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1
Akin, J. E., i J. Bass. "Asymmetric turbulent jet flows". Computer Methods in Applied Mechanics and Engineering 191, nr 6-7 (grudzień 2001): 515–24. http://dx.doi.org/10.1016/s0045-7825(01)00299-7.
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Polezhaev, Yu V., A. V. Korshunov i G. V. Gabbasova. "Turbulence and turbulent viscosity in jet flows". High Temperature 45, nr 3 (czerwiec 2007): 334–38. http://dx.doi.org/10.1134/s0018151x07030091.
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Erdil, A., H. M. Ertunc i T. Yilmaz. "Decomposition of forced turbulent jet flows". Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 223, nr 4 (11.12.2008): 919–33. http://dx.doi.org/10.1243/09544062jmes1173.
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In many cases, turbulence is superimposed on an unsteady organized motion of a mean flow. Indeed, large ranges of scales are involved in these flows, and it is important to investigate their characteristics and interactions. Thus, the time—frequency decomposition provided by the wavelet analysis appears an efficient tool that complements the classical approach and the Fourier transform. In this study, the wavelet decomposition (WD) method has been applied to the forced turbulent jet flows. The obtained results of the WD are compared with those of the other most common techniques such as proper orthogonal decomposition and phase averaging. In addition, the spectrogram of the signals has been presented for a visual representation of the frequency contents. It is shown that the WD is a successful tool to decompose the forced turbulent jet flows into its components for various axial distances, Re numbers, and forcing frequencies.
4
Mostafa, A. A. "Turbulent Diffusion of Heavy-Particles in Turbulent Jets". Journal of Fluids Engineering 114, nr 4 (1.12.1992): 667–71. http://dx.doi.org/10.1115/1.2910083.
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The turbulent dispersion of heavy suspended particles in turbulent shear flows is analyzed when crossing trajectory effects are important. A semiempirical expression for particle diffusion coefficient is developed via a comparison with experimental data of two-phase turbulent jet flows. This expression gives the particle momentum diffusion coefficient in terms of the gas diffusion coefficient, mean relatively velocity, and root mean square of the fluctuating fluid velocity. The proposed expression is used in a two-phase flow mathematical model to predict different particle-laden jet flows. The good agreement between the predictions and data suggests that the developed expression for particle diffusion coefficient is reasonably accurate in predicting particle dispersion in turbulent free shear flows.
5
NICKELS, T. B., i IVAN MARUSIC. "On the different contributions of coherent structures to the spectra of a turbulent round jet and a turbulent boundary layer". Journal of Fluid Mechanics 448 (26.11.2001): 367–85. http://dx.doi.org/10.1017/s002211200100619x.
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This paper examines and compares spectral measurements from a turbulent round jet and a turbulent boundary layer. The conjecture that is examined is that both flows consist of coherent structures immersed in a background of isotropic turbulence. In the case of the jet, a single size of coherent structure is considered, whereas in the boundary layer there are a range of sizes of geometrically similar structures. The conjecture is examined by comparing experimental measurements of spectra for the two flows with the spectra calculated using models based on simple vortex structures. The universality of the small scales is considered by comparing high-wavenumber experimental spectra. It is shown that these simple structural models give a good account of the turbulent flows.
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Alekseenko, Sergey, Artur Bilsky, Vladimir Dulin, Boris Ilyushin i Dmitriy Markovich. "TURBULENT ENERGY BALANCE IN FREE AND CONFINED JET FLOWS(Free and Confined Jet)". Proceedings of the International Conference on Jets, Wakes and Separated Flows (ICJWSF) 2005 (2005): 281–86. http://dx.doi.org/10.1299/jsmeicjwsf.2005.281.
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Stoellinger, Michael K., Stefan Heinz, Celestin P. Zemtsop, Harish Gopalan i Reza Mokhtarpoor. "Stochastic-Based RANS-LES Simulations of Swirling Turbulent Jet Flows". International Journal of Nonlinear Sciences and Numerical Simulation 18, nr 5 (26.07.2017): 351–69. http://dx.doi.org/10.1515/ijnsns-2016-0069.
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AbstractMany turbulent flow simulations require the use of hybrid methods because LES methods are computationally too expensive and RANS methods are not sufficiently accurate. We consider a recently suggested hybrid RANS-LES model that has a sound theoretical basis: it is systematically derived from a realizable stochastic turbulence model. The model is applied to turbulent swirling and nonswirling jet flow simulations. The results are shown to be in a very good agreement with available experimental data of nonswirling and mildly swirling jet flows. Compared to commonly applied other hybrid RANS-LES methods, our RANS-LES model does not seem to suffer from the ’modeled-stress depletion’ problem that is observed in DES and IDDES simulations of nonswirling jet flows, and it performs better than segregated RANS-LES models. The results presented contribute to a better physical understanding of swirling jet flows through an explanation of conditions for the onset and the mechanism of vortex breakdown.
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Alvani, R. F., i M. Fairweather. "Ignition Characteristics Of Turbulent Jet Flows". Chemical Engineering Research and Design 80, nr 8 (listopad 2002): 917–23. http://dx.doi.org/10.1205/026387602321143471.
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Louda, Petr, Jaromír Příhoda i Karel Kozel. "Numerical solution of turbulent jet flows". PAMM 8, nr 1 (grudzień 2008): 10629–30. http://dx.doi.org/10.1002/pamm.200810629.
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Walker, D. T., C. Y. Chen i W. W. Willmarth. "Turbulent structure in free-surface jet flows". Journal of Fluid Mechanics 291 (25.05.1995): 223–61. http://dx.doi.org/10.1017/s0022112095002680.
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Results of an experimental study of the interaction of a turbulent jet with a free surface when the jet issues parallel to the free surface are presented. Three different jets, with different exit velocities and jet-exit diameters, all located two jet-exit diameters below the free surface were studied. At this depth the jet flow, in each case, is fully turbulent before significant interaction with the free surface occurs. The effects of the Froude number (Fr) and the Reynolds number (Re) were investigated by varying the jet-exit velocity and jet-exit diameter. Froude-number effects were identified by increasing the Froude number from Fr = 1 to 8 at Re = 12700. Reynolds-number effects were identified by increasing the Reynolds number from Re = 12700 to 102000 at Fr = 1. Qualitative features of the subsurface flow and free-surface disturbances were examined using flow visualization. Measurements of all six Reynolds stresses and the three mean velocity components were obtained in two planes 16 and 32 jet diameters downstream using a three-component laser velocimeter. For all the jets, the interaction of vorticity tangential to the surface with its ‘image’ above the surface contributes to an outward flow near the free surface. This interaction is also shown to be directly related to the observed decrease in the surface-normal velocity fluctuations and the corresponding increase in the tangential velocity fluctuations near the free surface. At high Froude number, the larger surface disturbances diminish the interaction of the tangential vorticity with its image, resulting in a smaller outward flow and less energy transfer from the surface-normal to tangential velocity fluctuations near the surface. Energy is transferred instead to free-surface disturbances (waves) with the result that the turbulence kinetic energy is 20% lower and the Reynolds stresses are reduced. At high Reynolds number, the rate of evolution of the interaction of the jet with the free surface was reduced as shown by comparison of the rate of change with distance downstream of the local Reynolds and Froude numbers. In addition, the decay of tangential vorticity near the surface is slower than for low Reynolds number so that vortex filaments have time to undergo multiple reconnections to the free surface before they eventually decay.
