The influence of Laval nozzle throat size on supersonic molecular beam injection

In this study, finite element analysis （FEA） has been used to investigate the effects of different Laval nozzle throat sizes on supersonic molecular beam. The simulations indicate the Mach numbers of the molecular stream peak at different positions along the center axis of the beam, which correspond to local minimums of the molecular densities. With the increase of the throat diameter, the first peak of the Mach number increases first and then decreases, while that of the molecular number density increases gradually. Moreover, both first peaks shift progressively away from the throat. At the last part, we discuss the possible applications of our FEA approach to solve some crucial problems met in modern transportations.

The gas jet behavior in submerged Laval nozzle flow

The behavior of the combustion gas jet in a Laval nozzle flow is studied by numerical simulations. The Laval nozzle is installed in an engine and the combustion gas comes out of the engine through the nozzle and then injects into the surrounding environment. First, the jet injection into the air is simulated and the results are verified by the theoretical solutions of the 1-D isentropic flow. Then the behavior of the gas jet in a submerged Laval nozzle flow is simulated for various water depths. The stability of the jet and the jet evolution with a series of expansion waves and compression waves are analyzed, as well as the mechanism of the jet in a deep water depth. Finally, the numerical results are compared with existing experimental data and it is shown that the characteristics of the water blockage and the average values of the engine thrust are in good agreement and the unfixed engine in the experiment is the cause of the differences of the frequency and the amplitude of the oscillation.

Design and Atomization Characteristic of Laval-style Annular Slot Nozzle

Gas mass flux rate,metal mass flux rate and outlet gas velocity are three atomization scale parameters which greatly affect the atomization efficiency. A Laval-style annual slot supersonic nozzle is designed by optimizing the geometric parameters of delivery tube outlet and gas outlet to obtain applicable atomization scale parameters. A computational fluid flow model is adopted to investigate the effect of atomization gas pressure ( P0 ) on the gas flow field in gas atomization progress. The numerical results show that the outlet gas velocity of the nozzle is not affected by P0 and the maximum gas velocity reaches 452 m / s. The alternation of aspiration pressure ( ΔP) is caused by the variations of stagnation pressure and location of Mach shock disk, and hardly by the location of stagnation point. The aspiration pressure is found to decrease as P0 increases when P0 < 1. 3 MPa. However,at a higher atomization gas pressure increasing P0 causes an opposite: the aspiration pressure atomization increases with the gas pressure,and keeps a plateau when P0 > 2. 0 MPa. The minimum aspiration pressure ΔP = - 70 kPa is obtained at P0 = 1. 3 MPa. The results indicate that the designed Laval- style annual slot nozzle has well atomization characteristic at lower atomization pressure.

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.

Numerical simulation of the dimensional transformation of atomization in a supersonic aerodynamic atomization dust-removing nozzle based on transonic speed compressible flow

To simulate the transonic atomization jet process in Laval nozzles,to test the law of droplet atomization and distribution,to find a method of supersonic atomization for dust-removing nozzles,and to improve nozzle efficiency,the finite element method has been used in this study based on the COMSOL computational fluid dynamics module.The study results showed that the process cannot be realized alone under the two-dimensional axisymmetric,three-dimensional and three-dimensional symmetric models,but it can be calculated with the transformation dimension method,which uses the parameter equations generated from the two-dimensional axisymmetric flow field data of the three-dimensional model.The visualization of this complex process,which is difficult to measure and analyze experimentally,was realized in this study.The physical process,macro phenomena and particle distribution of supersonic atomization are analyzed in combination with this simulation.The rationality of the simulation was verified by experiments.A new method for the study of the atomization process and the exploration of its mechanism in a compressible transonic speed flow field based on the Laval nozzle has been provided,and a numerical platform for the study of supersonic atomization dust removal has been established.

Comparative study on the flow fields of three atomization nozzles

In this paper, the flow fields of three types of nozzles （ Hartmann, Laval and Laminar nozzles ） under the same conditions are simulated, and the corresponding to pressure, temperature, velocity and turbulence intensity are obtained. The results suggest that two crushing presents in the atomization process using Hartmann nozzle, but only one crushing presents in the atomization process using the other nozzles, through the comparative research on the flow field features of three types of nozzle. Furthermore, the shockwave plays a more important role in crushing of liquid metal than velocity.

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.

