A vortex-street model of the flow in the similarity region of a two-dimensional free turbulent jet

1982 ◽  
Vol 123 ◽  
pp. 523-535 ◽  
Author(s):  
J. W. Oler ◽  
V. W. Goldschmidt
Keyword(s):  
Experimental Data ◽  
Reynolds Stress ◽  
Turbulent Jet ◽  
Vortex Street ◽  
Two Dimensional ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Core ◽  
The Mean ◽  
Similarity Relationships

The mean-velocity profiles and entrainment rates in the similarity region of a two-dimensional jet are generated by a simple superposition of Rankine vortices arranged to represent a vortex street. The spacings between the vortex centres, their two-dimensional offsets from the centreline, as well as the core radii and circulation strengths, are all governed by similarity relationships and based upon experimental data.Major details of the mean flow field such as the axial and lateral mean-velocity components and the magnitude of the Reynolds stress are properly determined by the model. The sign of the Reynolds stress is, however, not properly predicted.

scholarly journals WKB theory for rapid distortion of inhomogeneous turbulence

1999 ◽  
Vol 390 ◽  
pp. 325-348 ◽  
Author(s):  
S. NAZARENKO ◽  
N. K.-R. KEVLAHAN ◽  
B. DUBRULLE
Keyword(s):  
Large Scale ◽  
Isotropic Turbulence ◽  
Two Dimensional ◽  
Turbulent Spot ◽  
Mean Flow ◽  
Mean Velocity ◽  
Inhomogeneous Turbulence ◽  
Large Scale Vortex ◽  
The Mean ◽  
Mean Strain

A WKB method is used to extend RDT (rapid distortion theory) to initially inhomogeneous turbulence and unsteady mean flows. The WKB equations describe turbulence wavepackets which are transported by the mean velocity and have wavenumbers which evolve due to the mean strain. The turbulence also modifies the mean flow and generates large-scale vorticity via the averaged Reynolds stress tensor. The theory is applied to Taylor's four-roller flow in order to explain the experimentally observed reduction in the mean strain. The strain reduction occurs due to the formation of a large-scale vortex quadrupole structure from the turbulent spot confined by the four rollers. Both turbulence inhomogeneity and three-dimensionality are shown to be important for this effect. If the initially isotropic turbulence is either homogeneous in space or two-dimensional, it has no effect on the large-scale strain. Furthermore, the turbulent kinetic energy is conserved in the two-dimensional case, which has important consequences for the theory of two-dimensional turbulence. The analytical and numerical results presented here are in good qualitative agreement with experiment.

Turbulence characteristics of the boundary layer on a rotating disk

1994 ◽  
Vol 266 ◽  
pp. 175-207 ◽  
Author(s):  
Howard S. Littell ◽  
John K. Eaton
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Reynolds Stress ◽  
Structural Model ◽  
Rotating Disk ◽  
Two Dimensional ◽  
Mean Flow ◽  
Velocity Correlation ◽  
Dimensional Boundary ◽  
The Mean

Measurements of the boundary layer on an effectively infinite rotating disk in a quiescent environment are described for Reynolds numbers up to Reδ2 = 6000. The mean flow properties were found to resemble a ‘typical’ three-dimensional crossflow, while some aspects of the turbulence measurements were significantly different from two-dimensional boundary layers that are turned. Notably, the ratio of the shear stress vector magnitude to the turbulent kinetic energy was found to be at a maximum near the wall, instead of being locally depressed as in a turned two-dimensional boundary layer. Also, the shear stress and the mean strain rate vectors were found to be more closely aligned than would be expected in a flow with this degree of crossflow. Two-point velocity correlation measurements exhibited strong asymmetries which are impossible in a two-dimensional boundary layer. Using conditional sampling, the velocity field surrounding strong Reynolds stress events was partially mapped. These data were studied in the light of the structural model of Robinson (1991), and a hypothesis describing the effect of cross-stream shear on Reynolds stress events is developed.

Measurements in Two-Dimensional Plumes in Crossflow

1989 ◽  
Vol 111 (2) ◽  
pp. 130-138 ◽  
Author(s):  
B. R. Ramaprian ◽  
H. Haniu
Keyword(s):  
Experimental Data ◽  
Short Distance ◽  
Two Dimensional ◽  
Mean Flow ◽  
Buoyant Jets ◽  
Laser Velocimetry ◽  
Buoyancy Forces ◽  
The Mean

The mean-flow and turbulent properties of two-dimensional buoyant jets discharged vertically upward into a crossflowing ambient have been measured in a hydraulic flume, using laser velocimetry and microresistance thermometry. The trajectory of the resulting inclined plume is found to be nearly straight, beyond a short distance from the source. The flow is essentially characterized by the presence of buoyancy forces along (s-direction) and perpendicular (n-direction) to the trajectory. While the s-component buoyancy tends to destabilize the flow and hence raise the overall level of turbulence in the flow, the n-component buoyancy tends to augment turbulence on the upper part of the flow and inhibit turbulence on the lower part. The experimental data are used to examine these effects quantitatively.

