STUDY ON THE FUEL AIR MIXING INDUCED BY A SHOCK WAVE PROPAGATING INTO A H_2-AIR INTERFACE

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An experimental investigation of the sonic criterion for transition from regular to Mach reflection of weak shock waves

The signal speed, namely the local sound speed plus the flow velocity, behind the reflected shocks produced by the interaction of weak shock waves (M _i < 1.4) with rigid inclined surfaces has been measured for several shock strengths close to the point of transition from regular to Mach reflection. The signal speed was measured using piezo-electric transducers, and with a multiple schlieren system to photograph acoustic signals created by a spark discharge behind a small aperture in the reflecting surfaces. Both methods yielded results with equal values within experimental error. The theoretical signal speeds behind regularly reflected shocks were calculated using a non-stationary model, and these agreed with the measured results at large angles of incidence. As the angle of incidence was reduced, for the same incident shock Mach number, so as to approach the point of transition from regular to Mach reflection, the measured values of the signal speed deviated significantly from the theoretical predictions. It was found, within experimental uncertainty, that transition from regular to Mach reflection occurred at the experimentally observed sonic point, namely, when the signal speed was equal to the speed of the reflection point along the reflecting surface. This sonic condition did not coincide with the theoretical value.     

Characteristics of counter-rotating vortex rings formed ahead of a compressible vortex ring

Characteristics of high Mach number compressible vortex ring generated at the open end of a short driver section shock tube is studied experimentally using high-speed laser sheet-based flow visualization. The formation mechanism and the evolution of counter rotating vortex ring (CRVR) formed ahead of the primary vortex ring are studied in details for shock Mach number (M) 1.7, with different driver section lengths. It has been observed that the strength of the embedded shock, which appears at high M, increases with time due to the flow expansion in the generating jet. Strength of the embedded shock also varies with radius; it is strong at smaller radii and weak at larger radii; hence, it creates a velocity gradient ahead of the embedded shock. At critical Mach number (M _c ≥ 1.6), this shear layer rolls up and forms a counter rotating vortex ring due to Biot-Savart induction of the vortex sheet. For larger driver section lengths, the embedded shock and the resultant shear layer persists for a longer time, resulting in the formation of multiple CRVRs due to Kelvin–Helmholtz type instability of the vortex sheet. CRVRs roll over the periphery of the primary vortex ring; they move upstream due to their self-induced velocity and induced velocity imparted by primary ring, and interact with the trailing jet. Formation of these vortices depends strongly upon the embedded shock strength and the length of the generating jet. Primary ring diameter increases rapidly during the formation and the evolution of CRVR due to induced velocity imparted on the primary ring by CRVR. Induced velocity of CRVR also affects the translational velocity of the primary ring considerably.     

Effect of Partial Closure of the Channel on the Pressure Pulse in a Shock Wave Emerging from a Duct

The temporal-spatial development of the flow pattern behind a shock wave emerging from open-ended and half-closed ducts at M₀=1.15 to 3.0 Mach number is investigated both experimentally and numerically and the action of the diffracted wave on a barrier placed at different distances from the duct exit is studied. Flow toeplerograms are obtained and the pressure on the barrier is measured. The distinctive features of the interaction between the shock wave and a barrier mounted perpendicular to the duct axis are established. It is found that partial closing of the duct results in a decrease in the barrier pressure in the case of a strong shock (M₀ > 2.2) and leads to a pressure decrease when a weak shock is diffracted (M₀=1.1 to 1.7). A dependence characterizing the dynamic action of the shock wave on the barrier and specifying the threshold value of a combination of the shock Mach number and the distance from the barrier determining whether the pressure pulse on the barrier increases or decreases, is obtained.     

