High Convective Mach Number Research Articles

1604 超音速平面ジェットにおける斜めモードの組み合せに対する遷移構造に及ぼす影響(S35-1 圧縮性流れの基礎と応用(1),S35 圧縮性流れの基礎と応用)

The three-dimensional time dependent compressible Navier-Stokes equations are numerically solved to study acoustic emission mechanism in a supersonic plane jet at high convective Mach numbers using high-order compact upwind schemes. Three cases for convective Mach number Mc=1.17 are presented. The fast case is the jet flow forced randomly. The second case is the jet forced by random disturbances and two pair of most unstable oblique modes with a subsonic phase speed. The third case is the jet forced by random disturbances, two pairs of most unstable oblique modes and a pair of subharmonic oblique modes. The numerical results provide new physical insights into three-dimensional structures and acoustic wave generation mechanisms in a plane turbulent jet. Upstream disturbance conditions play an important role for the evolution of the jet flow structures. The numerical results show that the jet meandering is suppressed in the jet forced by oblique modes. Therefore, the intense sound radiation observed in the randomly forced jet can be reduced by forcing with a pair of oblique modes.

Effects of Unstable Oblique Modes on the Acoustic Filed in a Supersonic Plane Turbulent Jet

The three-dimensional time dependent compressible Navier-Stokes equations are numerically solved to study acoustic emission mechanism in a supersonic plane jet at high convective Mach numbers using high-order compact upwind schemes. High-order compact schemes of 5th order developed by Deng and Maekawa (1996, 1997) (1)(2) are used for spatial derivatives and a 4th order Runge-Kutta scheme is employed for time advancement. Navier-Stokes characteristic boundary conditions are used in the streamwise and vertical directions and periodic boundary conditions in the spanwise direction. Two cases for convective Mach number Mc=1.17 are presented. The first case is the jet flow forced randomly. The second case is the jet forced by random disturbances and a pair of linear unstable oblique modes with a subsonic phase speed. The numerical results provide new physical insights into three-dimensional structures and acoustic wave generation mechanisms in a plane turbulent jet. Intense Mach waves radiating at low-frequencies are attributable to the growth of two-dimensional radiating mode with a supersonic phase speed in the jet shear layers. Upstream disturbance conditions play an important role for the evolution of the jet shear layers. The growth of a pair of oblique modes is responsible for the Λ structure in the jet shear layers, which yields sooner decay of the centerline velocity due to the shear layer rapid evolution. Therefore, the intense sound radiation observed in the randomly forced jet can be reduced by forcing with a pair of oblique modes.

908 超音速平面ジェットの音響場に対する斜めモードの影響(2)(OS9-2 高速流れと衝撃波現象の解明と制御,OS9高速流れと衝撃波現象の解明と制御)

The three-dimensional time dependent compressible Navier-Stokes equations are numerically solved to study acoustic emission mechanism in a supersonic plane jet at high convective Mach numbers using high-order compact upwind schemes. High-order compact schemes of 5th order are used for spatial derivatives and a 4th order Runge-Kutta scheme is employed for time advancement. Navier-Stokes characteristic boundary conditions are used in the streamwise and vertical directions and periodic boundary conditions in the spanwise direction. Two cases for convective Mach number Mc=1.17 are presented. The first case is the jet flow forced randomly. The second case is the jet forced by random disturbances and a pair of linear unstable oblique modes with a subsonic phase speed. The numerical results provide new physical insights into three-dimensional structures and acoustic wave generation mechanisms in a plane turbulent jet. Upstream disturbance conditions play an important role for the evolution of the jet shear layers. The growth of a pair of oblique modes is responsible for the Λ structure in the jet shear layers, which yields sooner decay of the centerline velocity due to the shear layer rapid evolution. Therefore, the intense sound radiation observed in the randomly forced jet can be reduced by forcing with a pair of oblique modes.

Effect of Rocket Exhaust Configurations on Ejector Performance in RBCC Engines

The results of a study of several rocket-based combined cycle engine ejector flowfield configurations, those using a single rocket located along the axisymmetric axis and those incorporating an additional annular rocket located along the outer wall of the ejector are detailed. Steady-state solutions of the axisymmetric Favre averaged Navier-Stokes equations closed by the Wilcox k-w turbulence model (including the Wilcox dilatational dissipation correction) are obtained using WARP, a finite difference flow solver using the Yee-Roe flux limiting scheme. It is shown that by having 75% of the rocket exhaust enter the ejector through the annular rocket a compression ratio of nearly 2.5 can be achieved for the case where both the air and rocket exhaust mass flows are equal. It is also shown that the effectively mixed area using this configuration extends over the outer 95% of the ejector exit area. A grid convergence analysis shows the resulting total pressure increase to be conservative by approximately 10%. In addition, WARP's ability to simulate mixed subsonic/supersonic shear layers accurately with high convective Mach numbers is demonstrated through comparison with experimental data.

