Shock structure in separated nozzle flows

In the case of high overexpansion, the exhaust jet of the supersonic nozzle of rocket engines separates from nozzle wall because of the large adverse pressure gradient. Correspondingly, to match the pressure of the separated flow region, an oblique shock is generated which evolves through the supersonic jet starting approximately at the separation point. This shock reflects on the nozzle axis with a Mach reflection. Thus, a peculiar Mach reflection takes place whose features depend on the upstream flow conditions, which are usually not uniform. The expected features of Mach reflection may become much difficult to predict, depending on the nozzle shape and the position of the separation point along the divergent section of the nozzle.      

Effect of Spherical Recesses on the Characteristics of Coanda Flow

Sub- and supersonic flows past curvilinear surfaces with spherical recesses are investigated. The Coanda flow was created by a jet flowing out from a plane convergent nozzle into a submerged space along the tangent to a circular cylinder. The forces exerted on the cylinder and the total and static pressure profiles in Coanda jet cross-sections were measured. It is shown that the spherical recesses increase the friction drag at both sub- and supersonic velocities.     

Supersonic flow separation in planar nozzles

We present experimental results on separation of supersonic flow inside a convergent–divergent (CD) nozzle. The study is motivated by the occurrence of mixing enhancement outside CD nozzles operated at low pressure ratio. A novel apparatus allows investigation of many nozzle geometries with large optical access and measurement of wall and centerline pressures. The nozzle area ratio ranged from 1.0 to 1.6 and the pressure ratio ranged from 1.2 to 1.8. At the low end of these ranges, the shock is nearly straight. As the area ratio and pressure ratio increase, the shock acquires two lambda feet. Towards the high end of the ranges, one lambda foot is consistently larger than the other and flow separation occurs asymmetrically. Downstream of the shock, flow accelerates to supersonic speed and then recompresses. The shock is unsteady, however, there is no evidence of resonant tones. The separation shear layer on the side of the large lambda foot exhibits intense instability that grows into large eddies near the nozzle exit. Time-resolved wall pressure measurements indicate that the shock oscillates in a piston-like manner and most of the energy of the oscillations is at low frequency.      

Experimental Investigation of Nozzle Exit Reflector Effect on Supersonic Jet

The present study describes an experimental work to investigate the effect of a nozzle exit reflector on a supersonic jet that is discharged from a convergent–divergent nozzle with a design Mach number of 2.0. An annular reflector is installed at the nozzle exit and its diameter is varied. A high-quality spark schlieren optical system is used to visualize detailed jet structures with and without the reflector. Impact pressure measurement using a pitot probe is also carried out to quantify the reflector’s effect on the supersonic jet which is in the range from an over-expanded to a moderately under-expanded state. The results obtained show that for over-expanded jets, the reflector substantially increases the jet spreading rate and reduces the supersonic length of the jet, compared with moderately under-expanded jets. The reflector’s effect appears more significant in imperfectly expanded jets that have strong shock cell structures, but is negligible in correctly expanded jet.     

Shock pattern in the plume of rocket nozzles: needs for design consideration

For ideal nozzles, basically two different types of shock structures in the plume may appear for overexpanded flow conditions, a regular shock reflection or a Mach reflection at the nozzle centreline. Especially for rocket propulsion, other nozzle types besides the ideal nozzles are often used, including simple conical, thrust-optimized or parabolic contoured nozzles. Depending on the contour type, another shock structure may appear: the so-called cap-shock pattern. The exact knowledge of the plume pattern is of importance for mastering the engine operation featuring uncontrolled flow separation inside the nozzle, appearing during engine start-up and shut-down operation. As consequence of uncontrolled flow separation, lateral loads may be induced. The side-load character strongly depends on the nozzle design, and is a key feature for the nozzle’s mechanical structure layout. It is shown especially for the VULCAIN and VULCAIN 2 nozzle, how specific shock patterns evolve during transients, and how - by the nozzle design - undesired flow phenomena can be avoided.     

