Investigation of the effect of nozzle shape on supersonic/hypersonic impactors designed for size discrimination of nanoparticles

In this study the flow field and the nanoparticle collection efficiency of supersonic/hypersonic impactors with different nozzle shapes were studied using a computational modeling approach.The aim of this study was to develop a nozzle design for supersonic/hypersonic impactors with the smallest possible cut-off size d_(50) and rather sharp collection efficiency curves.The simulation results show that the changes in the angle and width of a converging nozzle do not alter the cut-off size of the impactor;however,using a conical Laval nozzle with an L/D_n ratio less than or equal to 2 reduced d_(50).The effect of using a cap as a focuser in the nozzle of a supersonic/hypersonic impactor was also investigated.The results show that adding a cap in front of the nozzle had a noticeable effect on decreasing the cut-off size of the impactor.Both flat disks and conical caps were examined,and it was observed that the nozzle with the conical cap had a lower cut-off size.     

Asymptotic nature of hypersonic flow in a conical nozzle

This study investigates hypersonic flow in a conical nozzle at large distances from the throat with account for the interaction with the laminar boundary layer.A study of the asymptotic nature of the hypersonic flow of an ideal gas in an expanding nozzle whose wall was close to a kth-power parabola was made by Ladyzhenskii [1], who showed in particular that for 00)_0* the nonuniformity in the distribution of all the gasdynamic parameters in the flow is hydraulic in nature; in this case the maximal Mach number is determined from the boundary-layer joining condition at the nozzle centerline; 2) for Reynolds numbers much larger than (R₀)_0*, when most of the gas is concentrated near the outer edge of the potential core, the region of isentropic flow is bounded in the direction of the stream by the interaction of the compressed gas layers.The author wishes to thank V. N. Gusev and V. N. Zhigulev for helpful discussions of this study.     

Optimal 3D impactors penetrating into layered targets

Optimization of 3D sharp high speed impactors with given form of a longitudinal contour, length, and volume, penetrating into layered ductile targets, both for conical and thin non-conical strikers using approximate models is studied. It is found that the impactor with the minimum drag moving in a homogenous target with a constant velocity penetrates to the maximal depth into a semi-infinite target and has the minimal ballistic limit when it penetrates into a finite thickness target, regardless of the distribution of the material properties of the target along its depth, the number of the layers, etc. Using the analogy with the hypersonic flow over the flying projectiles it is predicted that the optimal impactor should have a star-shaped form of the cross section. If an impactor has a polygonal cross sections allowing the inscribed circles, the ballistic limit and maximum depth of penetration are independent not only of the properties of the target but also of the form of the polygon in the cross section and equal to the corresponding values for the inscribed body of revolution.     

不同重力场下颗粒冲击过程的离散元分析

开展不同重力场下颗粒材料冲击动力学研究有助于加深对颗粒运动机制的理解和深空探测任务的实施。本文采用离散元模拟对颗粒介质受球形冲击物的冲击过程进行了数值模拟，并与地球重力下冲击的试验结果进行对比验证。在此基础上，进一步研究了重力加速度对冲击物动力学的影响规律。计算结果表明，在所有重力加速度下，冲击物的穿透深度d与冲击速度v₀的关系可以用Poncelet模型表达；d与冲击物下落的总高度H表现为d～Hⁿ的幂律关系，当H<10 m时，d与H的幂率标度为0.322,而H>10 m时，d与H的幂率标度下降到0.211。此外，穿透深度小于冲击物半径时，重力加速度对冲击物减速过程无影响。在所有的重力加速度下，当冲击速度大于5 m/s时，冲击物的持续碰撞时间t_c是恒定的，且与重力的-1/2次方呈正比。     

Numerical study of rheological behaviors of a compound droplet in a conical nozzle

