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.     

Gas and Particle Dynamics of a Contoured Shock Tube for Pre-clinical Microparticle Drug Delivery

We investigate the gas-particle dynamics of a device designed for biological pre-clinical experiments. The device uses transonic/supersonic gas flow to accelerate microparticles such that they penetrate the outer skin layers. By using a shock tube coupled to a correctly expanded nozzle, a quasi-one-dimensional, quasi-steady flow (QSF) is produced to uniformly accelerate the microparticles. The system utilises a microparticle “cassette” (a diaphragm sealed container) that incorporates a jet mixing mechanism to stir the particles prior to diaphragm rupture. Pressure measurements reveal that a QSF exit period – suitable for uniformly accelerating microparticles – exists between 155 and 220 mus after diaphragm rupture. Immediately preceding the QSF period, a starting process secondary shock was shown to form with its (x,t) trajectory comparing well to theoretical estimates. To characterise the microparticle, flow particle image velocimetry experiments were conducted at the nozzle exit, using particle payloads with varying diameter (2.7–48 μm), density (600–16,800 kg/m³) and mass (0.25–10 mg). The resultant microparticle velocities were temporally uniform. The experiments also show that the starting process does not significantly influence the microparticle nozzle exit velocities. The velocity distribution across the nozzle exit was also uniform for the majority of microparticle types tested. For payload masses typically used in pre-clinical drug and vaccine applications (≤ 1 mg), it was demonstrated that payload scaling does not affect the microparticle exit velocities. These characteristics show that the microparticle exit conditions are well controlled and are in agreement with ideal theory. These features combined with an attention to the practical requirements of a pre-clinical system make the device suitable for investigating microparticle penetration into the skin for drug delivery.     

LES and RANS modelling of under-expanded jets with application to gaseous fuel direct injection for advanced propulsion systems

A density-based solver with the classical fourth-order accurate Runge-Kutta temporal discretization scheme was developed and applied to study under-expanded jets issued through millimetre-size nozzles for applications in high-pressure direct-injection (DI) gaseous-fuelled propulsion systems. Both large eddy simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) turbulence modelling techniques were used to evaluate the performance of the new code. The computational results were compared both quantitatively and qualitatively against available data from the literature. After initial evaluation of the code, the computational framework was used in conjunction with RANS modelling (k-ω SST) to investigate the effect of nozzle exit geometry on the characteristics of gaseous jets issued from millimetre-size nozzles. Cylindrical nozzles with various length to diameter ratios, namely 5, 10 and 20, in addition to a diverging conical nozzle, were studied. This study is believed to be the first to provide a direct comparison between RANS and LES within the context of nozzle exit profiling for advanced high-pressure injection systems with the formation of under-expanded jets. It was found that reducing the length of the straight section of the nozzle by 50% resulted in a slightly higher level of under-expansion (∼2.6% higher pressure at the nozzle exit) and ∼1% higher mass flow rate. It was also found that a nozzle with 50% shorter length resulted in ∼6% longer jet penetration length. At a constant nozzle pressure ratio (NPR), a lower nozzle length to diameter ratio resulted in a noticeably higher jet penetration. It was found that with a diverging conical nozzle, a fairly higher penetration length could be achieved if an under-expanded jet formed downstream of the nozzle exit compared to a jet issued from a straight nozzle with the same NPR. This was attributed to the radial restriction of the flow and consequently formation of a relatively smaller reflected shock angle. With the conical nozzle used in this study and a 30 bar injection pressure, an under-expanded hydrogen jet exhibited ∼60% higher penetration length compared to an under-expanded nitrogen jet at 100 μs after start of injection. Moreover, the former jet exhibited ∼22% higher penetration compared to a nitrogen jet issued through the conical profile with 150 bar injection pressure.     

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.     

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.      

The structure of particle-laden,underexpanded free jets

Underexpanded, supersonic gas-particle jets were experimentally studied using the shadowgraph technique in order to examine the influence of the dispersed particles on the shape of the free jet and the structure of the imbedded shock waves. The particle mass loading at the nozzle exit was varied between zero and one, and two sizes of particles (i.e. spherical glass beads) with mean number diameters of 26 and 45 m were used. It was found that the Mach-disc moves upstream towards the orifice with increasing particle loading. The laser light sheet technique was also used to visualize the particle concentration distribution within the particle jet and the spreading rate of the particle jet. Furthermore, the particle velocity along the jet centerline was measured with a modified laser-Doppler anemometer. These measurements revealed that the particles move considerably slower than the gas flow at the nozzle exit. This is mainly the result of the particle inertia, whereby the particles are not accelerated to sonic speed in the converging part of the nozzle.In order to further explore the particle behavior in the free jet, numerical studies were performed by a combined Eulerian/Lagrangian approach for the gas and particle phases, including full coupling between the two phases. The numerical results showed that the application of different particle velocities at the nozzle exit as the inlet conditions, which were below the sonic speed of the gas phase has a significant influence on the free jet shape and the configuration of the shock waves. These results demonstrate that the assumption of equilibrium flow (i.e. zero slip between the phases) at the nozzle exit which has been applied in most of the previous numerical studies is not justified in most cases. Furthermore, the numerical calculations of the free jet shape and the particle velocity along the jet axis were compared with the measurements. Although correlations for rarefaction and compressibility effects in the drag coefficient were taken into account, the particle velocity along the center line was considerably overpredicted.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

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.     