11
Gerodimos, G., i R. M. C. So. "Near-Wall Modeling of Plane Turbulent Wall Jets". Journal of Fluids Engineering 119, nr 2 (1.06.1997): 304–13. http://dx.doi.org/10.1115/1.2819135.
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In most two-dimensional simple turbulent flows, the location of zero shear usually coincides with that of vanishing mean velocity gradient. However, such is not the case for plane turbulent wall jets. This could be due to the fact that the driving potential is the jet exit momentum, which gives rise to an outer region that resembles a free jet and an inner layer that is similar to a boundary layer. The interaction of a free-jet like flow with a boundary-layer type flow distinguishes the plane wall jet from other simple flows. Consequently, in the past, two-equation turbulence models are seldom able to predict the jet spread correctly. The present study investigates the appropriateness of two-equation modeling; particularly the importance of near-wall modeling and the validity of the equilibrium turbulence assumption. An improved near-wall model and three others are analyzed and their predictions are compared with recent measurements of plane wall jets. The jet spread is calculated correctly by the improved model, which is able to replicate the mixing behavior between the outer jet-like and inner wall layer and is asymptotically consistent. Good agreement with other measured quantities is also obtained. However, other near-wall models tested are also capable of reproducing the Reynolds-number effects of plane wall jets, but their predictions of the jet spread are incorrect.
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Ferreira, V. G., A. C. Brandi, F. A. Kurokawa, P. Seleghim Jr., A. Castelo i J. A. Cuminato. "Incompressible Turbulent Flow Simulation Using theκ-ɛModel and Upwind Schemes". Mathematical Problems in Engineering 2007 (2007): 1–26. http://dx.doi.org/10.1155/2007/12741.
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In the computation of turbulent flows via turbulence modeling, the treatment of the convective terms is a key issue. In the present work, we present a numerical technique for simulating two-dimensional incompressible turbulent flows. In particular, the performance of the high Reynoldsκ-ɛmodel and a new high-order upwind scheme (adaptative QUICKEST by Kaibara et al. (2005)) is assessed for 2D confined and free-surface incompressible turbulent flows. The model equations are solved with the fractional-step projection method in primitive variables. Solutions are obtained by using an adaptation of the front tracking GENSMAC (Tomé and McKee (1994)) methodology for calculating fluid flows at high Reynolds numbers. The calculations are performed by using the 2D version of theFreeflowsimulation system (Castello et al. (2000)). A specific way of implementing wall functions is also tested and assessed. The numerical procedure is tested by solving three fluid flow problems, namely, turbulent flow over a backward-facing step, turbulent boundary layer over a flat plate under zero-pressure gradients, and a turbulent free jet impinging onto a flat surface. The numerical method is then applied to solve the flow of a horizontal jet penetrating a quiescent fluid from an entry port beneath the free surface.
13
Kohli, Atul, i David G. Bogard. "Turbulent Transport in Film Cooling Flows". Journal of Heat Transfer 127, nr 5 (1.05.2005): 513–20. http://dx.doi.org/10.1115/1.1865221.
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This experimental study was performed on a single row of round holes with a 35° surface angle, representing film cooling geometry commonly used in turbine engines. Simultaneous velocity and temperature measurements were made using a cold-wire in conjunction with a LDV. The experimentally determined cross correlations provide a direct indication of the extent of turbulent transport of heat and momentum in the flow, which in turn governs dispersion of the film cooling jet. Actual engine environments have elevated mainstream turbulence levels that can severely reduce the cooling capability of film cooling jets. Clearly, the turbulent transport for very high mainstream turbulence is expected to be markedly different than that with low mainstream turbulence, and would improve our understanding of the mechanisms involved in the dispersion of film cooling jets. Experimental cross-correlation data was obtained for two vastly different freestream turbulence levels (0.6% and 20%) in this study. For this purpose, eddy diffusivities for momentum and heat transport were estimated from the measured data. These results will help develop new turbulence models and also explain why gradient diffusion based models do not give good predictions relative to experimental results.
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Lilley, G. M. "The generation of sound in turbulent motion". Aeronautical Journal 112, nr 1133 (lipiec 2008): 381–94. http://dx.doi.org/10.1017/s0001924000002347.
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Abstract The present paper reviews and discusses the physical mechanisms of noise generation and reduction in turbulent flows with their applications towards aircraft noise reduction at takeoff and on the approach. This work began in 1948 when Lilley undertook an experimental investigation into the source of jet noise as a necessary precursor to finding methods for the reduction of high speed jet engine noise on civil jet airliners. Westley and Lilley completed this experimental programme in 1951, which included the design of a range of devices for high speed jet noise reduction. It was about this time that similar studies on jet noise were being started elsewhere and in particular by Lassiter and Hubbard in USA. The major contribution to the subject of turbulence as a source of noise came from Sir James Lighthill’s remarkable theory in 1952. In spite of the difficulties attached to theoretical and experimental studies on noise from turbulence, it is shown that with the accumulated knowledge on aerodynamic noise over the past 50 years, together with an optimisation of aircraft operations including flight trajectories, we are today on the threshold of approaching the design of commercial aircraft with turbofan propulsion engines that will not be heard above the background noise of the airport at takeoff and landing beyond 1-2km, from the airport boundary fence. It is evident that in the application of this work, which centres on the physical mechanisms relating to the generation of noise from turbulence and turbulent shear flows, to jet noise, there is not one unique mechanism of jet noise generation for all jet Mach numbers. This author in this publication has concentrated on what appears to be the dominant mechanism of noise generation from turbulence, where the mean convection speeds of the turbulence are subsonic. The noise generated at transonic and supersonic jet speeds invariably involves extra mechanisms, which are only briefly referred to here.
