Experimental evaluation of side-loads in LE-7A prototype engine nozzle

During development tests of the LE-7A prototype engine, severe side-loads were observed. The side-load peaks appeared only in certain limited conditions during start-up and shut-down transients. To investigate phenomena causing those severe side-loads observed in the LE-7A prototype engine nozzle, series of cold-flow tests and hot-firing tests as well as CFD analyses were conducted. As a result of the hot-firing tests, two different phenomena were found to cause severe side-loads in the LE-7A prototype engine nozzle. One was a restricted shock separation (RSS) flow structure and the other was a phenomenon termed “separation jump,” the rapid movement of the separation location in the vicinity of the step. A step was installed in the LE-7A prototype to supply film-cooling gas. Hot-firing test results showed that RSS can occur for a limited mixture ratio. Detailed flow structure of RSS on the nozzle surface was revealed by the cold-flow tests. Measured pressures and visualized images of cold-flow tests clarified the mechanism causing the separation jump. The key phenomenon ruling the separation jump was found to be the base flow behind the step. Based on the results of the present study, the latest LE-7A engine nozzle design has been changed to eliminate the severe side-load.

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Numerical confirmation of the hysteresis phenomenon in the regular to the Mach reflection transition in steady flows

Numerical calculations based on the Navier-Stokes equations are carried out to investigate the reflection of shock waves over straight reflecting surfaces in steady flows. The results for a flow Mach number of M₀=4.96 confirm the recent experimental findings of Chpoun et al. (1995) concerning the transition from regular to Mach reflection. Numerical calculations as well as experimental results show a hysteresis phenomenon during this transition and the regular reflection is found to be stable in the dual-solution domain in which theoretically both regular and Mach reflection wave configurations are possible.     

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.     

Changes in the type of the shock-wave structure in high-velocity flows

Physical aspects of nonuniqueness of shock-wave structures in supersonic and hypersonic flows are considered. Thermodynamic conditions determining the dual solution domains are analyzed, and the boundaries of the transition from Mach to regular reflection are examined.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 23–32, March–April, 2005.     

Shock unsteadiness in a thrust optimized parabolic nozzle

This paper discusses the nature of shock unsteadiness, in an overexpanded thrust optimized parabolic nozzle, prevalent in various flow separation modes experienced during start up and shut down sequences. The results are based on simultaneously acquired data from real-time wall pressure measurements using Kulite pressure transducers, high-speed schlieren (2 kHz) of the exhaust flow-field and from strain-gauges installed on the nozzle bending tube. Shock unsteadiness in the separation region is seen to increase significantly just before the onset of each flow transition, even during steady nozzle operation. The intensity of this measure (rms level) is seen to be strongly influenced by relative locations of normal and overexpansion shock, the decrease in radial size of re-circulation zone in the back-flow region, and finally, the local nozzle wall contour. During restricted shock separation, the pressure fluctuations in separation region exhibit periodic characteristics rather than the usually observed characteristics of intermittent separation. The possible physical mechanisms responsible for the generation of flow unsteadiness in various separation modes are discussed. The results are from an experimental study conducted in P6.2 cold-gas subscale test facility using a thrust optimized parabolic nozzle of area-ratio 30.

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On the RR→MR transition of asymmetric shock waves in steady flows

In this paper, RR→MR transition of asymmetric shock waves has been theoretically studied. The transition can occur between the sonic-point and maximum-deflection criteria due to the the effects of expansion fans which are inherent flow structures. Comparison shows a better agreement among experiments and the analytical results. Some discrepancies reported in previous studies among experiments and theory have also been explained based on the threshold for RR→MR transition.      

Advances in the study of separated flows

This paper consists of three parts. The first deals with the separation conditions for three dimensional steady viscous separated flows, in which the behaviour of separated flow described by Navier-Stokes equations and boundary layer equations is studied. The second part involves an application of differential topology to qualitative analysis of flow fields. Here the distribution rule of singular points on the separation line is studied. The last part discusses the numerical method solving Navier-Stokes equations for separated flows. The obtained computational results are analysed by the above mentioned theories and methods.     

