Numerical investigation of transient nozzle flow

Abstract. The starting process of two-dimensional and axisymmetric nozzle flows has been investigated numerically. Special attention has been paid to the early phase of the starting process and to the appearance of a strong secondary shock wave. For both cases, shock intensities and velocities are obtained and discussed. The flow evolution in the axisymmetric case is proved to be more complex and the transient starting process is slower than in the plane case. Finally, the effects of changing the nozzle angle and the incident shock wave Mach number on the transient flow are addressed. It is shown that a faster start-up can be induced either by decreasing the nozzle angle or increasing the Mach number of the incident shock wave. Received 16 November 2001 / Accepted 24 September 2002 / Published online 4 December 2002 Correspondence to:A.-S. Mouronval (e-mail: mouronv@coria.fr)     

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 d₅₀ 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 d₅₀. 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.     

Numerical study on the effect of nozzle pressure and yarn delivery speed on the fiber motion in the nozzle of Murata vortex spinning

Murata vortex spinning (MVS) is a recently developed spinning technology which utilizes high speed swirling airflow to insert twist into the yarn. The motional characteristics of the flexible fibers in the airflow inside the MVS nozzle are of vital importance to the yarn formation mechanism and properties. The fiber motion in the MVS nozzle involves fluid-structure interaction (FSI) and contact problems. In this paper, a two-dimensional FSI model combined with the fiber-wall contact is introduced to simulate a single fiber moving in the airflow inside the MVS nozzle. The model is solved using a finite element code ADINA. Based on the model, the motional characteristics of the fiber are analyzed and the effect of two process parameters - the nozzle pressure and yarn delivery speed - on the fiber motion and, in turn, the yarn tenacity is discussed. The results indicate that the fiber firstly undergoes a false-twisting process. Subsequently, its trailing end splays out and whirls within the nozzle chamber for several turns to helically wrap and make the spun yarn. The results also show that the effect of the nozzle pressure on the tenacity of the produced MVS yarn is not obvious. The increased yarn delivery speed leads to the decreased MVS yarn tenacity. The numerical results show good agreement with the experimental results provided by other researchers.     

Supersonic ideal-gas flow of in the throat region of a nozzle

The problem of profiling a supersonic nozzle with uniform outlet flow is considered when the contour is constructed from a point on a given convergent section of the nozzle. It is shown that there are contours such that the flow in the throat is supersonic in choked regimes (as distinct from common notions of mixed or uniform sonic flow). The influence of flow nonuniformity in the throat region on the thrust of a supersonic nozzle is analyzed.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 132–139, May–June, 1996.     

Experimental investigation of CO vibrational deactivation in a supersonic cooling gas flow

Abstract. The vibrational relaxation time of CO molecules at collisions with H atoms was measured in shock tube experiments by means of the CARS-spectroscopy method. The measurements of the CO vibrational temperature at gas temperatures of 1800–3000 K were performed in a supersonic cooling gas flow. The gas was heated behind the incident and reflected shock wave and then flowed out of a wedge-shaped nozzle. H atoms were generated in the reflected shock wave because of dissociation of H and HO admixtures. The extremely high efficiency of H atoms in CO vibrational deactivation was confirmed. Received 1 February 2000 / Accepted 20 February 2000     

Thrust of a contracting nozzle

A study is made of the influence of the nonuniformity of the parameters due to the two-dimensional nature of the flow on the specific thrust of a contracting nozzle. It is shown that for continuous flow of an ideal (inviscid and nonheat-conducting) gas the specific thrust in the supercritical regimes exceeds the value determined using the one-dimensional theory for the same stagnation parameters of the gas; in the subcritical regimes the specific thrust of the contracting nozzle is equal to the value found from the one—dimensional approximation.     

Profiling the Supersonic Part of a Plug Nozzle with a Nonuniform Transonic Flow

The effect of transonic flow nonuniformity on the profiling of optimal plug nozzles is studied in the inviscid gas approximation. Sonic and supersonic regions providing maximum thrust for given nozzle dimensions and a given outer pressure are designed for given subsonic contours and calculated nonuniform transonic flows. As in the case of uniform flow on a cylindrical sonic surface, the initial regions of the designed contours satisfy the condition that in these regions the flow Mach number is unity or near-unity. In all the examples calculated, the optimal plug nozzles produce a greater thrust than the optimal axisymmetric and annular nozzles with a near-axial flow for the same lengths and the same gas flow rates through the nozzle. It is established that contouring without regard for transonic flow nonuniformity can result in considerable thrust losses. However, these losses are due only to a decrease in the flow rate, while the specific thrust may even increase slightly.     

