Specific momentum of a flow in the minimal cross section of a laval nozzle and in the outlet cross section of a contracting nozzle

The article discusses the question of the effect of nonuniformity of the parameters, brought about by the two-dimensional character of the flow on the value of the specific momentum of the flow under supercritical conditions. It is shown, that, in the approximation of an ideal (nonviscous and non-heat-conducting) gas, the corresponding value with a continuous flow always exceeds the value calculated in accordance with the one-dimensional theory for the same nozzle and the same stagnation parameters of the gas.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 186–188, January–February, 1976.     

Thrust shock vector control of an axisymmetric conical supersonic nozzle via secondary transverse gas injection

Transverse secondary gas injection into the supersonic flow of an axisymmetric convergent–divergent nozzle is investigated to describe the effects of the fluidic thrust vectoring within the framework of a small satellite launcher. Cold-flow dry-air experiments are performed in a supersonic wind tunnel using two identical supersonic conical nozzles with the different transverse injection port positions. The complex three-dimensional flow field generated by the supersonic cross-flows in these test nozzles was examined. Valuable experimental data were confronted and compared with the results obtained from the numerical simulations. Different nozzle models are numerically simulated under experimental conditions and then further investigated to determine which parameters significantly affect thrust vectoring. Effects which characterize the nozzle and thrust vectoring performances are established. The results indicate that with moderate secondary to primary mass flow rate ratios, ranging around 5 %, it is possible to achieve pertinent vector side forces. It is also revealed that injector positioning and geometry have a strong effect on the shock vector control system and nozzle performances.     

Mass transport in a converging-diverging nozzle

The local concentration has been determined for a viscous liquid flowing through a converging-diverging tube with constant wall- and initial concentration. The liquid flow was considered as creeping flow and its velocity distribution was determined by solving the biharmonic differential equation of the stream function. The mass transport was presented in form of an infinite series of Legendre functions, which rendered with the Galerkin condition a determinant of finite order for the determination of the eigenvalues. The local concentration was evaluated numerically for differently diverging tubes, of which the case of mass transport for viscous (linearized) flow through an orifice of circular cross-section presented a special case.

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Stofftransport in einem konvergierenden-divergierenden Rohr

Znsammenfassung Es wird die lokale Konzentration eines in einer viskosen Strömung durch ein Venturirohr befindlichen Stoffes bei konstanter Wand-und Einlaßkonzentration bestimmt. Die viskose (kriechende) Strömungsgeschwindigkeit wurde aus der Lösung der biharmonischen Differentialgleichung der Stromfunktion bestimmt. Die Bestimmung des Massentransportes im Rohr wird mit einer Lösung in Form einer unendlichen Reihe von Legendrefunktionen bewältigt, wobei die Eigenwertgleichung eine Determinante unendlicher Ordnung ergibt. Die lokale Konzentration wurde für verschieden divergierende Rohre numerisch ausgewertet, wobei der Massentransport bei Strömung durch eine kreisförmige Öffnung als Sonderfall auftrat.

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Nomenclature a radius of throat area - c (, ) concentration - c _w wall concentration - c _i initial concentration - D diffusion coefficient - P _n ⁰ Legendre function - u (, ) flow velocity of liquid (in-direction) - flow volume per time unit - _n roots ofP ⁰ ( ₀)=0 - stream function - , , oblate spheroidal coordinates - ₀ wall of the nozzle     

Separated two-phase flow in a nozzle

This work was performed to extend and further test the method of handling separated two-phase flow by studying each phase separately and, particularly, by placing emphasis on the study of the gas phase with interface transport expressions showing the influence of the liquid phase on it. A one-dimensional flow model for accelerating flows was used in conjunction with experimental data to obtain the pressure distribution and velocity distribution in a converging nozzle for several values of flow quality and nozzle inlet stagnation pressure. The results tend to support the use of the model (which includes the assumption that the gas is in critical flow when the two-phase mixture is in critical flow) and give some insight regarding the nature of the liquid distribution near the nozzle throat.     

Flow of a two-phase medium in a laval nozzle

The back reaction of particles on a gas flow in Laval nozzles was investigated experimentally. Experimental data were obtained that characterize the change produced by the particles of a solid phase in the shape of the sonic line, the pressure distribution on the nozzle profile, and the configuration of the shock waves in the jet. Flow rate coefficients are given for different nozzle profiles and mass fraction and sizes of the particles in the flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 107–111, January–February, 1981.     

Thrust production by a mechanical swimming lamprey

To develop a comprehensive model of lamprey locomotion, we use a robotic lamprey to investigate the formation of the wake structure, the shedding vorticity from the body, and the relationship between thrust production and pressure on the surface of the robot. The robot mimics the motion of living lamprey in steady swimming by using a programmable microcomputer to actuate 13 servomotors that produce a traveling wave along the length of the lamprey body. The amplitude of the phase-averaged surface pressure distribution along the centerline of the robot increases toward the tail, which is consistent with previous momentum balance experiments. This indicates that thrust is produced mainly at the tail. The phase relationship between the pressure signal and the vortex shedding from the tail is also examined, showing a clear connection between the location of vortex structures and the fluctuations of the pressure signal.     

Nonequilibrium gas-condensate flow in a laval nozzle

A scheme is proposed which simplifies the algorithm and reduces the labor involved in solving the system of quasi-linear hyperbolic equations describing supersonic nonequilibrium two-phase flow in an axisymmetric nozzle.     

