Two-dimensional Turbulent Wake Research Articles

Instability of energy spectrum disturbance for ship turbulent wakes: SAR imaging simulation and analysis

We present a ship turbulent wake synthetic aperture radar (SAR) simulator (STW-SARSim) producing two-dimensional true-scale turbulent wakes in SAR images that extend for kilometers. In this paper, we innovatively overcome the sea surface time-varying problem in solving the spectral energy balance equation by transforming the unsteady problem into a steady problem and considering the dark trailing centerline region of the turbulent wake in SAR images as a texture modulation effect of the Bragg wave for sea surface scattering. We also present SAR images simulated in three different bands: (i) Sentinel-1A C-band, (ii) TerraSAR X-band, and (iii) ALOS PALSAR L-band to validate the reliability of our proposed method and analyze the effects of wind speed, wind direction, and dissipation rates on the turbulent wake simulation. This paper provides new insights into the simulation of turbulent wakes in SAR images of large scenes inspired by recent research on detection algorithms. It sets the stage for future dataset generation for detection.

Two-dimensional turbulent thermal classical far wake

The two-dimensional turbulent thermal classical far wake is investigated. The turbulence is described by the Boussinesq hypothesis for the Reynolds stresses with Prandtl’s mixing length model for the eddy viscosity and eddy thermal conductivity. Two conservation laws are derived for the thermal boundary layer equations for the far wake using the multiplier method and two conserved quantities are obtained from the conserved vectors and boundary conditions. The Lie point symmetry associated with the momentum and thermal conserved vectors is derived. It is found that the momentum and thermal mixing lengths are proportional. In obtaining the invariant solution the cases ν≠0, κ≠0 and ν=0, κ=0 needed to be treated separately, where ν is the kinematic viscosity and κ is the thermal conductivity of the fluid. When ν≠0, κ≠0 the associated Lie point symmetry is determined in full but an analytical solution of the reduced ordinary differential equations could not be derived. The invariant solution is obtained numerically using a shooting method with the two conserved quantities as targets. The width of the wake is infinite. When ν=0, κ=0 the width of the wake is finite. In order to obtain the associated Lie point symmetry in full, Prandtl’s hypothesis that the mixing length is proportional to the width of the wake was imposed. The invariant solution is obtained analytically. The lines of constant mean temperature difference and the streamlines for the mean velocity deficit are plotted. The numerical and analytical solutions agree in the limit ν→0, κ→0.

End effects of nominally two-dimensional thin flat plates

Differences in the structure and dynamics of nominally two-dimensional turbulent wakes are investigated experimentally for a thin flat plate, normal to a uniform flow, with two different end conditions: with and without end plates. Both cases are characterized by Karman-like vortex shedding with broadband low frequency unsteadiness. Both wakes evidence a low frequency flapping motion in addition to the slowly drifting base flow common to cylinder wakes. For the case without end plates, an interaction between the drift motion and the vortex formation process is associated with a much stronger modulation of the quasiperiodic vortex shedding amplitude when compared to the case with end plates where a flapping motion is more strongly expressed. These dynamics underlie structural differences in the mean wake and Reynolds stress fields.

Compressible plane turbulent wakes under pressure gradients evolving in a constant area section