An analysis of unsteady highly turbulent swirling flow in a model vortex combustor

This paper reports an experimental investigation of a non-reacting turbulent swirling flow in a practical vortex combustor. The flow was examined for the conditions characteristic of the presence of a breakdown zone and a strong flow instability appearing at swirl numbers S>0.5. Flow visualization techniques, LDA measurements and acoustic probes were employed to study the unsteady flow characteristics. Based on the experimental results a positive first helical mode of instability was identified with a wavelength and frequency depending on swirl. The wavelength was confirmed to grow monotonically with S, while the dominant frequency of the flow pulsations was found to have an unusual parabolic evolution with swirl, with a minimum at S _min=0.88. This finding was interpreted using a proposed kinematic model based on the contribution of two mechanisms: rotation and axial motion of the helical vortex. It was concluded that for S<S _min the instability frequency is essentially dominated by the axial translation of the spiral vortex being inversely proportional to S and therefore giving a decreasing trend. For S>S _min the frequency of the flow precession is more dependent on the angular transportation of the vortex core, which resulted in the expected growing dependence on S.     

Mach reflection of a plane shock wave passing a mountain of 45° inclination

The transition from regular reflection (RR) to Mach reflection (MR) as a plane shock wave diffracts around a triangular mountain of 45° inclination is analysed in this paper, both by optical measurement in a shock tube and by numerical simulation the numerical method developed by Li Yingfan^[1] is of the FLIC type with triangular mesh. The dependence of the critical transition point Lk ofRR→MR on shock Mach numberM _i is analyzed and the variations of the incidence angle ω _i of the impinging shock and the reflection angle ω _r with the distanceL ^* are investigated. Our experimental and numerical results agree well with the theoretical results of Iton and Italya.     

TR-PIV measurement of the wake behind a grooved cylinder at low Reynolds number

A comparative study of the wakes behind cylinders with grooved and smooth surfaces was performed with a view to understand the wake characteristics associated with the adult Saguaro cacti. A low-speed recirculation water channel was established for the experiment; the Reynolds number, based on the free-stream velocity and cylinder diameter (D), was kept at Re_D=1500. State-of-the-art time-resolved particle image velocimetry (TR-PIV) was employed to measure a total of 20 480 realizations of the wake field at a frame rate of 250 Hz, enabling a comprehensive view of the time- and phase-averaged wake pattern. In comparison to the wake behind the smooth cylinder, the length of the recirculation zone behind the grooved cylinder was extended by nearly 18.2%, yet the longitudinal velocity fluctuation intensity was considerably weakened. A global view of the peaked spectrum of the longitudinal velocity component revealed that the intermediate region for the grooved cylinder, which approximately corresponds to the transition region where the shear layer vortices interact, merge and shed before the formation of the Karman-like vortex street, was much wider than that for the smooth one. The unsteady events near St=0.3-0.4 were detected in the intermediate region behind the grooved cylinder, but no such events were found in the smooth cylinder system. Although the formation of the Karman-like vortex street was delayed by about 0.6D downstream for the grooved cylinder, no prominent difference in the vortex street region was found in the far wake for both cylinders. The Proper Orthogonal Decomposition (POD) method was used extensively to decompose the vector and swirling strength fields, which gave a close-up view of the vortices in the near wake. The first two POD modes of the swirling strength clarified the spatio-temporal characteristics of the shear layer vortices behind the grooved cylinder. The small-scale vortices superimposed on the shear layers behind the grooved cylinder were found to be generated and convected downstream in the same phase, which would significantly reduce the fluctuating force on the cylinder surface.     

Nonlinear Strong Shock Interactions: A Shock-Fitted Approach

This paper addresses nonlinear effects which result from the interaction of shock waves with vortices. A series of experiments are carried out, which involve the interaction of a strong shock wave with a single plane vorticity wave and a randomly distributed wave system. These experiments are first conducted in the linear regime to obtain a mutual verification of theory and computation. They are subsequently extended into the nonlinear regime. A systematic study of the interaction of a plane shock wave and a single vortex is then conducted. Specifically, we investigate the conditions under which nonlinear effects become important, both as a function of shock Mach number, M ₁, and incident vortex strength (characterized by its circulation Γ). The shock Mach number is varied from 2 to 8, while the circulation of the vortex is varied from infinitesimally small values (linear theory) to unity. Budgets of vorticity, dilatation, and pressure are obtained. They indicate that nonlinear effects become more significant as both the shock Mach number and the circulation increase. For Mach numbers equal to 5 and above, the dilatation in the vortex core grows quadratically with circulation. An acoustic wave propagates radially outward from the vortex center. As circulation increases, its upstream-facing front steepens at low Mach numbers, and its downstream-facing front steepens at high Mach numbers. A high Mach number asymptotic expansion of the Rankine--Hugoniot conditions reveals that nonlinear effects dominate both the shock motion and the downstream flow for ΓM ₁ > 1. Received 28 June 1997 and accepted 25 November 1997     