Flow of a dispersed phase in the Laval nozzle and in the test section of a two-phase hypersonic shock tunnel

An unsteady gas-particle flow in a hypersonic shock tunnel is studied numerically. The study is performed in the period from the instant when the diaphragm between the high-pressure and low-pressure chambers is opened until the end of the transition to a quasi-steady flow in the test section. The dispersed phase concentration is extremely low, and the collisions between the particles and their effect on the carrier gas flow are ignored. The particle size is varied. The time evolution of the particle concentration in the test section is obtained. Patterns of the quasi-steady flow of the dispersed phase in the throat of the Laval nozzle and the flow around a model (sphere) are presented. Particle concentration and particle velocity lag profiles at the test-section entrance are obtained. The particle-phase flow structure and the time needed for it to reach a quasi-steady regime are found to depend substantially on the particle size. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 102–113, September–October, 2008.     

Mixing of high speed coaxial jets

In this study, five different supersonic nozzles – conical, elliptical, tabbed, radially lobed and two-dimensional lobed – are compared experimentally for their mixing performance. With the background of studies by various groups conducted on the above nozzles, the present paper aims to provide an experimental comparison of their respective mixing performances with that of a conventional conical nozzle under identical operating conditions. The mixing of the supersonic stream coming from such nozzles with a coaxial sonic stream is investigated. The investigation is performed non-intrusively, using digital image processing of planar Mie-scattering images of the flow field. The results of these investigations reveal the superiority of mixing performance of the two-dimensional lobed nozzle over conventional circular and other non-conventional nozzles. Received: 15 July 1999/Accepted: 3 July 2000     

Shock wave driven microparticles for pharmaceutical applications

Ablation created by a Q-switched Nd:Yttrium Aluminum Garnet (Nd:YAG) laser beam focusing on a thin aluminum foil surface spontaneously generates a shock wave that propagates through the foil and deforms it at a high speed. This high-speed foil deformation can project dry micro- particles deposited on the anterior surface of the foil at high speeds such that the particles have sufficient momentum to penetrate soft targets. We used this method of particle acceleration to develop a drug delivery device to deliver DNA/drug coated microparticles into soft human-body targets for pharmaceutical applications. The device physics has been studied by observing the process of particle acceleration using a high-speed video camera in a shadowgraph system. Though the initial rate of foil deformation is over 5 km/s, the observed particle velocities are in the range of 900–400 m/s over a distance of 1.5–10 mm from the launch pad. The device has been tested by delivering microparticles into liver tissues of experimental rats and artificial soft human-body targets, modeled using gelatin. The penetration depths observed in the experimental targets are quite encouraging to develop a future clinical therapeutic device for treatments such as gene therapy, treatment of cancer and tumor cells, epidermal and mucosal immunizations etc.      

Large Eddy Simulation of Compressible Subsonic Turbulent Jet Starting From a Smooth Contraction Nozzle

Compressible subsonic turbulent starting jet with a relatively large Reynolds number of significant practical importance is investigated using large eddy simulation (LES), starting from a smooth contraction nozzle. The computational domain of truncated conical shape is determined through the comparison of the time-averaged numerical solution with the particle imaging velocimetry measurements for the steady jet. It is shown that the starting jet consists of a leading vortex ring followed by a quasi-steady jet, and the instantaneous velocity field exhibits contraction and expansion zones, corresponding to the high pressure (HP) and low pressure (LP) regions formed by the convecting vortex rings, and are related to the Kelvin-Helmholtz instability. The thin boundary layer inside the smooth contraction nozzle evolves into a shear layer at the nozzle exit and develops with the downstream penetration of the jet. Using λ ₂ criterion, the formation and evolution of the vortical structures are temporally visualized, illustrating distortion of vortex rings into lobed shapes prior to break-down. Rib-shape streamwise vortex filaments exist in the braid region between a pair of consecutive vortex rings due to secondary instabilities. Finally, formation and dynamics of hairpin vortices in the shear layer is identified.     

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.     