The dynamics of compound droplets is more and more attractive because of their applications in a wide range of industrial and natural processes. This study aims to improve the understanding of dynamical rheological behaviors of a compound droplet moving in a nozzle with a conical shape in the downstream region via front-tracking-based simulations. The numerical results show that the compound droplet experiences three stages of deformation: the entrance stage (in front of the conical region), the transit stage (within the conical region), and the exit stage (in the exit of the nozzle). The droplet receives the maximum deformation in the axial direction during the transit stage, and the radially maximum deformation occurs during the exit stage. Because of the acceleration induced by the conical region, the inner droplet of the compound droplet can break up into smaller droplets during the exit stage. To reveal the transition between the finite deformation and the breakup, many parameters including the Capillary number Ca (varied in the range of 0.0125–1.6), the droplet size relative to the nozzle size R₁/R₀ (varied in the range of 0.2–0.9), the droplet radius ratio R₂₁ (varied in the range of 0.3–0.8), the viscosity ratios μ₂₁ and μ₃₁ (varied in the range of 0.05–3.2), the interfacial tension ratio σ₂₁ (varied in the range of 0.125–8.0), the conical angle α (varied in the range of 4°–34°) and the initial location of the inner droplet (i.e. the droplet eccentricity) are considered. From the finite deformation mode, the transition to the breakup mode of the inner droplet occurs when increasing any of Ca, R₁/R₀, R₂₁ and α, or decreasing any of μ₂₁ and σ₂₁. The breakup mode is also enhanced when the inner droplet is initially located closer to the leading side of the outer droplet. However, varying μ₃₁ induces no transition between these modes. The regime diagrams of these modes, based on these parameters, are also proposed.     

Choking of ideal-gas flow in convergent nozzles and integral nozzle characteristics

The results of a numerical and theoretical investigation of the local and integral characteristics of convergent nozzles are presented. It is shown that self-similar (choked) nozzle flow, when the gas flow rate does not depend on the external pressure, may occur at subcritical values of the pressure ratio _c . If the nozzle contour consists of the contour of the conical nozzle and the convergent part corresponds to the boundary of the emerging jet, then on a certain interval of _c this nozzle will have a higher thrust coefficient than the initial conical nozzle.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 149–157, November–December, 1994.     

An experimental study of circular sand–water wall jets

Laboratory experiments were carried out to study the effects of sand particles on circular sand–water wall jets. Mean and turbulence characteristics of sand particles in the sand–water wall jets were measured for different sand concentrations c_o ranging from 0.5% to 2.5%. Effects of sand particle size on the centerline sand velocity of the jets were evaluated for sand size ranging from 0.21 mm to 0.54 mm. Interesting results with the range of measurements are presented in this paper. It was found that the centerline sand velocity of the wall jets with larger particle size were 15% higher than the jets with smaller particle size. Concentration profiles in the vertical direction showed a peak value at x/d = 5 (where x is the longitudinal distance from the nozzle and d is the nozzle diameter) and the sand concentration decreased linearly for x/d > 5. Experimental results showed that the turbulence level enhanced from the nozzle to x/d = 10. For sand–water wall jets with a higher concentration (c_o = 1.5–2.5%), the turbulence intensity became smaller than the corresponding single-phase wall jets by 34% due to turbulent modulation. A modified logarithmic formulation was introduced to model the longitudinal turbulent intensity at the centerline and along the axis of the jet.     

An implicit upwind parabolized Navier-Stokes code for chemically nonequilibrium flows

The previously developed single-sweep parabolized Navier-Stokes (SSPNS) space marching code for ideal gas flows has been extended to compute chemically nonequilibrium flows. In the code, the strongly coupled set of gas dynamics, species conservation, and turbulence equations is integrated with the implicit lower-upper symmetric Gauss-Seidel (LU-SGS) method in the streamwise direction in a space marching manner. The AUSMPW+ scheme is used to calculate the inviscid fluxes in the crossflow direction, while the conventional central scheme for the viscous fluxes. The k-g two-equation turbulence model is used. The revised SSPNS code is validated by computing the Burrows-Kurkov non-premixed H2/air supersonic combustion flows, premixed H2/air hypersonic combustion flows in a three-dimensional duct with a 15° compression ramp, as well as the hypersonic laminar chemically nonequilibrium air flows around two 10° half-angle cones. The results of these calculations are in good agreement with those of experiments, NASA UPS or Prabhu's PNS codes. It can be concluded that the SSPNS code is highly efficient for steady supersonic/ hypersonic chemically reaction flows when there is no large streamwise separation.     