Wave dynamic processes in cellular detonation reflection from wedges

When the cell width of the incident detonation wave (IDW) is comparable to or larger than the Mach stem height, self-similarity will fail during IDW reflection from a wedge surface. In this paper, the detonation reflection from wedges is investigated for the wave dynamic processes occurring in the wave front, including transverse shock motion and detonation cell variations behind the Mach stem. A detailed reaction model is implemented to simulate two-dimensional cellular detonations in stoichiometric mixtures of H ₂/O ₂ diluted by Argon. The numerical results show that the transverse waves, which cross the triple point trajectory of Mach reflection, travel along the Mach stem and reflect back from the wedge surface, control the size of the cells in the region swept by the Mach stem. It is the energy carried by these transverse waves that sustains the triple-wave-collision with a higher frequency within the over-driven Mach stem. In some cases, local wave dynamic processes and wave structures play a dominant role in determining the pattern of cellular record, leading to the fact that the cellular patterns after the Mach stem exhibit some peculiar modes. The English text was polished by Yumming Chen.     

On flows behind shock waves reflected from a solid wall

The flow fields associated with the interaction of a normal shock wave with a plane wall kept at a constant temperature were studied based on kinetic theory which can describe appropriately the shock structure and its reflection process. With the use of a difference scheme, the time developments of the distributions of the fluid dynamic quantities (velocity, temperature, pressure and number density of the gas) were obtained numerically from the BGK model of the Boltzmann equation subject to the condition of diffusive-reflection at the wall for several cases of incident Mach number:M ₁=1.2, 1.5, 2.0, 3.0, 4.0, 5.0 and 6.0. The reflection process of the shocks is shown explicitly together with the resulting formation of the flow fields as time goes on. The nonzero uniform velocity toward the wall occurring between the viscous boundary layer and the reflected shock wave is found to be fairly large, the magnitude of which is of the order of several percent of the velocity induced behind the incident shock, decreasing as the incident Mach number increases. It is also seen that a region of positive velocity (away from the wall) within the viscous boundary layer manifests itself in the immediate vicinity of the wall, which is distinct for larger incident Mach numbers. Some of the calculated density profiles are compared with available experimental data and also with numerical results based on the Navier-Stokes equations. The agreement between the three results is fairly good except in the region close to the wall, where the difference in the conditions of these studies and the inappropriateness of the Navier-Stokes equations manifest themselves greatly in the gas behavior.This article was processed using Springer-Verlag TEX Shock Waves macro package 1990.     

HLLE++格式在高马赫数空腔流动模拟中的应用

空腔流动存在剪切层运动、涡脱落与破裂,以及激波与激波、激波与剪切层、激波与膨胀波和激波/涡/剪切层相互干扰等现象,流动非常复杂,特别是高马赫数(M>2)时,剪切层和激波更强,激波与激波干扰更严重,对数值格式的要求更高,既需要格式耗散小,对分离涡等有很高的模拟精度,又需要格式在激波附近具有较大的耗散,可以很好地捕捉激波,防止非物理解的出现。Roe和HLLC等近似Riemann解格式在高马赫数强激波处可能会出现红玉现象,而HLLE++格式大大改善了这种缺陷,在捕捉高超声速激波时避免了红玉现象的发生,同时还保持在光滑区域的低数值耗散特性。本文在结构网格下HLLE++格式的基础上,通过改进激波探测的求解,建立了基于非结构混合网格的HLLE++计算方法,通过无粘斜坡算例,验证了HLLE++格式模拟高马赫数流动的能力,并应用于高马赫数空腔流动的数值模拟,开展了网格和湍流模型影响研究,验证了方法模拟高马赫数空腔流动的可靠性和有效性。     

The formation of a secondary shock wave behind a shock wave diffracting at a convex corner

