Local Solution of Three-Dimensional Axisymmetric Supersonic Flow in a Nozzle

In this paper, we construct a local supersonic flow in a 3-dimensional axis-symmetry nozzle when a uniform supersonic flow inserts the throat. We apply the local existence theory of boundary value problem for quasilinear hyperbolic system to solve this problem. The boundary value condition is set in particular to guarantee the character number condition. By this trick, the theory in quasilinear hyperbolic system can be employed to a large range of the boundary value problem.

Supersonic swirling characteristics of natural gas in convergent-divergent nozzles

The supersonic nozzle is a new apparatus which can be used to condense and separate water and heavy hydrocarbons from natural gas.The swirling separation of natural gas in the convergent-divergent nozzle was numerically simulated based on a new design which incorporates a central body. Axial distribution of the main parameters of gas flow was investigated,while the basic parameters of gas flow were obtained as functions of radius at the nozzle exit.The effect of the nozzle geometry on the swirling separation was analyzed.The numerical results show that water and heavy hydrocarbons can be condensed and separated from natural gas under the combined effect of the low temperature（-80℃） and the centrifugal field（482,400g,g is the acceleration of gravity）.The gas dynamic parameters are uniformly distributed correspondingly in the radial central region of the channel,for example the distribution range of the static temperature and the centrifugal acceleration are from -80 to -55℃and 220,000g to 500,000g,respectively,which would create good conditions for the cyclone separation of the liquids.However,high gradients of gas dynamic parameters near the channel walls may impair the process of separation.The geometry of the nozzle has a great influence on the separation performance. Increasing the nozzle convergent angle can improve the separation efficiency.The swirling natural gas can be well separated when the divergent angle takes values from 4°to 12°in the convergent-divergent nozzle.

Supersonic Two-Dimensional Minimum Length Nozzle Design at High Temperature. Application for Air

When the stagnation temperature of a perfect gas increases, the specific heat ratio does not remain constant any more, and start to vary with this temperature. The gas remains perfect, its state equation remains always valid, except it will name in more calorically imperfect gas or gas at High Temperature. The goal of this work is to trace the profiles of the supersonic Minimum Length Nozzle with centered expansion when the stagnation temperature is taken into account, lower than the threshold of dissociation of the molecules and to have for each exit Mach number several nozzles shapes by changing the value of the temperature. The method of characteristics is used with a new form of the Prandtl Meyer function at high temperature. The resolution of the obtained equations is done by the second order of fmite differences method by using the predictor corrector algorithm. A study on the error given by the perfect gas model compared to our model is presented. The comparison is made with a calorically perfect gas for goal to give a limit of application of this model. The application is for the air.

Effect of Stagnation Temperature on the Supersonic Two-Dimensional Plug Nozzle Conception. Application for Air

When the stagnation temperature of a perfect gas increases, the specific heats and their ratio do not remain constant any more and start to vary with this temperature. The gas remains perfect, its state equation remains always valid, except it will name in more calorically imperfect gas or gas at High Temperature. The goal of this research is to trace the profiles of the supersonic plug nozzle when this stagnation temperature is taken into account, lower than the threshold of dissociation of the molecules, by using the new formula of the Prandtl Meyer function, and to have for each exit Mach number, several nozzles shapes by changing the value of this temperature. A study on the error given by the PG （perfect gas） model compared to our model at high temperature is presented. The comparison is made with the case of a calorically perfect gas aiming to give a limit of application of this model. The application is for the air.

Effects of Supersonic Nozzle Geometry on Characteristics of Shock Wave Structure

Interaction between the normal shock wave and the turbulent boundary layer in a supersonic nozzle becomes complex with an increase of a Mach number just before the shock wave. When the shock wave is strong enough to separate the boundary layer, the shock wave is bifurcated, and the 2nd and 3rd shock waves are formed downstream of the shock wave. The effect of a series of shock waves thus formed, called shock train, is considered to be similar to the effect of one normal shock wave, and the shock train is called pseudo-shock wave. There are many researches on the configuration of the shock wave. However, so far, very few researches have been done on the asymmetric characteristics of the leading shock wave in supersonic nozzles. In the present study, the effect of nozzle geometry on asymmetric shock wave in supersonic nozzles has been investigated experimentally.

