Assessment of the SSG Pressure-Strain Model in Free Turbulent Jets With and Without Swirl

1996 ◽  
Vol 118 (4) ◽  
pp. 800-809 ◽  
Author(s):  
B. A. Younis ◽  
T. B. Gatski ◽  
C. G. Speziale
Keyword(s):  
Linear Models ◽  
Turbulent Jets ◽  
Spreading Rate ◽  
Energy Dissipation Rate ◽  
Quadratic Model ◽  
Turbulence Structure ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Plane Jet ◽  
Strain Model

Data from free turbulent jets both with and without swirl are used to assess the performance of the pressure-strain model of Speziale, Sarkar and Gatski, which is quadratic in the Reynolds stresses. Comparative predictions are also obtained with the two versions of the Launder, Reece and Rodi model, which are linear in the same terms. All models are used as part of a complete second-order closure based on the solution of differential transport equations for each nonzero component of uiuj together with an equation for the scalar energy dissipation rate. For nonswirling jets, the quadratic model underestimates the measured spreading rate of the plane jet but yields a better prediction for the axisymmetric case without resolving the plane jet/round jet anomaly. For the swirling axisymmetric jet, the same model accurately reproduces the effects of swirl on both the mean flow and the turbulence structure in sharp contrast with the linear models which yield results that are in serious error. The reasons for these differences are discussed.

A Counter-Rotating Pair of Turbulent Jets

1973 ◽  
Vol 95 (2) ◽  
pp. 207-213 ◽  
Author(s):  
B. D. Pratte ◽  
J. F. Keffer
Keyword(s):  
Turbulent Jets ◽  
Spreading Rate ◽  
Mean Flow ◽  
Linear Superposition ◽  
Mean Velocity ◽  
Cross Sectional ◽  
Free Jet ◽  
Intensity Measurements ◽  
Limited Application ◽  
Sectional Shape

A study has been made of a pair of swirling jets having opposite rotation. Mean flow and turbulent intensity measurements were obtained and characteristics of the spreading rate determined. The swirling component of mean velocity decayed rapidly in the streamwise direction and by about 35 dia, the flow had most of the characteristics of the single, free jet without swirl. A linear superposition was found to be of limited application near the jet source but gave reasonable results in the developed flow downstream. It was observed that the major and minor axes of the flow, defining the asymmetrical cross-sectional shape, underwent a reversal of position as the flow progressed downstream.

Linear and Non-Linear Turbulence Model Predictions of Vortical Flows in Lobed Mixers

2004 ◽  
Vol 108 (1080) ◽  
pp. 65-73 ◽  
Author(s):  
H. Salman ◽  
D. Jiang ◽  
G.J. Page ◽  
J.J. McGuirk
Keyword(s):  
Linear Model ◽  
Turbulence Model ◽  
Time Scale ◽  
Quadratic Model ◽  
Turbulence Structure ◽  
Mean Flow ◽  
Linear Quadratic ◽  
Linear Quadratic Model ◽  
Non Linear ◽  
Standard Linear

AbstractLobed mixers are widely used in gas turbine engines to increase mixing between hot and cold streams and consequently reduce jet noise. CFD predictions are presented for a simplified experimental configuration of a planar, three lobe geometry. Results are shown for a standard lineark–ε turbulence model, the same model with a time scale limitation invoked and a non-linear quadratic model also employing a time scale limitation. Comparisons are presented between the three models for axial velocity, velocity vectors, shear stress and turbulence kinetic energy at a selected plane in the mixing region. The non-linear model was found to have little influence on the mean flow but some effect on the turbulence structure was observed. Comparison with measurements showed that all major features were reproduced but detail differences were evident. The use of a time scale limit reduced peak values of predicted turbulence quantities by 20-30%. As compared to the standard linear model, the time scale limited non-linear model moved the position of the zero streamwise circulation location by about one lobe wavelength upstream so giving better agreement with experiment.

scholarly journals Experimental investigation of turbulent flows through a boulder array placed on a permeable bed

2020 ◽  
Vol 20 (4) ◽  
pp. 1281-1293
Author(s):  
Hui Cao ◽  
Chen Ye ◽  
Xu-Feng Yan ◽  
Xing-Nian Liu ◽  
Xie-Kang Wang
Keyword(s):  
Turbulent Flows ◽  
Turbulence Intensity ◽  
Diffusion Processes ◽  
Quadrant Analysis ◽  
Turbulence Structure ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Flume Experiments ◽  
Budget Analysis ◽  
Boulder Array

