scholarly journals Similarity Solutions of Jet Development Mixing Layers Using Algebraic and 1-Equation Turbulence Models

10.14311/804 ◽  
2006 ◽  
Vol 46 (1) ◽  
Author(s):  
V. Tesař
Keyword(s):  
Similarity Transformation ◽  
Mixing Layer ◽  
Turbulence Models ◽  
Algebraic Model ◽  
Similarity Solutions ◽  
Equation Model ◽  
Mixing Layers ◽  
Piv Measurements ◽  
Round Jets ◽  
Present Solution

Mixing layers are formed between two parallel fluid streams having different velocities. One of the velocities may be zero, as is the usual case of the mixing layer that surrounds, immediately downstream from the nozzle, the core of a developing jet issuing into stagnant surroundings. Earlier – but so far not properly published – experimental evidence shows a remarkably weak effect of transversal curvature, making the present solution applicable with acceptable precision to description of developing round jets. This paper presents solutions of a planar mixing layer by a similarity transformation, which reduces the problem to solving ordinary differential equations. Two solutions are investigated: one based on an algebraic model and the other using the 1-equation model of turbulence. They are compared with recent results of PIV measurements of a developing jet. 

scholarly journals Two-equation Turbulence Model Similarity Solution of the Axisymmetric Fluid Jet

10.14311/210 ◽  
2001 ◽  
Vol 41 (2) ◽  
Author(s):  
V. Tesař
Keyword(s):  
Turbulence Model ◽  
Similarity Transformation ◽  
Turbulence Models ◽  
Similarity Solutions ◽  
Mixing Length ◽  
Governing Equations ◽  
Satisfactory Solution ◽  
Submerged Jet ◽  
Valid Solution ◽  
Model Similarity

This paper presents a general, universally valid solution of axisymmetric turbulent submerged jet flow, for which no fully satisfactory solution has been known. What has been available so far are either computational solutions for individual particular cases, lacking universality, or similarity solutions with inadequate turbulence models, some of them based upon assumptions of a speculative character (e.g. constant mixing length across the jet profile). The present approach uses a similarity transformation of the governing equations, which incorporate an advanced turbulence model. The results are shown to be in excellent agreement with available experimental data. The new solution provides a suitable basis for analysis of enigmatic aspects of axisymmetric jets, such as their "spreading anomaly".

scholarly journals Prediction of Turbine Blade Passage Heat Transfer Using a Zero and a Two-Equation Turbulence Model

1994 ◽  
Author(s):  
Ali A. Ameri ◽  
Andrea Arnone
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Turbulence Model ◽  
Turbulence Models ◽  
Algebraic Model ◽  
Equation Model ◽  
Accurate Solution ◽  
Bypass Transition ◽  
Transfer Rates ◽  
Blade Passage

Predictions of the heat transfer rates on the hot surfaces of a turbine cascade blade passage as influenced by the turbulence models was examined. A zero equation turbulence model supplemented by a bypass transition model and a two equation low Reynolds number model were chosen for this study. The experimental data of Graziani et. al. were used for comparison. The comparisons suggest that at least for the experimental data considered in this work the use of a two-equation model does not provide an overall more accurate solution than the zero equation model. This conclusion is strengthened if one takes into account the relative economy of computations with the algebraic model.

Incorporating Turbulence Models into the Lattice-Boltzmann Method

1998 ◽  
Vol 09 (08) ◽  
pp. 1159-1175 ◽  
Author(s):  
Christopher M. Teixeira
Keyword(s):  
Lattice Boltzmann Method ◽  
Turbulent Flows ◽  
Lattice Boltzmann ◽  
Turbulence Models ◽  
Algebraic Model ◽  
Expansion Ratio ◽  
Equation Model ◽  
Recirculation Length ◽  
Boltzmann Method ◽  
Good Agreement

The Lattice-Boltzmann method (LBM) is extended to allow incorporation of traditional turbulence models. Implementation of a two-layer mixing-length algebraic model and two versions of the k-ε two-equation model, Standard and RNG, in conjunction with a wall model, are presented. Validation studies are done for turbulent flows in a straight pipe at three Re numbers and over a backwards facing step of expansion ratio 1.5 and Re H=44 000. All models produce good agreement with experiment for the straight pipes but the RNG k-ε model is best able to capture both the recirculation length, within 2% of experiment, and the detailed structure of the mean fluid flow for the backwards facing step.

scholarly journals Two-point similarity in the round jet

2007 ◽  
Vol 577 ◽  
pp. 309-330 ◽  
Author(s):  
D. EWING ◽  
B. FROHNAPFEL ◽  
W. K. GEORGE ◽  
J. M. PEDERSEN ◽  
J. WESTERWEEL
Keyword(s):  
Reynolds Number ◽  
Separation Distance ◽  
Similarity Solutions ◽  
Similarity Analysis ◽  
Velocity Correlation ◽  
Piv Measurements ◽  
Round Jet ◽  
Axisymmetric Jet ◽  
Round Jets ◽  
Point Velocity

