Local Solution of Three-Dimensional Axisymmetric Supersonic Flow in a Nozzle

In this paper, we construct a local supersonic flow in a 3-dimensional axis-symmetry nozzle when a uniform supersonic flow inserts the throat. We apply the local existence theory of boundary value problem for quasilinear hyperbolic system to solve this problem. The boundary value condition is set in particular to guarantee the character number condition. By this trick, the theory in quasilinear hyperbolic system can be employed to a large range of the boundary value problem.

CHAOTIC MOTIONS AND LIMIT CYCLE FLUTTER OF TWO-DIMENSIONAL WING IN SUPERSONIC FLOW

Based on the piston theory of supersonic flow and the energy method, the flutter motion equations of a two-dimensional wing with cubic stiffness in the pitching direction are established. The aeroelastic system contains both structural and aerodynamic nonlinearities. Hopf bifurcation theory is used to analyze the flutter speed of the system. The effects of system parameters on the flutter speed are studied. The 4th order Runge-Kutta method is used to calculate the stable limit cycle responses and chaotic motions of the aeroelastic system. Results show that the number and the stability of equilibrium points of the system vary with the increase of flow speed. Besides the simple limit cycle response of period 1, there are also period-doubling responses and chaotic motions in the flutter system. The route leading to chaos in the aeroelastic model used here is the period-doubling bifurcation. The chaotic motions in the system occur only when the flow speed is higher than the linear divergent speed and the initial condition is very small. Moreover, the flow speed regions in which the system behaves chaos axe very narrow.

Nonlinear aeroelastic analysis of a two-dimensional wing with control surface in supersonic flow

Based on the piston theory of supersonic flow and the energy method, a two dimensional wing with a control surface in supersonic flow is theoretically modeled, in which the cubic stiffness in the torsional direction of the control surface is considered. An approximate method of the cha- otic response analysis of the nonlinear aeroelastic system is studied, the main idea of which is that under the condi- tion of stable limit cycle flutter of the aeroelastic system, the vibrations in the plunging and pitching of the wing can approximately be considered to be simple harmonic excita- tion to the control surface. The motion of the control surface can approximately be modeled by a nonlinear oscillation of one-degree-of-freedom. The range of the chaotic response of the aeroelastic system is approximately determined by means of the chaotic response of the nonlinear oscillator. The rich dynamic behaviors of the control surface are represented as bifurcation diagrams, phase-plane portraits and PS diagrams. The theoretical analysis is verified by the numerical results.

Characteristics of supersonic flow in new type externally pressurized spherical air bearings

In order to predict accurately the characteristics of supersonic flow in new type externally pressurized spherical air bearings under large bearing clearance and high air supply pressure, which could decrease their load carrying capacity and stability, a CFD-based analysis was introduced to solve the three-dimensional turbulent complete compressible air flow governing equations. The realizable κ-ε model was used as a turbulent closure illustrate that the interaction exists between shock waves The supersonic flow field near air inlets was analyzed. The flow structures and boundary layer, and the flow separation is formed at the lower comer and the lower wall around the point of a maximum velocity. The numerical results show that the conversion from supersonic flow to subsonic flow in spherical air bearing occurs through a shock region （pseudo-shock）, and the viscous boundary layer results in the flow separation and reverse flow near the shock. The calculation results basically agree with the corresponding experimental data.

Numerical investigation of dynamical behavior of tethered rigid spheres in supersonic flow

The dynamical behavior of two tethered rigid spheres in a supersonic flow is numerically investigated. The tethered lengths and radius ratios of the two spheres are different. The two spheres, which are centroid axially aligned initially, are held stationary first, then released, and subsequently let fly freely in a supersonic flow. The mean qualities of the system and the qualities of the bigger sphere are considered and compared with the situations without the tether. In the separation process, six types of motion caused by the spheres, tether, and fluid interaction are found. The results show that the mean x-velocity of the system changes in a different manner for different radius ratios, and the x-velocity of the bigger sphere is uniformly reduced but through different mechanisms.

Numerical simulation of gap effect in supersonic flows

The gap effect is a key factor in the design of the heat sealing in super- sonic vehicles subjected to an aerodynamic heat load. Built on S-A turbulence model and Roe discrete format, the aerodynamic environment around a gap on the surface of a supersonic aircraft was simulated by the finite volume method. As the presented results indicate, the gap effect depends not only on the attack angle, but also on the Mach number.

