Experimental exploration of underexpanded supersonic jets

Two underexpanded free jets at fully expanded Mach numbers $M_\mathrm{j}$ = 1.15 and 1.50 are studied. Schlieren visualizations as well as measurements of static pressure, Pitot pressure and velocity are performed. All these experimental techniques are associated to obtain an accurate picture of the jet flow development. In particular, expansion, compression and neutral zones have been identified in each shock cell. Particle lag is considered by integrating the equation of motion for particles in a fluid flow and it is found that the laser Doppler velocimetry is suitable for investigating shock-containing jets. Even downstream of the normal shock arising in the $M_\mathrm{j}$ = 1.50 jet, the measured gradual velocity decrease is shown to be relevant.     

Measurements on supersonic free jets

Summary An experimental study of round supersonic air jets discharging into quiescent air is described. The initial stagnation enthalpy of the jets was equal to that of the atmosphere. Most of the experiments concerned a fully expanded jet with initial Mach number M _I =1.74. From the experimental results the turbulent Prandtl number and the turbulent coefficient of momentum transfer could be calculated in a large part of the mixing zone of the jets. A mixing parameter K has been introduced and calculated for the jets. The results of this investigation are compared with those obtained for low-speed jets.     

Visual observations of supersonic transverse jets

We present experimental results on penetration of round sonic and supersonic jets normal to a supersonic cross flow. It is found that penetration is strongly dependent on momentum ratio, weakly dependent on free-stream Mach number, and practically independent of jet Mach number, pressure ratio, and density ratio. The overall scaling of penetration is not very different from that established for subsonic jets. The flow is very unsteady, with propagating pressure waves seen emanating from the orifice of helium jets.     

Investigation of supersonic isobaric submerged turbulent jets

Turbulent supersonic submerged air jets have been investigated on the Mach number interval M_a = 1.5–3.4 and on the interval of ratios of the total enthalpies in the external medium and the jet i₀ = 0.01 – 1. Oxyhydrogen jets with oxidizer ratios = 0.3–5 flowing from a nozzle at Mach numbers M_a = 1 and 2.4 have also been investigated. When < 1 the excess hydrogen in the jet burns up on mixing with the air. Special attention has been paid to obtaining experimental data free of the influence on the level of turbulence in the jet of the initial turbulence in the nozzle forechamber, shock waves occurring in the nozzle or in the jet at the nozzle exit, and the external acoustic field. The jet can be divided into two parts: an initial part and a main part. The initial part extends from the nozzle exit from the section x, in which the dimensionless velocity on the jet axis u_m = u_x/u_d = 0.75. Here, u_x is the velocity on the jet axis at distance x from the nozzle exit, and u_a is the nozzle exit velocity. The main part of the jet extends downstream from the section x. For the dimensionless length of the initial part x_m = x/d_a, where d_a is the diameter of the nozzle outlet section, empirical dependences on M_a and i₀ are obtained. It is shown, that in the main part of the jet the parameters on the flow axis — the dimensionless velocity and temperature — vary in inverse proportion to the distance, measured in units of length x, and do not depend on the flow characteristics which determine the length of the initial part of the jet. The angles of expansion of the viscous turbulent mixing layer in the submerged heated or burning jet increase with decrease in i₀ and M_a and are practically independent of the afterburning process.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza. No. 4, pp. 56–62, July–August, 1988.     

Experimental investigation of the role of instability waves in noise radiation by supersonic jets

Existing ideas of instability waves as the main dynamic noise sources in supersonic jets are tested for conformity with the data of acoustic measurements of this noise. Methodologically, the problem consists in the verification of the main principles of Tam’s theory of noise radiation by supersonic jets based on the ideology of instability waves in the shear layer of the jet and their key role in noise generation. Technologically, the study is based on a new technique for measuring the noise, namely, the azimuthal decomposition method developed by the authors. It is shown that on the Strouhal number range from 0.03 to 0.35 the theory satisfactorily describes the radiation pattern of the individual harmonics, while the initial amplitudes of the instability waves are in qualitative agreement with the assumption of their uniform distribution near the nozzle edge.     

Linear stability analysis of supersonic axisymmetric jets

Stabilities of supersonic jets are examined with different velocities, momentum thicknesses, and core temperatures. Amplification rates of instability waves at inlet are evaluated by linear stability theory (LST). It is found that increased velocity and core temperature would increase amplification rates substantially and such influence varies for different azimuthal wavenumbers. The most unstable modes in thin momentum thickness cases usually have higher frequencies and azimuthal wavenumbers. Mode switching is observed for low azimuthal wavenumbers, but it appears merely in high velocity cases. In addition, the results provided by linear parabolized stability equations show that the mean-flow divergence affects the spatial evolution of instability waves greatly. The most amplified instability waves globally are sometimes found to be different from that given by LST.     