This paper deals with the formation of a secondary shock wave behind the shock wave diffracting at a two-dimensional convex corner for incident shock Mach numbers ranging from 1.03 to 1.74 in air. Experiments were carried out using a 60 mm 150 mm shock tube equipped with holographic interferometry. The threshold incident shock wave Mach number () at which a secondary shock wave appeared was found to be = 1.32 at an 81° corner and = 1.33 at a 120° corner. These secondary shock waves are formed due to the existence of a locally supersonic flow behind the diffracting shock wave. Behind the diffracting shock wave, the subsonic flow is accelerated and eventually becomes locally supersonic. A simple unsteady flow analysis revealed that for gases with specific heats ratio the threshold shock wave Mach number was = 1.346. When the value of is less than this, the vortex is formed at the corner without any discontinuous waves accompanying above the slip line. The viscosity was found to be less effective on the threshold of the secondary shock wave, although it attenuated the pressure jump at the secondary shock wave. This is well understood by the consideration of the effect of the wall friction in one-dimensional duct flows. In order to interpret the experimental results a numerical simulation using a shock adaptive unstructured grid Eulerian solver was also carried out. Received 1 May 1996 / Accepted 12 September 1996     

可压缩流向涡与激波轴对称干扰的数值模拟

用ＮＳ方程数值模拟了可压缩流向涡和激波轴对称相互作用现象．数值模拟包括定常和非定常两种情况,计算结果分别与相应的实验进行了比较．结果表明数值模拟成功地捕捉到了激波和旋涡相互作用过程中发生的激波波面变形,激波振荡,涡核变大以及激波波后出现驻点、回流区等流场特征．提出了判断流向涡与运动激波相互作用中旋涡破碎的准则     

Experimental investigations of a swirling jet in both stationary and rotating surroundings

The ‘plug’ flow emerging from a long rotating tube into a large stationary reservoir was used in the experimental investigation of swirling jets with Reynolds numbers, Re = 600, 1,000 and 2,000, and swirl numbers, S = ΩR/U, in the range 0–1.1, to cover flow regimes from the non-rotating jet to vortex breakdown. Here Ω is the nozzle rotation rate, R is the radius of the nozzle exit, and U is the mean mass axial velocity. The jet was more turbulent and eddies shed faster at larger Re. However the flow criticality and shear layer morphology remained unchanged with Re. After the introduction of sufficient rotation, co-rotating and counter-winding helical waves replaced vortex rings to become the dominant vortex structure. The winding direction of the vortex lines suggests that Kelvin–Helmholtz and generalized centrifugal instability dominated the shear layer. A quantitative visualization study has been carried out for cases where the reservoir was rotating independently with S _a  = Ω _a R/U = ±0.35, ±0.51 and ±0.70 at Re = 1,000 and 2000, where Ω _a is the rotation rate of the reservoir. The criterion for breakdown was found to be mainly dependent on the absolute swirl number of the jet, S. This critical swirl number was slightly different in stationary and counter-swirl surroundings but obviously smaller when the reservoir co-rotated, i.e. S _c  = 0.88, 0.85 and 0.70, respectively. These results suggest that the flow criticality depends mainly on the velocity distributions of the vortex core, while instabilities resulting from the swirl difference between the jet and its ambient seem to have only a secondary effect.     

Experimental study of the shock–bubble interaction with reshock

The interaction of a planar shock wave with a spherical density inhomogeneity is studied experimentally under reshock conditions. Reshock occurs when the incident shock wave, which has already accelerated the spherical bubble, reflects off the tube end wall and reaccelerates the inhomogeneity for a second time. These experiments are performed at the Wisconsin Shock Tube Laboratory, in a 9m-long vertical shock tube with a large square cross section (25.4×25.4 cm²). The bubble is prepared on a pneumatically retracted injector and released into a state of free fall. Planar diagnostic methods are used to study the bubble morphology after reshock. Data are presented for experiments involving two Atwood numbers (A = 0.17 and 0.68) and three Mach numbers (1.35 < M < 2.33). For the low Atwood number case, a secondary vortex ring appears immediately after reshock which is not observed for the larger Atwood number. The post-reshock vortex velocity is shown to be proportional to the incident Mach number, M, the initial Atwood number, A, and the incident shock wave speed, W _i.     