Title Supersonic Condensation and Separation Characteristics of CO_(2)-Rich Natural Gas under Different Pressures

Supersonic separation technology is a new natural gas sweetening method for the treatment of natural gas with high CO_(2)(carbon dioxide)content.The structures of the Laval nozzle and the supersonic separator were designed,and the mathematical models of supersonic condensation and swirling separation for CO_(2)-CH4 mixture gas were established.The supersonic condensation characteristics of CO_(2) in natural gas and the separation characteristics of condensed droplets under different inlet pressures were studied.The results show that higher inlet pressure results in a larger droplet radius and higher liquid phase mass fraction;additionally,the influence of centrifugal force is more pronounced,and the separation efficiency and removal efficiency of CO_(2) are higher.When the inlet pressure is 6 and 9 MPa,the liquefaction efficiency at the Laval nozzle outlet increases from 56.90%to 79.97%,and the outlet droplet radius increases from 0.39 to 0.72μm,and the removal efficiency is 31.25%and 54.52%,respectively.The effects of inlet pressures on the removal efficiency of the supersonic separator are complicated and are controlled by the combined effects of liquefaction capacity of the nozzle and centrifugal separation capacity of the swirl vane.

Characteristics of compressible flow of supercritical kerosene

In this paper, compressible flow of aviation kerosene at supercritical conditions has been studied both numerically and experimentally. The thermophysical properties of supercritical kerosene are calculated using a 10- species surrogate based on the principle of extended corresponding states （ECS）. Isentropic acceleration of supercritical kerosene to subsonic and supersonic speeds has been analyzed numerically. It has been found that the isentropic relationships of supercritical kerosene are significantly dif- ferent from those of ideal gases, A two-stage fuel heating and delivery system is used to heat the kerosene up to a tem- perature of 820 K and pressure of 5.5 MPa with a maximum mass flow rate of 100 g/s. The characteristics of supercritical kerosene flows in a converging-diverging nozzle （Laval nozzle） have been studied experimentally. The results show that stable supersonic flows of kerosene could be established in the temperature range of 730 K-820 K and the measurements in the wall pressure agree with the numerical calculation.

Continuous Detonation Engine and Effects of Different Types of Nozzle on Its Propulsion Performance

The rotating propagation of a continuous detonation engine (CDE) with different types of nozzles is investigated in three-dimensional numerical simulation using a one-step chemical reaction model. Flux terms are solved by the so-called monotonicity-preserving weighted essentially non-oscillatory (MPWENO) scheme. The simulated flow field agrees well with the previous experimental results. Once the initial transient effects die down, the detonation wave maintains continuous oscillatory propagation in the annular chamber as long as fuel is continuously injected. Using a numerical flow field, the propulsion per- formance of a CDE is computed for four types of nozzles, namely the constant-area nozzle, Laval nozzle, diverging nozzle and converging nozzle. The gross specific impulse of the CDE ranges 1 540-1 750 s and the mass flux per square meter ranges 313-330 kg/(m2·s) for different nozzles. Among these four types of nozzles, Laval nozzle performs the best, and these parameters are 1 800 N, 1 750 s and 313 kg/(m2.s). A nozzle can greatly improve the propulsion performance.

A COUPLING MODEL OF WATER FLOWS AND GAS FLOWS IN EXHAUSTED GAS BUBBLE ON MISSILE LAUNCHED UNDERWATER

The gas and water flows during an underwater missile launch are numerically studied. For the gas flow, the explicit difference scheme of Non-oscillation and Non-free-parameter Dissipation (NND) is utilized to solve the Euler equations for compressible fluids in the body-fitted coordinates. For the water flow, the Hess-Smith method is employed to solve the Laplace equation for the velocity potential of irrotational water flows based on the potential theory and the boundary element method. The hybrid Eulerian-Lagrangian formulation for the free boundary conditions is used to compute the changes of the free surface of the exhausted gas bubble in time stepping. On the free surface of the exhausted gas bubble, the matched conditions of both the normal velocities and pressures are satisfied. From the numerical simulation, it is found that the exhausted gas bubble grows more rapidly in the axial direction than in the radial direction and the bubble will shrink at its "neck" finally. Numerical results of the movement of the shock wave and the distribution of the Mach number and the gas pressure within the bubble were presented, which reveals that at some time, the gas flow in the Laval nozzle is subsonic and the gas pressure in the nozzle is very high. Influences of various initial missile velocities and chamber total pressures and water depths on both the time interval when the gas flow in the nozzle is subsonic and the peak of the gas pressure at the nozzle end were discussed. It was suggested that a reasonable adjustment of the chamber total pressure can improve the performance of the engine during the underwater launch of missiles.

Research on Wet Steam Spontaneous Condensing Flows Considering Phase Transition and Slip

A new dual-fluid model considering phase ansition and velocity slip was proposed in this paper and the Cunningham correction was used in the droplet resistance calculation. This dual-fluid model was applied to the numerical simulations of wet steam flow in a 2D LAVAL nozzle and in the White cascade respectively. The results of two simulations demonstrate that the model is reliable. Meanwhile, the spontaneous condensing flow in White cascade was analyzed and it infers that the irreversible loss caused by condensation accounts for the largest share （about 8.78% of inlet total pressure） in total pressure loss while the loss caused by velocity slip takes the smallest share （nearly 0.42%）, and another part of total pressure loss caused by pneumatic factors contributes a less share than condensation, i.e. almost 3.95% of inlet total pressure.