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     

Starting of an axisymmetric convergent-divergent nozzle in a hypersonic flow

The starting of an axisymmetric convergent-divergent nozzle, with the result that supersonic flow is formed within almost the entire channel, is modeled, as applied to the hypersonic aerodynamic setup of the Institute of Mechanics of Moscow State University. A successful starting is realized when the nozzle is thrown in a uniform supersonic air flow at a fairly high Mach number. The steady flow structure is studied. It is numerically shown that in the convergent section of the channel there arises an oblique shock wave whose interaction with the nozzle axis leads to the formation of a reflected shock and a curvilinear Mach disk with a region of unsteady subsonic flow in the vicinity of the throat. The mathematical model is based on the two-dimensional Euler equations for axisymmetric gas flows.     

Analysis of Annular Liquid Membranes and Their Singularities

The singularities of the equations governing the fluid dynamics of steady, axisymmetric, annular liquid membranes subject to gravity are analyzed by means of two techniques based on the membranes's slope and curvature, and the membrane's mean radius, mass per unit length, and axial and radial velocity components, respectively. It is shown that no singularity is possible at or downstream from the nozzle exit for Weber numbers greater than unity because of the gravitational pull. For a Weber number equal to one, a singularity at the nozzle exit appears and the flow slope there is undetermined; however, the slope acquires a finite value if the liquid is assumed to leave the nozzle at angle different from that of the annular orifice. It is also shown that, for Weber numbers smaller than one, a singularity may occur downstream from the nozzle exit which may also be removed, and that the shapes of annular liquid membranes for Weber numbers equal to or less than one take a rounded form which is in agreement with experimental observations. An asymptotic analysis shows that, to leading order, the shapes of capillary, annular liquid membranes are arcs of circumferences, and this result is again in accord with available experimental findings.     

环形喷管喷口气泡演化的实验研究

水下气泡的发展演化及气泡动力学行为是气液两相动力学的基础理论与水下射流应用的重要基础. 环形喷管/喷口形成的气泡及气体射流具有其不同于圆孔实心射流的特殊表现与规律机制,随着同心筒破水发射等特殊应用的出现,环形喷口气体射流/泡流的基础现象观测和机制分析成为迫切的需求. 基于环形喷管的设计和水下射流条件的分析,设计建立了一套环形喷管水箱实验系统,对水下环形喷管喷口气泡发展演化过程进行了初步的实验研究. 为观测研究气体通过环形喷管气泡生长发展过程,在较低压力、较低流速下,采用高速摄影仪记录气泡生长及发展演化过程. 结合对气泡发展演化过程的图像处理与分析,研究分析了环形喷口气泡形成区制、气泡生长过程形态发展特点、以及气泡形成时间及气泡体积变化特点. 研究表明:在本实验气体流量范围内(50.8~237.3 dm3/min),环形喷口气泡发展演化过程呈现较为明显的三周期区制,前泡尾流影响是环形气泡呈三周期区制的主要原因;不同周期内的气泡形成时间具有较稳定规律,并受到流量影响;气泡生长过程中有较为明显的下沉、回升特征;气泡表面张力、液体惯性与流动的共同作用,造成了典型的气泡顶部坍塌现象.      

Unsteady flow in a circular sector duct

Analytic solutions for the unsteady flow in a circular sector duct are found using series sums of Bessel integrals. For starting flow due to a step pressure gradient, the velocity profile is initially flat, then approaches the rounded steady state shape in a time scale proportional to the square of opening angle of the sector. For oscillatory flow, the velocity is quasi-steady for low frequencies, but shows “annular effect” at large frequencies. Increased opening angle increases the amplitude and the phase lag. In all cases, the shear stress at the apex is zero for acute sector angles but becomes infinite for obtuse sector angles.     

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.     

Effect of pipe rotation on downward co-current air–water flow in a vertical pipe

The present research experimentally studied the effect of pipe rotation on the flow patterns of downward gasliquid two-phase flow. Two-phase flow patterns and their transition boundaries were observed and analyzed at different pipe revolutions. The experimental setup was fabricated to show flow patterns in a downward direction. The setup includes a transparent vertical pipe with a diameter of 50 mm and an aspect ratio (L/d) of 80 that can rotate at different speeds. Eight flow maps were obtained at revolutions of 0, 60, 120, 180, 240, 300, 400 and 500 rpm by changing the air and water velocities at any revolution (a total of 2205 points). The gasliquid downward two-phase flow regimes were analyzed using image processing. The experimental results were compared with published flow maps for vertical flow. It was found that pipe rotation has major effect on flow patterns map and their transitions boundaries. Increasing pipe rotation cause slug and annular flow start at lower V_SG.     