Experimental study of boundary layer separation in truncated ideal contour nozzles

DLR Lampoldshausen carried out a cold flow test series to study the boundary layer separation and the related flow field in a truncated ideal contour nozzle. A special focus was set on low nozzle pressure ratios to identify the origin of a locally re-attached flow condition that was detected in previous test campaigns. A convex shaped Mach disc was found for nozzle pressure ratios less than 10 and a slight concave one for nozzle pressure ratios more than 20. Due to boundary layer transition at low nozzle pressure ratios the convex Mach disc is temporary tilted and redirects the flow towards the nozzle wall. A simple separation criterion for turbulent nozzle flows is presented that fits well for both cold and hot flows. It is shown that the oblique separation shock recompresses the flow to 90% of the ambience. The separation zone of the presented film cooled nozzle is compared with a conventional one around 40% longer. Furthermore a relation between shear layer shape and forced side loads is described.      

A procedure for the design of nozzles used for the production of turbulent liquid jets

Where turbulent liquid jets are used for cutting and mining purposes the pressure generated by impact must be maximized. Initial jet behaviour has an important influence on subsequent jet impact pressures at medium range. Nozzle wall boundary layer history has a strong influence on the initial jet, and certain boundary layer features can be linked to poor jet performance. The procedure outlined in this paper was developed to eliminate new nozzle designs or changes in operating conditions on the grounds of badly behaved nozzle boundary flow. The design procedure consists of a potential flow analysis and a boundary layer analysis coupled to empirical correlations for boundary layers in accelerated flows. The procedure is exemplified by application to the design of a nozzle to be used for the specific purpose of mining china clay.     

An experimental investigation of hypervelocity flow in a conical nozzle

The flow in a conical nozzle is examined experimentally for a range of hypervelocity conditions in a free-piston shock tunnel. The pitot pressure levels compare reasonably well with an inviscid numerical prediction which includes a correction for the growth of the nozzle wall boundary layer. The size of the nozzle wall boundary layer seems to be well predicted by semi-empirical expressions developed for perfect gas flows, as do data from other free-piston shock tunnels.     

On the possibility of blowing a gas jet into a supersonic flow without formation of a three-dimensional boundary-layer separation zone

We consider the flow formed by the interaction of a supersonic flow and a transverse sonic or supersonic jet blown at right angles to the direction of the main flow through a nozzle whose exit section is in a flat wall. When a gas jet is blown through a circular opening [1] the pressure rises in front of the jet because of the stagnation of the oncoming flow. This leads to separation of the boundary layer formed on the wall in front of the blowing nozzle. The resulting three-dimensional separation zone leads to a sharp increase in the pressure and the heat fluxes to the wall in front of the blowing nozzle, which is undesirable in many modern applications. The aim of the present investigation was to find a shape of the exit section of the blowing nozzle for which there is no three-dimensional separation zone of the boundary layer in front of the blowing nozzle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 162–165, May–June, 1979.     

The influence of sidewall cooling on boundary layer pressure fluctuations for a two-dimensional supersonic nozzle

Broadband root-mean-square (rms) values and frequency spectra for pressure fluctuations in the supersonic boundary layer on a Mach 3 DeLaval nozzle sidewall and in the freestream are reported for both adiabatic and cooled surface conditions. The flat sidewall of the nozzle contained four sections independently cooled by liquid nitrogen. During the experiments, the flat sidewall was operated (1) adiabatically, (2) cooled in an approximately uniform manner to ?40°C, and (3) cooled in a nonuniform manner. For all thermal boundary conditions on the sidewall, a dynamic pitot probe was traversed through the boundary layer and into the freestream to measure the broadband pressure fluctuations from 30 Hz to 100 kHz. The influence of sidewall cooling on the measured pressure fluctuations was dependent on the unit Reynolds number. Compared with the pressure fluctuations measured with an adiabatic sidewall, uniform cooling of the sidewall was found to reduce the rms pressure fluctuations in both the boundary layer and the freestream by approximately 50% at the highest stagnation pressures used (unit Reynolds numbers above 44,000/cm). Uniform cooling of the sidewall increased rms pressure fluctuations for lower stagnation pressures (unit Reynolds numbers below 44,000/cm). A reduction in the pressure fluctuation amplitude within the boundary layer resulted in a corresponding reduction in the pressure fluctuation amplitude in the test section freestream. Tests using a nonuniform temperature distribution on the sidewall indicated that cooling the portion of the sidewall covering the nozzle throat had the most influence on the pressure fluctuations in the boundary layer and in the freestream.     