Three-Dimensional Structure of Non-Equilibrium Homogeneous Condensation Flow in a Supersonic Rectangular Nozzle

Numerical simulations have been carried out for a supersonic three-dimensional rectangular arc nozzle, where a secondary flow toward the center of the curvature occurs due to the shape of the nozzle. It is known that secondary flow causes longitudinal vortices to form near the wall of the nozzle corner, making the nozzle outlet flow unstable and induces loss of transport energy. When the working fluid is a condensable gas with relatively large latent heat such as moist air or steam, rapid accelerated expansion in the nozzle causes non-equilibrium condensation due to supersaturation. After the release of latent heat during phase transition, nozzle flow continues expanding at an equilibrium saturation condition. In the absence of foreign particles, e.g. ions or dust particles, condensation nuclei are formed in the gas itself causing non-equilibrium homogeneous condensation. Supersonic nozzle flow properties vary considerably due to the occurrence of condensation phenomenon. The objective of this study is to investigate the effect of non-equilibrium homogeneous condensation on the longitudinal vortices which form in the range close to the corner of rectangular arc nozzle numerically.

Multi-Schlieren CT Measurements of Supersonic Microjets from Circular and Square Micro Nozzles

Instantaneous three-dimensional (3D) density distributions of a shock-cell structure of perfectly and imperfectly expanded supersonic microjets escaping into an ambient space are measured. For the 3D observation of supersonic microjets, non-scanning 3D computerized tomography (CT) technique using a 20-directional quantitative schlieren optical system with flashlight source is employed for simultaneous schlieren photography. The 3D density distributions data of the microjets are obtained by 3D-CT reconstruction of the projection’s images using maximum likelihood-expectation maximization. Axisymmetric convergent-divergent (Laval) circular and square micro nozzles with operating nozzle pressure ratio 5.0, 4.5, 4.0, 3.67, and 3.5 have been studied. This study examines perfectly expanded, overexpanded, and underexpanded supersonic microjets issued from micro nozzles with fully expanded jet Mach numbers Mj ranging from 1.47 - 1.71, where the design Mach number is Md = 1.5. A complex phenomenon for free square microjets called axis switching is clearly observed with two types “upright” and “diagonal” of “cross-shaped”. The initial axis-switching is 45° within the first shock-cell range. In addition, from the symmetry and diagonal views of square microjets for the first shock-cells, two different patterns of shock waves are viewed. The shock-cell spacing and supersonic core length for all nozzle pressure ratios are investigated and reported.

Time Characterization of High Density Gas Jet from a Pulsed Supersonic Nozzle via Laser Produced Plasma

A high-density gas jet supersonic nozzle is reported in this paper. The jitter and actuation time of the nozzle is determined by the pin discharge and laser spark radiation respectively. The jitter time of the nozzle is within 10μs with the backing pressure as high as 25 bar. With a nanosecond laser pulse focused on the gas jet about 1 mm below the nozzle, the actuation time is calculated to be about 15 ms by detecting the laser produced spark radiation, which reveals the existence of the gas jet and the relative gas density evolving with time. Consequently the gas density is estimated to be well above 10^19 cm^-3, compared with theoretical simulations from the nozzle parameters.

Improvement of a Propulsion Equipment with a Supersonic Nozzle for Single Pulse Detonation

A pulse detonation engine (PDE) is one of candidates of aerospace engines for supersonic cruse. In the paper, a supersonic nozzle ejector is designed to increase thrust of single pulse detonation for methane-oxygen and hydrogen-oxygen mixtures. The design method is based on the conventional characteristic method and inlet condition is averaged value of detonations of methane-oxygen and hydrogen-oxygen mixtures. Comparison of thrusts with a design nozzle and no nozzle (straight- type) is conducted to ensure the designed nozzle performance. Furthermore, the flow velocity, temperature and velocity of the designed nozzle are calculated to ensure its appropriateness with the commercial software ANSYS CFX. Consequently, we succeed in increasing the thrusts of the single pulse detonation with the nozzle, which are 1.4 and 2.0 times as large as ones of straight- type for methane-oxygen and hydrogen-oxygen mixtures respectively.

Study on the Role of Supersonic Nozzle in Fiber Laser Cutting of Stainless Steel

Striation-free laser cutting, especially for thick section steel, is hard to obtain due to several factors. The inside shape of the gas nozzle is considered to be one of the most vital factors in striation-free fiber laser cutting. 0.8 mm normal nozzle and a supersonic nozzle are used to cut 0.8 mm AISI316L stainless steel (022Cr17Ni12Mo2) separately. The orthogonal experiment takes nozzle standoff distance, cutting speed, Laser power and gas pressure as its impacting factors. The same orthogonal table is adopted in different condition, using normal nozzle and using supersonic nozzle. In the mean time, Ar gas is used as assisted cutting gas in the experiment. The data from this experiment show that supersonic nozzle seems to be a strong helper for fiber laser cutting. Feed rate’s effect seems stable and inconspicuous under the condition of using supersonic nozzle.