Simulation of the Mach reflection in supersonic flows by the CE/SE method

This study employs the Space-Time Conservation Element and Solution Element (CE/SE) method to determine the influence of downstream flow conditions on Mach stem height. The results indicate that the Mach stem height depends on the incident shock wave angle and the distance between the trailing edge and the symmetry plane. Furthermore, it is shown that the downstream length ratio and the trailing edge angle do not affect the Mach stem height nor the Mach reflection (MR) configuration, and the Space-Time Conservation Element and Solution Element method is able to simulate the MR as well as many other numerical schemes. Communicated by K. Takayama PACS 47.40.Nm     

Experimental analysis of unsteady separated flows in a supersonic planar nozzle

The unsteady aspects of shock-induced-separation patterns have been investigated inside a Mach 2 planar nozzle. The mean location of the shock can vary by changing, relatively to the nozzle throat, the height of the second throat which is positioned downstream of the square test section. This study focuses on the wall pressure fluctuations spectra and the unsteady behaviour of the shock. Symmetric shock configurations appear both for the largest openings of the second throat, and for the smallest openings. For an intermediate opening the shock system exhibits asymmetrical configurations. A coating with roughnesses sticked on the throat part of the nozzle in order to modify the state of the incoming boundary layers (from smooth to rought turbulent statement) is a driver for the asymmetry. The fluctuating displacements of the shock patterns were analysed by using an ultra fast shadowgraph visualization technique. A spectral analysis of the unsteady wall pressure measurements has revealed low frequency phenomena governed by large structure dynamics in the separated flows. Communicated by K. Takayama PACS 02.60.Cb; 05.10.Ln; 47.11.+j; 47.15.Cb; 47.40.Nm     

Vortex structure of separated flows on model wings at low freestream velocities

Flow past model wings is experimentally investigated in a subsonic wind tunnel at large angles of attack at which the laminar boundary layer separates near the leading edge of the wing (flow stall). The object of the study was the flow structure within the separation zone. The carbon-oil visualization of surface streamlines used in the experiments showed that in the separation zone there exist one or more pairs of large-scale vortices rotating in the wing plane. Certain general properties of the vortex structures in the separation zone are found to exist, whereas the flow patterns may differ depending on the model aspect ratio, the yaw angle, and other factors.     

Wave disturbances in transonic separated flows

The results of an investigation of the nature and role of wave disturbances in transonic separated flows are presented. The effect of these disturbances on flow formation and stability, as well as on the characteristics of the pressure fluctuations and the time-average flow parameters, is considered.     

Numerical simulations of shock wave reflection phenomena in non-stationary flows using regularized smoothed particle hydrodynamics (RSPH)

In this paper we wish to demonstrate to what extent the numerical method regularized smoothed particle hydrodynamics (RSPH) is capable of modelling shocks and shock reflection patterns in a satisfactory manner. The use of SPH based methods to model shock wave problems has been relatively sparse, both due to historical reasons, as the method was originally developed for studies of astrophysical gas dynamics, but also due to the fact that boundary treatment in Lagrangian methods may be a difficult task. The boundary conditions have therefore been given special attention in this paper. Results presented for one quasi-stationary and three non-stationary flow tests reveal a high degree of similarity, when compared to published numerical and experimental data. The difference is found to be below 5, in the case where experimental data was found tabulated. The transition from regular reflection (RR) to Mach reflection (MR) and the opposite transition from MR to RR are studied. The results are found to be in close agreement with the results obtained from various empirical and semi-empirical formulas published in the literature. A convergence test shows a convergence rate slightly steeper than linear, comparable to what is found for other numerical methods when shocks are involved.     

Near-wall damping in model predictions of separated flows

Different near-wall scalings are reviewed by the use of data from direct numerical simulations (DNS) of attached and separated adverse pressure gradient turbulent boundary layers. The turbulent boundary layer equation is analysed in order to extend the validity of existing wall damping functions to turbulent boundary layers under severe adverse pressure gradients. A proposed near-wall scaling is based on local quantities and the wall distance, which makes it applicable for general computational fluid dynamics (CFD) methods. It was found to have a similar behaviour as the pressure-gradient corrected analytical y^* scaling and avoids the inconsistencies present in the y⁺ scaling. The performance of the model is illustrated by model computations using explicit algebraic Reynolds stress models with near-wall damping based on different scalings.     

Steady shock wave reflections in thermochemical nonequilibrium flows

The shock wave reflection phenomena in hypersonic steady air flows, including thermochemical nonequilibrium effects, are investigated. The main objectives are to study the influence of these effects on the two shock wave reflections (regular and Mach reflections), on the Mach stem height and on the hysteresis behavior. The air computations are performed using a multi-block MUSCL-TVD finite-volume scheme. The computational results with and without thermochemical effects in the air mixture flow at an upstream Mach number equal to 7 are compared. The comparison reveals a strong dependence of the transition angles, of the height and location of the Mach stem on the physical modeling of the gas flow. Received 17 February 2000 / Accepted 30 August 2000     

Shock and wave dynamics in cavitating compressible liquid flows in injection nozzles