Thrust shock vector control of an axisymmetric conical supersonic nozzle via secondary transverse gas injection

Transverse secondary gas injection into the supersonic flow of an axisymmetric convergent–divergent nozzle is investigated to describe the effects of the fluidic thrust vectoring within the framework of a small satellite launcher. Cold-flow dry-air experiments are performed in a supersonic wind tunnel using two identical supersonic conical nozzles with the different transverse injection port positions. The complex three-dimensional flow field generated by the supersonic cross-flows in these test nozzles was examined. Valuable experimental data were confronted and compared with the results obtained from the numerical simulations. Different nozzle models are numerically simulated under experimental conditions and then further investigated to determine which parameters significantly affect thrust vectoring. Effects which characterize the nozzle and thrust vectoring performances are established. The results indicate that with moderate secondary to primary mass flow rate ratios, ranging around 5 %, it is possible to achieve pertinent vector side forces. It is also revealed that injector positioning and geometry have a strong effect on the shock vector control system and nozzle performances.     

Experimental investigation of the recovery of the total pressure in a hypersonic wind tunnel with conical and profiled nozzles

Measurements have been made of the coefficient of recovery of the total pressure of a gas flow exhausting from axisymmetric and conical profiled hypersonic nozzles into a cylindrical channel of diameter equal to or greater than the nozzle exit and also in the presence of an Eiffel chamber. The experiments were made at Mach numbers M = 4.83–12.4 in the isentropic core. It is shown that the values of differ slightly (by 5%) from the corresponding value for a normal shock wave at the number M determined for a onedimensional flow by the ratio of the area of the cylindrical channel to the area of the critical section of the nozzle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 170–173, January–February, 1984.     

Critical gas outflow from nozzles

The possibility of critical gas flow from Laval nozzles in overexpanded regimes behind a bridge shock is investigated theoretically with and without allowance for viscous mixing at the edge of the jet. The influence of the mixing effect and flow separation from the nozzle walls on the critical flow conditions is analyzed. It is shown experimentally that these regimes coincide closely with the displacement of the normal shock to the nozzle exit and cessation of the emission by the jet of a discrete tone. Mariupol. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 180–184, July–August, 1994.     

Investigation of the solid impurity distribution in axisymmetric nozzles

Results are presented of an experimental investigation of the influence of the entrance conditions, the coarseness of the solid impurities (the nozzle scale), the profiles of the sub- and transonic parts of the nozzle, and the initial concentration on the discrete phase distribution in the exit sections of axisymmetric nozzles. It is shown that profiling of the subsonic part of the nozzle plays a governing role as compared with the transonic part, and the greatest filling of the supersonic nozzle section by a solid impurity is observed in the conical entrance. The nonuniformity of the parameter distribution at the nozzle entrance does not substantially alter the solid impurity distribution at the exit.     

PIV Measurements in the Near and Intermediate Field Regions of Jets Issuing from Eight Different Nozzle Geometries

An experimental study was conducted to investigate the effect of nozzle geometry on the mixing characteristics and turbulent transport phenomena in turbulent jets. The nozzle geometry examined were round, square, cross, eight-corner star, six-lobe daisy, equilateral triangle as well as ellipse and rectangle each with aspect ratio of 2. The jets were produced from sharp linear contoured nozzles which may be considered intermediate to the more widely studied smooth contraction and orifice nozzles. A high resolution particle image velocimetry was used to conduct detailed velocity measurements in the near and intermediate regions. It was observed that the lengths of the potential cores and the growth rates of turbulence intensities on the jet centerline are comparable with those of the orifice jets. The results indicate that the decay and spreading rates are lower than reported for orifice jets but higher than results for smooth contoured jets. The jets issuing from the elliptic and rectangular nozzles have the best mixing performance while the least effective mixing was observed in the star jet. The distributions of the Reynolds stresses and turbulent diffusion clearly showed that turbulent transport phenomena are quite sensitive to nozzle geometry. Due to the specific shape of triangular and daisy jets, the profiles of mean velocity and turbulent quantities are close to each other in their minor and major planes while in the elliptic and rectangular jets are considerably different. They also exhibit more isotropic behavior compared to the elliptic and rectangular jets. In spite of significant effects of nozzle geometry on mean velocity and turbulent quantities, the integral length scales are independent of changes in nozzle geometry.     

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.     

A two-phase stream containing liquid particles in the sub- and transonic regions of plane nozzles

The results of experimental studies of the influence of the entrance conditions, the particle size, the profiles of the sub- and transonic parts of the nozzle, and the initial concentration on the distribution of the solid discrete phase in the exit cross sections of axisymmetric nozzles were analyzed in [1]. The results of a study of the influence of the profiling of the nozzle and the size of the particles at the nozzle entrance on the formation of the distribution fields of the discrete liquid phase and its size at the cut of a plane nozzle are presented in the present report, which is a continuation of [1]. The experimental data presented permit a deeper understanding of the mechanism of flow of a two-phase medium in a nozzle and are required for an evaluation of efficiency of the calculation methods.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 167–170, March–April, 1978.