Compressible spreading rates of supersonic coaxial jets

The compressible spreading rates of two supersonic coaxial jets were studied experimentally. The center jet had a fully-expanded Mach number of 3, and the outer jet of M = 1.8. The geometries of the center jet were circular and rectangular with two configurations, both with a 3∶1 aspect-ratio. The convective Mach numbers were varied in the range between 0.25 < M _c< 2.25. This was accomplished by varying the density ratio between the center jet and the coaxial jet, as well as the velocity ratio. The experimental compressible spreading rate was determined using Schlieren photography and total-pressure measurements. The spreading rate of the center circular jet decreased with increasing convective Mach number until it reached a constant value of 0.2 to 0.3 of the incompressible spreading rate for M _c>1.4. The rectangular jets exhibited a similar drop, at the same range of M _c, but their spreading rate was higher relative to the circular jet in the entire convective Mach number range.     

Generation of Mach waves by supersonic jets

Direct shadowgraphy is used to study the generation of Mach waves and jet noise in a wide range of frequencies by single supersonic jets and by groups of jets in the Mach number range M = 1–4.     

One-dimensional theory of off-design supersonic gas jets

A method based on the quasi-one-dimensional treatment of off-design supersonic jet flow is presented, together with the results of calculating the parameters of the jet on the interval of adaptation to the external conditions in the immediate vicinity of the nozzle exit section. On the jet formation interval the region of flow with strong discontinuities (shocks) is replaced by a surface of discontinuity. The mixing effect is taken into account by means of a concentrated mass flux in the section of discontinuity. It is shown that taking into account the real properties of the jet flow on the formation interval makes it possible considerably to improve the accuracy of a number of important flow parameters and to obtain a series of quantitative results that coincide with the experimental data.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 48–56, January–February, 1993.The author is grateful to E. A. Kapustin for his interest in the work and useful discussions.     

Structure of three-dimensional turbulent jets

The results are presented of an experimental investigation of the aerodynamics of three-dimensional turbulent jets in natural and artificially heightened conditions of turbulence. On the basis of measurements of mean and pulsation values, a study is made of the characteristics of the development of jets formed when an incompressible fluid issues from a rectangular nozzle and from an obliquely cut circular nozzle. The experimental results are generalized on the basis of the method of equivalent problems of the theory of thermal conductivity and of pulsation-energy balance.     

Self-excited oscillations in rarefied, impact supersonic jets

The effect of rarefaction on self-excited oscillations in impact supersonic jets (underexpanded jets interacting with a normally located, planar, bounded obstacle) is investigated. Amplitude-frequency characteristics of pressure fluctuations at the obstacle are obtained. Baltiisk State Engineering University, St.-Petersburg 198005. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 109–115, May–June, 1999.     

On the flow in underexpanded supersonic water jets

The problem of a supersonic water jet exhausting from a cylindrical nozzle in the underexpansion regime is solved. The calculations are made with allowance lor splitting. The distributions of the parameters over the jet are given. It is shown that the splitting region depends on the degree of underexpansion of the regime. The solution is found by the method of stabilization based on the difference scheme of Godunov, Zabrodin, and Prokopov [3] generalized to the case of flow with splitting.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 155–157, March–April, 1982.I thank G. A. Atanov for discussing the work.     

Oscillation flow induced by underwater supersonic gas jets

This paper describes an experimental study on the oscillation flow characteristics of submerged supersonic gas jets issued from Laval nozzles. The flow pattern during the jet development and the jet expansion feedback phenomenon are studied using a high-speed camera and a pressure measurement system. The experimental results indicate that along the downstream distance, the jet has three flow regimes: (1) momentum jet; (2) buoyant jet; (3) plume. In the region near the nozzle exit a so-called bulge phenomenon is found. Bulging of the jet occurs many times before the more violent jet expansion feedback occurs. During the feedback process, the jet diameter can become several times that of the original one depending on the jet Mach number. The frequencies of the jet bulging and the jet expansion feedback are measured.     

Numerical study of spatial supersonic flow of a perfect gas with transverse injection of jets

Three-dimensional supersonic turbulent flow in the presence of symmetric transverse injection of round jets through slots in the walls is studied numerically. The simulation is based on Favre averaged Navier-Stokes equations solved using the Beam-Warming method. The influence of the ratio of the pressure in the jet to that in the flow (pressure ratio) on the spatial interaction of the injected jet with the oncoming flow is studied. Experimental pressure distributions on the wall near the jet approximated by curvilinear closed ellipses are reproduced numerically. The mechanism of the formation of two symmetric vortices in the mixing layer between the jet and the oncoming flow is studied. The results of the calculations are found to be in satisfactory agreement with the experimental dependence of the length of the separation zone on the pressure ratio of the jet to the flow.