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.

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.

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.

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.

Mode transition and oscillation suppression in supersonic cavity flow

Supersonic flows past two-dimensional cavities with/without control are investigated by the direct numerical simulation （DNS）. For an uncontrolled cavity, as the thickness of the boundary layer declines, transition of the dominant mode from the steady mode to the Rossiter Ⅱ mode and then to the Rossiter III mode is observed due to the change of vortex-corner interactions. Meanwhile, a low frequency mode appears. However, the wake mode observed in a subsonic cavity flow is absent in the current simulation. The oscillation frequencies obtained from a global dynamic mode decomposition （DMD） approach are consistent with the local power spectral density （PSD） analysis. The dominant mode transition is clearly shown by the dynamic modes obtained from the DMD. A passive control technique of substituting the cavity trailing edge with a quarter-circle is studied. As the effective cavity length increases, the dominant mode transition from the Rossiter Ⅱ mode to the Rossiter Ⅲ mode occurs. With the control, the pressure oscillations are reduced significantly. The interaction of the shear layer and the recirculation zone is greatly weakened, combined with weaker shear layer instability, responsible for the suppression of pressure oscillations. Moreover, active control using steady subsonic mass injection upstream of a cavity leading edge can stabilize the flow.

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.

An efficient unstructured WENO method for supersonic reactive flows

An efficient high-order numerical method for supersonic reactive flows is proposed in this article.The reactive source term and convection term are solved separately by splitting scheme.In the reaction step,an adaptive time-step method is presented,which can improve the efficiency greatly.In the convection step,a third-order accurate weighted essentially non-oscillatory（WENO）method is adopted to reconstruct the solution in the unstructured grids.Numerical results show that our new method can capture the correct propagation speed of the detonation wave exactly even in coarse grids,while high order accuracy can be achieved in the smooth region.In addition,the proposed adaptive splitting method can reduce the computational cost greatly compared with the traditional splitting method.

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.

Model reduction for supersonic cavity flow using proper orthogonal decomposition(POD)and Galerkin projection

The reduced-order model （ROM） for the two-dimensional supersonic cavity flow based on proper orthogonal decomposition （POD） and Galerkin projection is investigated. Presently, popular ROMs in cavity flows are based on an isentropic assumption, valid only for flows at low or moderate Mach numbers. A new ROM is constructed involving primitive variables of the fully compressible Navier-Stokes （N-S） equations, which is suitable for flows at high Mach numbers. Compared with the direct numerical simulation （DNS） results, the proposed model predicts flow dynamics （e.g., dominant frequency and amplitude） accurately for supersonic cavity flows, and is robust. The comparison between the present transient flow fields and those of the DNS shows that the proposed ROM can capture self-sustained oscillations of a shear layer. In addition, the present model reduction method can be easily extended to other supersonic flows.

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.

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.

Velocity Slip and Interfacial Momentum Transfer in the Transient Section of Supersonic Gas-Droplet Two-Phase Flows

Modelling and simulations are conducted on velocity slip and interfacial momentum transfer for supersonic two-pha.se (gas-droplet) flow in the transient section inside and outside a Laval jet(LJ). The initial velocity slip between gas and droplets causes an interfacial momentum transfer flux as high as (2.0-5.0) x 104 Pa. The relaxation time corresponding to this transient process is in the range of 0.015-0.090ms for the two-phase flow formed inside the LJ and less than 0.5ms outside the LJ. It demonstrates the unique performance of this system for application to fast chemical reactions using electrically active media with a lifetime in the order of 1 ms. Through the simulations of the transient processes with initial Mach number Mg from 2.783 to 4.194 at different axial positions inside the LJ, it is found that Mg has the strongest effect on the process. The momentum flux increases as the Mach number decreases. Due to compression by the shock wave at the end of the LJ, the flow pattern becomes two dimensional and viscous outside the LJ. Laser Doppler velocirneter (LDV) measurements of droplet velocities outside the LJ are in reasonably good agreement with the results of the simulation.

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 .

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.

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.

Thermoelastic Stability of Closed Cylindrical Shell in Supersonic Gas Flow

In a linear framework,the problem of stability of closed cylindrical shell is briefly discussed.The cylindrical shell is immersed in a supersonic gas flow and under the influence of temperature field varying along the thickness.An unperturbed uniform velocity flow field,directed along the short edges of the shell,is applied.Due to the inhomogeneity of the temperature field distribution across the thickness shell buckling instability occurs.This instability accounts for the deformed shape of the shell,to be referred as the unperturbed state.Stability conditions and boundary for the unperturbed state of the system under consideration are presented following the basic theory of aero-thermo-elasticity.The stability boundary depends on the variables characterizing the flow speed,the temperature at the middle plane of the shell and the temperature gradient in the direction normal to that plane.It is shown that the combined effect of the temperature field and flowing stream regulates the process of stability,and the temperature field can significantly change the flutter critical speed.

Flow Characteristics of Two-Dimensional Supersonic Under-Expanded Coanda-Reattached Jet

When there is a wall near the jet, it deflects and flows while being attached to the wall owing to the Coanda effect. The flow characteristics of the incompressible and two-imensional (2D) Coanda-reattached jets have been considerably explained. However, 2D supersonic under-expanded jets, reattached to side walls, have not been sufficiently investigated. These jets are used in gas-atomization to produce fine metal powder particles of several micrometers to several tens micrometers. In this case, the supersonic under-expanded jets are issued from an annular nozzle, which is set around a vertically installed circular nozzle for molten metal. The jet flow at the center cross-section of the annular jet resembles a 2D Coanda-reattached jet that deflects and attaches on the central axis. In this study, the flow characteristics of a supersonic under-expanded Coanda air jet from a 2D nozzle that reattaches to an offset side wall are elucidated through experiment and numerical analysis. For numerical analysis, we show how much it can express experimental results. The effects of supply pressure P0 on the flow characteristics such as the flow pattern, size of shock cell, reattachment distance, and velocity and pressure distributions, etc. are examined. The flow pattern was visualized by Schlieren method and the velocity distribution was measured using a Pitot tube. These results will be also useful in understanding the flow characteristics of a gas-atomization annular nozzle approximately.

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.