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 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.     

Two-way coupled simulation of a flow laden with metallic particulates in overexpanded TIC nozzle

A simulation of non-reacting dilute gas–solid flow in a truncated ideal contour nozzle with consideration of external stream interactions is performed. The Eulerian–Lagrangian approach involving a two-way momentum and thermal coupling between gas and particles phases is also adopted. Of interests are to investigate the effects of particles diameter and mass flow fraction on the flow pattern, Mach number, pressure and temperature contours and their distributions along the nozzle centerline and wall. The main goal is to determine the separation point quantitatively when the particles characteristics change. Particles sample trajectories are illustrated throughout the flow field and a qualitative discussion on the way that physical properties of the nozzle exit flow and particles trajectories oscillate is prepared. The existence of solid particulates delays the separation prominently in the cases studied. The bigger particles and the higher particles mass flow fractions respectively advance and delay the separation occurrence. The particles trajectories oscillate when they expose to the crisscrossing (or diamond-shape) shock waves generated outside the nozzle to approach the exit jet conditions to the ambient. The simulation code is validated and verified, respectively, against a one-phase 2D convergent–divergent nozzle flow and a two-phase Jet Propulsion Laboratory nozzle flow, and acceptable agreements are achieved.     

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.      

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.     

Shock wave configurations and flow structures in non-axisymmetric underexpanded sonic jets

An experimental and numerical study of underexpanded free sonic jet flows issuing from rectangular, elliptical and slot nozzles has been undertaken. Aspect ratios (AR) of 1, 2, and 4 are described at pressure ratios (exit plane pressure to ambient pressure), of 2 and 3. There is good qualitative agreement between the experimental observations and the numerical predictions. In the case of rectangular jets, a complex system of shock waves forming the incident shock system is identified. This shock wave system originates at the corners of the nozzle exits, and proceeds downstream. Mach reflections are found to occur on the incident shock wave surface as well as the presence of a Mach disk terminating the first jet cell. This Mach disk has the shape of a square, a hexagon, or an octagon depending on the nozzle shape. For slot and elliptical jets, the formation of the incident shock wave was not observed along the minor axis plane of the nozzle for AR > 2. The incident shock wave was observed to originate downstream of the nozzle exit in the major axis plane. This wave system undergoes a transition to Mach reflection as it propagates downstream of the nozzle exit. In all cases tested, the shape of the jet boundary is significantly distorted. In rectangular jets, the narrowing of the jet boundary along the diagonal axis of the nozzle exit is observed, and in the case of the elliptical and slot jets axis switching is noted.     

Optimal Profiling of the Supersonic Part of a Plug Nozzle Contour

The problem of the optimal profiling of the supersonic part of a plug nozzle contour is solved within the framework of the ideal (inviscid and non-heat-conducting) gas model. The contours obtained provide a thrust maximum for given uniform sonic flow in the radial critical section of the nozzle, given constraints on the nozzle dimensions, and a given outer pressure (counterpressure). The initial sonic regions of the optimal contours are profiled on the basis of the condition that there the flow Mach number is unity. Varying the initial sonic region length makes it possible to construct nozzles of different sizes. The possibilities of the computational programs developed are demonstrated with reference to the example of plug nozzles, optimal when operated in a vacuum. It is shown that low thrust losses are obtained even for moderate nozzle dimensions. In the examples calculated, the optimal plug nozzles provide a greater thrust than the optimal axisymmetric and two-dimensional nozzles with an axial sonic flow for the same lengths and gas flow rates.     

Profiling the Supersonic Part of a Plug Nozzle with a Nonuniform Transonic Flow

The effect of transonic flow nonuniformity on the profiling of optimal plug nozzles is studied in the inviscid gas approximation. Sonic and supersonic regions providing maximum thrust for given nozzle dimensions and a given outer pressure are designed for given subsonic contours and calculated nonuniform transonic flows. As in the case of uniform flow on a cylindrical sonic surface, the initial regions of the designed contours satisfy the condition that in these regions the flow Mach number is unity or near-unity. In all the examples calculated, the optimal plug nozzles produce a greater thrust than the optimal axisymmetric and annular nozzles with a near-axial flow for the same lengths and the same gas flow rates through the nozzle. It is established that contouring without regard for transonic flow nonuniformity can result in considerable thrust losses. However, these losses are due only to a decrease in the flow rate, while the specific thrust may even increase slightly.     

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.     

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.     

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.      

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.      

Influence of nozzle geometry on the near-field structure of a highly underexpanded sonic jet

Detailed near-field structures of highly underexpanded sonic free jets have been investigated with the help of computational fluid dynamics. Two-dimensional, axisymmetric Euler equations have been chosen to predict the underexpanded jets, and the third-order total variation diminishing finite-difference scheme has been applied to solve the system of governing equations numerically. Several different nozzles have been employed to investigate the influence of the nozzle geometry on the near-field structures of highly underexpanded sonic free jets. The results obtained show that the distance from the nozzle exit to the Mach disk is an increasing function of the jet–pressure ratio, which also significantly influences the shape of the jet boundary. The diameter of the Mach disk increases with the jet–pressure ratio, and it is further significantly influenced by the nozzle geometry, unlike the distance of the Mach disk from the nozzle exit. However, such a dependence on the nozzle geometry is no longer found when an effective-diameter concept is taken into account for the flow from a sharp-edged orifice. A good correlation in the diameters of the Mach disk is obtained, so that the near-field structure of highly underexpanded sonic free jets is a unique function of the pressure ratio, regardless of the nozzle geometry.     