A numerical investigation of side‐loads resulting from rigid body motions of an overexpanded engine nozzle

A numerical model for fluid–structure interactions is presented. Its purpose, within the context of 2D overexpanded engine nozzles, is to improve understanding of interactions between side‐loads and rigid body rotations, and more generally of the underlying physics between a shock in motion and nozzle movements. The model is based on three different solvers, for fluid, structure and mesh deformation respectively, which are linked to a coupling scheme in a parallel environment. In particular it is shown that the nozzle has a natural torsional frequency for which the measured side‐loads are the greatest. This phenomenon is associated with a transversal wave in the flow between the two internal walls of the nozzle. For free coupling cases, our calculations go some way to explain how the mechanical energy is dissipated with a transfer of energy to the shock that encounters the largest motions to dissipate it. It has also been observed that the compression shock may adopt a quasi‐steady state response with regard to nozzle rotations at low frequencies, whereas this will no longer be the case at higher frequencies, where a phase shift may occur between side‐loads and rotational position. This study is aimed at enhancing the only current aeroelastic stability model for overexpanded nozzles (AIAA, 29th Joint Propulsion Conference and Exhibit, Monterey, CA, 28–30 June 1993). Copyright © 2010 John Wiley & Sons, Ltd.     

TVD格式在超音速喷管三维粘性流动求解中的应用

详细给出了任意三维曲线坐标系中Ｎｏｖｉｅｒ－Ｓｔｏｋｅｓ方程的对流项ＴＶＤ格式的构造过程，建立了数值求解三维粘性流动的计算方法，应用该方法对三维超音速喷管中有激波及无激波情况下的两种工况的层流流场进行了数值求解，并与实验做了对比。结果表明本文建立的计算方法具有较高的精度，同时也证明ＴＶＤ格式具有分辩率高，稳定收敛等优点，为进一步开展叶栅流场及紊流的研究打下了基础。     

Relationship between vortex and sound in under‐expanded supersonic impinging jets

The study of an under‐expanded supersonic jet impinging on a flat plate by using large‐eddy simulation is reported. A third‐order upwind compact difference and a fourth‐order symmetric compact scheme are employed to discretize the nondimensional axisymmetric compressible Favre‐filtered Navier–Stokes equations in space, whereas the third‐order Runge–Kutta method with the total variation diminishing property is adopted to deal with the temporal discretization. The numerical simulation successfully captures the shock wave and vortex structures with different scales in the flow field. Waves with high and low frequencies traveling forward and reflecting back, and sound sources in different locations can be observed. By comparison with the frequency of the impinging tone from the experiment, it can be deduced that the change of pressure and swirling strength in the shear layer, pressure change on the impinging plate, and vortex merging in the jet shear layer are interdependent with the impinging tone. The effects of nozzle lip thickness on the impinging jet flow field have been investigated. The results show that the values of pressure fluctuation and vortex swirling strength in the shear layer near the nozzle have an extremum with the variation of the nozzle lip thickness. The results provide a theoretical foundation for the design of supersonic nozzles. Copyright © 2011 John Wiley & Sons, Ltd.     

Visualization and numerical simulation of supersonic microjets

Very narrow supersonic jets expanding from a small size convergent-divergent nozzle are visualized by the laser induced fluorescence method and simulated numerically using the piecewise linear method. Good agreement between the experiment and the numerical result is obtained in the jet structure, i.e. the shape of the barrel shock, the location of its reflection point on the axis, and the shape of the jet boundary.     

Two-dimensional numerical calculation of the flow field about a scoop inlet by the piecewise linear method

The piecewise linear method (PLM) based on time operator splitting is used to solve the unsteady compressible Euler equations describing the two-dimensional flow around and through a straight wall inlet placed stationary in a rapidly rotating supersonic flow. The PLM scheme is formulated as a Lagrangian step followed by an Eulerian remap. The inhomogeneous terms in the Euler equations written in cylindrical coordinates are first removed by Sod's method and the resulting set of equations is further reduced to two sets of one-dimensional Lagrangian equations, using time operator splitting. The numerically generated flow fields are presented for different values of the back pressure imposed at the downstream exit of the inlet nozzle. An oblique shock wave is formed in front of the almost whole portion of the inlet entrance, the incoming streamlines being deflected towards the higher pressure side after passing through the oblique shock wave and then bending down to the lower pressure side. A reverse flow appears inside the inlet nozzle owing to the recovery pressure of the incoming streams being lower than the back pressure of the inlet nozzle.     