Imaging of supersonic flow over a double elliptic surface

The coherent structures of flow over a double elliptic surface are experimentally investigated in a supersonic low- noise wind tunnel at Mach number 3 using nano-tracer planar laser scattering （NPLS） and particle image velocimetry （PIV） techniques. High spatiotemporal resolution images and velocity fields of both laminar and turbulent inflows over the test model are captured. Based on the time-correlation images, the spatial and temporal evolutionary characteristics of the coherent structures are investigated. The flow structures in the NPLS images are in good agreement with the velocity fluctuation fields by PIV. From statistically significant ensembles, spatial correlation analysis of both cases is performed to quantify the mean size and the orientation of coherent structures. The results indicate that the mean structure is elliptical in shape and the structural angles in the separated region of laminar inflow are slightly smaller than that of turbulent inflow. Moreover, the structural angles of both cases increase with their distance away from the wall.

Numerical Investigation of Particle Temperature Change in Supersonic Flows

Gas-particle two-phase flow is a very important consideration in designing various machines. Although a great deal of theoretical, experimental, and numerical research has been carried out, particle motion in a supersonic flow has not been sufficiently clarified. Hence, in order to clarify the interactions between flow and particles, the authors consider the characteristics of particle motion, especially at high temperatures. In the present study, the flow of a gas with a diluted particle load is to be simulated in a conventional converging-diverging supersonic nozzle. The turbulent gas flow in the nozzle is computed with the finite difference and RANS （raynolds averaged navier-stokes simulation） methods. The particle motion is simulated in a Lagrangian manner. In addition, taking into account the light particle loading, a weak coupling method is used. Through this investigation, it is shown that the particle velocity increases monotonically from the nozzle throat to the outlet. And it is shown that particles can be accelerated to higher velocities in helium than in nitrogen, and smaller particles tend to attain higher speed and lower static temperature.

Shock Wave Spectrum Forming around the Compound Five-Hole Probe and its Influence on Pneumatic Parameters Acquisition during Subsonic to Supersonic Flow

Supersonic wind tunnel experiment is one of the important measurements for developing advanced gas turbines,and supersonic multi-hole probes are sophisticated tools to measure pneumatic parameters in such experiments.However,shock waves form around the probe head in supersonic flow,which affect the accuracy of results.In this study,a supersonic five-hole probe is selected as the research object.Firstly,a compound five-hole pressure-temperature probe was designed and produced with 3D-printing technology.Then,the shock wave spectrum was numerically calculated by three methods,which were the Mach number,density gradient,and shock function;in contrast to the other two methods,the shock function could accurately identify the types and ranges of shock and expansion waves.The results show that a strong shock wave is formed at the front section of the probe head,and the shock wave generated around the pressure measuring tube affects the total pressure and Mach number of the flow field,which causes the increase of entropy.The intensity of the shock wave at the head of the pressure measuring tube is the largest,causing a decrease in the total pressure around the flow field.Aferwards,to reduce the calculation errors caused by neglecting the compressibility of gases and the entropy increase,a gas compression factor d,was introduced.It is proved that the error of the calculated pneumatic parameters is less than 5%and 10%in subsonic and supersonic condition,respectively,with the gas compression factor considered.The research results of this paper provide theoretical reference for the design and use of pneumatic probes during subsonic to supersonic flow.

NUMERICAL SIMULATION OF SUPERSONIC AXISYMMETRIC FLOW OVER MISSILE AFTERBODY WITH JET EXHAUST USING POSITIVE SCHEMES

Supersonic axisymmetric jet flow over a missile afterbody containing exhaust jet is simulated using the second order accurate positive schemes method developed for solving the axisymmetric Euler equations based on the 2-D conservation laws.Comparisons between the numerical results and the experimental measurements show excellent agreements.The computed results are in good agreement with the numerical solutions obtained by using third order accurate RKDG finite element method.The results show larger gradient at discontinuous points compared with those obtained by second order accurate TVD schemes.It indicates that the presented method is efficient and reliable for solving the axisymmetric jet with external freestream flows,and shows that the method captures shocks well without numerical noise.

Tracking characteristics of tracer particles for PIV measurements in supersonic flows

The tracking characteristics of tracer particles for particle image velocimetry（PIV） measurements in supersonic flows were investigated.The experimental tests were conducted at Mach number 4 in Multi-Mach Wind Tunnel（MMWT） of Shanghai Jiao Tong University.The motion of tracer particles carried by the supersonic flow across Shockwaves was theoretically modelled,and then their aerodynamic characteristics with compressibility and rarefaction effects were evaluated.According to the proposed selection criterion of tracer particles,the PIV measured results clearly identified that the Shockwave amplitude is in good agreement with theory and Schlieren visualizations.For the tracer particles in nanoscales,their effective aerodynamic sizes in the diagnostic zone can be faithfully estimated to characterize the tracking capability and dispersity performance based on their relaxation motion across oblique Shockwaves.On the other hand,the seeding system enabled the tracer particles well-controlled and repeatable dispersity against the storage and humidity.

