The mathematical simulation of various condensation regimes in turbulent isobaric jets

Mathematical models are considered and calculations made for flows in turbulent isobaric steam—air jets in the presence of condensation of the water vapor they contain. The models consist of gasdynamic equations for a turbulent jet, equations for a differential two-parameter model of turbulence, thermodynamic relations, and kinetic equations. A study is made of steam—air jets in a regime of condensation in equilibrium, when the flow region is broken down into zones of frozen flow and flow in equilibrium, described by the equations for a turbulent jet with the use of the traditional thermodynamic relations and of the thermodynamic relations for condensation in equilibrium. An analysis is made of the influence of pulsating motion on the kinetic parameters: rate of nucleation, the critical size of the nuclei, and rate of growth of the drops. It is shown that the rate of nucleation, determined from a quasilaminar averaging model, is several orders of magnitude less than the mean value obtained by averaging using the density distribution of the passive admixture concentration probability. A numerical study is made of the heterogeneous condensation in turbulent jets on extraneous particles entering from the nozzle. Kinetic equations are written down for the case when the rate of growth of the drops does not depend on their radius. A study is made of the dynamics of the transition of heterogeneous condensation from disequilibrium to equilibriumTranslated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 59–67, January–February, 1985.     

Investigation of turbulent vapor-air jets in the presence of condensation and the injection of foreign particles

A study is made of flow in turbulent jets when there is condensation of the water vapor contained in them. A necessary condition for condensation in vapor-air jets is formulated. Relations are obtained for the regime of equilibrium condensation. An experimental investigation was made of the local characteristics of an isobaric turbulent vapor jet exhausting into air at rest when condensation develops in the jet and foreign condensation nuclei (smoke particles) and charged particles (ions produced in a corona discharge) are introduced into the flow. Measurements were made of the local characteristics of the condensed disperse phase — the Sauter diameter d₃₂ of the drops and their volume concentration c_s — using the optical method of an integrating diaphragm. It is shown that d₃₂ and₃₂ c_s increase downstream in the main section of the jet. Specific features of temperature measurements using an end-type microthermocouple were established. Quantitative data were obtained about the influence on the condensation of the thermal conditions and the presence of the foreign particles. The conditions under which there is an intensification of the condensation in vapor-air jets in the presence of ions were determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 53–61, May–June, 1984.     

A study of the flow characteristics in micro-abrasive jets

An experimental study of particle velocities in micro-abrasive jets by using the particle image velocimetry (PIV) technique is presented. It has been found that the particle jet flow has a nearly linear expansion downstream. The particle velocities increase with air pressure, and the increasing rate increases with nozzle diameter within the range considered. The instantaneous velocity profile of the particle flow field in terms of the particle velocity distribution along the axial and radial directions of the jets is discussed. For the axial profile in the jet centerline downstream, there exists an extended acceleration stage, a transition stage, and a deceleration stage. For the radial velocity profiles, a relatively flat shape is observed at a jet cross-section near the nozzle exit. Mathematical models for the particle velocities in the air jet are then developed. It is shown that the results from the models agree well with experimental data in both the variation trend and magnitude.     

The structure of particle-laden,underexpanded free jets

Underexpanded, supersonic gas-particle jets were experimentally studied using the shadowgraph technique in order to examine the influence of the dispersed particles on the shape of the free jet and the structure of the imbedded shock waves. The particle mass loading at the nozzle exit was varied between zero and one, and two sizes of particles (i.e. spherical glass beads) with mean number diameters of 26 and 45 m were used. It was found that the Mach-disc moves upstream towards the orifice with increasing particle loading. The laser light sheet technique was also used to visualize the particle concentration distribution within the particle jet and the spreading rate of the particle jet. Furthermore, the particle velocity along the jet centerline was measured with a modified laser-Doppler anemometer. These measurements revealed that the particles move considerably slower than the gas flow at the nozzle exit. This is mainly the result of the particle inertia, whereby the particles are not accelerated to sonic speed in the converging part of the nozzle.In order to further explore the particle behavior in the free jet, numerical studies were performed by a combined Eulerian/Lagrangian approach for the gas and particle phases, including full coupling between the two phases. The numerical results showed that the application of different particle velocities at the nozzle exit as the inlet conditions, which were below the sonic speed of the gas phase has a significant influence on the free jet shape and the configuration of the shock waves. These results demonstrate that the assumption of equilibrium flow (i.e. zero slip between the phases) at the nozzle exit which has been applied in most of the previous numerical studies is not justified in most cases. Furthermore, the numerical calculations of the free jet shape and the particle velocity along the jet axis were compared with the measurements. Although correlations for rarefaction and compressibility effects in the drag coefficient were taken into account, the particle velocity along the center line was considerably overpredicted.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Dynamics of heavy particles in two swirling jets