Numerical simulations of underexpanded supersonic jet and free shear layer using WENO schemes

Numerical simulations of the flowfield structures and properties of underexpanded supersonic jet and planar shear layer are performed by solving the time-dependent, compressible Euler equations. The numerical code uses the high-order weighted essentially non-oscillatory (WENO) finite difference schemes with the fifth-order-accurate for spatial discretization and the fourth-order-accurate Runge–Kutta scheme for time integration. The present predictions are compared with the available experimental data and other numerical results using different numerical schemes. Good agreements between the predicted and experimental data are achieved for both cases. The results show that the near-field region of the jet and shear layer is influenced by compressibility, which reduces turbulent mixing rates and suppresses vortex roll-up and pairings at high-convective Mach number. Analyses of sound pressure level of the jet indicate that the broadband shock noise is generated from the shock cells and radiates in the direction of 40°–50° to the jet axis. Various forcing frequencies are applied at the inflow boundary to demonstrate mixing enhancement and shock cell destruction for the underexpanded jet. The computation of an underexpanded free shear layer indicates that the numerical turbulence model inherent with WENO algorithm can satisfactorily predict turbulence properties at a convective Mach number of 0.64 even without including subgrid-scale turbulence models.

SUPERSONIC PLANE JET AT HIGHT CONVECTIVE MACH NUMBER(Plane Jet)

The three-dimensional time dependent compressible Navier-Stokes equations are numerically solved to study acoustic emission mechanism in a supersonic plane jet at high convective Mach numbers using high-order compact upwind schemes. High-order compact schemes of 5th order developed by Deng and Maekawa (1996, 1997) [1] [2] are used for spatial derivatives and a 4th order Runge-Kutta scheme is employed for time advancement. Navier-Stokes characteristic boundary conditions are used in the streamwise and vertical directions and periodic boundary conditions in the spanwise direction. Numerical results for the convective Mach number Mc=1.17 are presented (Mc is denned by eq. (16) in Section 2). Two cases were investigated. The first case is the jet flow forced randomly. The second case is the jet forced by random disturbamces and linear unstable oblique modes. The numerical results provide new physical insights into three-dimensional structures and acoustic wave generation mechanisms in a plane turbulent jet. Upstream disturbance conditions play an important role for the evolution of the downstream structure, such as development of shear layers in a jet. Growth of the oblique mode is responsible for the A structure in a plane jet, which yields sooner decay of the centerline velocity. The result indicates that the jet forced with the oblique modes can mix faster with the surounding fluid medium than the jet forced randomly. The intense sound radiation observed in the randomly forced jet can be reduced by forcing with a pair of oblique modes.

Hypersonic Mixing Enhancement by Compression at a High Convective Mach Number

The effect of an oblique shock and of a Prandtl‐Meyer compression fan on the characteristics of the turbulent mixing of a square-cross-section hydrogen jet in hypervelocity air is presented. The air properties before the compression process are set to those found after the first shock of a two-shock external compression shcramjet inlet at a flight Mach number of 11 and an altitude of 34.5 km. The hydrogen properties are such that the convective Mach number is 1.2, the global equivalence ratio is 0.68, and the pressure of the hydrogen matches the pressure of the air at injection. Also presented is an algebraic expression approximating increase in mixing efficiency growth through compression. The algebraic expression is based on available empirical correlations for the turbulent mixing layer and is simplified for the special case of a high-convective-Mach-number mixing layer in which the Mach numbers of both streams are high. The numerical results are obtained by using the WARP code to solve the Favre-averaged Navier‐Stokes equations closed by the Wilcox kω turbulence model and the Wilcox dilatational dissipation correction, discretized by the Yee‐Roe flux-limited scheme. Results obtained indicate increase in the mixing efficiency growth by 5.7 and 6.3 times through the oblique shock and the compression fan, respectively. Despite generating weaker axial vortices, the compression fan results into a greater increase mixing efficiency growth because of a higher density increase.

