Numerical study for hysteresis phenomena of shock wave reflection in overexpanded axisymmetric supersonic jet

When the high-pressure gas is exhausted to the vacuum chamber from the supersonic nozzle,the overexpandedsupersonic jet is formed at specific condition.In two-dimensional supersonic jet,furthermore,it is known that thehysteresis phenomena for the reflection type of shock wave in the flow field is occurred under the quasi-steadyflow and for instance,the transitional pressure ratio between the regular reflection(RR)and Mach reflection(MR) is affected by this phenomenon.Many papers have described the hysteresis phenomena for underexpandedsupersonic jet,but this phenomenon under the overexpanded axisymmetric jet has not been detailed in the pastpapers.The purpose of this study is to clear the hysteresis phenomena for the reflection type of shock wave at theoverexpanded axisymmetric jet using the TVD method and to discuss the characteristic of hysteresis phenomena.     

Shock wave in supersonic moist air jet for a low pressure ratio

In the present study,a computational fluid dynamics work was performed to investigate the occurrence of the shock wave by condensation in supersonic moist air jet.The unsteady,compressible axisymmetric Navier-Stokes equation is solved by TVD(Total Variation Diminishing) scheme in this study.The numerical simulations have been performed for low pressure ratio and various humidities.The results show the occurrence of the shock wave in supersonic moist air jet for a low pressure ratio when Mach disk does not occur,depending on humidity of the air.     

Navier—Stokes Computations of the Supersonic Ejector—Diffuser System with a Second Throat

The supersonic ejector-diffuser system with a second throat was simulated using CFD.An explicit finite volume scheme was applied to solve two-dimensional Navier-Stokes equations with standard κ-εturbulence model.The vacuum performance of the supersonic ejector-diffuser system was investigated by changing the ejector throat area ration and the operating pressure ratio.Two convergent-divergent nozzles with design Mach number of 2.11 and 3.41 were selected to give the supersonic operation of the ejector-diffuser system.The presence of a second throat strongly affected the shock wave structure inside the mixing tube as well as the spreading of the under-expanded jet discharging from the primary nozzle.There were optimum values of the operating pressure ratio and ejector throat area ratio for the vacuum performance of the system to maximize.     

A Study of Under-expanded Moist Air Jet Impinging on a Flat Plate

When a gas expands through a convergent nozzle in which the ratio of the ambient to the stagnation pressures is higher than that of the critical one, the issuing jet from the nozzle is under-expanded. If a flat plate is placed normal to the jet at a certain distance from the nozzle, a detached shock wave is formed at a region between the nozzle exit and the plate. In general, supersonic moist air jet technologies with non-equilibrium condensation are very often applied to industrial manufacturing processes. In spite of the importance in major characteristics of the supersonic moist air jets impinging to a solid body, its qualitative characteristics are not known satisfactorily. In the present study, the effect of the non-equilibrium condensation on the under-expanded air jet impinging on a vertical flat plate is investigated numerically in the case with non-equilibrium condensation, frequency of oscillation for the flow field becomes larger than that without the non-equilibrium condensation, and amplitudes of static pressure become small compared with those of dry air. Furthermore, the numerical results are compared with experimental ones.     

A study of the gas flow through air jet loom

Air jet loom,as one of the shuttleless looms,transports a yarn into warps using viscosity and kinetic energy of anair jet.Performance of this picking system depends on the ability of instantaneous inhalation/exhaust,configura-tion of nozzle,operation characteristics of a check valve,etc.In the recent past,many studies have been reportedon the air jet discharged from a nozzle exit,but studies for understanding the flow field characteristics associatedwith shear layer and shock wave/boundary layer interaction in the nozzle were not conducted enough.In this pa-per,a computational study was performed to explain the flow field in the air jet nozzle with an acceleration tubeand validated with previous experimental data available.The results obtained from the computational study showthat,in the supersonic flow regime,the flow field depends significantly on the length of acceleration tube.Asnozzle pressure ratio increases,drag force acting on the string also increases.For a longer acceleration tube,thetotal pressure loss is large,owing to the frictional loss.     

