Turbulent Plane Jet Research Articles

Detection of the irrotational boundary using machine learning methods

Four machine learning methods, i.e., self-organizing map (SOM), Gaussian mixture model (GMM), eXtreme gradient boosting (XGBoost), and contrastive learning (CL), are used to detect the irrotational boundary (IB), which represents the outer edge of the turbulent and non-turbulent interface layer. To accurately evaluate the detection methods, high-resolution databases from direct numerical simulations of a temporally evolving turbulent plane jet are used. It is found that except for the SOM method, the general contour of the IB appears to be effectively captured using the GMM, XGBoost, and CL methods, which indicate the turbulent and non-turbulent regions can be roughly recognized. Furthermore, the intrinsic features of the detected IB using the GMM, XGBoost, and the CL methods are quantitatively evaluated. Unlike the conventional vorticity norm method, the three machine learning methods do not rely on a single threshold of vorticity magnitude to separate the turbulent and non-turbulent regions. A small part of the detected IB using the three machine learning methods is characterized by the rotational motions, which are expected to be only found inside the turbulent sublayer and turbulent core region. Compared to the vorticity norm and XGBoost methods, the fractal dimensions of the IB detected by the GMM and CL methods are relatively small, which are related to the missing detection of some highly contorted elements. With the three machine learning methods, a large part of the detected IB is characterized by a convex shape, similarly as with the vorticity norm. However, the probability density function profiles of the local curvature of the detected IB differ greatly between the three machine learning methods and the vorticity norm. A mild variation of the mean conditional distributions of the vorticity magnitude can be observed across the detected IB by the three machine learning methods. This study first implies that using the machine learning methods the turbulent and non-turbulent regions can be roughly distinguished, but it is still challenging to obtain the intrinsic features of the detected IB.

A developed transition simulation model for turbulent plane jet impingement heat transfer

Jet impingement has been widely used due to its high heat transfer rate, but numerical simulation of this flow is highly challenging because of complex flow phenomena. In this paper, a turbulence model based on the physics of jet impingement is developed using the shear stress transport (SST) four-equation transition model and the SST with cross-diffusion correction (SSTCD) model. The proposed method is evaluated for plane jet impingement under various nozzle-plate spacings (2.6, 4 and 6) and different Reynolds numbers ranging from 10,200 to 20,000 in terms of heat transfer and flow fields. The results show that the developed model has the ability to capture the second peak of heat transfer and skin friction at low nozzle-plate spacing. Even at high nozzle-plate spacing, this approach also gives accurate trends for the above two features. However, without the cross-diffusion correction, the transition model provides too high energy and low velocity peaks. With the developed model in hand, the effects of pressure gradient on heat transfer and skin friction coefficient are further investigated. It is found that when the adverse pressure gradient becomes strong, the position of the secondary peak of skin friction occurs earlier than that of the secondary peak of heat transfer rate. Conversely, if the adverse pressure gradient disappears, the positions of these features coincide.

Experimental investigation of the structure of plane turbulent wall jets. Part 1. Spectral analysis

Plane turbulent wall jets are traditionally considered to be composed of a turbulent boundary layer (TBL) topped by a half-free jet. However, certain peculiar features, such as counter-gradient momentum flux occurring below velocity maximum in experiments and numerical simulations, suggest a different structure of turbulence therein. Here, we hypothesize that turbulence in wall jets has two distinct structural modes, wall mode scaling on wall variables and free-jet mode scaling on jet variables. To investigate this hypothesis, experimental data from our wall jet facility are acquired using single hot-wire anemometry and two-dimensional particle image velocimetry at three nozzle Reynolds numbers 10 244, 15 742 and 21 228. Particle image velocimetry measurements with four side-by-side cameras capture the longest field of view studied so far in wall jets. Direct spatial spectra of these fields reveal modal spectral contributions to variances of velocity fluctuations, Reynolds shear stress, shear force, turbulence production, velocity fluctuation triple products and turbulent transport. The free-jet mode has wavelengths scaling on the jet length scale ${z_{T}}$ , and contains two dominant submodes with wavelengths $5{z_{T}}$ and $2.5{z_{T}}$ . The region of flow above the velocity maximum shows the presence of the outer jet mode whereas the region below it shows robust bimodal behaviour attributed to both wall and inner jet modes. Counter-gradient momentum flux is effected by the outer jet mode intruding into the region below velocity maximum. These findings support the hypothesis of wall and free-jet structural modes, and indicate that the region below velocity maximum could be much complex than a conventional TBL.