Validation of the Wilcox k-omega Model for Flows Characteristic to Hypersonic Airbreathing Propulsion

Numerical results obtained with the WARP code solving the 1988 Wilcox k‐ω two-equation model are compared with experimental data of flowfields characteristic of hypersonic airbreathing propulsion. The problems chosen for the comparison include a shock/boundary-layer interaction case, a reacting and inert planar mixing case, and two ramp injector mixing cases. In addition, a comparison is performed with empirical correlations on the basis of skin friction for flow over a flat plate and shear layer growth for a free shear layer. The agreement between the numerical and experimental results varies between being reasonable and excellent, with a discrepancy generally not exceeding 20%. It is found that the grid-induced error can be reduced to an acceptable level for most problems with a reasonable mesh size. However, the free shear layer and the shock/boundary-layer interaction cases require a considerably finer mesh. The Wilcox dilatational dissipation correction is seen to be beneficial in predicting the growth of a free shear layer at a high convective Mach number, but its use is considered either questionable or detrimental for the other cases. A proper choice of the turbulent Schmidt number is observed to be crucial in predicting the injectant mole fraction contours for one of the ramp injector cases, with the best agreement obtained with Schmidt number Sct fixed to 0.25. For the inert planar mixing case, overall better agreement is obtained when setting both the turbulent Prandtl and Schmidt number to 0.5.

Impact of Axial Vortices on Mixing at a High Convective Mach Number

Impact of Axial Vortices on Mixing at a High Convective Mach Number

Computation of supersonic mixing layers

Direct numerical simulation is used to investigate three-dimensional temporal supersonic mixing layers at two convective Mach numbers 1.2 and 1.6. At the convective Mach number of 1.2, the compressibility effects, characterized by the shear layer growth rate reduction, are more pronounced than at high subsonic convective Mach numbers. In this case, the flow structure becomes three dimensional, and Λ structures are clearly observed which accelerate the occurrence of turbulence. For the Mc=1.2 case, the absence of symmetry leads to a strong interaction between Λ structures. At Mc=1.6, the use of a computational box size of one fundamental wavelength maintains the symmetry of the flow. The Λ structures, strongly inclined, are distorted by the shear layer and split into two symmetrical parts. Finally, shocklets occur in the flow for both convective Mach numbers. These viscous shocks are developed in three dimensions and are stronger for the 1.6 case. In this paper, transition mechanisms are analyzed and the existence of shocklets and their influences are studied.

Transverse Injection from Circular and Elliptic Nozzles into a Supersonic Crossflow

An investigation of sonictransverse injection from circular and elliptic nozzles into a supersoniccrosse ow using planar Rayleigh/Mie scattering is reported. Instantaneous images allow examination of the structural details, whereas ensemble-averaged images provide transverse penetration and lateral spread data for each jet. Standard deviation images produce information regarding the large-scale mixing/entrainment and reveal the mixing zones. Results show a highly three-dimensional near-e eld interaction dominated by shear-layer eddies and a counterrotating vortex pair. Ensemble-averaged results show that the elliptic jet spreads more rapidly in the lateral direction than the circular jet, cone rming that an axis-switching phenomenon is present. Near-e eld transverse penetration data collapse well with low-speed scaling conventions; however, the jet produced by the elliptic nozzle suffersa20%reductioninpenetrationcomparedto thecircularjet.Compressibilityleveldoesnotplaya signie cant roleintheaveragepenetrationorspreadofthesejets,althoughitstronglyaffectsthemixing/entrainmentandlargescale structure. Analysis of mixing potential from the standard deviation images indicates that the low and high convective Mach number Mc injection cases are signie cantly different; low Mc injection yields better large-scale mixing potential than high Mc injection regardless of the injector geometry.

Modelling of compressible flows with highly oscillating initial data by homogenization

We introduce a mathematical modelling of slightly compressible viscous flows with two well-separated space scales. We use as mean tool formal mathematical homogenization techniques. In the model derived, there appear closure terms, much as in usual physical turbulence models. Here, the closure terms are computed from the solution of a PDE system that governs the turbulent perturbation. This system is coupled to the mean flow PDE system. Starting from this model, we derive another of the k- ε family, including eddy diffusion terms. We solve this model by an explicit mixed finite volume-finite element technique with upwinding. We test it for a compressible steady mixing layer with different convective Mach numbers. The numerical results show a good qualitative prediction of the relevant mean quantities of the flow for moderately high convective Mach numbers. This is consistent with the theoretical foundations of the model.