Transient supersonic release of hydrogen from a high pressure vessel: A computational analysis

Understanding the characteristics of a hydrogen gas jet exiting from a compressed vessel during vessel rupture or venting is crucial for determining safety requirements for distribution and use of hydrogen. Such jets can undergo several flow regimes during venting, from initial supersonic flow, to transonic, to subsonic flow regimes as the pressure in the vessel decreases. A bow shock wave is a characteristic flow structure during the initial stage of the jet development, and this paper focuses on the development of the bow shock wave and the jet structure behind it. The transient behaviour of an impulsively initiated jet is investigated using unsteady, compressible flow simulations. Both the cases of a hydrogen jet exiting into quiescent hydrogen and of a hydrogen jet exiting into air are presented. The gases are considered to be ideal, and the computational domain is axisymmetric. The jet structure, including the shock wave and flow separation due to an adverse pressure gradient at the nozzle is investigated with a focus on the differences between the single- and multi-component flow scenarios.     

Study on Transonic Tone in an Axisymmetric Supersonic Nozzle

This paper describes experimental and numerical works to investigate noise phenomenon in supersonic flow dis- charged from a convergent-divergent nozzle. The noise phenomenon of flow is generated by an emission of ＇transonic tones＇. The results obtained show that the frequency of a transonic tone, that differs from the frequency of a screech tone due to the shock-cell structures in a jet and originates in the shock wave in the nozzle, increases in proportion to the nozzle pressure ratio. The high-order transonic tone has the directivity in the direction of the flow. As for the transonic tone＇s frequency, the separated zone was calculated by using a simple flow model con- sidering the propagating perturbation. The results of the model corresponded to the results of this experiment well.     

Boundary layer effects on the critical nozzle of hydrogen sonic jet

When hydrogen flows through a small finite length constant exit area nozzle the viscous effects create a fluid throat which acts as a converging-diverging nozzle and lead to Mach number greater than one at the exit if the jet is under-expanded. This phenomenon influences the mass flow rate and the dispersion cloud size. In this study, the boundary layer effect on the unsteady hydrogen sonic jet flow through a 1 mm diameter pipe from a high pressure reservoir (up to 70 MPa) is studied using computational fluid dynamics with a large eddy simulation turbulence model. This viscous flow simulation is compared with a non-viscous simulation to demonstrate that the velocity is supersonic at the exit of a small exit nozzle and that the mass flow is reduced.     

Numerical investigation of a high pressure hydrogen jet of 82 MPa with adaptive mesh refinement: The starting transient evolution and Mach disk stabilization

A three-dimensional (3D) strongly under expanded hydrogen jet flow is numerically investigated with a storage pressure of 82 MPa and a tiny jet orifice diameter of 0.2 mm. The full compressible Navier–Stokes equations are utilized in a domain with a size of about 3 × 3 × 6 m which is discretized by employing adaptive mesh refinement (AMR) technology to reduce the number of grid cells. The highly under expanded hydrogen jet flow with a nozzle pressure ratio (NPR) of about 809 is then captured from the very beginning when hydrogen is ejected out of the jet orifice. The starting transient evolution and Mach disk stabilization are then discussed in details. It is found that with the AMR technology, the grid number can be greatly reduced and high resolutions can be easily installed to deal with the small jet orifice size together with those flow microscales. Jet flow is numerically captured and discussed. It is found that over expansion occurs in this under expanded jet. The secondary shock is generated to match the pressure which plays the most important physics in the starting transient period of an under expanded hydrogen jet. The Mach shock and the lateral barrel shock which are originated from the secondary shock play central roles. The jet flow is divided into subsonic and supersonic branches in the near-nozzle region, which makes the highly under-expanded jets have two annular shear layers, the inner and outer layer, in this region.     

Configuration of Shock Waves in Two-Dimensional Overexpanded Jets

An experimental and analytical study has been carried out to obtain the clear understanding of a shock wave transition associated with a steady two-dimensional overexpanded flow. Two-dimensional inviscid theory with respect to a shock wave reflection is used in the present study on the characteristic of shock waves. The results obtained from the flow analysis are compared with those obtained from flow visualizations. It is shown that in the region of regular reflection, the angle of an incident shock wave becomes lower than that calculated by two shock theory with an increment in the ratio pe/pb of the nozzle exit pressure pe to the back pressure pb. It is indicated that the configuration of shock waves in overexpanded jets is influenced by the divergent angle at the nozzle exit. Also it is shown from the flow visualization that a series of shock waves move into the nozzle inside with a decrease in pressure ratio pe/pb, even if the pe/pb is under overexpanded conditions.     