Coherent structures in elastic turbulent planar jets

At low Reynolds numbers, the flow of a Newtonian planar jet remains laminar, thus easy to characterize. In contrast, the presence of elasticity (e.g., attained dissolving polymers in a Newtonian solvent) enables a highly-complex turbulent-like behavior termed elastic turbulence. In this work, we run data-driven modal decomposition algorithms on high-fidelity data collected from the simulation of an elastic turbulent planar jet. The large-scale motions are expressed as a finite expansion of modes that condense the dominant dynamics. The modes associated with lower frequencies weight the most on the reconstruction of the original data, thus they are further decomposed in space to investigate their implications on the sustainment of the elastic turbulent state. Our findings suggest that slower dynamics are crucial for the sustainment of elastic turbulence, which is connected to the interaction of spanwise-coherent structures, steady in space, with spanwise-periodic traveling waves, causing the breakdown of the structures close to the inlet.

Hybrid large eddy simulation and Lagrangian simulation of a compressible turbulent planar jet with a chemical reaction

AbstractLarge eddy simulation (LES) coupled with Lagrangian particle simulation (LPS) is applied to investigate high‐speed turbulent reacting flows. Here, LES solves a velocity field while LPS solves scalar transport equations with notional particles. Although LPS does not require sub‐grid scale models for chemical source terms, molecular diffusion has to be modeled by a so‐called mixing model, for which a mixing volume model (MVM), that is originally proposed for an inert scalar in incompressible flow, is extended to reactive scalars in compressible flows. The extended model is based on a relaxation process toward the average of nearby notional particles and assumes a common mixing timescale for all species. LES/LPS with the MVM is applied to a temporally‐evolving compressible turbulent planar jet with an isothermal reaction and is tested by comparing the results with direct numerical simulation (DNS). The results show that LES/LPS well predicts the statistics of mass fractions. As the jet Mach number increases, the reaction progress delays due to the delayed jet development. This Mach number dependence is also well reproduced in LES/LPS. The mean molecular diffusion term of the product calculated as a function of its mass fraction also agrees well between LES/LPS and DNS. An important parameter for the MVM is the distance among particles, for which the requirement for accurate prediction is presented for the present test case. LES/LPS with the MVM is expected to be a promising method for investigating compressible turbulent reactive flows at a moderate computational cost.

Integral Turbulent Length and Time Scales of Higher Order Moments

Turbulent length and time scales represent a fundamental quantity for analysing and modelling turbulent flows. Although higher order statistical moments have been conveniently used for decades to describe the mean behaviour of turbulent fluid flow, the definition of the integral turbulent scales seems to be limited to the velocity or its fluctuation itself (i.e. the first moment). Higher order moments are characterized by smaller integral scales and a framework is proposed for estimating autocorrelation functions and integral turbulent length or time scales of higher order moments under the assumption that the probability distribution of the velocity field is Gaussian. The new relations are tested for synthetic turbulence as well as for DNS data of a turbulent plane jet at Reynolds number 10000. The present results in particular suggest that the length or time scales of higher order moments can be markedly smaller than those of the turbulent variable itself, which has implications for statistical uncertainty estimates of higher order moments.

Aerodynamic sealing using a segmented recirculating horizontal air curtain for buoyancy-driven flows in doorways