Oscillating annular liquid membranes

Summary The response of annular liquid membranes to sinusoidal mass flow rate fluctuations at the nozzle exit is analyzed as a function of the amplitude and frequency of the axial velocity fluctuations at the nozzle exit and thermodynamic compression of the gas enclosed by the membrane. It is shown that both the pressure of the gases enclosed by the annular membrane and the axial distance at which the annular membrane merges on the symmetry axis are periodic functions of time which have the same period as that of the mass flow rate fluctuations at the nozzle exit. They are also nearly sinusoidal functions of time for small amplitudes of the mass flow rate fluctuations at the nozzle exit, and exhibit delay and lag times with respect to the sinusoidal axial velocity fluctuations at the nozzle exit. Both the delay and the lag times are functions of the amplitude and frequency of the mass flow rate fluctuations at the nozzle exit and the polytropic exponent. The amplitudes of both the pressure of the gases enclosed by the annular liquid membrane and the convergence length increase and decrease, resp., as the amplitude and frequency of the mass flow rate fluctuations at the nozzle exit, resp., are increased. They also increase as the polytropic exponent is increased.

---

Oszilierende rotationsschalenförmige Flüssigkeitsmembranen

Übersicht Untersucht wird das Verhalten rotationsschalenförmiger Flüssigkeitsmembranen in Abhängigkeit von der Amplitude und Frequenz der axialen Geschwindigkeitsschwankungen an der Düsenmündung und der thermodynamischen Verdichtung des eingeschlossenen Gases, wenn sich der Massestrom an der Düsenmündung sinusförmig ändert. Es wird gezeigt, daß der Druck des eingeschlossenen Gases und der axiale Mündungsabstand des Scheitels der geschlossenen Membran periodische Zeitfunktionen mit der Frequenz der Masseflußschwankung am Düsenaustritt sind. Für kleine Amplituden des Massestroms ist ihr Zeitverhalten ebenfalls fast-sinusförmig, wobei sie bezüglich der sinusförmigen axialen Geschwindigkeitsschwankungen an der Düsenmündung eine Ansprechzeit und Phasenverschiebung aufweisen. Ansprechzeit und Phasenverschiebung sind Funktionen von Amplitude und Frequenz der Massestromschwankung sowie des polytropen Exponenten. Die Amplitude von Gasdruck und Abstand des Membranscheitels von der Düse wächst bzw. fällt mit wachsender Amplitude und Frequenz des Massestroms. Beide nehmen außerdem mit dem polytropen Exponenten zu.

     

Modelling the complete operation of a free-piston shock tunnel for a low enthalpy condition

Only a limited number of free-stream flow properties can be measured in hypersonic impulse facilities at the nozzle exit. This poses challenges for experimenters when subsequently analysing experimental data obtained from these facilities. Typically in a reflected shock tunnel, a simple analysis that requires small amounts of computational resources is used to calculate quasi-steady gas properties. This simple analysis requires initial fill conditions and experimental measurements in analytical calculations of each major flow process, using forward coupling with minor corrections to include processes that are not directly modeled. However, this simplistic approach leads to an unknown level of discrepancy to the true flow properties. To explore the simple modelling techniques accuracy, this paper details the use of transient one and two-dimensional numerical simulations of a complete facility to obtain more refined free-stream flow properties from a free-piston reflected shock tunnel operating at low-enthalpy conditions. These calculations were verified by comparison to experimental data obtained from the facility. For the condition and facility investigated, the test conditions at nozzle exit produced with the simple modelling technique agree with the time and space averaged results from the complete facility calculations to within the accuracy of the experimental measurements.     