Capability Assessment of Five Different RANS-Based Turbulence Models to Simulate the Various Regions of Slot Turbulent Impingement Jet Flow

2017 ◽  
Author(s):  
Mahmoud Charmiyan ◽  
Ahmed-Reza Azimian ◽  
Ebrahim Shirani ◽  
Fethi Aloui
Keyword(s):  
Experimental Data ◽  
Turbulence Models ◽  
Jet Flows ◽  
Two Dimensional ◽  
Mean Flow ◽  
Impingement Jet ◽  
Image Velocimetry ◽  
The Mean ◽  
Bottom To Top ◽  
Plate Distance

In this paper, impingement of a turbulent rectangular flow to a fixed wall is investigated. The jet flows from bottom-to-top and the output jet Reynolds is 16000. The nozzle-to-plate distance is equal to 10 (H/e = 10). Five turbulence models, including k-ε, RNG k-ε, k-ω SST, RSM and v2f model have been used for two-dimensional numerical simulation of the turbulent flow. Because of the complexities of the impingement flow, such as curved streamlines, flow separation, normal strains and sudden deceleration in different areas, different turbulence models are proposed to simulate different regions of the flow. To investigate the capability of these turbulence models in simulating different regions of the impinging jet, the mean flow velocity field and turbulent kinetic energy are extracted and compared with the experimental data of a two-dimensional particle image velocimetry (PIV). The calculated error of these five turbulence models was presented for the various flow regions, while it have not been clearly investigated earlier. Results indicate the highest conformity of the v2f model with the experimental data at the jet centerline. However, this model does not predict well the flow at the shear layer and wall-jet areas. RSM Gibson and Lander model has the highest conformity with the experimental data in these regions.

Stabilization and destabilization of turbulent shear flow in a rotating fluid

1992 ◽  
Vol 241 ◽  
pp. 503-523 ◽  
Author(s):  
D. J. Tritton
Keyword(s):  
Experimental Data ◽  
Shear Flow ◽  
Reynolds Stress ◽  
Rotation Rate ◽  
Turbulent Shear ◽  
Rotating Fluid ◽  
Mean Flow ◽  
Rotation Rates ◽  
Principal Axes ◽  
The Mean

We consider turbulent shear flows in a rotating fluid, with the rotation axis parallel or antiparallel to the mean flow vorticity. It is already known that rotation such that the shear becomes cyclonic is stabilizing (with reference to the non-rotating case), whereas the opposite rotation is destabilizing for low rotation rates and restabilizing for higher. The arguments leading to and quantifying these statement are heuristic. Their status and limitations require clarification. Also, it is useful to formulate them in ways that permit direct comparison of the underlying concepts with experimental data.An extension of a displaced particle analysis, given by Tritton & Davies (1981) indicates changes with the rotation rate of the orientation of the motion directly generated by the shear/Coriolis instability occurring in the destabilized range.The ‘simplified Reynolds stress equations scheme’, proposed by Johnston, Halleen & Lezius (1972), has been reformulated in terms of two angles, representing the orientation of the principal axes of the Reynolds stress tensor (αa) and the orientation of the Reynolds stress generating processes (αb), that are approximately equal according to the scheme. The scheme necessarily fails at large rotation rates because of internal inconsistency, additional to the fact that it is inapplicable to two-dimensional turbulence. However, it has a wide range of potential applicability, which may be tested with experimental data. αa and αb have been evaluated from numerical data for homogeneous shear flow (Bertoglio 1982) and laboratory data for a wake (Witt & Joubert 1985) and a free shear layer (Bidokhti & Tritton 1992). The trends with varying rotation rate are notably similar for the three cases. There is a significant range of near equality of αa and αb. An extension of the scheme, allowing for evolution of the flow, relates to the observation of energy transfer from the turbulence to the mean flow.