Dealing with buoyancy-driven flow to reduce infiltration heat is challenging for buildings such as cold storages where the indoor-outdoor temperature differences are significant. In this study, a segmented recirculating horizontal air curtain (SRHAC) is proposed to respond to the vertical thermal buoyancy profile in doorways and recover the cold air entrained by the air curtain. Specifically, SRHAC is a planar turbulent impingement jet discharged through a vertically mounted rectangular nozzle. The discharge nozzle is divided into segments and the return vent recirculates the discharged air to the rear of the discharge nozzle. In this study, the aerodynamic sealing performance of the SRHAC is investigated by considering structural, operational, and ambient parameters. Orthogonal analysis reveals the flow rate, nozzle width, and discharge angle as significant factors affecting the thermal separation efficiency of the SRHAC. Increasing the flow rate and decreasing the nozzle width leads to an increase in the jet momentum flux, thereby enhancing the thermal separation efficiency, with a maximum efficiency of 75.9 %. Setting the discharge parameters in the three sections along the height improves the thermal separation efficiency by 16.5% points. The maximum efficiencies of two-, three-, and five-segment air curtains are 83.6 %, 87.3 %, and 90.3 %, respectively. The separation efficiency of the SRHAC remains relatively stable even when the indoor-outdoor temperature difference varies between 32 and 57 K. These results establish that the SRHAC is an efficient energy-saving device, with the ratio of reduced infiltration load to energy consumption as high as 110.9.

The mixing field and flame structure near the reaction zone of turbulent planar flames at different levels of mixture inhomogeneity

Turbulent flames with compositionally inhomogeneous mixtures are commonly used in many combustion systems. In this work, turbulent planar jet flames issued from a concentric flow slot burner, CFSB, were used to study the impact of mixture inhomogeneity near the flame sheet. The CFSB burner can control the mixing inhomogeneity by changing the mixing length “L” between the concentric fuel and air slot nozzles. At various levels of mixture inhomogeneity, the mixing field, presented by mixture fraction, Z, distribution, and the flame structure was investigated via simultaneous Rayleigh and OH-PLIF imaging technique. Our previous study investigated the mixing field immediately downstream of the burner exit in non-reacting conditions. The PDFs of Z showed that the mixing field covered a wide range of mixture fractions, where the high flame stabilization occurred when a large portion of the PDF(Z) was located within the fuel flammability limits. This work showed that further downstream, the highly stabilized flames were also obtained when the range of fluctuations in the mixture fraction was close to the stoichiometric mixture fraction. Moreover, plotting the mixing field using the scatter plot within the mixing regime diagram for various flame conditions showed that the mixing field downstream of the burner exit consistently follows the mixing diagram classification. Moreover, a close inspection of the flame structure showed that the flame sheet varies from thick, and corrugated at a low and high levels of mixing to thin flame sheet but less corrugated and that at a particular mixing normalized length L/D = 7. The flame corrugation data showed that the flame stability occurs at a minimum corrugation factor.

Non-Newtonian turbulent jets at low-Reynolds number

We perform direct numerical simulations of planar jets of non-Newtonian fluids at low Reynolds number, in typical laminar conditions for a Newtonian fluid. We select three different non-Newtonian fluid models mainly characterized by shear-thinning (Carreau), viscoelasticity (Oldroyd-B) and shear-thinning and viscoelasticity together (Giesekus), and perform a thorough analysis of the resulting flow statistics. We characterize the fluids using the parameter γ, defined as the ratio of the relevant non-Newtonian time scale over a flow time scale. We observe that, as γ is increased, the jet transitions from a laminar flow at low γ, to a turbulent flow at high γ. We show that the different non-Newtonian features and their combination give rise to rather different flowing regimes, originating from the competition of viscous, elastic and inertial effects. We observe that both viscoelasticity and shear-thinning can develop the instability and the consequent transition to a turbulent flowing regime; however, the purely viscoelastic Oldroyd-B fluid exhibits the onset of disordered fluid motions at a lower value of γ than what observed for the purely shear-thinning Carreau fluid. When the two effects are both present, an intermediate condition is found, suggesting that, in this case, the shear-thinning feature is acting against the fluid elasticity. Despite the qualitative differences observed in the flowing regime, the bulk statistics, namely the centerline velocity and jet thickness, follow almost the same power-law scalings obtained for laminar and turbulent Newtonian planar jets. The simulations reported here are, to the best of our knowledge, the first direct numerical simulations showing the appearance of turbulence at low Reynolds number in jets, with the turbulent motions fully induced by the non-Newtonian properties of the fluid, since the Newtonian case at the same Reynolds number is characterized by steady, laminar flow.