Methodology of a combined ground based testing and numerical modelling analysis of supersonic combustion flow paths

In the framework of the European Commission co-funded LAPCAT (Long-Term Advanced Propulsion Concepts and Technologies) project, the methodology of a combined ground-based testing and numerical modelling analysis of supersonic combustion flow paths was established. The approach is based on free jet testing of complete supersonic combustion ramjet (scramjet) configurations consisting of intake, combustor and nozzle in the High Enthalpy Shock Tunnel Göttingen (HEG) of the German Aerospace Center (DLR) and computational fluid dynamics studies utilising the DLR TAU code. The capability of the established methodology is demonstrated by applying it to the flow path of the generic HyShot II scramjet flight experiment configuration.     

Hysteresis phenomena in a plane rotatable nozzle

The flow in a rotatable nozzle is calculated within the framework of the Reynolds equations and the Spalart-Allmaras turbulence model on the pressure difference range 1.1 < π < 5 for four configurations of the nozzle with the area ratio ε = 1.52 and two angles of the nozzle axis rotation. The flow structure is determined and the thrust characteristics and the angles of the thrust vector rotation are obtained. It was found that in the overexpansion regime the flows in plane symmetric and rotatable nozzles involve hysteresis phenomena due the Coanda effect and the interaction between the boundary layer and a shock generated within the nozzle on its supersonic walls. The hysteresis phenomena detected provide an up-to-4% divergence in the thrust coefficient for the same problem parameters. The results of the numerical modeling are compared with the experimental data and the results of calculations in accordance with Sekundov’s model.     

超音速冲击射流离散频率噪声的屏蔽抑制方法

根据导致超音速冲击射流离散频率噪声的反馈机理，提出了一种能够有效地破坏反馈环的形成，从而抑制超音速冲击射流离散频率噪声的喷嘴屏蔽方法。这种方法是通过阻隔反馈波使其不能到达喷嘴唇口从而破坏反馈环、同时屏蔽罩不与射流接触来实现降噪的目的的。本文介绍了这种方法的基本思想并提出了屏蔽罩的设计要点。实验结果表明，对于合适的屏蔽罩的参数，降噪效果达5分贝以上。应用LDV方法对超声速射流轴线速度进行了测量和比较，发现应用屏蔽降噪方法以后射流轴线速度显著增加，核心区长度增加50%左右。分析表明这种降噪方法对射流冲击障碍物的推力和除尘除水效率的提高有帮助。     

The compressible Coanda wall jet—an experimental study of jet structure and breakaway

An underexpanded jet issuing from a convergent slot and blowing over a surface of convex streamwise curvature was studied experimentally. The jet was confined between side walls, with the slot aspect ratio varying between 40 and 6, but tests showed that in the area of interest close to the slot the flow was effectively two-dimensional. The ratio of slot width to the radius of curvature of the downstream surface varied between 0.05 and 0.33. The main techniques used were Schlieren and shadowgraph to show the jet structure, and surface flow visualization which revealed areas of separation and reattachment. Surface static pressures were also measured on the curved surface. The curved jet proved to have a shock cell structure similar to that of a plane jet. However, the cell structure disappeared more rapidly as the outer shear layer grew more quickly due to the destabilizing effect of the curvature on the turbulence in the shear layer. Even at modest upstream jet pressures, a separated region on the Coanda surface became evident. This region was characterized by a stagnant constant pressure part followed by a region of strongly reversed flow before reattachment took place. The separation was caused by the compression at the end of the first shock cell, with reattachment taking place where expansion in the second cell started. The separated region grew rapidly as the upstream pressure was increased, until, finally, reattachment failed to occur and the jet suddenly broke away from the surface. This work is related to studies of the Coanda flare, where the jet is axisymmetric. The high level of turbulence causes rapid entrainment of air and so gives us clean combustion. However there should be more general application to devices that use the Coanda effect, varying from fluidic devices to blown jet flaps on wings.     

超音速气流粉碎喷嘴数值模拟

对气流粉碎装置的喷嘴结构和参数进行设计与优化,采用流体动力学软件对所设计喷嘴进行流场模拟,对所喷嘴效果进行检验。分别讨论了锥顶角和内腔造型对超音速喷嘴性能的影响,通过结果比较得出,入口压力3.5MPa、入口直径为6mm的喷嘴为设计的最佳喷嘴。超音速喷嘴锥顶角在8度到12度之间变化时,对喷嘴的性能影响不大,内腔造型为光滑曲面的超音速喷嘴性能最佳。