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An approximate calculation method is developed for the transition sections of plane and axisymmetric turbulent jets in a co-moving stream. It is shown why earlier methods, based on differentiation between the initial and final sections, are not applicable in the transition (mixing) region. The velocity profiles obtained by this method in the transition region turn out to be the same for plane and axisymmetric jets, and can be used to calculate the variation of the jet parameters along the stream axis by using the set of integral equations connecting the angular momentum and the energy. Limiting parameters are defined under which the results coincide with the velocity profile of the main section of the turbulent jet. It is concluded that in first approximation the external boundary of the transition layer is straight and is a continuation of the outer boundary of the outer section. The method is then demonstrated to be suitable for a determination of continuous velocity-profile deformation in the transition region. (Author).
The Science & Applications of Heat and Mass Transfer: Reports, Reviews, & Computer Programs, Volume 6: Turbulent Buoyant Jets and Plumes focuses on the formation, properties, characteristics, and reactions of turbulent jets and plumes. The selection first offers information on the mechanics of turbulent buoyant jets and plumes and turbulent buoyant jets in shallow fluid layers. Discussions focus on submerged buoyant jets into shallow fluid, horizontal surface or interface jets into shallow layers, fundamental considerations, and turbulent buoyant jets (forced plumes). The manuscript then examines a turbulence model for buoyant flows and its application to vertical buoyant jets, including mathematical model, calculation of vertical buoyant jets, and explanation of velocity and temperature spreading in pure jets and pure plumes. The publication is a dependable reference for scientists and readers interested in turbulent buoyant jets and plumes.
Some experimental and theoretical studies have been made of axisymmetric free jets exhausting from sonic and supersonic nozzles into still air and into supersonic streams with a view toward problems associated with propulsive jets and the investigation of these problems. For jets exhausting into still air, consideration is given to the effects of jet Mach number, nozzle divergence angle, and jet static-pressure ratio upon jet structure, jet wavelength, and the shape and curvature of the jet boundary. Studies of the effects of the ratio of specific heats of the jets are included as are observations pertaining to jet noise and jet simulation. For jets exhausting into supersonic streams, an attempt has been made to present primarily theoretical curves of the type that may be useful in evaluating certain jet interference effects and in formulating experimental studies. The primary variables considered are jet Mach number, free-stream Mach number, jet static-pressure ratio, ratio of specific heats of the jet, nozzle exit angle, and boattail angle. The simulation problem and the case of a hypothetical hypersonic vehicle are examined. A few experimental observations are included.
Three-dimensional, incompressible turbulent jets with rectangular and elliptical cross-sections are simulated with a finite-difference numerical method. The full Navier- Stokes equations are solved at low Reynolds numbers, whereas at high Reynolds numbers filtered forms of the equations are solved along with a sub-grid scale model to approximate the effects of the unresolved scales. A 2-N storage, third-order Runge-Kutta scheme is used for temporary discretization and a fourth-order compact scheme is used for spatial discretization. Although such methods are widely used in the simulation of compressible flows, the lack of an evolution equation for pressure or density presents particular difficulty in incompressible flows. The pressure-velocity coupling must be established indirectly. It is achieved, in this study, through a Poisson equation which is solved by a compact scheme of the same order of accuracy. The numerical formulation is validated and the dispersion and dissipation errors are documented by the solution of a wide range of benchmark problems. Three-dimensional computations are performed for different inlet conditions which model the naturally developing and forced jets. The experimentally observed phenomenon of axis-switching is captured in the numerical simulation, and it is confirmed through flow visualization that this is based on self-induction of the vorticity field. Statistical quantities such as mean velocity, mean pressure, two-point velocity spatial correlations and Reynolds stresses are presented. Detailed budgets of the mean momentum and Reynolds stresses are presented. Detailed budgets of the mean momentum and Reynolds stress equations are presented to aid in the turbulence modeling of complex jets. Simulations of circular jets are used to quantify the effect of the non-uniform curvature of the non-circular jets. Wilson, Robert V. and Demuren, Ayodeji O. Langley Research Center NASA-CR-203976, NAS 1.26:203976, ICAM-97-101 NCC1-232...