Turbulent flow between a rotating and a stationary disk

2001 ◽  
Vol 426 ◽  
pp. 297-326 ◽  
Author(s):  
MAGNE LYGREN ◽  
HELGE I. ANDERSSON
Keyword(s):  
Shear Stress ◽  
Boundary Layers ◽  
Coherent Structures ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Mean Flow ◽  
Mean Velocity ◽  
Stationary Disk ◽  
Dimensional Boundary ◽  
The Mean

Turbulent flow between a rotating and a stationary disk is studied. Besides its fundamental importance as a three-dimensional prototype flow, such flow fields are frequently encountered in rotor–stator configurations in turbomachinery applications. A direct numerical simulation is therefore performed by integrating the time-dependent Navier–Stokes equations until a statistically steady state is reached and with the aim of providing both long-time statistics and an exposition of coherent structures obtained by conditional sampling. The simulated flow has local Reynolds number r2ω/v = 4 × 105 and local gap ratio s/r = 0.02, where ω is the angular velocity of the rotating disk, r the radial distance from the axis of rotation, v the kinematic viscosity of the fluid, and s the gap width.The three components of the mean velocity vector and the six independent Reynolds stresses are compared with experimental measurements in a rotor–stator flow configuration. In the numerically generated flow field, the structural parameter a1 (i.e. the ratio of the magnitude of the shear stress vector to twice the mean turbulent kinetic energy) is lower near the two disks than in two-dimensional boundary layers. This characteristic feature is typical for three-dimensional boundary layers, and so are the misalignment between the shear stress vector and the mean velocity gradient vector, although the degree of misalignment turns out to be smaller in the present flow than in unsteady three-dimensional boundary layer flow. It is also observed that the wall friction at the rotating disk is substantially higher than at the stationary disk.Coherent structures near the disks are identified by means of the λ2 vortex criterion in order to provide sufficient information to resolve a controversy regarding the roles played by sweeps and ejections in shear stress production. An ensemble average of the detected structures reveals that the coherent structures in the rotor–stator flow are similar to the ones found in two-dimensional flows. It is shown, however, that the three-dimensionality of the mean flow reduces the inter-vortical alignment and the tendency of structures of opposite sense of rotation to overlap. The coherent structures near the disks generate weaker sweeps (i.e. quadrant 4 events) than structures in conventional two-dimensional boundary layers. This reduction in the quadrant 4 contribution from the coherent structures is believed to explain the reduced efficiency of the mean flow in producing Reynolds shear stress.

scholarly journals The Development of the Mean Flow and Turbulence Structure in an Annular S-Shaped Duct

1994 ◽  
Author(s):  
K. M. Britchford ◽  
J. F. Carrotte ◽  
S. J. Stevens ◽  
J. J. McGuirk
Keyword(s):  
Reynolds Stress ◽  
Laser Doppler Anemometry ◽  
Reynolds Shear Stress ◽  
Turbulence Models ◽  
Test Facility ◽  
Turbulence Structure ◽  
Mean Flow ◽  
Mean Velocity ◽  
Curvature Effects ◽  
The Mean

This paper describes an investigation of the mean and fluctuating flow field within an annular S-shaped duct which is representative of that used to connect the compressor spools of aircraft gas turbine engines. Data was obtained from a fully annular test facility using a 3-component Laser Doppler Anemometry (LDA) system. The measurements indicate that development of the flow within the duct is complex and significantly influenced by the combined effects of streamwise pressure gradients and flow curvature. In addition CFD predictions of the flow, using both the k-ε and Reynolds stress transport equation turbulence models, are compared with the experimental data. Whereas curvature effects are not described properly by the k-ε model, such effects are captured more accurately by the Reynolds stress model leading to a better prediction of the Reynolds shear stress distribution. This, in turn, leads to a more accurate prediction of the mean velocity profiles, as reflected by the boundary layer shape parameters, particularly in the critical regions of the duct where flow separation is most likely to occur.

On the periodically excited plane turbulent mixing layer, emanating from a jagged partition

2007 ◽  
Vol 589 ◽  
pp. 479-507 ◽  
Author(s):  
E. KIT ◽  
I. WYGNANSKI ◽  
D. FRIEDMAN ◽  
O. KRIVONOSOVA ◽  
D. ZHILENKO
Keyword(s):  
Turbulent Mixing ◽  
Mixing Layer ◽  
Two Dimensional ◽  
Streamwise Vortices ◽  
Mean Flow ◽  
Trailing Edge ◽  
Mean Velocity ◽  
Turbulent Mixing Layer ◽  
Arithmetic Average ◽  
The Mean

