Effects of global density ratio on the centerline mixing behavior of axisymmetric turbulent jets

Measurements, utilizing Rayleigh light scattering, of timeaveraged concentration and unmixedness have been made along the centerlines of axisymmetric turbulent jets formed from six pairs of jet and ambient gases. Jet to ambient density ratios range from 0.14 to 5.11. Findings are compared with predictions of an approx. similarity analysis and with extensive previous literature measurements. It is shown that virtual origins for plots of inverse time-averaged concentration are strongly dependent on global density ratio. Unmixedness values first grow with increasing distance from the jet source and then achieve an asymptote. The flow distance required to reach this asymptote is a strong function of density ratio.     

Measurement of product concentration of two parallel reactive jets using digital image processing

The chemically sensitive LIF technique [9] is employed to study the mixing of two reactive axisymmetric jets, one of which carries fluorescein, in an ambient quiescent fluid. The degree of mixing depends on the jet spacing and the axial position downstream of the jets and power laws are found to hold for some concentration characteristics. Unlike the far velocity field of dual plane jets, self preservation laws are not found to hold in general for the concentration field.     

A comparative study of sound generation by laminar,combusting and non-combusting jet flows

Sound production by two-dimensional, laminar jet flows with and without combustion is studied numerically and theoretically. The compressible Navier–Stokes, energy and progress variable equations are solved by resolving both the near field and the acoustics. The combusting jet flows are compared to non-combusting jets of the same jet Mach number, with the non-combusting, non-isothermal jets having the same steady temperature difference as the combusting jets. This infers that the magnitude of entropic and density disturbances is similar in some of the combusting and non-combusting cases. The flows are perturbed by a sinusoidal inlet velocity fluctuation at different Strouhal numbers. The computational domain is resolved to the far field in all cases, allowing direct examination of the sound radiated and its sources. Lighthill’s acoustic analogy is then solved numerically using Green’s functions. The radiated sound calculated using Lighthill’s equation is in good agreement with that from the simulations for all cases, validating the numerical solution of Lighthill’s equation. The contribution of the source terms in Dowling’s reformulation of Lighthill’s equation is then investigated. It is shown that the source term relating to changes in the momentum of density inhomogeneities is the dominant source term for all non-reacting, non-isothermal cases. Further, this source term has similar magnitude in the combusting cases and is one of the several source terms that have similar magnitude to the source term involving fluctuations in the heat release rate.     

Opposed round jets issuing into a small aspect ratio channel cross flow

Round jets (diameter D) discharging into a confined cross flow (dimension 3.16D × 21.05D) are investigated experimentally. Two configurations are considered: (1) a single jet (momentum flux ratio, J = 155) and (2) two opposed jets with two different momentum flux ratios (J = 60, and 155). A two-component laser-Doppler anemometer is used to make a detailed map of the normal stresses and mean velocities in the symmetry plane of the jets. In addition, smoke-wire and laser-sheet visualization are used to study the flow.

The rate of bending of the single confined jet is found to be higher than the rate of bending of an unconfined jet with the same momentum flux ratio. In the far field, the jet centerline velocity is observed to decay more slowly than the unconfined jet, indicating poor turbulent diffusion of linear momentum. Annular shear layer vortices are visualized on the upstream edge of the jet in the near field. In the far field, the flow visualization suggests that the jet loses its integrity and fragments into independent regions that are convected by the cross flow.

In the opposed jet configuration at the high momentum flux ratio (J = 155), the jets impinge in the center of the duct, and a pair of vortices is observed upstream of the impingement region. The flow visualization implies that the impingement vortices form quasi periodically and have a finite life span. In the impingement region, the jets are observed to penetrate alternately beyond the symmetry plane of the duct. In the two-jet configuration with J = 60, the jets do not impinge on each other owing to the higher rate of bending. Instead, the flow visualization indicates that the shear layers of the jets penetrate to the central region and periodically pinch off regions of the potential-like cross-flow fluid where they meet. The pinch-off regions of cross-flow fluid are convected by the turbulent flow for large distances, yet remain essentially unmixed.     