A hybrid pressure–density‐based algorithm for the Euler equations at all Mach number regimes

In the present work, we propose a reformulation of the fluxes and interpolation calculations in the PISO method, a well‐known pressure‐correction solver. This new reformulation introduces the AUSM⁺ ? up flux definition as a replacement for the standard Rhie and Chow method of obtaining fluxes and central interpolation of pressure at the control volume faces. This algorithm tries to compatibilize the good efficiency of a pressure based method for low Mach number applications with the advantages of AUSM⁺ ? up at high Mach number flows. The algorithm is carefully validated using exact solutions. Results for subsonic, transonic and supersonic axisymmetric flows in a nozzle are presented and compared with exact analytical solutions. Further, we also present and discuss subsonic, transonic and supersonic results for the well known bump test‐case. The code is also benchmarked against a very tough test‐case for the supersonic and hypersonic flow over a cylinder. Copyright © 2011 John Wiley & Sons, Ltd.     

Simplified Navier-Stokes Equations for Internal Mixed Flows and a Numerical Method of Solution

Simplified Navier-Stokes equations, of the elliptic and hyperbolic type in the subsonic and supersonic flow regions, respectively, are derived for viscous flows in channels and nozzles with curved walls whose local radii of longitudinal curvature are comparable with the transverse channel dimensions. A new numerical method is developed for the system of equations obtained. This method is of the evolution type along the longitudinal coordinate and includes global iterations of the streamline direction field and the longitudinal pressure gradient field. The effectiveness of the method is illustrated with reference to the solution of the direct Laval nozzle problem for an air flow at Reynolds numbers Re10⁴ and 10⁶ in conical nozzles with throat curvatures K _w=1.0 and 1.6 (K _w is the curvature divided by the inverse radius of the nozzle throat). Two iterations are sufficient to calculate the nozzle flow rate and power correct to 0.01%.     

Investigation of hypersonic nozzle flow uniformity using NO fluorescence

Planar laser-induced fluorescence visualisation is used to investigate nonuniformities in the flow of a hypersonic conical nozzle. Possible causes for the nonuniformity are outlined and investigated, and the problem is shown to be due to a small step at the nozzle throat. Entrainment of cold boundary layer gas is postulated as the cause of the signal nonuniformity. PACS 47.80.Jk, 47.40.Ki, 47.60.+i     

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     

Visualization of high-speed gas jets and their airblast sprays of cross-injected liquid

A planar and instantaneous visualization study of high-speed gas jets and their airblast sprays was performed to qualitatively examine the different atomization performances of different gas nozzles. For the visualization of high-speed gas jets (with no liquid injected), Nd:YAG pulsed laser sheets imaged the clustered vapor molecules in the Rayleigh range (d?λ), condensed from the natural humidity during the isentropic gas expansion through a nozzle. This method visualized both underexpanded sonic gas jets from a converging nozzle (SN-Type) and overexpanded supersonic gas jets from a converging-diverging nozzle (CD-Type). When liquid is cross-injected, the same laser sheet images the spray droplets of relatively large sizes (d?λ). The present visualization results show that the SN-Type nozzle develops a wider spray than the CD-Type nozzle, quite probably because the SN-Type nozzle has a wider gas jet (in the absence of liquid) than the CD-Type. Also, the wider spray of the SN-Type nozzle lowers the probability of droplet coalescence and generates finer sprays compared to the CD-Type nozzle. These visualization results qualitatively agree with the previous quantitative finding of the different atomization characteristics of the two types of nozzles (Park et al. 1996).     