The flow in a turbulent mixing layer resulting from two parallel different velocity streams, that were brought together downstream of a jagged partition was investigated experimentally. The trailing edge of the partition had a short triangular ‘chevron’ shape that could also oscillate up and down at a prescribed frequency, because it was hinged to the stationary part of the partition to form a flap (fliperon). The results obtained from this excitation were compared to the traditional results obtained by oscillating a two-dimensional fliperon. Detailed measurements of the mean flow and the coherent structures, in the periodically excited and spatially developing mixing layer, and its random constituents were carried out using hot-wire anemometry and stereo particle image velocimetry.The prescribed spanwise wavelength of the chevron trailing edge generated coherent streamwise vortices while the periodic oscillation of this fliperon locked in-phase the large spanwise Kelvin–Helmholtz (K-H) rolls, therefore enabling the study of the inter- action between the two. The two-dimensional periodic excitation increases the strength of the spanwise rolls by increasing their size and their circulation, which depends on the input amplitude and frequency. The streamwise vortices generated by the jagged trailing edge distort and bend the primary K-H rolls. The present investigation endeavours to study the distortions of each mode as a consequence of their mutual interaction. Even the mean flow provides evidence for the local bulging of the large spanwise rolls because the integral width (the momentum thickness, θ), undulates along the span. The lateral location of the centre of the ensuing mixing layer (the location where the mean velocity is the arithmetic average of the two streams,y0), also suggests that these vortices are bent. Phase-locked and ensemble-averaged measurements provide more detailed information about the bending and bulging of the large eddies that ensue downstream of the oscillating chevron fliperon. The experiments were carried out at low speeds, but at sufficiently high Reynolds number to ensure naturally turbulent flow.

Turbulent rotating flow calculations: An assessment of two-equation anisotropic and Reynolds stress models

1998 ◽  
Vol 212 (3) ◽  
pp. 193-212 ◽  
Author(s):  
S P Yuan ◽  
R M C So
Keyword(s):  
Stress Tensor ◽  
Turbulent Flows ◽  
Reynolds Stress ◽  
Dissipation Rate ◽  
Rotating Flow ◽  
Mean Flow ◽  
Mean Velocity ◽  
Anisotropic Stress ◽  
The Mean ◽  
Anisotropic Stress Tensor

The stress field in a rotating turbulent internal flow is highly anisotropic. This is true irrespective of whether the axis of rotation is aligned with or normal to the mean flow plane. Consequently, turbulent rotating flow is very difficult to model. This paper attempts to assess the relative merits of three different ways to account for stress anisotropies in a rotating flow. One is to assume an anisotropic stress tensor, another is to model the anisotropy of the dissipation rate tensor, while a third is to solve the stress transport equations directly. Two different near-wall two-equation models and one Reynolds stress closure are considered. All the models tested are asymptotically consistent near the wall. The predictions are compared with measurements and direct numerical simulation data. Calculations of turbulent flows with inlet swirl numbers up to 1.3, with and without a central recirculation, reveal that none of the anisotropic two-equation models tested is capable of replicating the mean velocity field at these swirl numbers. This investigation, therefore, indicates that neither the assumption of anisotropic stress tensor nor that of an anisotropic dissipation rate tensor is sufficient to model flows with medium to high rotation correctly. It is further found that, at very high rotation rates, even the Reynolds stress closure fails to predict accurately the extent of the central recirculation zone.

The maintenance of Reynolds stress in turbulent shear flow

1967 ◽  
Vol 27 (1) ◽  
pp. 131-144 ◽  
Author(s):  
O. M. Phillips
Keyword(s):  
Shear Flow ◽  
Velocity Profile ◽  
Reynolds Stress ◽  
Mixing Layer ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Mean Flow ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
The Mean

A mechanism is proposed for the manner in which the turbulent components support Reynolds stress in turbulent shear flow. This involves a generalization of Miles's mechanism in which each of the turbulent components interacts with the mean flow to produce an increment of Reynolds stress at the ‘matched layer’ of that particular component. The summation over all the turbulent components leads to an expression for the gradient of the Reynolds stress τ(z) in the turbulence\[ \frac{d\tau}{dz} = {\cal A}\Theta\overline{w^2}\frac{d^2U}{dz^2}, \]where${\cal A}$is a number, Θ the convected integral time scale of thew-velocity fluctuations andU(z) the mean velocity profile. This is consistent with a number of experimental results, and measurements on the mixing layer of a jet indicate thatA= 0·24 in this case. In other flows, it would be expected to be of the same order, though its precise value may vary somewhat from one to another.

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