Turbulence effects on the formation and growth of nano-particles in three-dimensional premixed and non-premixed flames

This study examines the impact of turbulence on particle-forming flames via three-dimensional direct numerical simulations. The simulations employ the finite rate chemistry approach to simulate both premixed and non-premixed methane-air turbulent planar jet flames. These flames are doped with titanium tetraisopropoxide (TTIP) to form titanium dioxide TiO2 nanoparticles. The sectional model is employed to solve the population balance equation governing particle dynamics. Through these simulations, a number of the Batchelor scales pertaining to the smaller nanoparticle structures are effectively captured. The analysis conducted on these simulations is to identify and quantify the respective influences of diffusion, coagulation, and inception on variations in particle concentration across different regions within the flame. Several regions of the computational domain with different turbulence intensities are analyzed. Results show that the physical mechanisms that contribute to particle growth are not negligible on the particle concentrations. The impact of normal aN and tangential aT strain rates, which govern the thickness of particle-loaded zones affected by turbulence effects, is also evaluated. Conditional mean values of the strain rates upon the particle number concentration fields and the PDFs of aN and aT confirm that on the iso-surfaces of the particle fields the compressive and stretching effects are predominant. The aforementioned information is used to gain a deeper understanding of the influence of turbulence on premixed and non-premixed particle-forming flames, which will help us to develop transferable models for the simulation of nanoparticle synthesis.

Length scales and the turbulent/non-turbulent interface of a temporally developing turbulent jet

The temporally developing self-similar turbulent jet is fundamentally different from its spatially developing namesake because the former conserves volume flux and has zero cross-stream mean flow velocity whereas the latter conserves momentum flux and does not have zero cross-stream mean flow velocity. It follows that, irrespective of the turbulent dissipation's power-law scalings, the time-local Reynolds number remains constant, and the jet half-width $\delta$ , the Kolmogorov length $\eta$ and the Taylor length $\lambda$ grow identically as the square root of time during the temporally developing self-similar planar jet's evolution. We predict theoretically and confirm numerically by direct numerical simulations that the mean centreline velocity, the Kolmogorov velocity and the mean propagation speed of the turbulent/non-turbulent interface (TNTI) of this planar jet decay identically as the inverse square root of time. The TNTI has an inner structure over a wide range of closely spatially packed iso-enstrophy surfaces with fractal dimensions that are well defined over a range of scales between $\lambda$ and $\delta$ , and that decrease with decreasing iso-enstrophy towards values close to $2$ at the viscous superlayer. The smallest scale on these isosurfaces is approximately $\eta$ , and the length scales between $\eta$ and $\lambda$ contribute significantly to the surface area of the iso-enstrophy surfaces without being characterised by a well-defined fractal dimension. A simple model is sketched for the mean propagation speeds of the iso-enstrophy surfaces within the TNTI of temporally developing self-similar turbulent planar jets. This model is based on a generalised Corrsin length, on the multiscale geometrical properties of the TNTI, and on a proportionality between the turbulent jet volume's growth rate and the growth rate of $\delta$ . A prediction of this model is that the mean propagation speed at the outer edge of the viscous superlayer is proportional to the Kolmogorov velocity multiplied by the $1/4$ th power of the global Reynolds number.

Visualization of the rotational and irrotational motions in a temporally evolving turbulent plane jet

Visualization of the rotational and irrotational motions in a temporally evolving turbulent plane jet

Comparison of Turbulence Models in Simulation of Plane Jet Flow

Plane turbulent jets are widely used in a variety of applications. Such as jets in drying processes, air curtains for room conditioning, heating, mixing, ventilating applications etc., therefore, jet flow is a very important research topic in both experimental and analytical research.
 Depending upon the position and forces acts on the jet, jets are broadly classified as turbulent free jet and turbulent wall jet. The studies conducted herein provide the comparison between various turbulence model present Computational Fluid Dynamics(CFD). Numerical approaches were used in the present investigation. CFD technique helped to understand better the hydrodynamics of the jet flow and correlate the numerical result.
 Among the all turbulence model studied, the k-ε turbulence model performed the best. Performance of k-ω model was found to be somewhat superior to Spalart-Allmaras and Reynolds stress model.