We report flow visualisations and laser Doppler anemometry (LDA) velocity measurements in the near field of two swirling jets. The Reynolds number based on jet diameter and bulk velocity at the nozzle exit is 1.4 × 10⁵. In the first jet, a small recirculation region is formed around the jet axis, while, in the second, the streamwise velocity remains positive and overshoots near the jet centre. In both cases, flow visualisations show that the vortex core of the jets is depleted of seeding particles. By using time-averaged distributions of the streamwise and tangential velocities measured at the nozzle outlet, the dynamics of the particles is simulated, by integrating their simplified equations of motion. The particles trajectory thus computed agrees well with that observed in the flow visualisations. Although the turbulence intensity is substantially different in the core of the two jets, its effect on the seeding concentration is localised near the edge of the core.     

Numerical modeling of the formation of aerosol particles in jet engine plumes

The formation of liquid sulfate aerosols in the isobaric axisymmetric plume of a subsonic aircraft is modeled numerically. The specific features of the appearance and evolution of sulfate aerosols attributable to 2D effects, such as the parameter nonuniformity in the initial section (at the nozzle outlet), mixing of the hot engine jet with the cold air stream, and the transverse turbulent diffusion of aerosol particles and gas mixture components. The equations of gas dynamics for a turbulent axisymmetric jet, the equations of chemical kinetics, the equations for the liquid fractions (water and sulfuric acid), and the relations for the binary nucleation, condensation growth and coagulation of aerosol particles are used. The distributions of the parameters determining the formation of the aerosol phase in the exhaust plume of a B-747 aircraft are obtained and the geometry of the nucleation zone in this plume is determined.     

Evaluation of stochastic particle dispersion modeling in turbulent round jets

ODT (one-dimensional turbulence) simulations of particle-carrier gas interactions are performed in the jet flow configuration. Particles with different diameters are injected onto the centerline of a turbulent air jet. The particles are passive and do not impact the fluid phase. Their radial dispersion and axial velocities are obtained as functions of axial position. The time and length scales of the jet are varied through control of the jet exit velocity and nozzle diameter. Dispersion data at long times of flight for the nozzle diameter (7 mm), particle diameters (60 and 90 µm), and Reynolds numbers (10, 000–30, 000) are analyzed to obtain the Lagrangian particle dispersivity. Flow statistics of the ODT particle model are compared to experimental measurements. It is shown that the particle tracking method is capable of yielding Lagrangian prediction of the dispersive transport of particles in a round jet. In this paper, three particle-eddy interaction models (Type-I, -C, and -IC) are presented to examine the details of particle dispersion and particle-eddy interaction in jet flow.     

Special characteristics of the propagation of three-dimensional viscous jets

Numerical investigations were made of the propagation, in a supersonic wake, of uncalculated jets, flowing out of nozzles of square and rectangular cross section, and of lumped jets, made up of from two to nine individual jets; the special characteristics of their flow were investigated in the initial, transitional, and main sections. Specifically, for lumped jets, the possibility of replacing them by a single axisymmetric jet, equivalent in mass-flow rate, is discussed. To calculate a three-dimensional unexpanded supersonic jet, flowing out into a wake, in [1] it was proposed to use a numerical method for solving a simplified system of Navier-Stokes equations for steady-state flow, and numerical investigations were made of the three-dimensional interaction of four jets in a supersonic wake, at small distances from the outlet cross section of the nozzle, i.e., mainly in the initial sections of the jets, where the mixing layers along the boundaries of the jets are still not closed. Here the method of [1] is used to study the special characteristics of three-dimensional viscous jets at large distances from the outlet cross section of the nozzle in the region of the main section, where the mixing layers have come together and a single three-dimensional jet has been formed. The system of equations, the boundary conditions, the numerical method, the system of coordinates, and the nomenclature used are the same as in [1].     

Doubly spiraled supersonic jet

The instability of supersonic underexpanded submerged air jet outflow from a nozzle with a central cone in the form of two convergent interlaced spirals is described. A technique for controlling this structure by means of extending the central cone streamwise is proposed. It is shown that the central cone position makes it possible to control the gas outflow and to go over from the Mach reflection regime to the regime of wave spiral and gaseous phase condensation, which before were not observable. The results of the measurements of the dynamic head of jets issuing from the nozzle with and without the central cone are presented.     