Abstract Glass beads were used to model permeable beds and boulders (simulated by plastic spherical balls) placed on the centre section of the bed. Flume experiments were conducted to investigate the hydrodynamics through a boulder array over impermeable and permeable beds (i.e. IMPB and PB). For background reference, hydrodynamics investigation was made over smooth beds (SB) with the boulder array. Through measuring the instantaneous velocity field, the major flow characteristics such as mean flow velocity, turbulence intensity, turbulent kinetic energy (TKE) and instantaneous Reynolds stresses (through quadrant analysis) were presented. The results show that the increase in bed permeability through decreasing the exposure height of boulders has little impact on the magnitude of streamwise velocity, but tends to decrease the near-bed velocity gradient, thus affecting the bed shear-stress. For turbulence, similar to the previous studies, the bed permeability is identified to enable a downward shift of the peak of turbulence intensity. The TKE budget analysis shows that bed permeability tends to inhibit the transport and diffusion processes of TKE generation. Finally, the quadrant analysis of turbulence structure clearly shows that the ejections (Q2) and sweeps (Q4) with and without the boulder array are dominated by turbulence structure of different scales.

Experimental Investigation of Turbulent Flow With Separation Over a NACA 4412 Airfoil at Angle of Attack 20 Degree

2002 ◽  
Author(s):  
Omar O. Badran ◽  
Hans H. Bruun
Keyword(s):  
Separation Bubble ◽  
Angle Of Attack ◽  
Shear Stresses ◽  
Turbulence Structure ◽  
Separation Flow ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Trailing Edge ◽  
Mean Velocity ◽  
Airfoil Surface

This paper presents the measured mean flow and Reynolds stresses results, obtained on the center-line plane of the airfoil, covering the boundary layers over the upper surface, the potential flow region and the wake downstream of the trailing edge, at αa = 20°. The flying X-hot-wire probe was used to measure mean velocity and turbulence structure over the airfoil. An improved understanding of the physical characteristics of separation on the airfoil sections and in the region of the trailing edge is of direct value for the improvement of high lift wings for aircraft. From the study of the separation flow at angle of attack αa = 20°, the following can be concluded: A stable separation bubble has developed near the trailing edge of the airfoil, covering around 0.6c of the airfoil surface. Also it is found that values of the Reynolds normal and shear stresses move away from the surface with downstream distance, showing turbulence diffusion to be more evident in this flow. In the wake region, relatively large values of Reynolds stresses occurred, which were related to the vertical oscillations in the upper wake.

scholarly journals Instability wave models for the near-field fluctuations of turbulent jets

2011 ◽  
Vol 689 ◽  
pp. 97-128 ◽  
Author(s):  
K. Gudmundsson ◽  
Tim Colonius
Keyword(s):  
Flow Field ◽  
Large Scale ◽  
Microphone Array ◽  
Near Field ◽  
Turbulent Jets ◽  
Instability Wave ◽  
Mean Flow ◽  
Velocity Fluctuations ◽  
The Mean ◽  
Scale Structures

AbstractPrevious work has shown that aspects of the evolution of large-scale structures, particularly in forced and transitional mixing layers and jets, can be described by linear and nonlinear stability theories. However, questions persist as to the choice of the basic (steady) flow field to perturb, and the extent to which disturbances in natural (unforced), initially turbulent jets may be modelled with the theory. For unforced jets, identification is made difficult by the lack of a phase reference that would permit a portion of the signal associated with the instability wave to be isolated from other, uncorrelated fluctuations. In this paper, we investigate the extent to which pressure and velocity fluctuations in subsonic, turbulent round jets can be described aslinearperturbations to the mean flow field. The disturbances are expanded about the experimentally measured jet mean flow field, and evolved using linear parabolized stability equations (PSE) that account, in an approximate way, for the weakly non-parallel jet mean flow field. We utilize data from an extensive microphone array that measures pressure fluctuations just outside the jet shear layer to show that, up to an unknown initial disturbance spectrum, the phase, wavelength, and amplitude envelope of convecting wavepackets agree well with PSE solutions at frequencies and azimuthal wavenumbers that can be accurately measured with the array. We next apply the proper orthogonal decomposition to near-field velocity fluctuations measured with particle image velocimetry, and show that the structure of the most energetic modes is also similar to eigenfunctions from the linear theory. Importantly, the amplitudes of the modes inferred from the velocity fluctuations are in reasonable agreement with those identified from the microphone array. The results therefore suggest that, to predict, with reasonable accuracy, the evolution of the largest-scale structures that comprise the most energetic portion of the turbulent spectrum of natural jets, nonlinear effects need only be indirectly accounted for by considering perturbations to the mean turbulent flow field, while neglecting any non-zero frequency disturbance interactions.