Effect of Excitation on Supersonic Jet Afterburning

High-temperature Mach 2 jets that consisted of ethylene-oxygen combustion products diluted with nitrogen were used in an experimental study of supersonic jet excitation. Afterburning reaction was observed under certain conditions in which excess fuel was present, as a result of the fuel-rich gas mixing with fresh oxygen in the surrounding air. By fitting an adjustable-geometry cavity at the nozzle exit, the jets were passively excited at various frequencies via a flow-induced cavity resonance mechanism. Mie-scattering flow visualization and chemiluminescence measurements were used to measure the response of the excited jets under both afterburning and non-afterburning conditions. The effects on supersonic mixing and afterburning reaction were quantified in terms of changes in initial shear layer growth rate and chemiluminescence from the flames. Three cases having similar compressibility conditions but with different exit temperature and composition were investigated ; the shear-flow convective Mach numbers ranged between 1.3 and 1.4 for all cases while the exit temperature ranged between 1300 K and 1510 K. Mie-scattering images revealed that the excited shear layers in the near-jet region rolled up into organized large-scale structures, which are extraordinary at such a high convective Mach number. The dynamics of the large coherent structures was manipulated by varying the excitation frequencies. The results showed that flow excitation increased the initial shear layer growth rate by an amount that was sensitive to excitation frequency. For the present compressibility condition, the increase of as much as 50 % was observed when the frequency was at or near the jet preferred mode. However, the net effect on afterburning reaction was determined by a delicate balance between afterburning suppression due to large-scale cold-flow entrainment that caused quenching and afterburning enhancement which was a result of faster mixing. The results showed that global emission from the afterburning flames could be either reduced or increased from the natural state by as much as 80% depending on the excitation frequency and flow conditions. While the effect of excitation was strongest when the frequency was within the jet-preferred-mode bandwidth, the afterburning reaction in general appeared to be intensified at higher frequencies.

Computation of turbulent axisymmetric and nonaxisymmetric jet flows using the K-epsilon model

It is known that the standard K-e model does not provide an accurate prediction of the mean flow of turbulent jets. This is so even when the Pope and Sarkar correction terms are included. It is suggested that the K-e model, together with the Pope and Sarkar terms for nonplanar and high convective Mach number flow corrections, does contain the essential ingredients of turbulence physics for adequate jet mean flow prediction. The problem lies in the standard coefficients that were calibrated by using boundary-layer and low Mach number plane mixing layer data. By replacing these coefficients by a new set of empirical coefficients, it is demonstrated that the model can offer good predictions of axisymmetric, rectangular, and elliptic jet mean flows over the Mach number range of 0.4-2.0 and jet total temperature to ambient temperature ratio of 1.0-4.0. The present result conveys the message that it is possible that there is no universally applicable turbulence model. The reason is that although the characteristics and dynamics of fine-scale turbulence may be the same for all turbulent flows, the large turbulence structures, having dimensions comparable to the local length scale of the flow, are significantly influenced by local boundary conditions and geometry. Thus overall turbulence dynamics are somewhat problem type dependent.

Compressibility effects and mixing enhancement in turbulent free shear flows

Computational simulations have been performed to study compressible, spatially developing turbulent free shear layers with various velocity regimes—subsonic/subsonic, supersonic/subsonic, and supersonic/supersonic— for convective Mach numbers in the range of 0.14-1.28. The numerical code used the finite volume technique and a modified Godunov's scheme. The computed results for the supersonic/subsonic case are first compared with experimental axial mean-velocity profiles, vorticity thickness, and turbulence parameters. Mixing layers with various velocity regimes are then calculated to investigate compressibility effects on the evolution of large-scale structures through the flow visualization of the vorticity field, growth rate of the vorticity thickness, and vorticity dynamics analysis. Various forcing frequencies are applied at the inflow boundary to examine mixing enhancement for free shear layers with higher convective Mach numbers. It is found for the first time that the growth rate of supersonic/supersonic free shear layers increases markedly when the forced layers move up and down with time instead of forming vortex roll-up and pairing.

Mean and turbulent velocity measurements of supersonic mixing layers

The behavior of supersonic mixing layers under three conditions has been examined by schlieren photography and laser Doppler velocimetry. In the schlieren photographs, some largescale, repetitive patterns were observed within the mixing layer; however, these structures do not appear to dominate the mixing layer character under the present flow conditions. It was found that higher levels of secondary freestream turbulence did not increase the peak turbulence intensity observed within the mixing layer, but slightly increased the growth rate. Higher levels of freestream turbulence also reduced the axial distance required for development of the mean velocity. At higher convective Mach numbers, the mixing layer growth rate was found to be smaller than that of an incompressible mixing layer at the same velocity and freestream density ratio. The increase in convective Mach number also caused a decrease in the turbulence intensity (σ u /ΔU).