15
CAMUSSI, R., i G. GUJ. "Orthonormal wavelet decomposition of turbulent flows: intermittency and coherent structures". Journal of Fluid Mechanics 348 (10.10.1997): 177–99. http://dx.doi.org/10.1017/s0022112097006551.
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Experimental data obtained in various turbulent flows are analysed by means of orthogonal wavelet transforms. Several configurations are analysed: homogeneous grid turbulence at low and very low Reλ, and fully developed jet turbulence at moderate and high Reλ. It is shown by means of the wavelet decomposition in combination with the form of scaling named extended self-similarity that some statistical properties of fully developed turbulence may be extended to low-Reλ flows. Indeed, universal properties related to intermittency are observed down to Reλ≃10. Furthermore, the use of a new conditional averaging technique of velocity signals, based on the wavelet transform, permits the identification of the time signatures of coherent structures which may or may not be responsible for intermittency depending on the scale of the structure itself. It is shown that in grid turbulence, intermittency at the smallest scales is related to structures with small characteristic size and with a shape that may be related to the passage of vortex tubes. In jet turbulence, the longitudinal velocity component reveals that intermittency may be induced by structures with a size of the order of the integral length. This effect is interpreted as the signature of the characteristic jet mixing layer structures. The structures identified on the transverse velocity component of the jet case turn out on the other hand not to be affected by the mixing layer and the corresponding shape is again correlated with the signature of vortex tubes.
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Savitskii, Alexey, Aleksei Lobasov, Dmitriy Sharaborin i Vladimir Dulin. "Testing Basic Gradient Turbulent Transport Models for Swirl Burners Using PIV and PLIF". Fluids 6, nr 11 (25.10.2021): 383. http://dx.doi.org/10.3390/fluids6110383.
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The present paper reports on the combined stereoscopic particle image velocimetry (PIV) and planar laser induced fluorescence (PLIF) measurements of turbulent transport for model swirl burners without combustion. Two flow types were considered, namely the mixing of a free jet with surrounding air for different swirl rates of the jet (Re = 5 × 103) and the mixing of a pilot jet (Re = 2 × 104) with a high-swirl co-flow of a generic gas turbine burner (Re = 3 × 104). The measured spatial distributions of the turbulent Reynolds stresses and fluxes were compared with their predictions by gradient turbulent transport models. The local values of the turbulent viscosity and turbulent diffusivity coefficients were evaluated based on Boussinesq’s and gradient diffusion hypotheses. The studied flows with high swirl were characterized by a vortex core breakdown and intensive coherent flow fluctuations associated with large-scale vortex structures. Therefore, the contribution of the coherent flow fluctuations to the turbulent transport was evaluated based on proper orthogonal decomposition (POD). The turbulent viscosity and diffusion coefficients were also evaluated for the stochastic (residual) component of the velocity fluctuations. The high-swirl flows with vortex breakdown for the free jet and for the combustion chamber were characterized by intensive turbulent fluctuations, which contributed substantially to the local turbulent transport of mass and momentum. Moreover, the high-swirl flows were characterized by counter-gradient transport for one Reynolds shear stress component near the jet axis and in the outer region of the mixing layer.
17
Barata, J. M. M., D. F. G. Dura˜o i M. V. Heitor. "Velocity Characteristics of Multiple Impinging Jets Through a Crossflow". Journal of Fluids Engineering 114, nr 2 (1.06.1992): 231–39. http://dx.doi.org/10.1115/1.2910020.
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The mean and turbulent velocity characteristics of the flowfield resulting from the impingement of two and three jets against a wall through a low-velocity crossflow are quantified in detail making use of a laser-Doppler velocimeter and are discussed together with the visualization of the flow. The experiments have been carried out for a velocity ratio between the jets and the crossflow of 30, for a Reynolds number based on the jet exit of 105,000, and for the jet exit five jet-diameters above the ground plate, and provided a basis to improve knowledge of several related complex flow fields in engineering applications. The results characterize the turbulent transport typical of multiple impinging flows associated with a large penetration of the impinging jets through a crossflow, and quantify the formation of fountain flows due to collision of consecutive wall jets. The turbulence measurements include those of Reynolds shear stress and identify large effects of flow distortion on the turbulence structure parameters that determine the empirical constants in engineering models of turbulence.
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Liu, Hongmei, i Tat Leung Chan. "A coupled LES-Monte Carlo method for simulating aerosol dynamics in a turbulent planar jet". International Journal of Numerical Methods for Heat & Fluid Flow 30, nr 2 (7.09.2019): 855–81. http://dx.doi.org/10.1108/hff-11-2018-0657.
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Purpose The purpose of this paper is to study the evolution and growth of aerosol particles in a turbulent planar jet by using the newly developed large eddy simulation (LES)-differentially weighted operator splitting Monte Carlo (DWOSMC) method. Design/methodology/approach The DWOSMC method is coupled with LES for the numerical simulation of aerosol dynamics in turbulent flows. Findings Firstly, the newly developed and coupled LES-DWOSMC method is verified by the results obtained from a direct numerical simulation-sectional method (DNS-SM) for coagulation occurring in a turbulent planar jet from available literature. Then, the effects of jet temperature and Reynolds number on the evolution of time-averaged mean particle diameter, normalized particle number concentration and particle size distributions (PSDs) are studied numerically on both coagulation and condensation processes. The jet temperature and Reynolds number are shown to be two important parameters that can be used to control the evolution and pattern of PSD in an aerosol reactor. Originality/value The coupling between the Monte Carlo method and turbulent flow still encounters many technical difficulties. In addition, the relationship between turbulence, particle properties and collision kernels of aerosol dynamics is not yet well understood due to the theoretical limitations and experimental difficulties. In the present study, the developed and coupled LES-DWOSMC method is capable of solving the aerosol dynamics in turbulent flows.
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Yang, Xingtuan, Nan Gui, Gongnan Xie, Jie Yan, Jiyuan Tu i Shengyao Jiang. "Anisotropic Characteristics of Turbulence Dissipation in Swirling Flow: A Direct Numerical Simulation Study". Advances in Mathematical Physics 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/657620.
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This study investigates the anisotropic characteristics of turbulent energy dissipation rate in a rotating jet flow via direct numerical simulation. The turbulent energy dissipation tensor, including its eigenvalues in the swirling flows with different rotating velocities, is analyzed to investigate the anisotropic characteristics of turbulence and dissipation. In addition, the probability density function of the eigenvalues of turbulence dissipation tensor is presented. The isotropic subrange of PDF always exists in swirling flows relevant to small-scale vortex structure. Thus, with remarkable large-scale vortex breakdown, the isotropic subrange of PDF is reduced in strongly swirling flows, and anisotropic energy dissipation is proven to exist in the core region of the vortex breakdown. More specifically, strong anisotropic turbulence dissipation occurs concentratively in the vortex breakdown region, whereas nearly isotropic turbulence dissipation occurs dispersively in the peripheral region of the strong swirling flows.