Due to the exceptional high inlet pressures up to 2,000 bar flow dynamics and efficiency of modern injection systems are controlled by high frequency wave dynamics of the compressible liquid flow. Corresponding to alternating shock and expansion waves the liquid fluid evaporates and recondenses instantaneously. Here we present CFD simulations of the time accurate evolution of cavitating flows in 2-D plane and in six-hole injection nozzles with focus on the wave dynamics just after initialisation of the flow and within the time scale Δt ≤ 10^?4 s of pilot and multi-point injection. Due to shock reflections at the bottom of the sack hole the instantaneous maximum pressure increases more than three times higher as compared with the prescribed pressure at the nozzle inlet. For instance, in case of an inlet pressure of 600 bar the maximum pressure in the sack and therefore ahead of the nozzle bore holes reaches about 2,100 bar. It is quite reasonable that this amplification of the pressure affects the evolution of the convective flow and therefore the mass flow through the nozzle bore holes.     

Numerical simulation of Mach reflections

In this paper, the “FLIC” difference method with triangular mesh is adopted to numerically simulate the regular and Mach reflections that occur when a shock wave pass around a wedge. The compuational result is compared with the shock tube experimental results of G. Ben-Dor and I. I. Glass. The comparison shows that the position, shape of shock wave and height of Mach stem all show a good agreement. Consequently, the “FLIC” difference method with triangular mesh is quite satisfactory in numerical simulation of the regular and Mach reflections.     

Conical Mach reflection of moving shock waves, Part 2: Physical and CFD experimentation

Analytical consideration of Mach reflections over cones using the ray-shock theory showed that they differ from those of the two-dimensional Mach reflection over wedges. Conical configurations include both self-similar and non-self-similar cases. However, even when self-similar, the conical configurations exhibit triple-point locus trajectory angles with values which, for any given reflection angle, differ from those of self-similar, wedge cases. Additionally, within the range of possible conical configurations, different values of self-similar triple-point locus angles exist for any given reflection angle depending on the geometry of the particular reflection process. While the ray-shock theory, as discussed in a previous paper on this research, provides a useful guide and a means of readily identifying these variations, verification using both shock tube and numerical simulations is required and is now available. Results of experimentation for both self-similar and non-self-similar axisym metric cases using these techniques are reported here and comparisons are made with the previous analysis. These support the calculations of the ray-shock theory over much of the reflection angle, Mach number range as well as highlighting some limitations of the theory. Received 15 October 1996 / Accepted 14 April 1997     

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.      

Convergence properties of high-Reynolds-number separated flow calculations

The convergence properties of an iterative solution technique for the Reduced Navier–Stokes equations are examined for two-dimensional steady subsonic flow over bump and trough geometries. Techniques for decreasing the sensitivity to the initial pressure approximation, for fine meshes in particular, are investigated. They are shown to improve the robustness of the relaxation process and to decrease the computational work required to obtain a converged solution. A semi-coarsening multigrid technique that has previously been found to be particularly advantageous for high-Reynolds-number (Re) flows with flow separation and with highly stretched surface-normal grids is applied herein to further accelerate convergence. Solutions are obtained for the laminar flow over a trough that is more severe than has been considered to date. Sufficient axial grid refinement in this case leads to a shock-like reattachment and, for sufficiently large Re, to a local ‘divergence’ of the numerical computations. This ‘laminar flow breakdown’ appears to be related to an instability associated with high-frequency fine-grid modes that are not resolvable with the present modelling. This behaviour may be indicative of dynamic stall or of incipient transition. The breakdown or instability is shown to be controllable by suitable introduction of transition turbulence models or by laminar flow control, i.e. small amounts of wall suction. This lends further support to the hypothesis that the instability is of a physical rather than numerical character and suggests that full three-dimensional analysis is required to properly capture the flow behaviour. Another inference drawn from this investigation is that there is a need for careful grid refinement studies in high-Re flow computations, since coarser grids may yield oscillation-free solutions that cannot be obtained on finer grids.     

Massively separated flows due to transverse sonic jet in laminar hypersonic stream

A numerical simulation of flow interactions due to a transverse sonic jet ejected from a two-dimensional slot into a hypersonic stream is carried out to examine the capability of Navier–Stokes solutions in predicting a massively separated flow upstream of the jet exit. Grid sensitivity has been studied using gradually refined meshes to address the numerical accuracy of the discretised solution of the governing equations. Comparison has been made with published experimental data regarding the separation and reattachment points and the pressure distribution in the separated region. Flow field visualisation provides further insight into the interaction region and reveals a small clockwise vortex immediately ahead of the jet exit, which is found to be responsible for the second peak in the surface pressure distribution. Received 30 June 1998 / Accepted 27 September 1998