An experimental study of circular sand–water wall jets

Laboratory experiments were carried out to study the effects of sand particles on circular sand–water wall jets. Mean and turbulence characteristics of sand particles in the sand–water wall jets were measured for different sand concentrations c_o ranging from 0.5% to 2.5%. Effects of sand particle size on the centerline sand velocity of the jets were evaluated for sand size ranging from 0.21 mm to 0.54 mm. Interesting results with the range of measurements are presented in this paper. It was found that the centerline sand velocity of the wall jets with larger particle size were 15% higher than the jets with smaller particle size. Concentration profiles in the vertical direction showed a peak value at x/d = 5 (where x is the longitudinal distance from the nozzle and d is the nozzle diameter) and the sand concentration decreased linearly for x/d > 5. Experimental results showed that the turbulence level enhanced from the nozzle to x/d = 10. For sand–water wall jets with a higher concentration (c_o = 1.5–2.5%), the turbulence intensity became smaller than the corresponding single-phase wall jets by 34% due to turbulent modulation. A modified logarithmic formulation was introduced to model the longitudinal turbulent intensity at the centerline and along the axis of the jet.     

PIV Measurements in the Near and Intermediate Field Regions of Jets Issuing from Eight Different Nozzle Geometries

An experimental study was conducted to investigate the effect of nozzle geometry on the mixing characteristics and turbulent transport phenomena in turbulent jets. The nozzle geometry examined were round, square, cross, eight-corner star, six-lobe daisy, equilateral triangle as well as ellipse and rectangle each with aspect ratio of 2. The jets were produced from sharp linear contoured nozzles which may be considered intermediate to the more widely studied smooth contraction and orifice nozzles. A high resolution particle image velocimetry was used to conduct detailed velocity measurements in the near and intermediate regions. It was observed that the lengths of the potential cores and the growth rates of turbulence intensities on the jet centerline are comparable with those of the orifice jets. The results indicate that the decay and spreading rates are lower than reported for orifice jets but higher than results for smooth contoured jets. The jets issuing from the elliptic and rectangular nozzles have the best mixing performance while the least effective mixing was observed in the star jet. The distributions of the Reynolds stresses and turbulent diffusion clearly showed that turbulent transport phenomena are quite sensitive to nozzle geometry. Due to the specific shape of triangular and daisy jets, the profiles of mean velocity and turbulent quantities are close to each other in their minor and major planes while in the elliptic and rectangular jets are considerably different. They also exhibit more isotropic behavior compared to the elliptic and rectangular jets. In spite of significant effects of nozzle geometry on mean velocity and turbulent quantities, the integral length scales are independent of changes in nozzle geometry.     

Comparison-speed liquid jets

The performance of a small high-speed liquid jet apparatus is described. Water jets with velocities from 200 to 700 m/s were obtained by firing a deformable lead slug from an air rifle into a stainless steel nozzle containing water sealed with a rubber diaphragm. Nozzle devices using the impact extrusion (IE) and cumulation (CU) methods were designed to generate the jets. The effect of the nozzle diameter and the downstream distance on the jet velocity is examined. The injection sequences are visualized using both shadowgraphy and schlieren photography. The difference between the IE and CU methods of jet generation is found.     

The influences of jet precession on near field particle distributions

The effects of jet precession on the mean and fluctuating components of the distributions of 20 μm spherical particles in the first 10 nozzle diameters downstream from a simulated pulverised fuel burner have been investigated experimentally. Precessing jets are a class of oscillating flow with application in the combustion of pulverised fuels, especially in rotary kilns. The particle distributions have been determined using planar nephelometry, a laser-based instantaneous concentration technique. The influence of the momentum ratio of precessing jet to co-annular jet flow on the distribution of particles is assessed. Mean and fluctuating components of centreline particle distributions, half-widths and radial profiles are presented. It is found that small amounts of jet precession result in an elongation and narrowing of the overall particle distributions. Further increases of precessing jet momentum leads to a wider distribution of particles.     