Comparison of the mean flow and turbulence characteristics of a single offset jet and a dual offset jet

This study compares the mean flow characteristics of a dual offset jet, comprising two 2-dimensional or plane turbulent offset jets, to a single offset jet. An in-house computational model is used to solve the incompressible form of the governing equations which are based on the standard k−ϵ Reynolds Averaged Navier–Stokes turbulence model. The offset ratio, defined as the vertical distance from the solid wall to the jet centreline divided by the nozzle width, of the upper jet is varied from 7 to 13, while the same for the lower jet is equal to 3. The jets’ inlet Reynolds number is 10,000 with a turbulence intensity of 5%. The mean flow results reveal that the presence of the second offset jet greatly influences the flow patterns compared to those of the single offset jet, although at some distance downstream of the inlet, the flow fields of both jet configurations resemble that of a classical wall jet. A single recirculation zone is formed underneath the single offset jet, whereas the flow field of the dual offset jet comprises two recirculation zones, one below the lower jet and the other between the two jets. In the pre-impingement region, the dual offset jet experiences a more rapid decay of the jet half width as compared to the single offset jet; however, the rate of growth of the jet half width for the single offset jet is faster than the dual offset jet. The self-similar solutions confirm that the dual offset jet begins to preserve self-similar characteristics for the mean flow field at a downstream distance greater than that for the single offset jet. For a given offset ratio, the total momentum flux for the single offset jet is found to be greater than that for the dual offset jet. Furthermore, the turbulent Reynolds stresses in the neighbourhood of the merging point are greater for the dual offset jet, but near the reattachment point, they are greater for the single offset jet. No self-similar characteristic of turbulence Reynolds stresses is obtained for both the jets. The turbulent kinetic energy budget reveals the highest value of the production term in the outer shear layer of the lower offset jet for the dual offset jet, which is greater than that for the single offset jet.

Implicit large-eddy simulation of turbulent plane jet at Re = 104

In this study, implicit large-eddy simulations (ILESs) are performed for a turbulent plane jet at a Reynolds number 104 to assess the capability of ILESs in simulating turbulent transport in free shear flows. To investigate the effect of resolved turbulent scales on the self-similar behavior of the plane jet, ILESs are conducted using fifth- (ILES+P5), seventh- (ILES+P7), and ninth-order polynomial (ILES+P9) interpolation methods, as well as the third-order MUSCL method (ILES+M3). ILES+P5, ILES+P7, and ILES+P9 reproduced the results of the direct numerical simulation (DNS) for a plane jet at Re = 104. The resolution of the power spectral density of ILESs with high-order interpolation schemes, which agrees well with the DNS, increases as the order of spatial accuracy increases and resolves more than 80% of the total energy. Hence, we conclude that the spatial resolution to resolve up to the frequency region that contains approximately 80% of the turbulent energy is required to obtain good agreement with the results of DNS, which is widely accepted in LES with the subgrid-scale (SGS) model and is also valid for ILES.

Air curtains: validation of results from small-scale laboratory waterbath experiments by real-scale measurements in climate chambers and numerical simulations

An air curtain is a planar turbulent air jet, which is used to separate two zones maintained at different temperatures. One of the aims of using an air curtain in the doorway of a building is to minimise the heat losses from the warm room to the cold environment and thus, to save energy. It is important to know how well an air curtain performs in a given operating scenario in order to assess its energy saving potential. In recent literature, it was proposed to use the waterbath experimental technique as a quick and inexpensive tool for testing the performance of an air curtain in a given scenario. The first central objective of the present study is to validate whether results obtained from small-scale waterbath experiments (WB) are adequate to describe the performance of a real-scale air curtain. To this end, we selected scenarios previously investigated by means of WB experiments and conducted real-scale measurements (RS) with a commercially available air curtain device (ACD) in a climate chamber, and RANS numerical simulations (NS) reproducing the configuration of the ACD in the climate chamber. These scenarios include (I) the base case of a downwards discharging air curtain when the doorway is the only connection between the two rooms, (II) the case when there is an additional top-level ventilation pathway between the rooms as well as (III) the case of a downwards blowing heated air curtain when the rooms are again joined only by the doorway. The second main goal of the present study is to verify the previously developed theoretical models for scenarios (II) and (III) by real-scale measurements and numerical simulations. As the main results, we establish that the effectiveness curves for an ACD obtained from WB experiments on the one hand as well as RS and NS measurements on the other exhibit the same general trends but also possess some minor differences for which we offer possible explanations. Furthermore, we find that RS and NS data are very well described by the previously proposed theoretical models in scenarios (II) and (III). The main finding of the present study is that the waterbath technique can be used as a reliable investigation tool to assess the general trends of the performance of an ACD in a given scenario but should be complemented by a small amount of RS or NS measurements if the finer details are important.