Wall jet similarity of impinging planar underexpanded jets

Velocity profiles and wall shear stress values in the wall jet region of planar underexpanded impinging jets are parameterized based on nozzle parameters (stand-off height, jet hydraulic diameter, and nozzle pressure ratio). Computational fluid dynamics is used to calculate the velocity fields of impinging jets with height-to-diameter ratios in the range of 15–30 and nozzle pressure ratio in the range of 1.2–3.0. The wall jet has an incomplete self-similar profile with a typical triple-layer structure as in traditional wall jets. The effects of compressibility are found to be insignificant for wall jets with Ma < 0.8. Wall jet analysis yielded power-law relationships with source dependent coefficients describing maximum velocity, friction velocity, and wall distances for maximum and half-maximum velocities. Source dependency is determined using the conjugate gradient method. These power-law relationships can be used for mapping wall shear stress as a function of nozzle parameters.     

Convective-Region Top Front Propagation in a Uniform Medium under the Action of Point, Linear, and Plane Heat and Momentum Sources

A relation between the height of a convective front rising in an unstratified medium and the momentum and heat fluxes released on the substrate surface is proposed for point, linear, and uniform plane sources arbitrarily dependent on time. This relation makes it possible to determine the integral power of a plume on the basis of optical observations of the height of the propagating convective front. As particular solutions, three classes of self-similar regimes related with the heat and momentum sources, whose rate is a step-shaped, power-law, or exponential function of time, are obtained. A one-dimensional integral model of a rising convective jet is constructed. The classes of self-similar jets corresponding to power or exponential heat and momentum sources are described. It is shown that all self-similar jets corresponding to heat and momentum sources governed by a power law with a fairly large exponent are characterized by the same temperature and velocity profiles.     

Jet Outflow from a Small Hole in a Plane

On the basis of the method of matched asymptotic expansions, the problem of the outflow of a nonswirling axisymmetric laminar jet from a hole in a plane is solved for large Reynolds numbers. Since directly matching the leading terms of the asymptotic expansions for the axial boundary layer and the main flow region is impossible, the problem is solved by introducing an intermediate region. In the axial region the solution is the Schlichting solution [1] for an axisymmetric jet in the boundary-layer approximation, in the intermediate region the solution is found analytically, and in the main flow region the problem is reduced to that of viscous flow induced by a sink line in the presence of a transverse wall [2].     

The free jets as boundary-layer flows induced by continuous stretching surfaces

This paper proves that the free laminar jets of the classical hydrodynamics may be identified with certain boundary-layer flows induced by continuous surfaces immersed in quiescent incompressible fluids and stretched with well-defined velocities. In this sense: (i) Schlichting's round jet of momentum flow coincides with the axisymmetric flow induced by a thin continuous wire issuing from a small orifice at x=0 and stretching along the x-axis with velocity U _w(x) = 3J˙/(8πρνx), and (ii) the Schlichting–Bickley plane jet of momentum flow J˙ coincides with the boundary-layer flow induced by an impermeable plane wall issuing from a long slit (of length l) and stretching with velocity U _w(x)= [{3J˙ ²/(32νρ² l ² x)}]^1/3.     

Investigation of the microstructure a turbulent jet in a wake

The study of the characteristics of the turbulence in the boundary layer and in free jets is one of the most important problems of the aerodynamics of viscous fluids. The accumulation of information on the pulsation characteristics of jet flows and the establishment of the corresponding governing laws may serve to verify the basic hypotheses of the semiempirical theories of turbulence, and also for the development of more advanced computational methods. In many cases the measurement of the pulsation characteristics of turbulent jets is of practical interest.The studies made up till now [1–5] of the microstructure of turbulent flow in the primary region of submerged axisymmetric jets have made it possible to obtain several interesting results. In particular, in addition to the average velocity profiles, hot-wire anemometric equipment has been used to measure the normal and tangential Reynolds stresses and also the intermittency factor in cross sections of the jet, the distribution of the intensity of the longitudinal and lateral velocity pulsations along the axis, the correlation coefficients and the corresponding integral turbulence scales, etc. These measurements have made it possible to draw several important conclusions on the mechanism of turbulent exchange, on the order of the terms omitted in the equation of motion, and on the semiempirical theories of turbulence [6–9].The common deficiency of the studies mentioned above is that near the boundary of a submerged jet, where the average velocity is practically equal to zero, the intensity of the pulsations is so great that it makes the reliability of the results obtained by means of the hotwire anemometer questionable. In this connection Townsend [6] indicated the advisability of studying the microstructure of a turbulent jet issuing into a low-velocity ambient flow.The present study had as its objective the investigation of the microstructure of the primary region of an axisymmetric jet in a wake flow over quite a broad range of the flow ratio parameter m=u/u₀;here u₀ is the average velocity at the nozzle exit, u is the velocity of the ambient stream. For various values of the parameter m in the primary region of the jet measurements were made of the profiles of the three components of the pulsation velocity and the Reynolds shear stresses, and also the values of the average velocity and two components of the pulsation velocity at a large number of points on the jet axis. The measured profiles of the Reynolds shear stresses were compared with the corresponding profiles calculated on the basis of the boundary layer equations from the experimentally determined average velocity profiles. For two values of the parameter m, in one of the sections of the jet measurements were made of the correlation coefficients of the longitudinal components of the pulsation velocity and the variation across the jet of the integral turbulence scale was determined.The results obtained give an idea of the influence of the parameter m on the characteristics of the turbulent jet in an ambient stream.     