Supersonic flow over a pitching delta wing using surface pressure measurements and numerical simulations

Experimental and numerical methods were applied to investigating high subsonic and supersonic flows over a 60°swept delta wing in fixed state and pitching oscillation. Static pressure coefficient distributions over the wing leeward surface and the hysteresis loops of pressure coefficient versus angle of attack at the sensor locations were obtained by wind tunnel tests. Similar results were obtained by numerical simulations which agreed well with the experiments. Flow structure around the wing was also demonstrated by the numerical simulation. Effects of Mach number and angle of attack on pressure distribution curves in static tests were investigated. Effects of various oscillation parameters including Mach number, mean angle of attack, pitching amplitude and frequency on hysteresis loops were investigated in dynamic tests and the associated physical mechanisms were discussed. Vortex breakdown phenomenon over the wing was identified at high angles of attack using the pressure coefficient curves and hysteresis loops, and its effects on the flow features were discussed.

Experimental investigations of detonation initiation by hot jets in supersonic premixed flows

A new method to initiate and sustain the detonation in supersonic flow is investigated. The reaction activity of coming flow may influence the result of detonation initiation. When a hot jet initiates a detonation wave successfully, there may exist two types of detonations. If the detonation velocity is greater than the velocity of coming flow, there will be a normal detonation here. Because of the influence of boundary layer separation, the upstream detonation velocity is much greater than the Chapman-Jouguet （C J） detonation velocity. On the other hand, if the detonation velocity is less than the velocity of coming flow, an oblique detonation wave （ODW） will form. The ODW needs a continuous hot jet to sustain itself. If the jet pressure is lower than a certain value, the ODW will decouple. In contrast, the normal detonation wave can sustain itself without the hot jet.

Instantaneous and time-averaged flow structures around a blunt double-cone with or without supersonic film cooling visualized via nano-tracer planar laser scattering

In a Mach 3.8 wind tunnel, both instantaneous and time-averaged flow structures of different scales around a blunt double-cone with or without supersonic film cooling were visualized via nano-tracer planar laser scattering （NPLS）, which has a high spatiotemporal resolution. Three experimental cases with different injection mass flux rates were carried out. Many typical flow structures were clearly shown, such as shock waves, expansion fans, shear layers, mixing layers, and turbulent boundary layers. The analysis of two NPLS images with an interval of 5 us revealed the temporal evolution characteristics of flow structures. With matched pressures, the laminar length of the mixing layer was longer than that in the case with a larger mass flux rate, but the full covered region was shorter. Structures like K-H （Kelvin-Helmholtz） vortices were clearly seen in both flows. Without injection, the flow was similar to the supersonic flow over a backward- facing step, and the structures were relatively simpler, and there was a longer laminar region. Large scale structures such as hairpin vortices were visualized. In addition, the results were compared in part with the schlieren images captured by others under similar conditions.

Detached-eddy simulation of supersonic flow past a spike-tipped blunt nose

Space vehicle in atmosphere travels mostly at supersonic speed and generates a very strong bow shockwave around its blunt nose. Oblique shock and conical separated flow zone generated by a forward disk-tip spike significantly reduce the drag by reducing the high pressure area on the blunt nose. This study employs improved delayed detached eddy simulation to investigate the characteristic flow structures around a spike-tipped blunt nose at Mach number of 3 and Reynolds number（based on the blunt-body diameter） of 2.72x10;. The calculated time-averaged quantities agree well with experimental data. Characteristic frequencies in different flow regions are extracted using fast Fourier transform. It is found that two distinct instability modes exist: oscillation mode and pulsation mode. The former is related to the foreshock/turbulence interaction with nondimensional frequency at around 0.004. The latter corresponds to the interaction between turbulence and shock structures around the blunt nose, with a typical coherent structure shedding frequency at 0.092.