Development of statistically two-dimensional (2-D) turbulent wakes under pressure gradients is a common feature of many industrial and aerodynamic flows. The usual set-up is to generate a wake, and study its development through a passage with a variable area; if the downstream area decreases (increases) a favourable pressure gradient or FPG (adverse pressure gradient or APG) is imposed. In applications such as in turbomachinery, however, the wakes develop in a periodic constant area passage in the stator–rotor gap and with an imposed pressure gradient. To study these flows, here, we develop a canonical set-up for this new kind of wake evolution in FPG and APG of different strengths by placing a 2-D flat plate normal to the flow in a periodic constant area passage and a fixed inflow mass flux. Employing compressible direct numerical simulations, we impose pressure gradients through a ramped body force term to the momentum and total energy equations while the wake is allowed to develop spatially in a region of fixed width. The resultant mean velocity statistics, wake width, energy budgets and entropy generation rates are scrutinised to assess the effect of the pressure gradients, and where possible, the similarities and differences to the conventional case of variable area pressure gradients are discussed. The results show that the effect of a constant area pressure gradient on flow statistics is non-trivial, resulting from significant density changes. The pressure gradients also have an effect on the different energy budgets, which produces a gain for FPG and loss for APG in the mean kinetic energy. Consequently, the entropy generation rate diminishes and augments for the FPG and APG, respectively, compared to the zero pressure gradient. Finally, the effect of different passage heights ( ) relative to the wake half-width ( ) is studied using large eddy simulations. We find that wake width and hence the spreading, depends primarily on the wake–wake interaction for small and pressure gradients for larger , and this has implications for the design of turbomachinery.

Revised Prandtl mixing length model applied to the two-dimensional turbulent classical wake

Previous applications of Prandtl׳s mixing length model to turbulent wake flows, which neglect the kinematic viscosity of the fluid, have underestimated the width of the boundary layer. In this paper, we present a revised Prandtl mixing length model by including the kinematic viscosity of the fluid. We show that this model predicts a boundary that lies outside the one predicted by Prandtl. We also prove that the results for the two models converge for very large Reynolds number wake flows.

Experimental sensitivity analysis of the global properties of a two-dimensional turbulent wake

AbstractThe sensitivity of the global properties of a two-dimensional turbulent wake produced by the separated flow of a ‘D’-shaped cylinder at$\mathit{Re}= 13\hspace{0.167em} 000$is investigated experimentally using a small circular control cylinder as a local disturbance. The height of the main cylinder is$D= 25~\mathrm{mm} $and control cylinders are of diameters$d= 0. 04D$and$d= 0. 12D$, the former being smaller than the shear layer thickness detaching from the main cylinder, while the latter is larger. In both cases, the control cylinder is able to modify the global frequency, base pressure and spanwise velocity correlation. The results are presented as sensitivity maps. Reynolds stresses spatial structure and the recirculation bubble length are examined in detail when the control cylinder is displaced vertically across the wake at a fixed downstream location. It is found that the increase of the recirculation bubble length is accompanied by a damping of Reynolds stresses with a downstream shift of their spatial structures together with the base pressure increase. The global frequency can be either decreased or increased independently of the bubble length modification. The sensitivity of these global properties is interpreted on the basis of the ability of the control cylinder to change the size of the formation region of the Kármán vortex street by interacting with the primary detached shear layers. The corresponding physical mechanisms are discussed. The impact of a two-dimensional control cylinder on the three-dimensional properties of the wake is examined through spanwise correlation. This is found to be improved whenever the control cylinder is placed inside the recirculation region of the main cylinder wake.

Partially premixed flamelets in LES of nonpremixed turbulent combustion

Partially premixed flames are observed in nonpremixed turbulent combustion when fuel and oxidizer have mixed before burning. This combustion regime combines the properties of both premixed and diffusion flames. A procedure based on the resolved fields is proposed to associate premixed and diffusion flame descriptions in large eddy simulation. Using basic and well known subgrid modelling of premixed and diffusion flames, the proposed methodology is tested for flames lifted in a two-dimensional turbulent wake. Very recent experimental observations concerning the dynamics of the flow field at the turbulent flame base are reproduced.

Airfoil-Boundary Layer Subjected to a Two-Dimensional Asymmetrical Turbulent Wake

The results of an experimental study of interaction between an incompressible two-dimensional asymmetrical turbulent wake produced by a symmetrical airfoil at incidence and a boundary layer formed on a similar airfoil immediately downstream are discussed. Extensive measurements of time-averaged quantities of the e ow and turbulence characteristics in the interaction region are performed. Particular attention is paid to analysis of the e ow structure with the downstream airfoil position being changed across the wake. In particular, a signie cant reduction in thelevel of turbulent velocity e uctuations hasbeen found in the boundary layer if the airfoil is located in the wake periphery. A similar effect also has been registered in the outer e ow region (outside the boundary layer) for the case when the wing is located in the central part of the wake. Although the interaction process has rather a complicated character, the distribution of the normalized mean velocity defect in the outer region of the interactinge owcanberoughlydescribedin theframeofwell-knowncorrelationsvalidforawakee owimmediately downstream of a transverse-positioned circular cylinder. A detailed analysis of the interacting e ow components (i.e., isolated turbulent wake and boundary layer ) is presented, and a possibility of their description in self-similar variables is shown.