Rarefied planar jets into vacuum

This paper presents a fundamental gaskinetic study on high speed rarefied jets expanding into vacuum from a cluster of planar exits. Based on the corresponding exact expressions for one planar jet, this paper straightforwardly derives the combined multiple jet flowfield solutions of density and velocity components, however, for the combined temperature and pressure solutions, extra attention shall be practiced. Several direct simulation Monte Carlo simulation results are provided and they validate these analytical solutions of rarefied planar jet flows.     

Absolute instability in variable density round jets

This is a brief report on the properties of round jets of different densities issuing into the ambient air. Different densities were obtained by premixing helium and air in various proportions. We show that these jets have two types of behaviour depending on the density ratio between the jet and the ambient fluids, one characterized by very sharp peaks in the power spectral density of the velocity in the near field of the jet, and another with broadened and much less prominant spectral peaks. We examine the possibility that the first state corresponds to absolute instability, and the second to convective instability. It appears that the nature of instability can be changed from absolute to convective by very simple means reminiscent of similar possibilities in low Reynolds number wakes of circular cylinders. Flow visualization reveals that the low-density jets intermittently breakdown, and spread spectacularly, beyond a certain small axial distance.     

入口速度比对射流拟序结构的影响

为了深入了解湍流流动机理以及湍流拟序结构发现过程的影响因素，本文采用大涡模拟方法对不同入口射流伴流速度比的平面湍射流流动进行了数值模拟。采用分步投影法求解动量方程，亚格子项采用标准Smagorinsky亚格子模式模拟，压力泊松方程采用修正的循环消去法快速求解，空间方程采用二阶精度的差分格式，在时间方向上采用二阶精度的显式差分格式。模拟结果给出了平面射流中湍流拟序结构的瞬态发展演变过程，分析了入口速度比对射流拟序结构发展演化过程及宏观流场形态的影响。为进一步研究射流拟序结构及其在湍流流动中的作用提供了基础。     

A gas jet superposition model for CFD modeling of group-hole nozzle sprays

In the present study, a jet superposition modeling approach is explored to model group-hole nozzle sprays, in which multiple spray jets interact with each other. An equation to estimate the merged jet velocity from each of the individual jets was derived based on momentum conservation for equivalent gas jets. Diverging and converging group-hole nozzles were also considered. The model was implemented as a sub-grid-scale submodel in a Lagrangian Drop–Eulerian Gas CFD model for spray predictions. Spray tip penetration predicted using the present superposition model was validated against experimental results for parallel, diverging and converging group-hole nozzles as a function of the angle between the two holes at various injection and ambient pressures. The results show that spray tip penetration decreases as the group hole diverging or converging angle increases. However, the spray penetration of the converging group-hole nozzle arrangement is more sensitive to the angle between the two holes compared to diverging nozzle because the radial momentum component is converted to axial momentum during the jet–jet impingement process in the converging group-hole nozzle case. The modeling results also indicate that for converging group-hole nozzles the merged sprays become ellipsoidal in cross-section far downstream of the nozzle exit with larger converging angles, indicating increased air entrainment.     