A Computational Study of the Gas-Solid Suspension Flow through a Supersonic Nozzle

The present study focuses on numerical simulation of the gas-solid suspension flow in a supersonic nozzle. The Euler- Lagrange approach using a Discrete Phase Model (DPM) has been used to solve the compressible Navier-Stokes equa- tions. A fully implicit finite volume scheme has been employed to discretize the governing equations. Based upon the present CFD results, the particle loading effect on gas-solid suspension flow was investigated. The results show that the presence of particles has a big influence on the gas phase behavior. The structure of shock train, the separation point, and the vortex of the backflow are all related to particle loading. As the particle loading increases the flow characteris- tics behave differently such as 1) the strength of shock train decreases, 2) the separation point moves toward the nozzle exit, 3) the number and strength of vortex increase, 4) the strength of first shock also increases while the other pseudo shocks decreases. The change of gas flow behavior in turn affects the particle distribution. The particles are concen- trated at the shear layers separated from the upper wall surface.

Numerical Analysis of Chevron Nozzle Effects on Performance of the Supersonic Ejector-Diffuser System

The supersonic nozzle is the most important device of an ejector-diffuser system.The best operation condition and optimal structure of supersonic nozzle are hardly known due to the complicated turbulent mixing,compressibility effects and even flow unsteadiness which are generated around the nozzle extent.In the present study,the primary stream nozzle was redesigned using convergent nozzle to activate the shear actions between the primary and secondary streams,by means of longitudinal vortices generated between the Chevron lobes.Exactly same geometrical model of ejector-diffuser system was created to validate the results of experimental data.The operation characteristics of the ejector system were compared between Chevron nozzle and conventional convergent nozzle for the primary stream.A CFD method has been applied to simulate the supersonic flows and shock waves inside the ejector.It is observed that the flow structure and shock system were changed and primary numerical analysis results show that the Chevron nozzle achieve a positive effect on the supersonic ejector-diffuser system performance.The ejector with Chevron nozzle can entrain more secondary stream with less primary stream mass flow rate.

Computational Analysis of Mixing Guide Vane Effects on Performance of the Supersonic Ejector-Diffuser System

The flow field in the ejector-diffuser system and its optimal operation condition are hardly complicated due to the complicated turbulent mixing, compressibility effects and even flow unsteadiness which are generated inside the ejector- diffuser system. This paper aims at the improvement in ejector-diffuser system by focusing attention on entrainment ratio and pressure recovery. Several mixing guide vanes were installed at the inlet of the secondary stream for the purpose of the performance improvement of the ejector system. A Computational Fluid Dynamics (CFD) method based on Fluent has been applied to simulate the supersonic flows and shock waves inside the ejector. A finite volume scheme and density-based solver with coupled scheme were applied in the computational process. Standard k-ω turbulent model, implicit formulations were used considering the accuracy and stability. Previous experimental results showed that more flow vortexes were generated and more vertical flow was introduced into the stream under a mixing guide vane influence. Besides these effects on the secondary stream, the mixing guide vane effects on the shock system of the primary stream were also investigated in this paper. Optimal analysis results of the mixing guide vane effects were also carried out in detail in terms of the positions, lengths and numbers to achieve the best operation condition. The comparison of ejector performance with and without the mixing guide vane was obtained. The ejector-diffuser system performance is discussed in terms of the entrainment ratio, pressure recovery as well as total pressure loss.

A novel contour design technique of super/hypersonic nozzle diverging section with sharing throat

A straightforward technique has been developed to quickly determine the wall contour of super/hypersonic nozzles working at multiply Mach number which share a common throat section.Mach number distribution along the centerline of the nozzle is specified in advance and divided into two sections,both of which are described by the b-spline function.The first section is shared by different exit Mach number nozzles.The nozzle contour is determined by the method of characteristics plus boundary layer correction.An example of this design method is employed to illustrate the technique with a computational fluid dynamics calculation.The simulation results indicate that desired Mach numbers are obtained at the nozzle exit,and the good flow quality is attained for different nozzles within δMa/Ma<±0.56% in the flow core region.This technique improves the design precision of the converging-diverging nozzle,cancels waves completely,and achieves nozzles with multiple Mach number exiting which share a common throat section.

Numerical Study on the Effect of Unsteady Downstream Conditions on Hydrogen Gas Flow through a Critical Nozzle

A critical nozzle (sonic nozzle) is used to measure the mass flow rate of gas. It is well known that the coefficient of discharge of the flow in the nozzle is a single function of Reynolds number. The purpose of the present study is to investigate the effect of unsteady downstream condition on hydrogen gas flow through a sonic nozzle, numerically. Navier-Stokes equations were solved numerically using 3rd-order MUSCL type TVD finite-difference scheme with a second-order fractional-step for time integration. A standard k-ε model was used as a turbulence model. The computational results showed that the discharge coefficients in case without pressure fluctuations were in good agreement with experimental results. Further, it was found that the pressure fluctuations tended to propagate upstream of nozzle throat with the decrease of Reynolds number and an increase of amplitude of pressure fluctuations.