This Philosophiae Doctor thesis presents the motivation, objectives and reasoning behind the undertaken project. This research, study the capability of compressible Implicit Large Eddy Simulation (ILES) in predicting free shear layer flows, under different free stream regimes (Static and Co-flow jets). Unsteady flows or jet flows are non-uniform in structure, temperature, pressure and velocity. Turbulent mixing is of particular importance for the developing of this class of flows. As a shear layer is formed immediately downstream of the jet exhaust, an early linear instability involving exponential growth of small perturbations is introduced at the jet discharge. Beyond this development stage, in the non-linear Kelvin-Helmholtz instability region large scale vortex rings roll up, and their dynamics of formation and merging become the defining feature of the transitional shear flow into fully developed regime. This class of flows is particularly relevant to numerical predictions, as the extreme nature of the flow in question is considered as a benchmark; however, experimental data should be selected carefully as some results are controversial. To qualify the behaviour of unsteady flows, some important criteria have been selected for the analysis of the flow quantities at different regions of the flow field (average velocities, Reynolds stresses and dissipation rates). A good estimation of high-order statistics (Standard Deviation, Skewness and Kurtosis) correspond to mathematical steadiness and convergence of results. From the physical point of view, similarity analysis between jet's wake sections reveals physical steadiness in results. Spectral analysis of the different regions of the flow field could be used as a sign that the energy cascade is correctly predicted or efficiently enough since this is where the smallest scales are usually present and which in effect require to be modelled by the different numerical schemes. The flow solver has been reviewed and improved. The former, a revised version of the reconstruction numerical schemes (WENO 5th and WENO 9th orders) has been performed and tested, the correspondent results have been compared against analytical data; the latter, correction of the method to compute the Jacobian of the transformation (singularity correction), by changing from the standard algebraic to geometric method, and augmented with transparent boundary condition, giving mathematical and physical meaning to the obtained results. The flow solver improvements and review have been verified and validated through simulations of a compressible Convergent-Divergent Nozzle (CDN), and the standard and a modified version of the Shock tube test cases, where the results are gained with minimal modelling effort. The study of numerical errors associated with the simulations of turbulent flows, for unsteady explicit time step predictions, have been performed and a new formula proposed. Ten different computational methods have been employed in the framework of ILES and computations have been performed for a jet flow configuration for which experimental data and DNS are available. It can be seen that a numerical error bar can be defined that takes into account the errors arising from the different numerical building blocks of the simulation method. The effects of different grids, Riemann solvers and numerical reconstruction schemes have been considered, however, the approach can be extended to take into account the effects of the initial and boundary conditions as well as subgrid scale modelling, if applicable. From the physical analysis several observations were established, revealing that differences in terms of jet's core size are not an important parameter in terms of quantification and qualification of predictions, in other words, data should be reduced to the jet's inertial reference system. Moreover, the comparative study has been performed to identify the differences between Riemann solvers (CBS and HLLC), Low Mach number Limiting/ Corrections (LMC), numerical reconstruction schemes (MUSCL and WENO) and spatial order of accuracy (2nd-order LMC, 5th-order LMC and 9th-order schemes) in combination with the most efficient cost/resolution discretization level (Medium mesh). The comparisons between results reveals for the Static and Co-Flow jets that the CBS MUSCL 5th-order LMC and the HLLC MUSCL 5th-order LMC as the most accurate schemes in predicting this class of flows, accordingly. Furthermore, the selected numerical methods show to be in accordance with the empirical (Static) and experimental (Co-flow) results in terms of resonance frequency and/or Strouhal number; also, the expected behaviour in terms of spectral energy decay rate throughout the jet's central line is observed. To conclude the study of the Static jet case, a possible explanation for the jet's buoyancy effect is presented.