Axisymmetric jets impinging on porous walls

The flow of axisymmetric turbulent jets impinging on porous walls has been studied experimentally. It is shown how the overall flow structure depends on the porosity of the surface. For high porosities (open area ratios, β, in excess of around 40% say) the porous wall, or screen, leads to a sudden increase in jet width and decrease in mean and fluctuating velocities, a direct consequence of the momentum flux extracted because of the screen drag. Lower porosities can lead to the appearance of radial wall jets on the upstream side of the screen but, in contrast to the corresponding case of planar jet impingement (Cant et al. in Exp Fluids 32:16–26, 2002), such wall jets never occur on the downstream side. The axial downstream velocities thus remain positive for all porosities. Jet growth rates for are initially increased by the screen, but once β≤0.4 momentum extraction by the screen is virtually complete, so that velocities become very small. Again, unlike in the corresponding planar case (for β≈0.4), recirculating regions upstream of the screen never occur. A simple argument is suggested to explain the fundamental differences in flow behaviour between planar and axisymmetric jet impingement onto porous screens and it is concluded that in the latter case the effects of the screen are generally more benign and unsurprising. Nonetheless, these axisymmetric flows, like the corresponding planar ones, provide a serious challenge for computational modelling.     

Solution of the problem of flow of a non-axisymmetric swirling submerged jets

This paper considers the problem of a non-axisymmetric swirling jet of an incompressible viscous fluid flowing in a space flooded with the same fluid. The far field of the jet is studied under the assumption that the angular momentum vector corresponding to the swirling of the jet is not collinear to the momentum vector of the jet. It is shown that the main terms of the asymptotic expansion of the full solution for the velocity field are determined by the exact integrals of conservation of momentum, mass, and angular momentum. An analytical solution of the problem describing the axisymmetric swirling jet is obtained.     

Theory of an Ideal Jet Thrust Augmentor

A theory of the ideal jet thrust augmentor is presented. The conditions of optimal outflow of the active (primary) and passive (secondary) jets from the device under consideration are obtained by solving the variational problem of maximum average thrust realization. The inlet values of the mass and total enthalpy fluxes for both flows, their entropies, and the inlet value of the passive-gas momentum component parallel to the flight velocity are preassigned. These conditions correspond to the use of jet engines, including a bypass turbojet gas generator, operating in steady mode, as well as a pulsed detonation rocket engine, as the high-pressure gas source. Along with the work done by the high-pressure gas on the low-pressure one, the gases may exchange heat. The possibility of heat transfer results in an appreciable increase in ideal thrust augmentor performance.     

The preheated Airy wall jet

The Airy jet is a wall-bounded flow belonging to the similarity class of the well known free jet but, in contrast to the latter, its far field behavior is an algebraically decaying rotational flow. The velocity and temperature distributions of a preheated Airy jet flowing over an insulated wall are investigated using both analytical and numerical methods, and are compared with those of the classical (preheated) exponentially decaying wall jet. For the same value of the dimensionless skin friction parameter, the maximum of the similar velocity profile of the Airy jet exceeds that of the classical wall jet by approximately 20%. The dimensionless temperature along the insulated wall scales for large values of the Prandtl number with Pr^2/3 for both jets, while for small values of the Prandtl number the temperature scales with Pr^1/3 for the Airy jet and goes to 1 for the classical wall jet.This work is dedicated to Michael B. Glauert who passed away on June 14, 2004     

Global mode-based control of laminar and turbulent high-speed jets

The emitted noise from round jets is reduced using linear feedback controllers designed using structural sensitivity analysis. Linear global modes inform the selection and placement of the controller, and Navier–Stokes simulations are used to demonstrate effectiveness in a Mach-1.5 cold axisymmetric jet and in a Mach-0.9 cold turbulent jet. In both jets, each fitted with a cylindrical nozzle, the control reduces the radiated noise and modifies the baseflow in a way that enhances the relative amplitudes of low-frequency $\mathit{St}\approx 0.05$ global modes that do not have significant support in the acoustic field.     

Investigation of density ratio effects on normally injected cold jets into a hot cross flow

In this work, hydrodynamic effects of multiple squared cross-section cold jets inclined normally into a hot cross flow were computationally simulated using large eddy simulation (LES) approach. The finite volume method and the SIMPLE algorithm on a multi-block non-uniform staggered grid were applied. The jet into cross flow velocity ratio and the jet Reynolds number were 0.5 and 4,700, respectively. Simulations were performed for three different jets into cross flow temperature ratios, namely, 2, 1, and 0.5, corresponding to density ratios of 0.5, 1, and 2. The experimental and numerical results of Ajersch et al. (J. Turbomachinery 119(2), 330–342, 1997) at unit density ratio were used for validation purposes. The density ratio effects on the flow characteristics were investigated. It was shown that the density ratio has significant effects on the hydrodynamics of the jet into cross flow problems and even though the flow Mach number may be low, its effects due to temperature differences between the jet and the cross flow cannot be easily ignored.