Small-scale turbulence characteristics of two-dimensional bluff body wakes

Measurements have been made in nominally two-dimensional turbulent wakes generated by five different bluff bodies. Each wake has a different level of large-scale organization which is reflected in different amounts of large-scale anisotropy. Structure functions of streamwise (u) and lateral (v) velocity fluctuations at approximately the same value of Rλ, the Taylor microscale Reynolds number, indicate that inertial-range scales are significantly affected by the large-scale anisotropy. The effect is greater on v than u and more pronounced for the porous-body wakes than the solid-body wakes. In particular, ‘relative’ values of the scaling (or power-law) exponents indicate that the magnitude of the transverse exponents can exceed that of the longitudinal ones in the porous-body wakes. This is supported by the inertial-range behaviour of the spectra of u and v. The difference between the transverse and longitudinal exponents appears to depend on the large-scale anisotropy of the flow, as measured by the ratio of the variances of v and u and ratio of the integral length scales of v and u. The spanwise vorticity spectra are much less affected by the anisotropy than the spectra of u and v.

The statistical properties of two-dimensional turbulent wake of a heated cylinder

By analyzing the experimental data, the statistical properties of 2D turbulent wake of a heated cylinder are studied. The coherent structures may have the stronger effect upon the transverse velocity and temperature than the longitudinal velocity. In the near wake, the transverse velocity v and the temperature T have the bimodal distribution and the χ 2 distribution, respectively. But the distribution of the longitudinal velocity u is near the Gaussian even in the near wake. The statistical distributions for the velocity differences and the temperature differences are studied. In the near wake, the pdfs of the transverse velocity differences are concave functions only for the time separations n Δt : n c 1 <n<n c 2 . Otherwise, they will be the convex functions. The pdf of the temperature difference will change from the nearly exponential distribution to the Gaussian distribution as the time separation nΔ t increasing in the near wake. Using the detrended fluctuation analysis, it is found out that the longitudinal velocity and temperature have the long-range correlation with the exponent α≈0.7 in the near and intermediate wake and the transverse velocity has the weakly anti-correlation with the exponent α≈0.44 in the intermediate wake.

Airfoil-boundary layer subjected to a two-dimensional asymmetrical turbulent wake

Airfoil-boundary layer subjected to a two-dimensional asymmetrical turbulent wake

Scalar transport in a quasi two-dimensional turbulent wake interacting with a boundary layer

An experimental study of heat transport in the interaction region between the wake of a cylinder and a turbulent boundary layer is presented in this work. The cylinder was placed parallel to a flat plate and normal to the flow. Its position was selected above the boundary layer edge, so that the lower part of the wake was interacting with the boundary layer. Heat was supplied to the boundary layer flow by means of a line heat source. Presence of surface roughness on the cylinder resulted in the deviation of the velocity power spectrum scaling region from the −5/3 power law which is characteristic of three-dimensional turbulence. Point measurements of the instantaneous values of two velocity components and temperature have been taken using hot-wire anemometry. Two turbulent scalar flux components and a Reynolds shear stress component have been obtained directly from the experimental data. Results were assessed in conjunction with the periodic coherent structures in the wake (a von Kármán vortex street) using a phase-averaging technique that provided a clear picture of the heat transport procedures involved.