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Nallasamy, M. "Computation of confined turbulent coaxial jet flows". Journal of Propulsion and Power 3, nr 3 (maj 1987): 263–68. http://dx.doi.org/10.2514/3.22983.
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Martynenko, O. G., I. A. Vatutin, N. I. Lemesh i P. P. Khramtsov. "Optical characteristics of turbulent nonisothermal jet flows". Journal of Engineering Physics 54, nr 4 (kwiecień 1988): 379–82. http://dx.doi.org/10.1007/bf00871106.
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Mitsotakis, K., E. Zauner i W. Schneider. "Turbulent jet flows with buoyancy and swirl". Ingenieur-Archiv 58, nr 3 (1988): 161–70. http://dx.doi.org/10.1007/bf00534327.
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Kannan, BT, i NR Panchapakesan. "Influence of nozzle configuration on the flow field of multiple jets". Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 232, nr 9 (2.04.2017): 1639–54. http://dx.doi.org/10.1177/0954410017699008.
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Turbulent jet flows with multiple nozzle inlets are investigated computationally using OpenFOAM. The configurations vary from single to five axisymmetric nozzles. First-order closure is used with Reynolds-averaged Navier–Stokes equations. Computed results are compared with the available experimental data. The effect of nozzle configuration on the jet flow field is discussed with predicted mean flow and turbulent flow data. Near-field of multiple jets shows the nonlinear behavior. Multiple jets show better performance in the near-field based on entrainment, secondary flows, and area-averaged turbulent kinetic energy. The downstream evolution of the multiple jets differs for configurations with and without central jet. The shape parameter confirms the evolution of the multiple jets towards an axisymmetric jet.
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Castro, Nicolas D., i Ayodeji O. Demuren. "Large eddy simulation of turbulent axially rotating pipe and swirling jet flows". Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, nr 9 (2.12.2015): 1749–61. http://dx.doi.org/10.1177/0954406215620823.
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Fully-developed, turbulent rotating pipe flow and swirling jet flow, emitted from the pipe, into open quiescent ambient are investigated numerically using large eddy simulation. Simulations are performed at various rotation rates and Reynolds numbers. Time-averaged large eddy simulation results are compared to experimental and simulation data from previous studies. Pipe flow results show deformation of the turbulent mean axial velocity profile towards the laminar-type Poiseuille profile, with increased rotation. The Reynolds stress anisotropy tensor experiences a component-level redistribution due to pipe rotation. Turbulent energy is transferred from the axial component to the tangential component as rotation is increased. The Reynolds stress anisotropy invariant map also shows a movement away from the one-component limit in the buffer layer, with increased rotation. Exit conditions for the pipe flow simulation are utilized as inlet conditions for the jet flow simulation. Jet flow without swirl and at a swirl rate of S = 0.5 are investigated. Swirl is observed to change the characteristics of the jet flow field, leading to increased jet spread and velocity decay, and a corresponding decrease in the length of the jet potential core. The Reynolds stress anisotropy invariant map shows that the turbulent stress field, with or without rotation straddles the axi-symmetric limit.
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Markesteijn, A. P., i S. A. Karabasov. "Simulations of co-axial jet flows on graphics processing units: the flow and noise analysis". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 377, nr 2159 (14.10.2019): 20190083. http://dx.doi.org/10.1098/rsta.2019.0083.
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Large-eddy simulations (LES) are performed for a range of perfectly expanded co-axial jet cases corresponding to conditions of the computation of coaxial jet noise (CoJeN) experiment by QinetiQ. In all simulations, the high-resolution Compact Accurately Boundary-Adjusting high-REsolution Technique (CABARET) is used for solving the Navier–Stokes equations on unstructured meshes. The Ffowcs Williams–Hawkings method based on the penetrable integral surfaces is applied for far-field noise predictions. To correctly model the turbulent flow downstream of the complex nozzle that includes a central body, a wall modelled LES approach is implemented together with a turbulent inflow condition based on synthetic turbulence. All models are run on graphics processing units to enable a considerable reduction of the flow solution time in comparison with the conventional LES. The flow and noise solutions are validated against the experimental data available with 1–2 dB accuracy being reported for noise spectra predictions on the fine grid. To analyse the structure of effective noise sources of the jets, the covariance of turbulent fluctuating Reynolds stresses is computed and their characteristic scales are analysed in the context of the generalized acoustic analogy jet noise models. Motivated by self-similarity of single-stream axi-symmetric jet flows, a suitable non-dimensionalization of the effective jet noise sources of the CoJeN jets is tested, and its implications for low-order jet noise models are discussed. This article is part of the theme issue ‘Frontiers of aeroacoustics research: theory, computation and experiment’.
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Hui, H., T. Kobayashi, S. Wu i G. Shen. "Changes to the vortical and turbulent structure of jet flows due to mechanical tabs". Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 213, nr 4 (1.04.1999): 321–29. http://dx.doi.org/10.1243/0954406991522284.
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The effect of mechanical tabs on the vortical and turbulent structures in the near fields of jet mixing flows is investigated in the present paper. In order to compare the changes of the vortical and turbulent structures of jet flows with and without mechanical tabs, flow visualization and instantaneous quantitative concentration field measurements were conducted in a water channel by using a laser induced fluorescence (LIF) technique. The flow visualization confirmed the existence of a pair of counter-rotating streamwise vortices produced by each mechanical tab in a jet flow. The generated streamwise vortices can cause an inward indentation of ambient flow into the core jet flow and an outward ejection of core jet flow into the ambient flow. It also showed that the process of Kelvin—Helmholtz vortex pairing was accelerated, the small-scale vortical structure appeared earlier and a large-scale helical coherent structure was found in the near fields of tabbed jet flows. Based on the flow visualization and instantaneous quantitative concentration field measurements, two aspects of the effect of the streamwise vortical pairs induced by mechanical tabs on the jet mixing flows were suggested.
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Chandrasekhara, M. S., i B. R. Ramaprian. "Intermittency and Length Scale Distributions in a Plane Turbulent Plume". Journal of Fluids Engineering 112, nr 3 (1.09.1990): 367–69. http://dx.doi.org/10.1115/1.2909413.