Flow characteristics of rectangular underexpanded impinging jets

In this paper, the flow fields of underexpanded impinging jet issued from rectangular nozzles of aspect ratio 1, 3 and 5 are numerically and experimentally studied. Two dimensional temperature and pressure distributions are measured by using infrared camera and the combination of a pressure scanning device and a stepping motor, respectively. The variation of the stagnation pressure on the impinging plate reveals that a hysteretic phenomenon exists during the increasing and decreasing of the pressure ratio for the aspect ratio of 3.0 and 5.0. It is also found that the nozzle of aspect ratio 1.0 caused the largest total pressure loss pc / p0 = 0.27 at the pressure ratio of p0 /pb = 6.5, where pc is the stagnation center pressure on the wall, p0 the upstream stagnation pressure, pb the ambient pressure. The other two nozzles showed that the pressure loss pc /p0 =0.52 and 0.55 were achieved by the nozzles of the aspect ratio 3,0 and 5.0, respectively. The comparison between the calculations and experiments is fairly good, showing the three dimensional streamlines and structures of the shock waves in the jets. However, the hysteresis of the pressure variations observed in the experiments between the pressure ratio of 3.5 and 4.5 cannot be confirmed in the calculations.     

Effect of Axisymmetric Sonic Nozzle Geometry on Characteristics of Supersonic Air Jet

The effect of nozzle geometry on sonic line and characteristics of supersonic air jet was studied. Computational fluid dynamics was applied in this study. The axisymmetric nozzle geometries investigated were two different contour converging nozzles, two different conically converging sharp-edged nozzles and a sharp-edged orifice. The results show that the supersonic jet structure, sonic line and streamlines in supersonic jet are strongly influenced by the nozzle geometry, and the total pressure loss increases with the increase of Mach disk diameter. The present numerical simulation is an effective tool to evaluate compressible flows in supersonic air jet.     

Effect of Nonequilibrium Homogenous Condensation on Flow Fields in a Supersonic Nozzle

INTRODUCTIONManystudies[1-131onthecondensationshockwaveoccurringinthecaseoftheraPidexPansionofmoistairorsteaminasupersonicnozzlehavebeenper-formed,andthecharacteristicsofcondensationshock'wavehavenearlybeenclarilied.Acondensationshockwavealsooccursinthebladepassageinasteamturbinel14,15]andsuchacondensationshockwavinteractswiththeboundarylayeronthesurfaceoftheblade.Thus,thefiowinthebladepassageofthesteamturbinewiththecondensationshockwavehasnotyetbeenclariliedl16'17].InthepreseDtstudythee…     

The initiation and propagation of detonation in supersonic combustible flow with boundary layer

Adaptive simulations solving the Navier-Stokes equations have been conducted in order to get a better understanding on the detonation initiation and propagation in a stoichiometric H₂/O₂/Ar supersonic mixture with boundary layer. The detonation is initiated by a continuous hot jet. When reflecting on the wall, the jet induced bow shock interacts with the boundary layer and forms the shock boundary layer interaction phenomena, while in Euler result the bow shock forms Mach reflection. The investigation shows that the Navier-Stokes simulation result is structurally in better agreement with the experiment compared with that of the inviscid Euler simulation result. The bow shock interacts with the separation shock, forming the shock induced combustion behind the interaction zone. Then the combustion front couples with shock and forms Mach stem induced detonation. The Mach stem induced detonation continues to getting higher and propagating upstream, initiating the main flow. The initiated partial detonation exists with the separation shock induced combustion front, forming an “oblique shock induced combustion-partial detonation” structure in the main flow. The investigation on the influence of free stream Mach number further confirms that the boundary layer has an important influence on detonation initiation. The parametric studies also show that there exists a free stream Mach number range to initiate the partial detonation in supersonic combustible flow successfully.     

Navier-Stokes Computstions of the Supersonic Ejector Diffuser System with a Second Throat

INTRODUCTIONUnloosetheconvenhonalfluidmachineryinwhichusuallyhavesomerotatingormovingparts,theejectorisadevicewhichemploysahigh-velocityprimalmotivefluidtoentrainandaccelerateasecondalsuctionfluidwhichmovesslower.Theresulhngkinehcenergyofthefutureissubsequentlyusedforself-compressiontOahigherPressure,thusPerformingthefunchonofacompressor.TheejectorsystemhaslongbeenappliedtOjetpumps,vacuumPumps,high-altitUdesimulators,V/STOLs,etc['-'l;becauseofthemajoradvantagesofitsstrUcturalsimplicit…     

