increases.