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Previous studies have shown that normalized Reynolds shear stress and turbulent heat fluxes in asymptotic plane turbulent plumes are significantly higher than in asymptotic plane turbulent jets. This paper describes an attempt to relate this increase to the length scales in the flow. Hot/cold interface intermittency and integral-length-scale distributions were measured in both these flows. The interface-intermittency distributions were found to be bell-shaped in the plume in contrast to a nearly top-hat shape in a jet, thus providing confirmation of the role of buoyancy in generating larger scales in plumes. These larger scales cause the integral length of turbulence in the plume to increase by nearly 15 percent relative to the non-buoyant jet.
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Namazian, M., J. Kelly i R. W. Schefer. "Concentration imaging measurements in turbulent concentric-jet flows". AIAA Journal 30, nr 2 (luty 1992): 384–94. http://dx.doi.org/10.2514/3.10929.
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Vinberg, A. A., L. I. Zaichik i V. A. Pershukov. "Computational model of turbulent gas-disperse jet flows". Journal of Engineering Physics 61, nr 4 (październik 1991): 1199–206. http://dx.doi.org/10.1007/bf00872586.
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Ewing, D. "Two-point similarity in turbulent planar jet flows". International Journal of Heat and Fluid Flow 67 (październik 2017): 131–38. http://dx.doi.org/10.1016/j.ijheatfluidflow.2017.06.006.
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Thomas, F. O., i V. W. Goldschmidt. "Acoustically Induced Enhancement of Widening and Fluctuation Intensity in a Two-Dimensional Turbulent Jet". Journal of Fluids Engineering 108, nr 3 (1.09.1986): 331–37. http://dx.doi.org/10.1115/1.3242582.
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The enhancement of widening rate and turbulence intensity in a turbulent plane jet, due to an acoustic disturbance are considered. Detailed data at a representative Strouhal number suggest a well organized symmetric structural array in the initial region of the flow. These highly organized flow structures act as efficient agents in the transport of energy to the fine-grained turbulence, leading to greater diffusivity, enhanced turbulence and an increase in widening. The data also suggest significant differences in the underlying structure of the natural and excited jet flows, hence putting in jeopardy any generalization of coherent motions especially excited to facilitate their study.
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Hussain, A. K. M. F., i M. A. Z. Hasan. "Turbulence suppression in free turbulent shear flows under controlled excitation. Part 2. Jet-noise reduction". Journal of Fluid Mechanics 150 (styczeń 1985): 159–68. http://dx.doi.org/10.1017/s0022112085000076.
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It is shown that reduction of broadband (even total) far-field jet noise can be achieved via controlled excitation of a jet at a frequency in the range 0.01 < Stθ < 0.02, where Stθ is the Strouhal number based on the exit momentum thickness of the shear layer. Hot-wire measurements in the noise-producing region of the jet reveal that the noise suppression is a direct consequence of turbulence suppression, produced by early saturation and breakdown of maximally growing instability modes.
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STANLEY, S. A., S. SARKAR i J. P. MELLADO. "A study of the flow-field evolution and mixing in a planar turbulent jet using direct numerical simulation". Journal of Fluid Mechanics 450 (9.01.2002): 377–407. http://dx.doi.org/10.1017/s0022112001006644.
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Turbulent plane jets are prototypical free shear flows of practical interest in propulsion, combustion and environmental flows. While considerable experimental research has been performed on planar jets, very few computational studies exist. To the authors' knowledge, this is the first computational study of spatially evolving three-dimensional planar turbulent jets utilizing direct numerical simulation. Jet growth rates as well as the mean velocity, mean scalar and Reynolds stress profiles compare well with experimental data. Coherency spectra, vorticity visualization and autospectra are obtained to identify inferred structures. The development of the initial shear layer instability, as well as the evolution into the jet column mode downstream is captured well.The large- and small-scale anisotropies in the jet are discussed in detail. It is shown that, while the large scales in the flow field adjust slowly to variations in the local mean velocity gradients, the small scales adjust rapidly. Near the centreline of the jet, the small scales of turbulence are more isotropic. The mixing process is studied through analysis of the probability density functions of a passive scalar. Immediately after the rollup of vortical structures in the shear layers, the mixing process is dominated by large-scale engulfing of fluid. However, small-scale mixing dominates further downstream in the turbulent core of the self-similar region of the jet and a change from non-marching to marching PDFs is observed. Near the jet edges, the effects of large-scale engulfing of coflow fluid continue to influence the PDFs and non-marching type behaviour is observed.
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Dritschel, D. G., i R. K. Scott. "Jet sharpening by turbulent mixing". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, nr 1937 (28.02.2011): 754–70. http://dx.doi.org/10.1098/rsta.2010.0306.
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Jets or localized strong currents in planetary atmospheres, as well as in the Earth’s oceans, are often associated with sharp potential-vorticity gradients owing to the inherent balance exhibited by these flows. Here, we explore and quantify jet sharpening in a simple idealized single-layer quasi-geostrophic model on a mid-latitude β -plane. The advantages of this idealization are that just two parameters control the flow development (the Rossby deformation length and the amplitude of the initial random flow perturbation), and that numerical experiments can comprehensively and accurately cover the parameter space. These experiments, carried out at unprecedented numerical resolution, reveal how an initially broad jet is sharpened, and the role played by coherent vortices in the vicinity of jets.
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CHEN, LI-WEI, CHANG-YUE XU i XI-YUN LU. "LARGE-EDDY SIMULATION OF OPPOSING-JET-PERTURBED SUPERSONIC FLOWS PAST A HEMISPHERICAL NOSE". Modern Physics Letters B 24, nr 13 (30.05.2010): 1287–90. http://dx.doi.org/10.1142/s021798491002344x.
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A supersonic flow past a hemispherical nose with an opposing jet placed on its axis has been investigated using large eddy simulation. We find that the flow behaviors depend mainly on the jet total pressure ratio and can be classified into three typical flow regimes of unstable, stable and transition. The unstable flow regime is characterized by an oscillatory bow shock with a multi-jet-cell structure and the stable flow regime by a steady bow shock with a single jet cell. The transition regime lies between the unstable and stable ones with a complex flow evolution. Turbulence statistics are further analyzed to reveal the relevant turbulent behaviors in the three flow regimes. The results obtained in this study provide a physical insight into the understanding of the mechanisms underlying this complex flow.
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Breda, M., i O. R. H. Buxton. "Behaviour of small-scale turbulence in the turbulent/non-turbulent interface region of developing turbulent jets". Journal of Fluid Mechanics 879 (20.09.2019): 187–216. http://dx.doi.org/10.1017/jfm.2019.676.