Assessment of total variation diminishing schemes in compressible mixing flow computations

Numerical simulations of temporally developing mixing layers using high-resolution total variation diminishing (TVD) schemes have been carried out to investigate the effects of grid resolution and inherent scheme dissipation on the solution quality. Owing to the sensitivity of the turbulence results to grid resolution, mixing flow computations generally require high grid density to resolve the shear-layer dynamics and to interpret the mean and turbulent flowfield interactions. Various limiters were tested in examining the numerical dissipation effect for which essentially nonoscillatory (ENO) solution is taken as a benchmark basis. The computations performed for scheme evaluation covered a broad spectrum including subsonic, transonic, and supersonic convective Mach numbers. Among the schemes considered, the performance of a minmod and van Leer limiters comply more consistently with the ENO results for a wide range of convective Mach numbers, whereas the superbee limiter, being the test TVD scheme for subsonic and low transonic Mach number flow, suffers from overcompression, which may lead to nonphysical solutions at high supersonic convective Mach numbers. The result obtained by each TVD scheme is sensitive to the design of the limiter. Dissipation introduced by the limiting procedure should be kept as minimal as possible, but a nonsmooth minimization should be avoided, because it may result in nonphysical overcompression, particularly for high convective Mach number flows.

Mean and turbulent velocity measurements of supersonic mixing layers

The behavior of supersonic mixing layers under three conditions has been examined by schlieren photography and laser Doppler velocimetry. In the schlieren photographs, some large-scale, repetitive patterns were observed within the mixing layer; however, these structures do not appear to dominate the mixing layer character under the present flow conditions. It was found that higher levels of secondary freestream turbulence did not increase the peak turbulence intensity observed within the mixing layer, but slightly increased the growth rate. Higher levels of freestream turbulence also reduced the axial distance required for development of the mean velocity. At higher convective Mach numbers, the mixing layer growth rate was found to be smaller than that of an incompressible mixing layer at the same velocity and freestream density ratio. The increase in convective Mach number also caused a decrease in the turbulence intensity (σu/ΔU).

The instability and acoustic wave modes of supersonic mixing layers inside a rectangular channel

At high supersonic convective Mach numbers the familiar Kelvin-Helmholtz instability of a thin unconfined two-dimensional shear layer becomes neutrally stable. In this paper, it is shown that when the same shear layer is put inside a rectangular channel the coupling between the motion of the shear layer and the acoustic modes of the channel produces new two-dimensional instability waves. The instability mechanism of these waves is examined. Extensive numerical computation of the properties of these new instability waves has been carried out. Based on these results two classes of these waves are identified. Some of the important characteristic features of these waves are reported in this paper. In addition to the unstable waves, a thorough analysis of the normal modes of a supersonic shear layer inside a rectangular channel reveals that there are basically two other families of neutral acoustic waves. Examples of some of the prominent characteristics of these neutral acoustic waves are also provided in this paper. The new instability waves are the dominant instabilities of a confined mixing layer at high supersonic convective Mach number. As such they are very relevant to the supersonic mixing and combustion processes inside a ramjet engine combustion chamber.

Structure of turbulent sonic underexpanded free jets

Turbulent mixing in adapted and weakly underexpanded (underexpansion ratios less than 1.4) round jets, involving fully developed pipe flows injected into still air, was studied experimentally. Measurements included mean and fluctuating concentrations and mean static pressures using laser-induced iodine flourescence and mean and fluctuating streamwise velocities using laser Doppler anemometry. Predictions were used to help interpret the measurements and to initiate evaluation of methods for analyzing these processes. The predictions were based on k-e turbulence models, including a proposed extension to treat compressibility effects at high convection Mach numbers. In conjunction with other measurements, the results show that the near-field region of underexpanded jets is influenced by compressibility, which tends to reduce turbulent mixing rates at high convective Mach numbers, and high turbulence levels at the jet exit, which tends to increase turbulent mixing rates. Predictions based on effective-ada pted-jet exit conditions yielded reasonably good estimates of mixing levels near the exit of underexpanded jets for both fully developed and slug flow jet exit conditions; however, such methods provide no information concerning the near-field region containing the shock waves. Predictions based on solution of parabolized Navier-Stokes governing equations, using the SCIPVIS algorithm, were encouraging for slug flow exit conditions, but this approach must be extended to treat fully developed flow at the jet exit.