Compressible swirling flow through convergent-divergent nozzles

The effects of swirl on the rate of mass flow and on the velocity field in the throat region of axi-symmetric nozzles are studied analytically and experimentally. In the analytical phase, methods are developed for treating either the direct or the inverse problem for flow in de Lavai and annular nozzles, taking account of either weak or strong swirl. The experiments were performed in an annular nozzle, with swirl being imparted to the flow by adjustable vanes situated upstream of the test section. The analytical results facilitated an examination of the effects of swirl strength, distribution of swirl, and nozzle geometry. The rate of mass flow was found to decrease with increasing swirl strength. The mass flow results were well correlated by a swirl strength parameter evaluated at the throat, with swirl type and geometry being of secondary importance. Another effect of swirl was to shift the sonic line upstream of the geometric nozzle throat. The experimentally determined mass flow results were in agreement with the analytical predictions. Also, all of the qualitative characteristics of the local flow field measurements were reproduced by the analytical results.     

Calculation of hysteresis and flow-rate oscillations of base pressure in supersonic annular nozzles

The interaction of the turbulent axisymmetric near wake behind the face of the central body of an annular nozzle with the supersonic annular jet discharging from this nozzle is analyzed. The flow in the monoparametric near wake is calculated by the integral method [1] while the flow in the nonviscous jet is calculated by the method of through calculation using a monotonic explicit difference system of the first order of accuracy [2]. The interaction between the nonviscous and turbulent streams is determined by the displacement thickness of the wake. The initial conditions of the wake are determined from the integral conditions of attachment with the mixing flow in the isobaric base region. The interaction flow is described by the particular solution of the equations which passes through the singular saddle point — the throat of the wake. The near wake and base pressure in different modes of discharge from an annular nozzle at the exit cross section of which the ratio of outer and inner radii is y₂/y₁ = 1.3 and the Mach number is M = 2.54 are calculated as an example. The region of hysteresis of the base pressure, connected with the ambiguity of the interaction flow owing to the formation of the throat of the wake within the first or second barrel of the jet, and the parameters of the low-frequency flow-rate oscillations of base pressure in this region are determined. The results of the calculations are in satisfactory agreement with experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 125–130, January–February, 1977.     

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.     

Reynolds number effects on leading edge vortex development on a waving wing

The waving wing experiment is a fully three-dimensional simplification of the flapping wing motion observed in nature. The spanwise velocity gradient and wing starting and stopping acceleration that exist on an insect-like flapping wing are generated by rotational motion of a finite span wing. The flow development around a waving wing at Reynolds number between 10,000 and 60,000 has been studied using flow visualization and high-speed PIV to capture the unsteady velocity field. Lift and drag forces have been measured over a range of angles of attack, and the lift curve shape was similar in all cases. A transient high-lift peak approximately 1.5 times the quasi-steady value occurred in the first chord length of travel, caused by the formation of a strong attached leading edge vortex. This vortex appears to develop and shed more quickly at lower Reynolds numbers. The circulation of the leading edge vortex has been measured and agrees well with force data.     

Numerical investigation of overexpanded nozzle flows

The flow in a planar overexpanded nozzle with a slope discontinuity is studied numerically by means of two- (2D) and three-dimensional (3D) Reynolds-averaged Navier–Stokes simulations and is compared to experimental results. The nozzle pressure ratios (NPR) vary from 1.6 to 10. A good agreement is found between experimental and numerical results and two configurations are observed: under a certain critical NPR, the flow is shown to be asymmetrical with respect to the nozzle axis, while it is perfectly symmetrical for higher NPRs. The value of the critical NPR is found to be very dependent on the turbulence model. Finally, an hysteresis phenomenon is evidenced since the NPR at which the change of flow configuration occurs is different whether the NPR is increasing or decreasing in the nozzle.     

圆柱形充液室中4股贴壁燃气射流扩展特性的实验研究

为了探索高温高压周向均布4股贴壁燃气射流在受限空间中的扩展特性,设计了贴壁燃气射流在圆柱形充液室内扩展的实验装置,借助数字高速录像系统,观察了4股贴壁燃气射流在充液室中的扩展过程,发现由Kelvin-Helmholtz不稳定性引起的表面不规则一直存在于整个射流扩展过程;通过处理拍摄记录的射流扩展序列图,获得不同时刻射流扩展的轴向和径向位移; 对比了不同破膜喷射压力和喷孔结构参数对4股贴壁燃气射流扩展过程的影响。实验结果表明:喷孔面积越大,贴壁射流初期轴向扩展速度越大,但由于径向扩展达到交汇的时间较早,湍流掺混和干涉强烈,衰减也越快;破膜喷射压力越高,射流径向扩展到达交汇的时间越短; 破膜喷射压力从12 MPa升高到20 MPa,射流轴向扩展速度大幅增加,气液湍流掺混效应增强。     