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Tomographic particle image velocimetry experiments were conducted in the near and intermediate fields of two different types of jet, one fitted with a circular orifice and another fitted with a repeating-fractal-pattern orifice. Breda & Buxton (J. Vis., vol. 21 (4), 2018, pp. 525–532; Phys. Fluids, vol. 30, 2018, 035109) showed that this fractal geometry suppressed the large-scale coherent structures present in the near field and affected the rate of entrainment of background fluid into, and subsequent development of, the fractal jet, relative to the round jet. In light of these findings we now examine the modification of the turbulent/non-turbulent interface (TNTI) and spatial evolution of the small-scale behaviour of these different jets, which are both important factors behind determining the entrainment rate. This evolution is examined in both the streamwise direction and within the TNTI itself where the fluid adapts from a non-turbulent state, initially through the direct action of viscosity and then through nonlinear inertial processes, to the state of the turbulence within the bulk of the flow over a short distance. We show that the suppression of the coherent structures in the fractal jet leads to a less contorted interface, with large-scale excursions of the inner TNTI (that between the jet’s azimuthal shear layer and the potential core) being suppressed. Further downstream, the behaviour of the TNTI is shown to be comparable for both jets. The velocity gradients develop into a canonical state with streamwise distance, manifested as the development of the classical tear-drop shaped contours of the statistical distribution of the velocity-gradient-tensor invariants $\mathit{Q}$ and $\mathit{R}$. The velocity gradients also develop spatially through the TNTI from the irrotational boundary to the bulk flow; in particular, there is a strong small-scale anisotropy in this region. This strong inhomogeneity of the velocity gradients in the TNTI region has strong consequences for the scaling of the thickness of the TNTI in these spatially developing flows since both the Taylor and Kolmogorov length scales are directly computed from the velocity gradients.
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Antošová, Zuzana, i Zdeněk Trávníček. "Control of a Round Jet Intermittency and Transition to Turbulence by Means of an Annular Synthetic Jet". Actuators 10, nr 8 (5.08.2021): 185. http://dx.doi.org/10.3390/act10080185.
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This paper deals with active control of a continuous jet issuing from a long pipe nozzle by means of a concentrically placed annular synthetic jet. The experiments in air cover regimes of laminar, transitional, and turbulent main jet flows (Reynolds number ranges 1082–5181). The velocity profiles (time-mean and fluctuation components) of unforced and forced jets were measured using hot-wire anemometry. Six flow regimes are distinguished, and their parameter map is proposed. The possibility of turbulence reduction by forcing in transitional jets is demonstrated, and the maximal effect is revealed at Re = 2555, where the ratio of the turbulence intensities of the forced and unforced jets is decreased up to 0.45.
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BASU, A. J., i R. NARASIMHA. "Direct numerical simulation of turbulent flows with cloud-like off-source heating". Journal of Fluid Mechanics 385 (25.04.1999): 199–228. http://dx.doi.org/10.1017/s0022112099004280.
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Direct numerical solutions of the incompressible Navier–Stokes equations have been obtained under the Boussinesq approximation for the temporal evolution of a turbulent jet-like flow subjected to off-source volumetric heating, of the kind that occurs in a cloud due to latent heat release on condensation of water vapour. The results show good qualitative agreement with available experimental data on spatially growing jets. Thus, heating accelerates the flow and arrests jet growth; and turbulence velocities increase with heating but not as rapidly as mean velocities, so normalized intensities drop. It is shown that the baroclinic torque resulting from the heating enhances the vorticity dramatically in all three directions, with a preferential amplification at the higher wavenumbers that results in a rich fine structure at later times in the evolution of the jet. Streamwise vortex pairs, rendered stronger by mean flow acceleration, appear to be responsible for large expulsive motions at certain transverse cross-sections in the ambient fluid near the heated flow; together with the disruption of the toroidal component of the coherent vorticity achieved by heating, this results in an entraining velocity field that is qualitatively different from that around unheated turbulent jets. This mechanism may provide a plausible explanation for the experimentally observed drop in entrainment with off-source heating.
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Bremhorst, K., i L. Krebs. "Eddy Diffusivity Based Comparisons of Turbulent Prandtl Number for Boundary Layer and Free Jet Flows With Reference to Fluids of Very Low Prandtl Number". Journal of Heat Transfer 115, nr 3 (1.08.1993): 549–52. http://dx.doi.org/10.1115/1.2910722.
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It is shown that turbulent Prandtl numbers for turbulent boundary layer and jet flows correlate well if compared on the basis of eddy diffusivity. Experimental data for liquid sodium (Pr= 0.0058) lead to a universal expression relating turbulent Prandtl number to eddy diffusivity of heat with the same expression applying to boundary layer and jet flows. This suggests that the length and velocity scale dependence of the turbulent Prandtl number is associated predominantly with the eddy diffusivity of momentum. Since turbulent flow codes generally include eddy diffusivity of momentum calculations, simple and accurate estimates of eddy diffusivity of heat are possible without reliance on a variety of turbulent Prandtl number functional relationships for prediction of the temperature field. Available results also indicate that turbulent Prandtl number can be set at 0.9–1.0 irrespective of molecular Prandtl number, provided that εM/ν > 3Pr−1 and the structures of the mean temperature gradient and mean shear are similar.
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VARGHESE, SONU S., STEVEN H. FRANKEL i PAUL F. FISCHER. "Direct numerical simulation of stenotic flows. Part 1. Steady flow". Journal of Fluid Mechanics 582 (14.06.2007): 253–80. http://dx.doi.org/10.1017/s0022112007005848.
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Direct numerical simulations (DNS) of steady and pulsatile flow through 75% (by area reduction) stenosed tubes have been performed, with the motivation of understanding the biofluid dynamics of actual stenosed arteries. The spectral-element method, providing geometric flexibility and high-order spectral accuracy, was employed for the simulations. The steady flow results are examined here while the pulsatile flow analysis is dealt with in Part 2 of this study. At inlet Reynolds numbers of 500 and 1000, DNS predict a laminar flow field downstream of an axisymmetric stenosis and comparison to previous experiments show good agreement in the immediate post-stenotic region. The introduction of a geometric perturbation within the current model, in the form of a stenosis eccentricity that was 5% of the main vessel diameter at the throat, resulted in breaking of the symmetry of the post-stenotic flow field by causing the jet to deflect towards the side of the eccentricity and, at a high enough Reynolds number of 1000, jet breakdown occurred in the downstream region. The flow transitioned to turbulence about five diameters away from the stenosis, with velocity spectra taking on a broadband nature, acquiring a -5/3 slope that is typical of turbulent flows. Transition was accomplished by the breaking up of streamwise, hairpin vortices into a localized turbulent spot, reminiscent of the turbulent puff observed in pipe flow transition, within which r.m.s. velocity and turbulent energy levels were highest. Turbulent fluctuations and energy levels rapidly decayed beyond this region and flow relaminarized. The acceleration of the fluid through the stenosis resulted in wall shear stress (WSS) magnitudes that exceeded upstream levels by more than a factor of 30 but low WSS levels accompanied the flow separation zones that formed immediately downstream of the stenosis. Transition to turbulence in the case of the eccentric stenosis was found to be manifested as large temporal and spatial gradients of shear stress, with significant axial and circumferential variations in instantaneous WSS.