Liquid flow in a simplex swirl nozzle

Pressure-swirl nozzles are widely used in applications such as combustion, painting, air-conditioning, and fire suppression. Understanding the effects of nozzle geometry and inlet flow conditions on liquid film thickness, discharge coefficient and spray angle is very important in nozzle design. The nozzle-internal flow is two-phase with a secondary flow which makes its detailed analysis rather complex. In the current work, the flow field inside a pressure-swirl nozzle is studied theoretically. Using the integral momentum method, the growth of the boundary layer from the nozzle entry to the orifice exit is investigated and the velocity through the boundary layer and the main body of the swirling liquid is calculated. A numerical modeling and a series of experiments have also been performed to validate the theoretical results. The effect of various geometrical parameters is studied and results are compared for viscous and inviscid cases. In addition, the condition in which the centrifugal force of the swirling flow overcomes the viscous force and induces an air core is predicted. The theoretical analysis discussed in this paper provides better criteria for the design and the performance analysis of nozzles.     

Hysteresis phenomena in a plane rotatable nozzle

The flow in a rotatable nozzle is calculated within the framework of the Reynolds equations and the Spalart-Allmaras turbulence model on the pressure difference range 1.1 < π < 5 for four configurations of the nozzle with the area ratio ε = 1.52 and two angles of the nozzle axis rotation. The flow structure is determined and the thrust characteristics and the angles of the thrust vector rotation are obtained. It was found that in the overexpansion regime the flows in plane symmetric and rotatable nozzles involve hysteresis phenomena due the Coanda effect and the interaction between the boundary layer and a shock generated within the nozzle on its supersonic walls. The hysteresis phenomena detected provide an up-to-4% divergence in the thrust coefficient for the same problem parameters. The results of the numerical modeling are compared with the experimental data and the results of calculations in accordance with Sekundov’s model.     

Slowly mixing cylinder in a cone-shaped nozzle

We report on a surprising phenomenon in a turbulent jet setup which uses a cone-shaped nozzle with an excentric inlet. Inside the nozzle a slowly mixing, rotating cylinder surface was observed. The speed of mixing on this cylinder surface is reduced by approximately a factor of 8 compared to the remaining flow field of the nozzle. The phenomenon seems to be independent of the Reynolds number and the pressure distribution inside the nozzle.     

Mixing enhancement in a multi-stream injection nozzle

We present quantitative analysis of image sequences of multi-stream injection nozzle flows with several different injection geometries in an experiment simulating mixing in a chemical oxygen-iodine laser. To visualize mixing, image sequences were acquired with planar laser-induced fluorescence (PLIF) in iodine that was injected into the main flow. The injection nozzle consisted of a slot, ejector, and injector block, with rows of ejector and injector holes along the slot length. The ejector flow exits in an underexpanded state so that upon expanding it forces the slot and injector flows together to enhance mixing. For this study, the diameter and geometry of ejector holes were varied to assess their effect on mixing. Two configurations of ejector holes were used, each with two different diameters for a total of four cases with data collected at downstream stations. We carry out a quantitative mixing analysis for these configurations, using two methods to quantify the mixing. The first method considers the statistics of the PLIF image intensity histograms, which are bimodal for poorly-mixed flows and have a single peak in well-mixed flows. The second method quantifies the properties of the mixing interface. Our analysis shows that two injection schemes significantly enhance mixing by stretching the mixing interface.     

Atomization of glycerin with a twin-fluid swirl nozzle

Atomization of liquids with high viscosity is always a challenge, especially when small diameter droplets and high liquid flow rates are simultaneously required. In the present research, the performance of a Venturi–vortex twin-fluid swirl nozzle is examined, attending to its capabilities to generate droplets with diameters below 20 µm when atomizing pure glycerin at room temperature. In this nozzle, air is injected tangentially in a central convergent section, and discharges suctioning the liquid fed to a coaxial chamber, here using a gear pump. The resulting spray is visualized and analyzed. Droplet size distributions are measured with a laser diffractometer. As expected, droplet diameter increases with liquid flow rate, and quickly diminishes when air flow rate is increased. Sauter mean diameters (SMD) below 15 µm can be obtained even when atomizing pure glycerin. However, these values are obtained for relatively low glycerin flow rates (∼5 l/h), and with rather wide distributions. For 10 l/h and an air-to-liquid mass flow rate ratio (ALR) of 13.7 more than 26% of the glycerin volume is atomized in droplets smaller than 20 µm. Liquid ligaments are observed near the nozzle exit, but they tend to break up while moving downstream.     

Formation of a pulsed jet behind a supersonic nozzle when the gas can relax at the entrance to the nozzle

The formation of a pulsed jet behind supersonic nozzles is considered when relaxation processes take place in the gas entering the nozzle. In a general formulation, the problem of the motion of the front of the exhausting matter and the disturbances accompanying it in the process of formation of a pulsed jet is determined by a large number of parameters, which characterize the exhausting gas and the residual gas of the pressure chamber and also the geometry of the flow conditions. A reliable computational model of a pulsed jet does not exist. To construct such a model, experiments are required in a wide range of boundary and initial conditions. An investigation was made into flow of shockheated argon, nitrogen, and carbon dioxide out of nozzles set up at the end of a shock tube. Generalized dependences were obtained for describing the motion of the front of the nonstationary jet and the wave in front of it in a wide range of the initial pressure-difference parameters and variation of the stagnation temperatures. The choice of the generalized parameters when relaxation of the excited internal degrees of freedom of the molecules of the gas can occur at the entrance to the nozzle is discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 129–135, November–December, 1980.     

Metering characteristics of a convergent-divergent nozzle with a cylindrical throat

Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 164–165, March–April, 1993.