Transonic flow around a solid of revolution during the outflow of a reactive jet from its stern section

A numerical method is developed for calculating the motion of a subsonic or transonic flow around a solid of revolution with due allowance for the effects of the reactive jet, the bottom projection, possible noncoincidence between the planes of the nozzle tip and the stern section, nonuniformity of the flow at the nozzle outlet, the ejecting action of the supersonic jet, and also the displacement of the boundary layer. Examples of such calculations are given for solids of revolution of different shapes and nozzles of different types; comparison is also made with experimental data.     

Investigation of the solid impurity distribution in axisymmetric nozzles

Results are presented of an experimental investigation of the influence of the entrance conditions, the coarseness of the solid impurities (the nozzle scale), the profiles of the sub- and transonic parts of the nozzle, and the initial concentration on the discrete phase distribution in the exit sections of axisymmetric nozzles. It is shown that profiling of the subsonic part of the nozzle plays a governing role as compared with the transonic part, and the greatest filling of the supersonic nozzle section by a solid impurity is observed in the conical entrance. The nonuniformity of the parameter distribution at the nozzle entrance does not substantially alter the solid impurity distribution at the exit.     

Extension of the DSMC method to high pressure flows

A collision-limiter method, designated as equilibrium direct simulation Monte Carlo (eDSMC), is proposed to extend the DSMC technique to high pressure flows. The method is similar to collision-limiter schemes considered in the past with the important distinction that for inviscid flows, equilibrium is enforced in the entire flow by providing a sufficient number of collisions, based on pre-simulation testing. To test the method with standard DSMC and Navier–Stokes (NS) methods, axi-symmetric nozzle and embedded-channel flows are simulated and compared with experimental temperature data and pre-existing calculations, respectively. The method is shown to agree with third-order Eulerian nozzle flows and first-order channel flows. Chapman–Enskog theory is utilized to predict the range of initial conditions where eDSMC is potentially useful for modeling flows that contain viscous boundary layer regions. Comparison with supersonic nozzle data suggests that the eDSMC method is not adequate for capturing the large variation in flow length scales occurring in supersonic expansions into a vacuum. However, when eDSMC is used in combination with the baseline-DSMC method a near-exact solution is obtained with a considerable computational savings compared to the exact DSMC solution. Viscous flow channel calculations are found to agree well with an exact Navier–Stokes (NS) calculation for a small Knudsen number case as predicted by Chapman–Enskog theory.     

Separated nozzle flow

A separated turbulent flow in an axisymmetrical nozzle is studied numerically. Two configurations nozzle are investigated. The first one is the truncated ideal contour nozzle, DLR-TIC, is fed with nitrogen. The second configuration is called the thrust optimized contour nozzle or TOC type, ONERA-TOC, where the operating gas is a hot air. The classical pattern of a free shock separation is obtained for different values of the nozzle pressure ratio. The results are compared and validated using experimental data.     

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     

Flow transition in dual bell nozzles

The dual bell nozzle is a concept of altitude adaptive nozzles. The flow adapts to the altitude by separation at the wall inflection at low altitude, and full flowing at high altitude. To understand the phenomenology of the flow by the transition from sea-level mode to high altitude mode, a series of tests have been made at the cold flow test bench P6.2 at DLR Lampoldshausen. A dual bell nozzle have been successively shorten and driven in the same conditions for each length. Hence it was possible to observe the flow in the vicinity of the wall inflection using Schlieren optics. Furthermore this study yields the influence of the length ratio between basis and extension on the transition conditions.

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The effect of nozzle layout on droplet ejection of a piezo-electrically actuated micro-atomizer

We study here effects of nozzle layout on the droplet ejection of a micro atomizer, which was fabricated with the arrayed nozzles by the MEMS technology and actuated by a piezoelectric disc. A theoretical model was first built for this piezoelectric-liquid-structure coupling system to characterize the acoustic wave propagation in the liquid chamber, which determined the droplet formation out of nozzles. The modal analysis was carried out numerically to predict resonant frequencies and simulate the corresponding pressure wave field. By comparing the amplitude contours of pressure wave on the liquid-solid interface at nozzle inlets with the designed nozzle layout, behaviors of the device under different vibration modes can be predicted. Experimentally, an impedance analyzer was used to measure the resonant frequencies of the system. Three types of atomizers with different nozzle layouts were fabricated for measuring the effect of nozzle distribution on the ejection performance. The visualization experiment of droplet generation was carried out and volume flow rates of these devices were measured. The good agreement between the experiment and the prediction proved that only the increase of nozzles may not enhance the droplet generation and a design of nozzle distribution from a viewpoint of frequency is necessary for a resonant related atomizer. The project supported by the National Natural Science Foundation of China (50405001).     