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Kobayashi, Hiromichi, Hiroki Shionoya i Yoshihiro Okuno. "Turbulent duct flows in a liquid metal magnetohydrodynamic power generator". Journal of Fluid Mechanics 713 (17.10.2012): 243–70. http://dx.doi.org/10.1017/jfm.2012.456.
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AbstractWe numerically assess the influence of non-uniform magnetic flux density and connected load resistance on turbulent duct flows in a liquid metal magnetohydrodynamic (MHD) electrical power generator. When increasing the magnetic flux density (or Hartmann number), an M-shaped velocity profile develops in the plane perpendicular to the magnetic field; the maximum velocity in the sidewall layer of the M-shaped profile increases to maintain the flow rate. Under the conditions of a relaminarized flow, the turbulence structures align along the magnetic field and flow repeatedly like a von Kármán vortex sheet. At higher Hartmann numbers, the wall-shear stress in the sidewall layer increases and the sidewall jets transit to turbulence. The sidewall jets in the MHD turbulent duct flows have profiles similar to the non-MHD wall jets, i.e. a mean velocity profile with outer scaling, Reynolds shear stress with the opposite sign in a sidewall jet, and two maxima for the turbulent intensities in a sidewall jet. The Lorentz force suppresses the vortices of the secondary mean flow near the Hartmann layer for low Hartmann numbers, whereas the secondary vortices remain near the Hartmann layer for high Hartmann numbers. An optimal load resistance (or load factor) to obtain a maximum electrical efficiency exists, because the strong Lorentz force for a low load factor and unextracted eddy currents for a high load factor reduce efficiency. When the value of the load factor is changed, the profiles of mean velocity and r.m.s. for the optimal load factor produce almost the same profiles as the high load factor near the open-circuit condition.
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Liou, T. M., i Y. Y. Wu. "Turbulent Flows in a Model SDR Combustor". Journal of Fluids Engineering 115, nr 3 (1.09.1993): 468–73. http://dx.doi.org/10.1115/1.2910162.
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An experimental study is reported on the isothermal flow fields in a model solid-propellant ducted rocket combustor with two opposing side inlets. The measurements were made by using a four-beam two-color laser-Doppler velocimeter (LDV). Three values of momentum ratio (Ma/Ms) of the axial- to side-inlet jet—0.025, 0.11, and 1.28—were selected to investigate their effects on the flow characteristics. The Reynolds number, based on the air density, combustor height, and bulk velocity, was 4.56 × 104. The flow field was characterized in terms of the mean-velocity vectors and contours, joint probability functions, mean reattachment lengths, spreading rate of the axial-jet width, and Reynolds stress and turbulence kinetic energy contours. The LDV measured mean reattachment lengths were found to well agree with the corresponding flow-visualization photograph. In addition, the three Ma/Ms values provided three characteristic flows which are useful in testing the computational models. Further, correlations between the present cold-flow and previous reading-flow studies were documented in detail. It was found that from the fluid dynamic point of view Ma/Ms = 0.11 was preferable to the other two values of Ma/Ms.
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Johnson, Blair A., i Edwin A. Cowen. "Turbulent boundary layers absent mean shear". Journal of Fluid Mechanics 835 (27.11.2017): 217–51. http://dx.doi.org/10.1017/jfm.2017.742.
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We perform an experimental study to investigate the turbulent boundary layer above a stationary solid glass bed in the absence of mean shear. High Reynolds number $(Re_{\unicode[STIX]{x1D706}}\sim 300)$ horizontally homogeneous isotropic turbulence is generated via randomly actuated synthetic jet arrays (RASJA – Variano & Cowen J. Fluid Mech. vol. 604, 2008, pp. 1–32). Each of the arrays is controlled by a spatio-temporally varying algorithm, which in turn minimizes the formation of secondary mean flows. One array consists of an $8\times 8$ grid of jets, while the other is a $16\times 16$ array. Particle image velocimetry measurements are used to study the isotropic turbulent region and the boundary layer formed beneath as the turbulence encounters a stationary wall. The flow is characterized with statistical metrics including the mean flow and turbulent velocities, turbulent kinetic energy, integral scales and the turbulent kinetic energy transport equation, which includes the energy dissipation rate, production and turbulent transport. The empirical constant in the Tennekes (J. Fluid Mech. vol. 67, 1975, pp. 561–567) model of Eulerian frequency spectra is calculated based on the dissipation results and temporal frequency spectra from acoustic Doppler velocimetry measurements. We compare our results to prior literature that addresses mean shear free turbulent boundary layer characterizations via grid-stirred tank experiments, moving-bed experiments, rapid-distortion theory and direct numerical simulations in a forced turbulent box. By varying the operational parameters of the randomly actuated synthetic jet array, we also find that we are able to control the turbulence levels, including integral length scales and dissipation rates, by changing the mean on-times in the jet algorithm.
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Tam, Christopher K. W. "Physics and Prediction of Supersonic Jet Noise". Applied Mechanics Reviews 47, nr 6S (1.06.1994): S184—S187. http://dx.doi.org/10.1115/1.3124402.
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Both the large turbulence structures and the fine scale turbulence of the flows of supersonic jets are sources of turbulent mixing noise. At moderately high supersonic Mach numbers especially for hot jets, the dominant part of the noise is generated directly by the large turbulence structures. The large turbulence structures propagate downstream at supersonic velocities relative to the ambient sound speed. They generate strong Mach wave radiation analogous to a supersonically travelling wavy wall. A stochastic instability wave model theory of the large turbulence structures and noise of supersonic jets has recently been developed. The theory can predict both the spectrum and directivity of the dominant part of supersonic jet noise up to a multiplicative empirical constant. Calculated results agree well with measurements.
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Lipatnikov, A. N. "Burning Rate in Impinging Jet Flames". Journal of Combustion 2011 (2011): 1–11. http://dx.doi.org/10.1155/2011/737914.
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A method for evaluating burning velocity in premixed turbulent flames stabilized in divergent mean flows is quantitatively validated using numerical approximations of measured axial profiles of the mean combustion progress variable, mean and conditioned axial velocities, and axial turbulent scalar flux, obtained by four research groups from seven different flames each stabilized in an impinging jet. The method is further substantiated by analyzing the combustion progress variable balance equation that is yielded by the extended Zimont model of premixed turbulent combustion. The consistency of the model with the aforementioned experimental data is also demonstrated.