Lifting bodies using the flow behind axisymmetric conical shock waves

One of the methods of designing aircraft with supersonic flight speeds involves solving an inverse problem by means of the well-known flow schemes and the substitution of rigid surfaces for the flow surfaces. Lifting bodies using the flows behind axisymmetric shock waves belong to these configurations. All lifting bodies using the flow behind a conical shock wave can be divided into two types [1]. Bodies whose leading edge passes through the apex of the conical shock wave pertain to the first type and those whose leading edge lies below the apex of the conical shock wave, to the second. For small apex angles of the basic cone at hypersonic flow velocities an approximate solution of the variation problem was obtained, which showed that the lift-drag ratio of lifting bodies of the second type is higher than that of the first [2]. The present paper gives a numerical solution of the problem for flow past lifting bodies of the second type using the flow behind axisymmetric conical shock waves with half-angles of the basic cone _S=9.5 and 18° The upper surfaces of the bodies are formed by intersecting planes parallel to the velocity vector of the oncoming flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 135–138, March–April, 1986.     

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     

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.     

Results of interferometer study of laval nozzle

Interferometric measurement of the air density in a supersonic nozzle of rectangular cross section is described. The flow structure is studied in a real Laval nozzle. It is shown that the core flow follows the laws of motion of an ideal gas and has a wave nature. The relation _Z=(3–4)_y is obtained for the boundary layer thickness on the nozzle walls for nozzle width-height ratio L/h=3.75–7.5.The flow structure in a real supersonic nozzle may differ significantly from the theoretical structure, both because of defects in nozzle fabrication and because of boundary layer growth on the nozzle walls. In many casesitis important to know the param'eters of the supersonic flow in the actual nozzle. The determination of these parameters (density , pressure , temperature T, velocity u, Mach number M) at any section of the nozzle in question is the objective of the present investigation.The authors wish to thank V. P. Koronkevich for his assistance in this study.     

Hydraulic characterization of high temperature hydrocarbon liquid jets

An experimental study has been conducted to investigate the hydraulic characteristics of a plain orifice nozzle issuing pressurized high-temperature liquid hydrocarbon, in order to simulate injection of aviation fuel after being used as coolant in an active cooling system in a hypersonic flight vehicle. The fuel was heated to 553 K (280°C) using an induction heater, at an upstream pressure of up to 1.0 MPa, and injected to atmospheric pressure conditions through a sharp-edged orifice of diameter 0.7 mm and length 4.3 mm. It has been observed that the isothermal lines on the plane of the mass flow rate versus the square root of the pressure drop (ΔP) were clearly affected by increased fuel temperatures, and the discharge coefficient (C_d) decreased sharply with increasing fuel injection temperature (T_inj) above the fuel boiling point of 460 K. The Reynolds number (Re) for three ΔPs with respect to T_inj reached maxima and then began to decrease as T_inj increased for each ΔP case, and the fuel temperature of maximum Re at a given pressure condition increased as ΔP increased. The effects of cavitation on the hydraulic characteristics of the high temperature fuel were explored by representing C_d with respect to three cavitation numbers and dissipation efficiency. The behaviors of C_d showed a clear dependency on cavitation number, and all of the results collapsed to a single curve, regardless of ΔP. In addition, the curve indicated that the C_d characteristics was divided into non-cavitating and cavitating regions by the critical cavitation numbers near the fuel boiling point, and a sharp decrease in C_d was found to be typical in the cavitating region. The relationship between C_d and Re showed that when T_inj exceeded the boiling point the high temperature liquid jets experienced a sharp decrease in C_d at a determined Reynolds number, due to the collapse of the mass flow rate induced by the choked cavitaiton.     

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.     

Effect of Streamline Curvature on Intensity of Streamwise Vortices in the Mixing Layer of Supersonic Jets

The structure of supersonic nonisobaric jets with Mach numbers M_a = 1 and 2 is considered experimentally to find the effect of streamline curvature on the evolution of streamwise vortices in the mixing layer. The spatial development of steady streamwise vortices in the mixing layer of supersonic jets is considered. A method for generation of steady streamwise vortices by applying microroughness elements of controlled size onto the inner surface of the nozzle is developed. Radial profiles and azimuthal variations of total pressure are obtained; the mixinglayer thickness and the curvature of streamlines in supersonic jets are determined. A significant effect of microroughness elements of prescribed shape located on the nozzle surface on the behavior of total pressure in the mixing layer of supersonic jets, as compared to natural disturbances, is obtained.