An experimental and numerical study into turbulent condensing steam jets in air

 Temperatures, velocities, and droplet sizes are measured in turbulent condensing steam jets produced by a facial sauna, for varying nozzle diameters and varying initial velocities (Re=3,600–9,200). The release of latent heat due to droplet condensation causes the temperature in the two-phase jet to be significantly higher than in a single-phase jet. At some distance from the nozzle, droplets reach a maximum size and start to evaporate again, which results in a change in sign of latent heat release. The distance of maximum size is determined from droplet size measurements. The experimental results are compared with semi-analytical expressions and with a fully coupled numerical model of the turbulent condensing steam jet. The increase in centreline temperature due to droplet condensation is successfully predicted. Received: 5 April 2000 / Accepted: 15 November 2000     

Numerical investigation of gas-particle flow in the primary air pipe of a low NOx swirl burner – The DEM-CFD method

The gas-particle flow in the primary air pipe (PAP) of a low NO_x swirl burner was investigated using the computational fluid dynamics (CFD) coupled with the discrete element method (DEM). The mathematical models were validated using the measured values obtained at the outlet of the primary pipe through a phase Doppler anemometer (PDA) system. Particles of different Stokes numbers in the primary air pipe (PAP) were investigated, and the effects of the structure of the primary air pipe and the particle–particle interaction on particle dispersion were analyzed. The results indicate that particles under the combined effects of the Venturi pipe and the spindle body are concentrated into a narrow band area and that the PAP structure can more efficiently concentrate particles with large Stokes numbers. The formed fuel rich/lean jet persists for a long distance out of the burner, thereby favoring of air-staged combustion and NO_x reduction. The particle collision frequency and its fluctuation range increase as the particle Stokes number increases. The collisions among particles result in an increase of the spanwise dispersion of particles. Experimental results indicate that the models that take particle–particle collision into consideration are more able to predict particle concentration.     

Flows of Supersonic Underexpanded Jets on the Range of Moderate Reynolds Numbers

The results of an experimental investigation of the gasdynamic structure of supersonic underexpanded air jets flowing out of a sonic nozzle into a low-pressure medium are presented. This setting of the experimentmakes it possible to achieve high values of the nozzle-to-ambient pressure ratio at moderate outflow Reynolds numbers characteristic of underexpanded jets issuing from micronozzles. The data on the supersonic core length, the laminar-turbulent transition location, and the jet flow characteristics are obtained. The results are compared with those obtained in microjets flowing out of sonic nozzles. Emphasis is placed on the earlier discovered effect of inverse transition of a turbulent jet into the laminar flow regime with increase in the Reynolds number.     

Investigation on the generation process of impact-driven high-speed liquid jets using a CFD technique

High-speed liquid jets have been applied to many fields of engineering, science and medicine. It is therefore of benefit to all these areas to investigate their characteristics by modern and inexpensive methods using a computational fluid dynamics (CFD) technique. Previously, high-speed liquid jets have been studied experimentally using a momentum exchange method, called the “impact driven method (IDM)”, by which the impact of a high-velocity projectile on the liquid package contained in the nozzle cavity produced the jet. The shock pulse reflections in the cavity caused by the impact then drove a multiple pulsed jet from the nozzle exit. In this study, a two-fluid simulation consisting of liquid and air can be successfully calculated by using a two-phase flow mixture model and a moving mesh for the projectile motion. The CFD results show good agreement to the results of previous experimental studies, both quantitatively and qualitatively. For the first time, the wave propagation within the liquid in the nozzle has been captured and analyzed, thereby demonstrating the dynamic characteristics of multiple pulsed high-speed liquid jets initiated by the IDM. This provides a breakthrough in the simulation of the supersonic injection of a liquid into air by using a well-known and user-friendly CFD software. It is useful fundamental knowledge for future studies of high-speed injection with applications in all its related fields.     

Expansion of a Helium Jet under the Influence of High-Intensity Sound

The results of a comparative investigation of the influence of high-intensity sound (sound pressure level at the nozzle edge L=165 dB) on the expansion of turbulent helium and air jets are given. The jets and sound waves were visualized by means of the direct schlieren method using a spark light source with an exposure of 2·10^-7 s. It is shown that the helium jet expands much faster than an air jet with the same dynamic pressure.     

An experimental investigation of jet screech by air jet impingement on solid boundaries

An experimental investigation has been completed to study several methods of avoiding the jet screech phenomenon due to air jet impingement on solid boundaries. Measurements were completed in the Mach number region of M=0.5 using a 25 mm diameter nozzle with the air jet impinging on flat, concave and convex boundaries. Sound pressure levels were recorded in the plane of the nozzle outlet at a distance of 1.46 m from the jet axis. Hot wire studies and the stagnation pressure at the impingement zone of the jet were also recorded.With the air jet impinging on the flat board normal to its surface a maximum sound pressure occurred at a spacing of approximately two nozzle diameters producing a distinct screech at a sound level of 20 dB above that of the free jet. Three methods of preventing this screech were studied. First, by inserting disturbances into the shear layer at the nozzle exit; second, by changing the geometry of the boundary shape to improve the jet stability in the impingement region; and third, by introducing disturbances at the stagnation region which had the effect of displacing the distinct screech to another frequency range.