Viscous simulation of shock reflection hysteresis in ideal and tapered overexpanded planar nozzles

While a CFD simulation of the flow in overexpanded planar nozzles shows, inside an ideal nozzle, the existence of a hysteresis process in the transition from regular to Mach and from Mach to regular reflections such a process does not appear in tapered nozzles. Previous simulations have dealt only with the flow outside the nozzle and thus concluded that the hysteresis phenomenon takes place outside the nozzle even when viscous effects were introduced. When including the geometry of the nozzle in the simulation it becomes evident that flow separation will occur before transition from regular to Mach reflection for all relevant flow Mach numbers. The simulation reveals complex changes in the flow structure as the ratio between the ambient and the stagnation pressures is increased and decreased. The pressure along the nozzle wall downstream of the separation point was found to be less than the ambient pressure with the effect being more pronounced in the case of the ideal nozzle. The present study complements a previous study that dealt only with flow separation in an ideal nozzle.     

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.      

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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Supersonic Gas Flows in Radial Nozzles

Results of experimental investigations and numerical simulations of supersonic gas flows in radial nozzles with different nozzle widths are presented. It is demonstrated that different types of the flow are formed in the nozzle with a fixed nozzle radius and different nozzle widths: supersonic flows with oblique shock waves inducing boundary layer separation are formed in wide nozzles, and flows with a normal pseudoshock separating the supersonic and subsonic flow domains are formed in narrow nozzles (micronozzles). The pseudoshock structure is studied, and the total pressure loss in the case of the gas flow in a micronozzle is determined.     

Near field shock structure of dual co-axial jets

Experimental results on the shock structure of dual co-axial jets are presented. The effects of the geometric parameters of the inner nozzle, jet static pressure ratio (ratio of the exit plane static pressures of the inner and outer nozzles) and the ratio of outer to inner nozzle throat area on the shock structure were studied. A superimposed outer and inner jet structure was observed in the schlieren photographs. The inner flow is compressed by the outer flow resulting in the formation of a Mach disc and an exit shock. A parameter incorporating the effect of Mach number of the inner nozzle and jet static pressure ratio was found to correlate the observations regarding the Mach disc location.     

Transient three-dimensional startup side load analysis of a regeneratively cooled nozzle

The objective of this effort is to develop a computational methodology to capture the side load physics and to anchor the computed aerodynamic side loads with the available data by simulating the startup transient of a regeneratively cooled, high-aspect-ratio nozzle, hot-fired at sea level. The computational methodology is based on an unstructured-grid, pressure-based, reacting flow computational fluid dynamics and heat transfer formulation, and a transient inlet history based on an engine system simulation. Emphases were put on the effects of regenerative cooling on shock formation inside the nozzle, and ramp rate on side load reduction. The results show that three types of asymmetric shock physics incur strong side loads: the generation of combustion wave, shock transitions, and shock pulsations across the nozzle lip, albeit the combustion wave can be avoided with sparklers during hot-firing. Results from both regenerative cooled and adiabatic wall boundary conditions capture the early shock transitions with corresponding side loads matching the measured secondary side load. It is theorized that the first transition from free-shock separation to restricted-shock separation is caused by the Coanda effect. After which the regeneratively cooled wall enhances the Coanda effect such that the supersonic jet stays attached, while the hot adiabatic wall fights off the Coanda effect, and the supersonic jet becomes detached most of the time. As a result, the computed peak side load and dominant frequency due to shock pulsation across the nozzle lip associated with the regeneratively cooled wall boundary condition match those of the test, while those associated with the adiabatic wall boundary condition are much too low. Moreover, shorter ramp time results show that higher ramp rate has the potential in reducing the nozzle side loads.

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Origin of flow asymmetry in planar nozzles with separation

An experimental investigation was conducted to study the mechanisms that lead to the origin of flow asymmetry in overexpanded planar nozzles, especially at low nozzle pressure ratios. Three Mach 2 planar nozzles with different divergent wall angles but same area-ratio were tested. For all three nozzles, a large portion of the dimensional pressure rise data across the separation shock shows the nature of boundary layer to be in the laminar/transitional state. Depending upon the local flow conditions, the flow can, therefore, experience either an early or a delayed separation on either wall. This can result in a free or a restricted shock separation condition on either wall which can initiate the beginning of flow asymmetry in nozzles at low nozzle pressure ratio. However, a higher nozzle wall angle was observed to prevent initiation of such a flow asymmetry. The present tests, therefore, indicate that in addition to the state of the boundary layer along the nozzle wall, the proximity of the separated shear layer to the nozzle walls also seems to play a dominant role in initiating conditions that favor the origin of flow asymmetry in nozzles. A significant drop in the shock unsteadiness levels was also indicated by increasing the wall angle.     