Study of the Standard k-ε Model for Tip Leakage Flow in an Axial Compressor Rotor

2016 ◽  
Vol 33 (4) ◽  
Author(s):  
Yanfei Gao ◽  
Yangwei Liu ◽  
Luyang Zhong ◽  
Jiexuan Hou ◽  
Lipeng Lu
Keyword(s):  
Flow Field ◽  
Large Scale ◽  
Turbulent Viscosity ◽  
Axial Compressor ◽  
Leakage Flow ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Tip Leakage Flow ◽  
Tip Leakage ◽  
Compressor Rotor

AbstractThe standard k-ε model (SKE) and the Reynolds stress model (RSM) are employed to predict the tip leakage flow (TLF) in a low-speed large-scale axial compressor rotor. Then, a new research method is adopted to “freeze” the turbulent kinetic energy and dissipation rate of the flow field derived from the RSM, and obtain the turbulent viscosity using the Boussinesq hypothesis. The Reynolds stresses and mean flow field computed on the basis of the frozen viscosity are compared with the results of the SKE and the RSM. The flow field in the tip region based on the frozen viscosity is more similar to the results of the RSM than those of the SKE, although certain differences can be observed. This finding indicates that the non-equilibrium turbulence transport nature plays an important role in predicting the TLF, as well as the turbulence anisotropy.

Tilting at wave beams: a new perspective on the St. Andrew’s Cross

2017 ◽  
Vol 830 ◽  
pp. 660-680 ◽  
Author(s):  
T. Kataoka ◽  
S. J. Ghaemsaidi ◽  
N. Holzenberger ◽  
T. Peacock ◽  
T. R. Akylas
Keyword(s):  
Wave Field ◽  
Finite Length ◽  
Line Source ◽  
Cutoff Frequency ◽  
Three Dimensional ◽  
Resonance Phenomenon ◽  
Buoyancy Frequency ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Viscous Effects

The generation of internal gravity waves by a vertically oscillating cylinder that is tilted to the horizontal in a stratified Boussinesq fluid of constant buoyancy frequency, $N$, is investigated. This variant of the widely studied horizontal configuration – where a cylinder aligned with a plane of constant gravitational potential induces four wave beams that emanate from the cylinder, forming a cross pattern known as the ‘St. Andrew’s Cross’ – brings out certain unique features of radiated internal waves from a line source tilted to the horizontal. Specifically, simple kinematic considerations reveal that for a cylinder inclined by a given angle $\unicode[STIX]{x1D719}$ to the horizontal, there is a cutoff frequency, $N\sin \unicode[STIX]{x1D719}$, below which there is no longer a radiated wave field. Furthermore, three-dimensional effects due to the finite length of the cylinder, which are minor in the horizontal configuration, become a significant factor and eventually dominate the wave field as the cutoff frequency is approached; these results are confirmed by supporting laboratory experiments. The kinematic analysis, moreover, suggests a resonance phenomenon near the cutoff frequency as the group-velocity component perpendicular to the cylinder direction vanishes at cutoff; as a result, energy cannot be easily radiated away from the source, and nonlinear and viscous effects are likely to come into play. This scenario is examined by adapting the model for three-dimensional wave beams developed in Kataoka & Akylas (J. Fluid Mech., vol. 769, 2015, pp. 621–634) to the near-resonant wave field due to a tilted line source of large but finite length. According to this model, the combination of three-dimensional, nonlinear and viscous effects near cutoff triggers transfer of energy, through the action of Reynolds stresses, to a circulating horizontal mean flow. Experimental evidence of such an induced mean flow near cutoff is also presented.

scholarly journals Jet Formation and Evolution in Baroclinic Turbulence with Simple Topography

2010 ◽  
Vol 40 (2) ◽  
pp. 257-278 ◽  
Author(s):  
Andrew F. Thompson
Keyword(s):  
Southern Ocean ◽  
Potential Vorticity ◽  
Baroclinic Instability ◽  
Length Scale ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Jet Formation ◽  
Meridional Transport ◽  
Jet Behavior ◽  
Jet Variability