The governing equations for the two-point velocity correlations in the far field of the axisymmetric jet are examined and it is shown that these equations can have equilibrium similarity solutions for jets with finite Reynolds number that retain a dependence on the growth rate of the jet. The two-point velocity correlation can be written as the product of a scale that depends on the downstream position of the two points and a function that only depends on the similarity variables. Physically, this result implies that the turbulent processes producing and dissipating energy at the different scales of motion, as well as transferring energy between the different scales of motion, are in equilibrium as the flow evolves downstream. A particularly interesting prediction from the analysis is that the two-point similarity solutions depend only on the separation distance between the points in the streamwise similarity coordinate (i.e. υ = ξ′ − ξ), that is, the logarithm of the streamwise coordinate itself (i.e. ξ = lnx1, wherex1is measured from a virtual origin). Thus, the measures of the turbulence are homogeneous in the streamwise similarity coordinate.The predictions from the similarity analysis for the streamwise two-point velocity correlation were compared with combined hot-wire and LDA measurements on the centreline of a round jet at a Reynolds number of 33000, and with two-point velocity correlations computed from PIV measurements in a round jet at a Reynolds number of 2000 performed by Fukushimaet al. In both cases, the measured two-point velocity correlations in the streamwise direction collapsed when they were scaled in the manner predicted by the similarity analysis. The results provide further evidence that the equilibrium similarity hypothesis does describe the development of the flow in fully developed turbulent round jets and that the two-point correlations are statistically homogeneous in the streamwise similarity coordinate.

The Investigation of Turbulence Models Based on Numerical Simulation

2014 ◽  
Vol 590 ◽  
pp. 91-95
Author(s):  
Rui Li ◽  
Chang Hong Tang
Keyword(s):  
Transport Model ◽  
Turbulence Models ◽  
Algebraic Model ◽  
Equation Model ◽  
Turbulent Model ◽  
Stress Equation ◽  
Advantages And Disadvantages ◽  
Development Direction ◽  
Shear Stress Transport Model ◽  
Improvement Measures

The algebraic model, one-equation model, two equation models are Analyzed in the paper. Focusing on the k-ε turbulent model contains (the standardk-εturbulence model, RNGk-εmodel, Realizablek-ε model), and the origin of the shear stress transport model, Reynolds stress equation model on mathematical and physical model is discussed.the advantages and disadvantages of each model is Pointed out ,And the future development direction of turbulent model and improvement measures are proposed on the paper.

scholarly journals Growth Rate Exponents of Richtmyer-Meshkov Mixing Layers

2005 ◽  
Vol 73 (3) ◽  
pp. 461-468 ◽  
Author(s):  
Timothy T. Clark ◽  
Ye Zhou
Keyword(s):  
Flow Field ◽  
Power Law ◽  
Mixing Layer ◽  
Power Laws ◽  
Mixing Layers ◽  
Spatial Gradients ◽  
Power Law Exponent ◽  
Virtual Time ◽  
Time Origin ◽  
Density Ratios

The Richtmyer-Meshkov mixing layer is initiated by the passing of a shock over an interface between fluid of differing densities. The energy deposited during the shock passage undergoes a relaxation process during which the fluctuational energy in the flow field decays and the spatial gradients of the flow field decrease in time. This late stage of Richtmyer-Meshkov mixing layers is studied from the viewpoint of self-similarity. Analogies with weakly anisotropic turbulence suggest that both the bubble-side and spike-side widths of the mixing layer should evolve as power-laws in time, with the same power-law exponent and virtual time origin for both sides. The analogy also bounds the power-law exponent between 2∕7 and 1∕2. It is then shown that the assumption of identical power-law exponents for bubbles and spikes yields fits that are in good agreement with experiment at modest density ratios.

The mixing layer over a deep cavity at high-subsonic speed

2003 ◽  
Vol 475 ◽  
pp. 101-145 ◽  
Author(s):  
NICOLAS FORESTIER ◽  
LAURENT JACQUIN ◽  
PHILIPPE GEFFROY
Keyword(s):  
High Speed ◽  
Mixing Layer ◽  
Interaction Mechanism ◽  
Boundary Layer Separation ◽  
Mixing Layers ◽  
Deep Cavity ◽  
Collective Interaction ◽  
Flow Over A Cavity ◽  
Conditional Statistics ◽  
Forced Mixing

The flow over a cavity at a Mach number 0.8 is considered. The cavity is deep with an aspect ratio (length over depth) L/D = 0.42. This deep cavity flow exhibits several features that makes it different from shallower cavities. It is subjected to very regular self-sustained oscillations with a highly two-dimensional and periodic organization of the mixing layer over the cavity. This is revealed by means of a high-speed schlieren technique. Analysis of pressure signals shows that the first tone mode is the strongest, the others being close to harmonics. This departs from shallower cavity flows where the tones are usually predicted well by the standard Rossiter’s model. A two-component laser-Doppler velocimetry system is also used to characterize the phase-averaged properties of the flow. It is shown that the formation of coherent vortices in the region close to the boundary layer separation has some resemblance to the ‘collective interaction mechanism’ introduced by Ho & Huang (1982) to describe mixing layers subjected to strong sub-harmonic forcing. Otherwise, the conditional statistics show close similarities with those found in classical forced mixing layers except for the production of random perturbations, which reaches a maximum in the structure centres, not in the hyperbolic regions with which turbulence production is usually associated. An attempt is made to relate this difference to the elliptic instability that may be observed here thanks to the particularly well-organized nature of the flow.