An experimental study of the under-expanded swirling jet with secondary coaxial stream

The present study addresses experimental results for investigating the details of the near field flow characteristics produced in an under-expanded, dual, coaxial, swirling jet. The under-expanded swirling jet is discharged from a sonic inner nozzle. An outer annular nozzle produces co- and counter-swirling streams relative to the inner primary swirling jet. The interaction between both the outer annular swirling stream and inner under-expanded swirling jet is quantified by impact and static pressure measurements, and visualized by using the shadowgraph method. Experiments are performed for several different pressure ratios. The results show that the outer secondary co-swirling jet significantly changes the structure of the inner under-expanded swirling jet, such as the shock structures and the recirculation region generated at the jet axis. The effect of the outer secondary stream on the major structures of the inner primary swirling jet is strongly dependent on the pressure ratio of the inner swirling jet, regardless of the swirl direction of the outer stream.Received: 17 May 2004, Accepted: 27 September 2004, Published online: 26 November 2004[/PUBLISHED]H.D. Kim: Correspondence to     

Numerical simulations of nozzle starting process

The starting process of two-dimensional nozzle flow is investigated both experimentally and numerically. Discussions are made on the comparison between experimental and numerical results. Performances of two numerical methods which are used in the present study of unsteady flow problem are also discussed and indications for future development of numerical tools to study nozzle problems are obtained. Received 16 June 1998 / Accepted 17 August 1998     

Simulation of the starting flow in a wedge–like nozzle

The starting process of the flow in a wedge-like expansion nozzle of a shock tunnel is simulated by an unsplit 2-D GRP scheme on an unstructured grid. The scheme is briefly outlined and results are presented and discussed in comparison to the experimental (shadowgraph) findings obtained by Amann. The simulated pattern of reflected and transmitted shock waves in the nozzle inlet region and inside the nozzle is found to agree well with the experimental data. Received 5 April 1996 / Accepted 16 June 1997     

Aerodynamic external pressure loads on a semi-circular bluff body under wind gusts

This brief communication concerns the unsteady aerodynamic external pressure loads acting on a semi-circular bluff body lying on a floor under wind gusts and describes the theoretical model, experimental setup, and experimental results obtained. The experimental setup is based on an open circuit, closed test section, low speed wind tunnel, which includes a sinusoidal gust generating mechanism, designed and built at the Instituto de Microgravedad “Ignacio Da Riva” of the Universidad Politécnica de Madrid (IDR/UPM). Based on the potential flow theory, a theoretical model has been proposed to analyse the problem, and experimental tests have been performed to study the unsteady aerodynamic loads on a semi-circular bluff body. By fitting the theoretical model predictions with the experimental results, influencing parameters of the unsteady aerodynamic loads are ascertained. The values of these parameters can help in clarifying the phenomenon of the external pressure loads on semi-circular bluff body under various gust frequencies. The theoretical model proposed allows the pressure variation to be split into two contributions, a quasi-steady term and an unsteady term with a simple physical meaning.     

Parametric study on supersonic flutter of angle-ply laminated plates using shear deformable finite element method

The influence of fiber orientation,flow yaw angle and length-to-thickness ratio on flutter characteristics of angle-ply laminated plates in supersonic flow is studied by finite element approach.The structural model is established using the Reissner-Mindlin theory in which the transverse shear deformation is considered.The aerodynamic pressure is evaluated by the quasi-steady first-order piston theory.The equations of motion are formulated based on the principle of virtual work.With the harmonic motion assumption,the flutter boundary is determined by solving a series of complex eigenvalue problems.Numerical study shows that (1) The flutter dynamic pressure and the coalescence of flutter modes depend on fiber orientation,flow yaw angle and length-to-thickness ratio;(2) The laminated plate with all fibers aligned with the flow direction gives the highest flutter dynamic pressure,but a slight yawing of the flow from the fiber orientation results in a sharp decrease of the flutter dynamic pressure;(3) The angle-ply laminated plate with fiber orientation angle equal to flow yaw angle gives high flutter dynamic pressure,but not the maximum flutter dynamic pressure;(4) With the decrease of length-to-thickness ratio,an adverse effect due to mode transition on the flutter dynamic pressure is found.