Supersonic expansion and condensation characteristics of hydrogen gas under different temperature conditions

This paper introduced supersonic expansion liquefaction technology into the field of hydrogen liquefaction.The mathematical model for supersonic condensation of hydrogen gas in a Laval nozzle model was established.The supersonic expansion and condensation characteristics of hydrogen gas under different temperature conditions were investigated.The simulation results show that the droplet number rises rapidly from 0 at the nozzle throat as the inlet temperature increases,and the maximum droplet number generated is 1.339×10^(18)kg^(-1)at inlet temperature of 36.0 K.When hydrogen nucleation occurs,the droplet radius increases significantly and shows a positive correlation with the increase in the inlet temperature,and the maximum droplet radii are 6.667×10^(-8)m,1.043×10^(-7)m,and 1.099×10^(-7)m when the inlet temperature is 36.0 K,36.5 K,and 37.0 K,respectively.The maximum nucleation rate decreases with increasing inlet temperature,and the nucleation region of the Laval nozzle becomes wider.The liquefaction efficiency can be effectively improved by lowering the inlet temperature.This is because a lower inlet temperature provides more subcooling,which allows the hydrogen to reach the thermodynamic conditions required for large-scale condensation more quickly.

Integrated supersonic wind tunnel nozzle

In supersonic wind tunnels, the airflow at the exit of a convergent-divergent nozzle is affected by the connection between the nozzle and test section, because the connection is a source of disturbance for supersonic flow and the source of disturbance generated by this disturbance propagates downstream. In order to avoid the disturbance, the test can only be carried out in the rhombus area. However, for the supersonic nozzle, the rhombus region is small, limiting the size and attitude angle of the test model. An integrated supersonic nozzle is a nozzle and a test section as a whole, which is designed to weaken or eliminate the disturbance. The inviscid contour of the supersonic nozzle is based on the method of characteristics. A new curve is formed by the smooth connection between the inviscid contour and test section, and the boundary layer is corrected for the overall curve. Integrated supersonic nozzles with Mach number 1.5 and 2 are designed, which are based on this method. The flow field is validated by numerical and experimental results. The results of the study highlight the importance of the connection about the nozzle outlet and test section. They clearly show that the wave system does not exist at the exit of the supersonic nozzle, and the flow field is uniform throughout the test section.

Acoustic measurements of models of military style supersonic nozzle jets

Modern military aircraft jet engines are designed with variable-geometry nozzles to provide optimal thrust in different operating conditions, depending on the flight envelope. How- ever, acoustic measurements for such nozzles are scarce, due to the cost involved in making full- scale measurements and the lack of details about the exact geometries of these nozzles. Thus the present effort at Pennsylvania State University （PSU） in partnership with GE Aviation and the NASA Glenn Research Center is aiming to study and characterize the acoustic field produced by supersonic jets issuing from converging-diverging military style nozzles, and to identify and test promising noise reduction techniques. An equally important objective is to develop methodology for using data obtained from small- and moderate-scale experiments to reliably predict the full-scale engine noise. The experimental results presented show reasonable agreement between small-scale and medium-scale jets, as well as between heated jets and heat-simulated ones.

Hysteretic Phenomenon of Shock Wave in a Supersonic Nozzle

In recent years, hysteretic phenomena in fluid flow systems drew attention for their great variety of industrial and engineering applications. When the high-pressure gas is exhausted to atmosphere from the nozzle exit, the expanded supersonic jet with the Mach disk is formed at a specific condition. In two-dimensional expanded supersonic jet, the hysteresis phenomenon for the reflection type of shock wave is occurred under the quasi-steady flow and the transitional pressure ratio between the regular reflection and Mach reflection is affected by this phe- nomenon. However, so far, there are very few researches for the hysteretic phenomenon of shock wave in a supersonic internal flow and the phenomenon has not been investigated satisfactorily. The present study was concemed with the experimental and numerical investigations of hysteretic phenomena of shock wave in a supersonic nozzle, and discussed the relationship between hysteresis phenomenon and rate of the change of pressure ratio with time.

Performance analysis of lobed nozzle ejectors for high altitude simulation of rocket engines

Ejectors are used in high altitude testing of rocket engines to create vacuum for simulat-ing the engine test in vacuum conditions.The performance of an ejector plays a vital role in creating vacuum at the exit of the engine nozzle and the nozzle design exit pressure at the time of ignition.Consequently,the performance of ejectors has to be improved to reduce the consumption of active fluid.In this investigation,the performance of an ejector has been improved by changing the exit shear plane of the nozzle.Conventionally,conical nozzles are used for creating the required momentum.Lobes of 4 no’s,6 no’s and 8 numbers for an equivalent area ratio=5.88 are used to increase the shear area.The influence of shear plane variation in the suction pressure is studied by a detailed CFD analysis.