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Stepanov, Rodion, Peter Frick, Vladimir Dulin i Dmitriy Markovich. "Analysis of mean and fluctuating helicity measured by TomoPIV in swirling jet". EPJ Web of Conferences 180 (2018): 02097. http://dx.doi.org/10.1051/epjconf/201818002097.
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Important role of helicity was theoretically predicted for the generation of large-scale magnetic fields and atmospheric vortices. Helicity can lead to a reduction of turbulent dissipation in the atmosphere or in a specific constrained flow, e.g. in pipe. We use the TomoPIV data (42 cube of grid points, resolution 0.84 mm) to measure 3D velocity field of turbulent swirling flows. We study spatial distribution of the mean and fluctuating components of energy and helicity. We find that helical turbulence excitation and decay along stream of the jet strongly depend on the inflow swirl. We observe spatial separation of turbulent flow with different sign of helicity while integrated values are conserves. It is shown that large scale swirling flow induces helicity at the small scales. Our results bring valuable materials for benchmark the modern numerical simulations with turbulent closure technique.
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Cimarelli, A., A. Fregni, J. P. Mollicone, M. van Reeuwijk i E. De Angelis. "Structure of turbulence in temporal planar jets". Physics of Fluids 34, nr 4 (kwiecień 2022): 045109. http://dx.doi.org/10.1063/5.0085091.
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A detailed analysis of the structure of turbulence in a temporal planar turbulent jet is reported. Instantaneous snapshots of the flow and three-dimensional spatial correlation functions are considered. It is found that the flow is characterized by large-scale spanwise vortices whose motion is felt in the entire flow field. Superimposed to this large-scale motion, a hierarchy of turbulent structures is present. The most coherent ones take the form of quasi-streamwise vortices and high and low streamwise velocity streaks. The topology of these interacting structures is analyzed by quantitatively addressing their shape and size in the different flow regions. Such information is recognized to be relevant for a structural description of the otherwise disorganized motion in turbulent free-shear flows and can be used for the assessment of models based on coherent structure assumptions. Finally, the resulting scenario provides a phenomenological description of the elementary processes at the basis of turbulence in free-shear flows.
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Garrick, Sean C. "Growth Mechanisms of Nanostructured Titania in Turbulent Reacting Flows". Journal of Nanotechnology 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/642014.
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Titanium dioxide (titania) is used in chemical sensors, pigments, and paints and holds promise as an antimicrobial agent. This is due to its photoinduced activity and, in nanostructured form, its high specific surface area. Particle size and surface area result from the interplay of fluid, chemical, and thermal dynamics as well as nucleation, condensation and coagulation. After nucleation, condensation, and coagulation are the dominant phenomena affecting the particle size distribution. Manufacture of nanostructured titania via gas-phase synthesis often occurs under turbulent flow conditions. This study examines the competition between coagulation and condensation in the growth of nanostructured titania. Direct numerical simulation is utilized in simulating the hydrolysis of titanium tetrachloride to produce titania in a turbulent, planar jet. The fluid, chemical, and particle fields are resolved as a function of space and time. As a result, knowledge of titania is available as a function of space, time, and phase (vapor or particle), facilitating the analysis of the particle dynamics by mechanism. Results show that in the proximal region of the jet nucleation and condensation are the dominant mechanisms. However once the jet potential core collapses and turbulent mixing begins, coagulation is the dominant mechanism. The data also shows that the coagulation growth-rate is as much as twice the condensation growth-rate.
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Akiyama, Shinsaku, Yusuke Waki, Shinya Okino i Hideshi Hanazaki. "Unstable jets generated by a sphere descending in a very strongly stratified fluid". Journal of Fluid Mechanics 867 (20.03.2019): 26–44. http://dx.doi.org/10.1017/jfm.2019.123.
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The flow around a sphere descending at constant speed in a very strongly stratified fluid ($Fr\lesssim 0.2$) is investigated by the shadowgraph method and particle image velocimetry. Unlike the flow under moderately strong stratification ($Fr\gtrsim 0.2$), which supports a thin cylindrical jet, the flow generates an unstable jet, which often develops into turbulence. The transition from a stable jet to an unstable jet occurs for a sufficiently low Froude number $Fr$ that satisfies $Fr/Re<1.57\times 10^{-3}$. The Froude number $Fr$ here is in the range of $0.0157<Fr<0.157$ or lower, while the Reynolds number $Re$ is in the range of $10\lesssim Re\lesssim 100$ for which the homogeneous fluid shows steady and axisymmetric flows. Since the radius of the jet can be estimated by the primitive length scale of the stratified fluid, i.e. $l_{\unicode[STIX]{x1D708}}^{\ast }=\sqrt{\unicode[STIX]{x1D708}^{\ast }/N^{\ast }}$ or $l_{\unicode[STIX]{x1D708}}^{\ast }/2a^{\ast }=\sqrt{Fr/2Re}$, this predicts that the jet becomes unstable when it becomes thinner than approximately $l_{\unicode[STIX]{x1D708}}^{\ast }/2a^{\ast }=0.028$, where $N^{\ast }$ is the Brunt–Väisälä frequency, $a^{\ast }$ the radius of the sphere and $\unicode[STIX]{x1D708}^{\ast }$ the kinematic viscosity of the fluid. The instability begins when the boundary-layer thickness becomes thin, and the disturbances generated by shear instabilities would be transferred into the jet. When the flow is marginally unstable, two unstable states, i.e. a meandering jet and a turbulent jet, can appear. The meandering jet is thin with a high vertical velocity, while the turbulent jet is broad with a much smaller velocity. The meandering jet may persist for a long time, or develop into a turbulent jet in a short time. When the instability is sufficiently strong, only the turbulent jet could be observed.
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Kerstein, Alan R. "Linear-eddy modelling of turbulent transport. Part 3. Mixing and differential molecular diffusion in round jets". Journal of Fluid Mechanics 216 (lipiec 1990): 411–35. http://dx.doi.org/10.1017/s0022112090000489.
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The linear-eddy model of turbulent mixing represents a spatially developing flow by simulating the time development along a comoving transverse line. Along this line, scalar quantities evolve by molecular diffusion and by randomly occurring spatial rearrangements, representing turbulent convection. The modelling approach, previously applied to homogeneous turbulence and to planar shear layers, is generalized to axisymmetric flows. This formulation captures many features of jet mixing, including differential molecular diffusion effects. A novel experiment involving two unmixed species in the nozzle fluid is proposed and analysed.