Investigations of gas and particle dynamics in first generation needle-free drug delivery devices

Abstract. Transdermal powdered drug delivery involves the propulsion of solid drug particles into the skin by means of high-speed gas-particle flow. The fluid dynamics of this technology have been investigated in devices consisting of a convergent-divergent nozzle located downstream of a bursting membrane, which serves both to initiate gas flow (functioning as the diaphragm of a shock tube) and to retain the drug particles before actuation. Pressure surveys of flow in devices with contoured nozzles of relatively low exit-to-throat area ratio and a conical nozzle of higher area ratio have indicated a starting process of approximately 200 s typical duration, followed by a quasi-steady supersonic flow. The velocity of drug particles exiting the contoured nozzles was measured at up to 1050 m/s, indicating that particle acceleration took place primarily in the quasi-steady flow. In the conical nozzle, which had larger exit area ratio, the quasi-steady nozzle flow was found to be overexpanded, resulting in a shock system within the nozzle. Particles were typically delivered by these nozzles at 400 m/s, suggesting that the starting process and the quasi-steady shock processed flow are both responsible for acceleration of the particle payload. The larger exit area of the conical nozzle tested enables drug delivery over a larger target disc, which may be advantageous. Received 12 March 2000 / Accepted 8 June 2000     

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.     

Numerical calculation of FSS/RSS transition in highly overexpanded rocket nozzle flows

Turbulent flow separation in over-expanded rocket nozzles is investigated numerically in a sub-scale parabolic nozzle fed with cold nitrogen. Depending upon the feeding to ambient pressure ratio either a free shock separation or a restricted shock separation is computed, with a significant hysteresis between these two flow regimes. This hysteresis was also found in experimental tests with the same nozzle geometry. The present study is mainly focused on the transition between the two shock separation patterns. The analysis of the numerical solutions aims to provide clues for the explanation of the hysteresis cycle.     

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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Calculation of supersonic steady-state flow in axisymmetric nozzles with an upwind difference scheme

This paper is on the application of the upwind difference scheme proposed by the author^[1] to the calculation of supersonic steady-state flow in axisymmetric nozzles. The upwind scheme is conservative (or weakly conservative), it yields results approximating those from the characteristic relations, and it has corresponding boundary difference schemes. The entropy phenomenon in the calculation of shock reflection on boundaries with the shock-capturing method will be discussed and a correction of this phenomenon will be proposed. From numerical experiments on an arbitrary nozzle, it is seen that the upwind difference scheme, its corresponding boundary scheme, and the improved treatment of shock reflection work well for the calculation of supersonic steady-state flow in axisymmetric nozzles.     

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.      

Separated nozzle flow

A separated turbulent flow in an axisymmetrical nozzle is studied numerically. Two configurations nozzle are investigated. The first one is the truncated ideal contour nozzle, DLR-TIC, is fed with nitrogen. The second configuration is called the thrust optimized contour nozzle or TOC type, ONERA-TOC, where the operating gas is a hot air. The classical pattern of a free shock separation is obtained for different values of the nozzle pressure ratio. The results are compared and validated using experimental data.     

Unsteadiness of Flow Separation and End-Effects Regime in a Thrust-Optimized Contour Rocket Nozzle

Turbulent flow separation in over-expanded rocket nozzles is investigated experimentally in a sub-scale model nozzle fed with cold air and having a thrust-optimized contour. Depending upon the pressure ratio either a free shock separation (FSS) or a restricted shock separation (RSS) is observed with a significant hysteresis between these two flow regimes. It is shown that the RSS configuration may involve several separated regions. Analysis of wall pressure fluctuations give quantitative information on the fluctuating pressure field directly connected with the occurrence of significant side loads. Direct measurements of the evolution of the side loads with respect to the pressure ratio show the occurrence of three distinct peaks which are explained by the wall pressure fluctuations measurements.     

Effect of Gas Non-Ideality on the Performance of Laval Nozzles with an Abrupt Constriction

The flows in Laval nozzles with a ero-length region of abrupt constriction and in nozzles with smooth entrance regions are studied on the basis of the Reynolds equations supplemented by a differential turbulence model. It is established that the viscosity effect does not lead to flow separation in the vicinity of the minimum section of optimal nozzles with an abrupt constriction. In all the examples calculated, the thrust of these nozzles is greater than that of nozzles with smooth a constriction and an optimally contoured supersonic part, the flow rate through the nozzle being larger when viscosity is taken into account than in the ideal (inviscid) case.     

Bifurcations of the flow characteristics of an adjustable supersonic nozzle

A ground-based experimental study of the flow characteristic of an adjustable highaltitude nozzle was performed. It is shown that the flow characteristic of the adjustable nozzle can significantly depend on the design of its supersonic part and operation conditions. It is found that the operation such nozzles can involve different flow regimes of the working fluid depending on the position of the regulator; under certain conditions, there may be an abrupt change in the flow regime, which leads to an abrupt change (bifurcation) of the flow characteristic of the nozzle.     

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.      

Shock wave propagation into a surface depression

An aircraft travelling at supersonic speeds close to the ground generates a bow wave which is reflected off the ground surface. If a valley is traversed a complex reflection pattern will be generated. Similar patterns will evolve with a plane wave traversing a depression on a surface or structure. To simulate the process a planar shock wave, generated in a shock tube, is moved over several notched wedge configurations. Schlieren photographs were produced to assist in identifying the resulting complex three-dimensional wave structures and then verified and extended by three- dimensional computations. The valley geometries investigated are rectangular, triangular, parabolic and conical with a number of valley floor inclinations. The main features are extracted in surface models to demonstrate the complexity of the flow, and in particular in the case where the reflection is regular on the ground plane and Mach reflection in the valley.