Delayed detached eddy simulation of the end-effect regime and side-loads in an overexpanded nozzle flow

The separated flow in an overexpanded nozzle featuring a restricted shock separation is investigated numerically using delayed detached eddy simulation and compared with the experimental data of Nguyen et al. (Int J Flow Turbul Combust 71(1):161–181, 2003). First, the enormous cost of a Large Eddy Simulation for such a nozzle flow is assessed before being performed to motivate the practical need for using an hybrid RANS/LES method. The calculation is then used to investigate the “end-effect” regime which involves a strong global unsteadiness with very large amplitude fluctuations of about 15–20% of nozzle divergent length. The flow regime is characterized by high wall pressure fluctuations which are hopefully nearly axisymmetric. The main properties (rms levels, amplitude of displacement of the separation) of the motion are rather well reproduced by DDES compared to the experiment. However, a major difference lies in the frequency of the computed motion which is higher than in the experiment. This major discrepancy is currently not explained by the author. The properties of the side-loads are also briefly discussed.      

Experimental investigation of forced flow regime transition in a dual bell nozzle by secondary fluidic injection

Experiments on an axisymmetric dual-bell nozzle were performed at EDITH nozzle test facility of CNRS in Orléans, France. The main purpose of the study was to explore the possibility of controlling the flow regime transition by a secondary fluidic injection in the dual bell nozzle. The main focus of the present paper is to investigate the impact of the secondary injection parameters on the flow regimes transition in such nozzles. Secondary injection has been found to effectively control the flow regime transition and consequently to increase the propulsive performance of the device. It has also been pointed out that even a very low injected secondary mass flow rate leads to the control of the transition and contributes to reducing the lateral loads which can exist, moreover, when transitions are operated without injection.     

Estigation of twisted flows of an ideal gas in nozzles under super- and subcritical conditions

The article discusses weakly twisted flows of an ideal gas with arbitrary thermodynamoc properties in a supersonic nozzle with a central body, under super- and subcritical working conditions. The results of the investigation are generalized for the case of flow with an arbitrary (not necessarily weak) nonuniformity of the stagnation parameters of the flow (the entropy and the total enthalpy) over the cross section of the nozzle. An evaluation is made of the range of applicability of the linear theory with respect to the rate of twisting. The investigation is a generalization of the ideas of Chernyi, developed in [1].     

Mixing in Circular and Non-circular Jets in Crossflow

Coherent structures and mixing in the flow field of a jet in crossflow have been studied using computational (large eddy simulation) and experimental (particle image velocimetry and laser-induced fluorescence) techniques. The mean scalar fields and turbulence statistics as determined by both are compared for circular, elliptic, and square nozzles. For the latter configurations, effects of orientation are considered. The computations reveal that the distribution of a passive scalar in a cross-sectional plane can be single- or double-peaked, depending on the nozzle shape and orientation. A proper orthogonal decomposition of the transverse velocity indicates that coherent structures may be responsible for this phenomenon. Nozzles which have a single-peaked distribution have stronger modes in transverse direction. The global mixing performance is superior for these nozzle types. This is the case for the blunt square nozzle and for the elliptic nozzle with high aspect ratio. It is further demonstrated that the flow field contains large regions in which a passive scalar is transported up the mean gradient (counter-gradient transport) which implies failure of the gradient diffusion hypothesis.     

A random simulation of droplet distribution in nozzle and plume flows

A simple entrainment model is used to estimate droplet streamlines, velocity and mass flux in rocket exhaust plumes. Since droplet mass flux constitutes only about 1% of the exhaust mass flux, the effect of droplet entrainment on the gas flow is neglected. The novelty of the present model is in obtaining the droplet distribution within the nozzle by assuming a small radial random velocity component for droplets at the throat. Gas flow in the nozzle is approximated as isentropic plus a correction for the boundary layer. The computed distribution of droplet mass flux is found to be in good agreement with experimental data. Received 15 January 1996 / Accepted 11 September 1996