Normal shock interaction with a yawed wedge moving at supersonic speed

In this article, the interaction of a normal shock with a yawed wedge moving at supersonic speed has been considered. The vorticity distribution of a particle over the diffracted shock wave for various combinations of yawed angles, Mach number of the shock wave and Mach number of the moving wedge have been obtained. Further triple point angle χ in Mach reflection has been calculated for the various parameters.      

Flow visualization of supersonic laminar flow over a backward-facing step via NPLS

An experimental study on a supersonic laminar flow over a backward-facing step of 5 mm height was undertaken in a low-noise indraft wind tunnel. To investigate the fine structures of Ma = 3.0 and 3.8 laminar flow over a backward-facing step, nanotracer planar laser scattering was adopted for flow visualization. Flow structures, including supersonic laminar boundary layer, separation, reattachment, redeveloping turbulent boundary layer, expansion wave fan and reattachment shock, were revealed in the transient flow fields. In the Ma = 3.0 BFS (backward-facing step) flow, by measuring four typical regions, it could be found that the emergence of weak shock waves was related to the K–H (Kelvin–Helmholtz) vortex which appeared in the free shear layer and that the convergence of these waves into a reattachment shock was distinct. Based on large numbers of measurements, the structure of time-averaging flow field could be gained. Reattachment occurred at the location downstream from the step, about 7–7.5 h distance. After reattachment, the recovery boundary layer developed into turbulence quickly and its thickness increased at an angle of 4.6°. At the location of X = 14h, the redeveloping boundary layer was about ten times thicker than its original thickness, but it still had not changed into fully developed turbulence. However, in the Ma = 3.8 flow, the emergence of weak shock waves could be seen seldom, due to the decrease of expansion. The reattachment point was thought to be near X = 15h according to the averaging result. The reattachment shock was not legible, which meant the expansion and compression effects were not intensive.     

Three-dimensional numerical simulation of detonations in coaxial tubes

Three-dimensional numerical simulation of detonations in both a circular tube and a coaxial tube are simulated to reveal characteristics of single spinning and two-headed detonations. The numerical results show a feature of a single spinning detonation which was discovered in 1926. Transverse detonations are observed in both tubes, however, the single spinning mode maintains the complex Mach reflection whereas the two-headed mode develops periodically from the single Mach reflection to the complex one. The calculated cell aspect ratio for the two-headed mode changes from 1.09 to 1.34 as the radius of axial insert increases from r ₁/R = 0.1 to 0.9. The calculated cell aspect ratio for r ₁/R = 0.1 is close to the experimental results without an axial insert. The formation of an unreacted gas pocket behind the detonation front was not observed in the single spinning mode; however, the two-headed mode has unreacted gas pocket behind the front near the axial insert.      

Formation and evolution of vortex rings induced by interactions between shock waves and a low-density bubble

The deformation and instability of a low-density spherical bubble induced by an incident and its reflected shock waves are studied by using the large eddy simulation method. The computational model is firstly validated by experimental results from the literature and is further used to examine the effect of incident shock wave strength on the formations and three-dimensional evolutions of the vortex rings. For the weak shock wave case (Ma?=?1.24), the baroclinic effect induced by the reflected shock wave is the key mechanism for the formation of new vortex rings. The vortex rings not only move due to the self-induced effect and the flow field velocity, but also generate azimuthal instability due to the pressure disturbance. For the strong shock wave case (Ma?=?2.2), a boundary layer is formed adjacent to the end wall owing to the approach of vortex ring, and unsteady separation of the boundary layer near the wall results in the ejection and formation of new vortex rings. These vortex rings interact in the vicinity of the end wall and finally collapse to a complicated vortex structure via azimuthal instability. For both shock wave strength cases, the evolutions of vortex rings due to the instability lead to the formation of the complicated structure dominated by the small-scale streamwise vortices.     

A numerical study of oblique shock wave reflections over wedges in an ideal quantum gas

The various oblique shock wave reflection patterns generated by a moving incident shock on a planar wedge using an ideal quantum gas model are numerically studied using a novel high resolution quantum kinetic flux splitting scheme. With different incident shock Mach numbers and wedge angles as flow parameters, four different types of reflection patterns, namely, the regular reflection, simple Mach reflection, complex Mach reflection and the double Mach reflection as in the classical gas can be classified and observed. Both Bose–Einstein and Fermi–Dirac gases are considered.