Development of a Two-Dimensional Turbulent Wake in a Curved Channel With a Positive Streamwise Pressure Gradient

The development of turbomachinery wake flows is greatly influenced by streamline curvature and streamwise pressure gradient. This paper is part of a comprehensive experimental and theoretical study on the development of the steady and periodic unsteady turbulent wakes in curved channels at different streamwise pressure gradients. This paper reports on the experimental investigation of the two-dimensional wake behind a stationary circular cylinder in a curved channel at positive streamwise pressure gradient. Measurements of mean velocity and Reynolds stress components are carried out using a X-hot-film probe. The measured quantities obtained in probe coordinates are transformed to a curvilinear coordinate system along the wake center line and are presented in similarity coordinates. The results show strong asymmetry in velocity and Reynolds stress components. The Reynolds stress components have higher values at the inner half of the wake than at the outer half of the wake. However, the mean velocity defect profiles in similarity coordinates are almost symmetric and follow the same Gaussian function for the straight wake data. A comparison with the wake development in a curved channel at zero streamwise pressure gradient suggests the decay rate of velocity defect is slower and the growth of wake width is faster for a positive streamwise pressure gradient.

Experimental study of plane turbulent wakes in a shallow water layer

Shallow two-dimensional turbulent wake flows have been studied experimentally on a large water table. In the experiments, the ambient Reynolds number Re h = U a H/ ν, in which U a is the depth-averaged ambient velocity, H the water depth, and ν the kinematic viscosity, is large, well above a lower critical value of the order of 500 for open-channel flows so that the ambient base flow is fully turbulent. Different types of blunt bodies extending over the full depth are inserted in that base flow, including cylinders and flat solid and porous plates oriented transversely to the ambient flow. In all cases, the transverse body dimension D greatly exceeds the water depthy, D H ⪢ 1 . With that condition, the wake Reynolds number Re d = U a D/ ν is very large, greater than 10 4. The shallow near-wake characteristics of plane wakes from blunt bodies extending over the full water depth have been found to fall into one of three classes: (i) the vortex street (VS) type with an oscillating vortex shedding mechanism, (ii) the unsteady bubble (UB) wake type with flow instabilities growing downstream of a recirculating bubble attached to the body, and (iii) the steady bubble (SB) wake type with an attached bubble followed by a turbulent wake that contains no growing instabilities. When Re h > 1500, the flow classification is uniquely dependent on a shallow wake parameter, S = c f D H in which c f is a quadratic law friction coefficient. For circular cylindrical bodies the VS-UB transition is characterized by a critical value, S ca ≈ 0.2, and the UB-SB transition by S cc ≈ 0.5. Solid plates, oriented transversely, differ by a factor of 1.25. The shallow far-wake behavior has been investigated with a special variable porosity wake device that reduces the wake velocity deficit and completely suppresses the VS instabilities in the near-field. Thus, only UB and SB wake types are found in that case. Furthermore, the shallow plane wake is obsserved to “stabilize” for large downstream distances, x H , in the sense that the growth and maintenance of the large scale structures in the wake flow become suppressed and the wake collapses into a more ordered flow that, however, still contains small scale (of scale H) turbulence. This wake stabilization is controlled by two factors: first, the usual evolution in a turbulent wake that reduces the velocity deficit while increasing the wake parameter S, and secondly, the exponential loss of the momentum deficit flux in the wake due to bottom friction.

Mean flow distortion due to finite-amplitude instability waves in a plane turbulent wake

The nonlinear interaction between the mean flow and a coherent disturbance in a two-dimensional (2-D) turbulent wake is investigated. Based on considerations from stability theory, a model that assumes a quasiparallel mean flow and constant eddy viscosity is developed. Detailed comparisons between the model and experimental results are made. It is found that for downstream distances, where the wave is still being amplified according to the linear stability theory, the model predicts very well the modification of the mean velocity profile and the spatial growth of both the forced wake and the disturbance amplitude.