Modeling of the Vortex-Structure in a Particle-Laden Mixing-Layer

2005 ◽  
Author(s):  
Jens A. Melheim ◽  
Stefan Horender ◽  
Martin Sommerfeld
Keyword(s):  
Vortex Structure ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Mixing Layer ◽  
Equation Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Calculated Concentration ◽  
Langevin Model ◽  
Particle Velocities

Numerical calculations of a particle-laden turbulent horizontal mixing-layer based on the Eulerian-Lagrangian approach are presented. Emphasis is given to the determination of the stochastic fluctuating fluid velocity seen by the particles in anisotropic turbulence. The stochastic process for the fluctuating velocity is a “Particle Langevin equation Model”, based on the Simplified Langevin Model. The Reynolds averaged Navier-Stokes equations are closed by the standard k-epsilon turbulence model. The calculated concentration profile and the mean, the root-mean-square (rms) and the cross-correlation terms of the particle velocities are compared with particle image velocimetry (PIV) measurements. The numerical results agree reasonably well with the PIV data for all of the mentioned quantities. The importance of the modeled vortex structure “seen” by the particles is discussed.

scholarly journals An Investigation of Turbulence Modelling in Transonic Fans Including a Novel Implementation of an Implicit κ–ϵ Turbulence Model

1992 ◽  
Author(s):  
Mark G. Turner ◽  
Ian K. Jennions
Keyword(s):  
Turbulence Models ◽  
Algebraic Model ◽  
Turbulence Modelling ◽  
Experimental Results ◽  
Navier Stokes ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Wall Functions ◽  
Solution Methods ◽  
Explicit Solver

An explicit Navier-Stokes solver has been written with the option of using one of two types of turbulence models. One is the Baldwin-Lomax algebraic model and the other is an implicit k-ϵ model which has been coupled with the explicit Navier-Stokes solver in a novel way. This type of coupling, which uses two different solution methods, is unique and combines the overall robustness of the implicit k-ϵ solver with the simplicity of the explicit solver. The resulting code has been applied to the solution of the flow in a transonic fan rotor which has been experimentally investigated by Wennerstrom. Five separate solutions, each identical except for the turbulence modelling details, have been obtained and compared with the experimental results. The five different turbulence models run were: the standard Baldwin-Lomax model both with and without wall functions, the Baldwin-Lomax model with modified constants and wall functions, a standard k-ϵ model and an extended k-ϵ model which accounts for multiple time scales by adding an extra term to the dissipation equation. In general, as the model includes more of the physics, the computed shock position becomes closer to the experimental results.

An experimental investigation of the effects of compressibility on a turbulent reacting mixing layer

1998 ◽  
Vol 356 ◽  
pp. 25-64 ◽  
Author(s):  
M. F. MILLER ◽  
C. T. BOWMAN ◽  
M. G. MUNGAL
Keyword(s):  
High Speed ◽  
Large Scale ◽  
Structural Changes ◽  
Density Ratio ◽  
Mixing Layer ◽  
Mixing Layers ◽  
Unexpected Result ◽  
Entrainment Ratio ◽  
Plan View ◽  
Compressible Mixing Layer

Experiments were conducted to investigate the effect of compressibility on turbulent reacting mixing layers with moderate heat release. Side- and plan-view visualizations of the reacting mixing layers, which were formed between a high-speed high-temperature vitiated-air stream and a low-speed ambient-temperature hydrogen stream, were obtained using a combined OH/acetone planar laser-induced fluorescence imaging technique. The instantaneous images of OH provide two-dimensional maps of the regions of combustion, and similar images of acetone, which was seeded into the fuel stream, provide maps of the regions of unburned fuel. Two low-compressibility (Mc=0.32, 0.35) reacting mixing layers with differing density ratios and one high-compressibility (Mc=0.70) reacting mixing layer were studied. Higher average acetone signals were measured in the compressible mixing layer than in its low-compressibility counterpart (i.e. same density ratio), indicating a lower entrainment ratio. Additionally, the compressible mixing layer had slightly wider regions of OH and 50% higher OH signals, which was an unexpected result since lowering the entrainment ratio had the opposite effect at low compressibilities. The large-scale structural changes induced by compressibility are believed to be primarily responsible for the difference in the behaviour of the high- and low-compressibility reacting mixing layers. It is proposed that the coexistence of broad regions of OH and high acetone signals is a manifestation of a more biased distribution of mixture compositions in the compressible mixing layer. Other mechanisms through which compressibility can affect the combustion are discussed.

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