Abstract Satellite altimetry and high-resolution ocean models indicate that the Southern Ocean comprises an intricate web of narrow, meandering jets that undergo spontaneous formation, merger, and splitting events, as well as rapid latitude shifts over periods of weeks to months. The role of topography in controlling jet variability is explored using over 100 simulations from a doubly periodic, forced-dissipative, two-layer quasigeostrophic model. The system is forced by a baroclinically unstable, vertically sheared mean flow in a domain that is large enough to accommodate multiple jets. The dependence of (i) meridional jet spacing, (ii) jet variability, and (iii) domain-averaged meridional transport on changes in the length scale and steepness of simple sinusoidal topographical features is analyzed. The Rhines scale, ℓβ = 2πVe/β, where Ve is an eddy velocity scale and β is the barotropic potential vorticity gradient, measures the meridional extent of eddy mixing by a single jet. The ratio ℓβ /ℓT, where ℓT is the topographic length scale, governs jet behavior. Multiple, steady jets with fixed meridional spacing are observed when ℓβ ≫ ℓT or when ℓβ ≈ ℓT. When ℓβ < ℓT, a pattern of perpetual jet formation and jet merger dominates the time evolution of the system. Zonal ridges systematically reduce the domain-averaged meridional transport, while two-dimensional, sinusoidal bumps can increase transport by an order of magnitude or more. For certain parameters, bumpy topography gives rise to periodic oscillations in the jet structure between purely zonal and topographically steered states. In these cases, transport is dominated by bursts of mixing associated with the transition between the two regimes. Topography modifies local potential vorticity (PV) gradients and mean flows; this can generate asymmetric Reynolds stresses about the jet core and can feed back on the conversion of potential energy to kinetic energy through baroclinic instability. Both processes contribute to unsteady jet behavior. It is likely that these processes play a role in the dynamic nature of Southern Ocean jets.

Influence of Turbulent Flow Characteristics and Coherent Vortices on the Pressure Recovery of Annular Diffusers: Part A — Experimental Results

2015 ◽  
Author(s):  
Marcus Kuschel ◽  
Bastian Drechsel ◽  
David Kluß ◽  
Joerg R. Seume
Keyword(s):  
Boundary Layer ◽  
High Pressure ◽  
Static Pressure ◽  
Turbulent Transport ◽  
Axial Flow ◽  
Pressure Recovery ◽  
Turbulence Structure ◽  
Reynolds Stresses ◽  
Wide Range ◽  
Operating Points

Exhaust diffusers downstream of turbines are used to transform the kinetic energy of the flow into static pressure. The static pressure at the turbine outlet is thus decreased by the diffuser, which in turn increases the technical work as well as the efficiency of the turbine significantly. Consequently, diffuser designs aim to achieve high pressure recovery at a wide range of operating points. Current diffuser design is based on conservative design charts, developed for laminar, uniform, axial flow. However, several previous investigations have shown that the aerodynamic loading and the pressure recovery of diffusers can be increased significantly if the turbine outflow is taken into consideration. Although it is known that the turbine outflow can reduce boundary layer separations in the diffuser, less information is available regarding the physical mechanisms that are responsible for the stabilization of the diffuser flow. An analysis using the Lumley invariance charts shows that high pressure recovery is only achieved for those operating points in which the near-shroud turbulence structure is axi-symmetric with a major radial turbulent transport component. This turbulent transport originates mainly from the wake and the tip vortices of the upstream rotor. These structures energize the boundary layer and thus suppress separation. A logarithmic function is shown that correlates empirically the pressure recovery vs. the relevant Reynolds stresses. The present results suggest that an improved prediction of diffuser performance requires modeling approaches that account for the anisotropy of turbulence.

Large-scale Structure and Turbulence Transport in the Young Solar Wind – Comparison of Parker Solar Probe Observations with a Global 3D Reynolds-averaged MHD Model

2021 ◽  
Author(s):  
Rohit Chhiber ◽  
Arcadi Usmanov ◽  
William Matthaeus ◽  
Melvyn Goldstein ◽  
Riddhi Bandyopadhyay
Keyword(s):  
Solar Wind ◽  
Large Scale ◽  
Transport Equations ◽  
Turbulence Energy ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Coulomb Collisions ◽  
Flow Equations ◽  
Simulation Results ◽  
Turbulence Transport

<div>Simulation results from a global <span>magnetohydrodynamic</span> model of the solar corona and the solar wind are compared with Parker Solar <span>Probe's</span> (<span>PSP</span>) observations during its first several orbits. The fully three-dimensional model (<span>Usmanov</span> <span>et</span> <span>al</span>., 2018, <span>ApJ</span>, 865, 25) is based on Reynolds-averaged mean-flow equations coupled with turbulence transport equations. The model accounts for effects of electron heat conduction, Coulomb collisions, Reynolds stresses, and heating of protons and electrons via nonlinear turbulent cascade. Turbulence transport equations for turbulence energy, cross <span>helicity</span>, and correlation length are solved concurrently with the mean-flow equations. We specify boundary conditions at the coronal base using solar synoptic <span>magnetograms</span> and calculate plasma, magnetic field, and turbulence parameters along the <span>PSP</span> trajectory. We also accumulate data from all orbits considered, to obtain the trends observed as a function of heliocentric distance. Comparison of simulation results with <span>PSP</span> data show general agreement. Finally, we generate synthetic fluctuations constrained by the local rms turbulence amplitude given by the model, and compare properties of this synthetic turbulence with PSP observations.</div>

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