Modal decomposition of velocity signals in a plane, turbulent wake

The Orr-Sommerfeld equation admits two solution modes for the two-dimensional plane wake. These are the sinuous mode with antisymmetric streamwise fluctuations and the varicose mode with symmetric streamwise fluctuations. The varicose mode is often ignored because its amplification rates are considerably less than those of the sinuous mode. An experimental investigation of the varicose mode in a two-dimensional turbulent wake was undertaken to determine if this mode of instability agrees as well with linear stability theory, as did the sinuous mode in previous experiments (Wygnanski, Champagne &amp; Marasli 1986). The experiments demonstrated that, although it is possible to generate a nearly pure symmetric disturbance wave, it is very difficult to do as the flow is very sensitive to the slightest asymmetries which might be present in the experiments. These asymmetries are preferentially amplified, resulting in the eventual distortion of an initially prominent symmetric wave. It was therefore necessary to decompose phase-averaged measurements of the streamwise component of the velocity fluctuations into their symmetric and antisymmetric parts, and the results were compared with the appropriate theoretical eigenfunctions from linear stability theory. The lateral distribution of the amplitude and the phase of each mode agree reasonably well with their theoretical counterparts from the Orr-Sommerfeld equation. Slowly diverging linear theory predicts the streamwise variation of the sinuous mode quite well, but fails to do so for the varicose mode. An eddy-viscosity model, coupled with the slowly diverging linear equations, predicts the streamwise variation of both modes reasonably well and describes the transverse distributions of the perturbation amplitudes for both modes, but it fails to predict the distribution of phase for the varicose mode.

A computational model for a symmetric turbulent wake

The study of wakes has many engineering applications. A wake is present behind any object placed in a fluid flow. The wake structure affects the pressure distribution on the object creating the wake. A wake is characterized by high turbulent intensities and mean velocity gradients in the lateral direction. The mathematical modeling of a general three-dimensional wake is very complicated. Work is therefore initiated by modeling a two-dimensional symmetric turbulent wake behind a flat plate. Another reason for choosing this simple flow situation is that very good quality experimental data can be produced for this simple flow. The results from the computational model and comparison with experimental data is the topic of this paper.

Curvature and pressure-gradient effects on a small-defect wake

A fully developed two-dimensional turbulent wake was deflected by an airfoil-like thin plate placed at small angles in the external flow. The response of the mean-flow and turbulence properties of the wake to the ‘mild’ pressure gradient and the ‘mild’ streamline curvature caused by the deflection is studied. Owing to the small defect velocity, the extra strain rates are large compared with the main shear strain and the Reynolds stresses are strongly influenced by both the pressure gradient and the streamline curvature. The defect velocity relative to an appropriately chosen ‘potential-flow velocity’, and the mean vorticity, however, are not as strongly influenced by the curvature. Changes in the magnitudes of the Reynolds-stress components are much larger than would be caused by the simple rotation of coordinates aligned with the wake path. Most turbulence-model parameters are influenced significantly, while some pure turbulence parameters, such as the Taylor microscale, are relatively uninfluenced. The rapid and lagged responses are apparent and the terms in the transport equation for turbulent kinetic energy indicate that the response of the production terms is almost instantaneous, while the diffusion and dissipation terms are delayed.

Spanwise Mixing in Multistage Axial Flow Compressors: Part I—Experimental Investigation

Spanwise mixing has been shown to be an essential feature of multistage compressor aerodynamics. The cause of spanwise mixing in multistage axial flow compressors has been investigated directly by using an ethylene tracer gas technique in two low-speed, four-stage machines. The results show that the dominant mechanism is that of turbulent type diffusion and not the radial convection of flow properties as has been previously suggested. The mixing was also found to be substantially uniform in magnitude all the way across the span with levels similar to those found in two-dimensional turbulent wakes.

Vortex shedding from a spinning cylinder

An experimental investigation of a two-dimensional turbulent wake behind a spinning cylinder at Re=9000 is carried out to determine the influence of the rotation on the initial development of the flow. Spectral analysis of the velocity data measured in the near wake shows that for peripheral velocities up to the value of the free-stream velocity, a distinct Kármán vortex activity exists within the wake, whereas for greater peripheral velocities, the Kármán activity deteriorates and disappears for values in excess of twice the free-stream velocity.