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.     

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.     

Swirling flows in circular-to-rectangular transition ducts

Miniature axisymmetric supersonic nozzles were produced with exit Mach numbers ranging from 1.0 to 2.8 by forming Pyrex^® capillary tubing of 0.6 and 1.2 mm inside diameter into converging-diverging channels. The nozzle contours were measured and were found to compare favorably to ideal solutions given by the axisymmetric method of characteristics. In addition, the surfaces of these nozzles were quite smooth, providing featureless flows at perfect expansion. Schlieren visualization and pitot pressure measurements of the resulting microjets were compared to the literature available for jets produced by larger-scale nozzles. A postponed transition to turbulence is noted in these microjets due to their low Reynolds number. The pitot pressure on centerline is nearly uniform at perfect expansion over core lengths up to 12 nozzle exit diameters. Supersonic microjet nozzles thus provide a more effective small-scale high-pressure gas delivery device than do sonic nozzles of comparable scale at equivalent mass flow rates. Supersonic microjets may therefore have several industrial applications.List of symbols ^* boundary layer displacement thickness, mm - d diameter of nozzle exit, mm - L length of nozzle diverging section, mm - L _c inviscid core length, mm - L _s supersonic region length, mm - M _c convective Mach number - M _e exit Mach number - P _b backpressure at nozzle exit, (equal to ambient pressure in this experiment) - P _e exit pressure of the supersonic jet - P _be exit pressure ratio (P _b /P _e ) - P _p impingement pressure (pitot pressure) - P ₀ stagnation pressure supplied to nozzle - P _n overall pressure ratio (P ₀/P _b ,) - r radial dimension (cylindrical coordinate system), mm - r ₀ radius of throat, mm - Re _d Reynolds number, based on nozzle exit diameter - V _e exit velocity, m/s - x axial dimension (cylindrical coordinate system), mm This research was sponsored by National Science Foundation Grant DMI 9400119, as part of a study of the assist-gas dynamics of laser cutting.     

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.     

Drag force on quasi-axisymmetric scramjets at various flight Mach numbers: theory and experiment

The net axial force on a non-fuelled quasi-axisymmetric scramjet model designed for operation at Mach 6 was measured in the T4 Stalker tube at The University of Queensland using a single-component stress wave force balance. The design used was a variant of a model that was tested previously at Mach 6. The new model was equipped with a modified thrust nozzle that was designed to improve the performance of the nozzle. Tests were performed to measure the drag force on the model for Mach 6, Mach 8 and Mach 10 shock tunnel nozzles for a range of flow conditions. The nozzle-supply enthalpy was varied from 3 to 10 MJ/kg and the nozzle-supply pressure from 35 to 45 MPa. For the test model, the drag coefficient increased with increasing nozzle-supply enthalpy. The test results are compared with a force prediction method based on simple hypersonic theories and three-dimensional CFD. The test results are in good agreement with the predictions over the wide range of conditions tested. The re-designed model has a more efficient nozzle but this comes at the expense of increased drag associated with the modifications required for the cowl. The results indicate that this type of vehicle design is not likely to be suitable for flight above Mach 8.

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采用NND方法计算三维喷管气流场

本文运用NND显式差分格式,计算了三维喷管气流场。气流场计算的基本方程为一般贴体坐标系下三维守恒型的欧拉方程。采用了时间分裂法和Steger-Warming矢通量分裂技术。在喷管内沿周向的每个由轴线和壁面构成的子午面上根据泊松方程生成贴体网格。本文运用三维程序计算了轴对称JPL喷管,同时与实验结果和前人采用轴对称二维程序所计算的结果做了对比。最后,本文还计算了三维矢量喷管,计算结果与现有的实验结果一致。通过轴对称JPL喷管和三维矢量喷管的计算考核,表明建立的算法和编写的计算程序是正确的。文中提出了采用子午面形式的贴体网格时奇性轴的处理方法。计算结果表明在喷管壁面处,马赫数与压强的计算结果与实验值吻合较好,而在喷管轴线处,只有当网格较密时,才能得出与实验结果接近的计算结果。     

Study on the characteristics of interaction flowfields induced by supersonic jet on a revolution body

The paper focuses on the triple jets interaction with a hypersonic external flow on a revolution body. The experimental model is a ogive-cylinder body with three supersonic nozzles, which are aligned along the flow direction. The freestream Mach numbers are 5 and 6. The spatial and surface flow characteristics are illustrated by the schlieren photographs and the typical pressure distribution. The results show that there are multi-wave system, separation, reattachment, multi-peak pressure, high-pressure and low-pressure zone boundaries obvious distinction in tri-jets interference flowfield. The present paper also analyzes how do the pressure ratio, the angle of attack, and Mach number effect on tri-jets interaction characteristics.