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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.

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 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.

This paper describes computational work to understand the unsteady flow-field of a shock wave discharging from an exit of a duct and impinging upon a flat plate. A flat plate is located downstream, and normal to the axis of the duct. The distance between the exit of the duct and flat plate is changed. In the present study, two different duct geometries (i.e., square and cross section) are simulated to investigate the effect of duct geometry on the un-steady flows of a shock wave. In computation, the total variation diminishing (TVD) scheme is employed to solve three-dimensional, unsteady, compressible, Euler equations. Computations are performed over the range of shock Mach number from 1.05 to 1.75. Computational results can predict the three-dimensional dynamic behaviour of the shock wave impinging upon the flat plate. The results obtained show that the pressure increase generated on the plate by the shock impingement depends on the duct geometry and the distance between the duct exit and plate, as well as the shock Mach number. It is also found that for the duct with cross-section, the unsteady loads acting on the flat plate are less, compared with the square duct.

The present study describes an experimental work to investigate the effect of a nozzle exit reflector on a supersonic jet that is discharged from a convergent–divergent nozzle with a design Mach number of 2.0. An annular reflector is installed at the nozzle exit and its diameter is varied. A high-quality spark schlieren optical system is used to visualize detailed jet structures with and without the reflector. Impact pressure measurement using a pitot probe is also carried out to quantify the reflector’s effect on the supersonic jet which is in the range from an over-expanded to a moderately under-expanded state. The results obtained show that for over-expanded jets, the reflector substantially increases the jet spreading rate and reduces the supersonic length of the jet, compared with moderately under-expanded jets. The reflector’s effect appears more significant in imperfectly expanded jets that have strong shock cell structures, but is negligible in correctly expanded jet.

In this paper, the characteristics of a pressure wave propagating against two parallel subsonic streams in a constant-area straight duct are investigated by one-dimensional analysis, two-dimensional numerical simulation, and experiments. Computations have been carried out by the two-dimensional Euler Equations using the Chakravarthy-Osher-type TVD scheme. Optical observations by the schlieren method as well as wall pressure measurements have been performed to clarify both the structure and the propagation velocity of pressure waves. The results show that the pressure wave propagating against the streams changes into a bifurcated pressure wave and the bifurcation occurs in the low speed streams. It is also found that the propagation velocity of the pressure wave obtained by the analysis and computation agrees well with the present experimental data.

It is well known that screech tones of supersonic jet are generated by a feedback loop driven by the instability waves. Near the nozzle lip where the supersonic jet mixing layer is receptive to external excitation, acoustic disturbances impinging on this area excite the instability waves. This fact implies that the nozzle lip thickness can influence the screech tones of supersonic jet. The objective of the present study is to experimentally investigate the effect of nozzle-lip thickness on screech tones of supersonic jets issuing from a convergent-divergent nozzle. A baffle plate was installed at the nozzle exit to change the nozzle-lip thickness. Detailed acoustic measurement and flow visualization were made to specify the screech tones. The results obtained obviously show that nozzle-lip thickness significantly affects the screech tones of supersonic jet, strongly depending on whether the jet at the nozzle exit is over-expanded or under-expanded.

This paper describes an experimental work to investigate the effect of a reflector on supersonic jet noise radiated from a convergent-divergent nozzle with a design Mach number 2.0. In the present study, a metal reflector and reflectors made of three different sound-absorbing materials (grass wool and polyurethane foam) were employed, and the reflector size was varied. Acoustic measurement is carried out to obtain the acoustic characteristics such as frequency, amplitude of screech tone and overall sound pressure level (OASPL). A high-quality schlieren optical system is used to visualize the detailed structure of supersonic jet. The results obtained show that the acoustic characteristics of supersonic jet noise are strongly dependent upon the jet pressure ratio and the reflector size. It is also found that the reflector with sound-absorbing material reduces the screech tone amplitude by about 5–13dB and the overall sound pressure levels by about 2–5dB, compared with those of the metal reflector.

An experimental and analytical study has been carried out to obtain the clear understanding of a shock wave transition associated with a steady two-dimensional overexpanded flow. Two-dimensional inviscid theory with respect to a shock wave reflection is used in the present study on the characteristic of shock waves. The results obtained from the flow analysis are compared with those obtained from flow visualizations. It is shown that in the region of regular reflection, the angle of an incident shock wave becomes lower than that calculated by two shock theory with an increment in the ratio p e/p b of the nozzle exit pressure p e to the back pressure p b. It is indicated that the configuration of shock waves in overexpanded jets is influenced by the divergent angle at the nozzle exit. Also it is shown from the flow visualization that a series of shock waves move into the nozzle inside with a decrease in pressure ratio p e/p b, even if the p e/p b is under overexpanded conditions.

The acoustic properties of supersonic jet noise from a convergent-divergent nozzle with a baffle have been studied experimentally over the range of nozzle pressure ratios from 2.0 to 8.0. Acoustic measurements were conducted in a carefully designed anechoic room providing a free-field environment. A new approach for screech noise suppression by a cross-wire is proposed. Schlieren photographs were taken to visualize the shock wave patterns in the supersonic jet with and without the cross-wire. The effects of the baffle and the cross-wire on acoustic properties are discussed. It is shown that the baffle has little effect on the screech frequency for the underexpanded supersonic jet without the cross-wire. Also, the cross-wire introduced in supersonic jets is found to lead to a significant reduction in overall sound pressure level.

Multiple shocklets are frequently generated in transonic diffuser flows. The present paper investigates the formation of these shocklets with a high-speed CCD camera combined with the schlieren method. It is observed that compression waves steepen while propagating upstream, and eventually become new shock waves. The ordinary shock wave is found to move upstream beyond the nozzle throat or to disappear while moving downstream depending on the pressure ratio across the nozzle. This phenomenon is also analyzed with the one-dimensional Euler equations by assuming a pressure disturbance given by the sine function at the channel exit. The calculated results are found to reproduce quite well the experimental behavior of the shocklets. The effect of the frequency of disturbance is also studied numerically, and it is shown that the multiple shocklet pattern appears when the amplitude of disturbance is not large and the diverging part of the channel downstream of the ordinary shock wave is long.

The choking of dual subsonic streams flowing through a convergent duct in contact has been investigated experimentally and theoretically. The experiment was conducted by using blow-down wind tunnel. The condition, when the dual stream flow choking (compound choking) occurs at the nozzle exit, was explained by one-dimensional analysis of compound sound wave propagation. The experimental results for the condition of compound choking were compared with the prediction from theoretical analysis, and the schlieren optical method using the spark light source has been used to visualize the flowfield.

The thermal choking phenomenon is of great importance in an inlet isolator in dual-mode ram jet/scramjet combustor. In some cases the choked flow creates a pseudo-shock wave including a shock train in it at the engine inlet and causes large amounts of drag and radically reduces the performance of the engine at high flight Mach numbers. The present paper describes a one-dimensional flow model taking account of the upstream boundary-layer as well as heat addition by using a mass-weighted averaging technique. The simple relationships for the flow field in a constant area duct in which the effect of the upstream boundary-layer is considered but the effect of the wall friction in the duct can be neglected are presented. The results of the calculation such as the maximum heat addition when the thermal choking occurs, the downstream Mach number and the static pressure ratio are presented and examined in detail.