NUMERICAL STUDIES ON THE MIXING OF CH_4 AND KEROSENE INJECTED INTO A SUPERSONIC FLOW WITH H_2 PILOT INJECTION

Two-fluid model and divisional computation techniques were used. The multispecies gas fully N-S equations were solved by upwind TVD scheme. Liquid phase equations were solved by NND scheme. The phases-interaction ODE equations were solved by 2nd Runge-Kutta approach. The favorable agreement is obtained between computational results and PLIF experimental results of iodized air injected into a supersonic flow. Then, the numerical studies,were carried out on the mixing of CH, and kerosene injected into a supersonic flow with H-2 pilot injection. The results indicate that the penetration of kerosene approaches maximum when it is injected from the second injector. But the kerosene is less diffused compared with the gas fuels. The free droplet region appears in the flow field. The mixing mechanism of CH4 with H-2 pilot injection is different from that of kerosene. In the staged duct, H-2 can be entrained into both recirculation zones produced by the step mid injectors. But CH, can only be carried into the recirculation between the injectors. Therefore, initiations of H, and CH4 carl occur in those regions. The staged duct is better in enhancing mixing and initiation with H-2 pilot flame.

Aero-Optical Characteristics of Supersonic Flow over Blunt Wedge with Cavity Window

The optical rays that form the image of an object and propagate a supersonic flow over a vehicle are refracted by the density variations.A numerical analysis of the aero-optical characteristics of supersonic flow over blunt wedge with a cavity window is carried out.A hybrid method of Reynold averaged Navier-Stokes and direct simulation Monte Carlo(RANS/DSMC) is employed to simulate the flowfield.Refraction factor is introduced to evaluate the flowfield's aero-optical characteristic.The results show that mean flow's aero-optical effects are mainly caused by the shock wave,the expansion wave and the turbulent boundary layer.Fluctuation flow's aero-optical effects are mainly caused by the turbulent boundary layer and the shock wave induced by the cavity window.The aero-optical effects at the leading side of window are caused by the mean density variations,while the effects at the trailing side are caused by the density fluctuations.Different draft angles of the cavity window are investigated.The airborne optical devices of supersonic vehicle should be mounted in the middle of the cavity window with a large draft angle.

FLOW PROPERTIES OF A DUSTY-GAS POINT SOURCE IN A SUPERSONIC FREE STREAM

By using Lagrangian method, the flow properties of a dusty-gas point source in a supersonic free stream were studied and the particle parameters in the near-symmetry-axis region were obtained . It is demonstrated that fairly inertial particles travel along oscillating and intersecting trajectories between the bow and termination shock waves . In this region, formation of ' mufti- layer structure' in panicle distribution with alternating low- and high density layers is revealed. Moreover, sharp accumulation of particles occurs near the envelopes of particle trajectories .

Ignition of Hydrocarbon-Air Supersonic Flow by Volumetric Ionization

The paper describes the results of the electron-beam initiation of the combustion in the mixtures of hydrogen,natural gas or kerosene vapors with air.Electron beam characteristics were studied in closed volume with immobile gas.The researches included definition of an integrated current of an electronic beam,distribution of a current density and an estimation of average energy of electrons.Possibility of fuel mixtures ignition by means of this approach in the combustor at high velocity at the entrance was demonstrated.Experiments were carried out at Mach numbers of 4 and 5.Process of ignition and combustion under electron beam action was researched.It was revealed that ignition of mixture occurs after completion of electron gun operation.Data obtained have confirmed effectiveness of electron beam application for ignition of hydrogen and natural gas.The numerical simulation of the combustion of mixture in channel was carried out by means of ANSYS CFD 12.0 instrumentation on the basis of Reynolds averaged Navier-Stokes equation using SST/k-ωturbulence model.For combustion modeling,a detailed kinetic scheme with 38 reactions of 8 species was implemented taking into account finite rate chemistry.Computations have shown that the developed model allow to predict ignition of a mixture and flame propagation even at low flow temperatures.

SUPERSONIC DUSTY-GAS FLOWS WITH KNUDSEN EFFECT IN INTERPHASE MOMENTUM EXCHANGE

On the basis of the two-continuum model of dilute gas-solid suspensions,the dynamic behavior of inertial particles in supersonic dusty-gas flows past a blunt body is studied for moderate Reynolds numbers,when the Knudsen effect in the interphase momentum exchange is significant. The limits of the inertial particle deposition regime in the space of governing parameters are found numerically under the assumption of the slip and free-molecule flow regimes around particles.As a model problem,the flow structure is obtained for a supersonic dusty-gas point-source flow colliding with a hypersonic flow of pure gas.The calculations performed using the full Lagrangian approach for the near-symmetry-axis region and the free-molecular flow regime around the particles reveal a multi-layer structure of the dispersed-phase density with a sharp accumulation of the particles in some thin regions between the bow and termination shock waves.