Characteristics of the Mach Disk in the Underexpanded Jet in which the Back Pressure Continuously Changes with Time

When the high-pressure gas is exhausted to the vacuum chamber from the nozzle, the underexpanded supersonic jet contained with the Mach disk is generally formed. The eventual purpose of this study is to clarify the unsteady phenomenon of the underexpanded free jet when the back pressure continuously changes with time. The characteristic of the Mach disk has been clarified in consideration of the diameter and position of it by the numerical analysis in this paper. The sonic jet of the exit Mach number Me=1 is assumed and the axisymmetric conservational equation is solved by the TVD method in the numerical calculation. The diameter and position of the Mach disk differs with the results of a steady jet and the influence on the continuously changing of the back pressure is evidenced from the comparison with the case of steady supersonic jet.     

Shock Wave—Boundary Layer Interaction in Forced Shock Oscillations

The flow in transonic diffusers as well as in supersonic air intakes becomes often unsteady due to shock wave boundary layer interaction. The oscillations may be induced by natural separation unsteadiness or may be forced by boundary conditions. Significant improvement of CFD tools, increase of computer resources as well as development of experimental methods have again.drawn the attention of researchers to this topic. To investigate the problem forced oscillations of transonic turbulent flow in asymmetric two-dimensional Laval nozzle were considered. A viscous, perfect gas flow, was numerically simulated using the Reynolds-averaged compressible Navier-Stokes solver SPARC, employing a two-equation, eddy viscosity, turbulence closure in the URANS approach.For time-dependent and stationary flow simulations, Mach numbers upstream of the shock between 1.2 and 1.4 were considered. Comparison of computed and experimental data for steady states generally gave acceptable agreement. In the case of forced oscilla     

Generation of overpressure due to condensation in moist air jet

In the present study,a computational fluid dynamics method has been applied to investigate the effects of initialdegree of supersaturation at reservoir condition on under-expanded sonic jet structures,such as Mach disk loca-tion and diameter,barrel shock wave and jet boundary.The axisymmetfic nozzle geometry investigated was aconverging nozzle with straight part.As a result,it was found that the overpressures due to condensation generateand the characteristics of flow with generation of overpressure due to condensation in the jet were different fromthose without condensation.     

Unsteady shock-flow characteristics in an over-expanded rocket nozzle

<正>A numerical investigation of transient side-loads in an axisymmetric over-expanded thrust optimized contour nozzle is presented.These nozzles experience side-loads during start-up and shut-down operations,because of the flow separation at nozzle walls.Two types of flow separations such as FSS and RSS shock structure occur.A two-dimension numerical simulation has been carried out over an axisymmetric TOC nozzle to validate present results and investigate oscillatory flow characteristics for start-up processes.Reynolds Averaged Navier-Stokes equations are numerically solved using a fully implicit finite volume scheme.Governing equations are solved by coupled implicit scheme.Reynolds Stress turbulence model is selected.Present computed pressure at the nozzle wall closely matched with experiment data.A hysteresis phenomenon has been observed between these two shock structures.The transition from FSS to RSS pattern during start-up process has shown maximum nozzle wall pressure.Nozzle wall pressure and shear stress values have shown fluctuations during the FSS to RSS transition. The oscillatory pressure has been observed on the nozzle wall for high pressure ratio.Present results have shown that magnitude of the nozzle wall pressure variation is high for the oscillatory phenomenon.     

A visual observation of the air flow pattern for the high speed nozzle applicable to high power laser cutting and welding

In this study, the flow pattern and pressure variation of the nozzles applicable to high power laser cutting and welding were studied. A total of five nozzles are made and tested with nozzle diameter ranging from 0.8 to 4 mm. The depth of focus and the width of focus are measured based on the flow visualization. It is found that the depth of focus is increased with the rise of exit Mach number while the width of focus is increased with the nozzle diameter. The visual results indicate that the supersonic nozzle reveals a more concentrated jet flow pattern even the flow has passed through the depth of focus. On the other hand, appreciate deviation of the flow pattern is observed for the subsonic nozzle after the depth of focus. As far as more concentrated air flow pattern is concerned, a supersonic nozzle with an exit diameter less than 3.0 mm is recommended. The total pressure decreasing tremendously with the exit Mach number is encountered while moderate decline of the static and dynamic pressure for supersonic nozzles is seen. However, its corresponding dynamic pressure is still higher than that of the subsonic nozzle.