Direct numerical simulation of planar turbulent jets: Effect of a pintle orifice

The effects of a pintle-shaped orifice on a planar turbulent jet flow at Reynolds number 4000, based on the inlet bulk mean velocity and the jet width, are studied using direct numerical simulations. Flapping of the jet along with a low-frequency modulation of the Kelvin–Helmholtz (KH) instability, in the presence of a pintle-shaped orifice, is observed. To compare the pintle-jet behavior, a free-jet is simulated as a reference case. The effects of the near-field region on the far-field flow characteristics have been investigated. In both the cases, the KH instability in the near-field influences the far-field jet, whereas the pintle-jet also exhibits a low-frequency flapping. In addition, oblique vortex pattern has been observed in the case of pintle-jet. The far-field flow statistics of the pintle-jet with a top-hat inlet interestingly agree with those of the free-jet with a hyperbolic tangent inlet. Temporal variation of the jet characteristics has been analyzed using spatiotemporal plots. In addition, the large- and small-scale turbulent motion have been studied using three anisotropic invariant maps (turbulence triangles, eigenvalue, and barycentric maps). Moreover, that the barycentric map gives a better visualization of the anisotropic behavior has been observed in the current study.

Effect of corrugated side-walls on plane turbulent wall jets in narrow channels

An experimental study is presented to investigate the effect of corrugated sidewalls on submerged wall jets in narrow channels. Experiments were performed in a flume 0.3 m wide, 0.5 m deep, and 13.5 m long. Jets issued under the gate with a fixed thickness of 2.5 cm and the tailwater depth was adjusted to 37.5 cm, giving a fixed tailwater depth ratio yt/bo = 15. Experiments were conducted for five slot Froude numbers 2, 3, 4. 5, and 6. The Reynolds number ranged between 24712 and 74136. Three sets of experiments of five runs each, were performed. In Set A, the experiments were performed with smooth sidewalls whereas in Sets B and C, two arrangements of corrugated sidewalls (with gaps and with no gaps) were used, respectively. Velocity profiles along the centerline of the flume, water surface profile and the eddy length were measured for each experiment. It was found that the corrugations with gaps caused the largest decay in the maximum velocity; however, the effect of the presence of the sidewall corrugations on the velocity decay diminishes with the Froude number. Furthermore, the corrugated sidewalls with no gaps were observed to induce more flow entrainment and therefore cause a steep increase in the jet discharge and momentum flux near the slot. However, the corrugated sidewalls with gaps induced more mixing and diffusion, farther downstream from the slot, and caused a faster decay in the jet discharge and momentum. The use of corrugated sidewalls is introduced in this study as an alternative technique, to corrugated beds, to be used for energy dissipation in narrow channels. The sidewall corrugations are easier to maintain as less debris/sediments are trapped in between the corrugations. In addition, if channel maintenance is required, the movement of the maintenance facilities on a smooth bed would be much easier than that on a corrugated bed. Moreover, the sidewall corrugations will not be damaged during the maintenance process.

Turbulent planar wakes of viscoelastic fluids analysed by direct numerical simulations

Direct numerical simulations employing the finitely extensible nonlinear elastic constitutive model closed with Peterlin's approximation (FENE-P) are used to investigate the far-field region of turbulent planar wakes of viscoelastic fluids and to develop the theory describing these flows. The theoretical results display excellent agreement with the simulations and provide new scaling laws for the evolution of the shear layer thickness $\delta (x) \sim x^{1/2}$ , mean velocity deficit ${\rm \Delta} U(x) \sim x^{-1/2}$ and, for very high Deborah numbers, of the maximum polymer shear stresses $\sigma ^{[p]}_c(x) \sim x^{-2}$ and averaged polymer chain extension $\textrm {tr}(\bar {C}(x) - \boldsymbol{\mathsf{I}}) \sim x^{-2}$ , where $x$ is the streamwise distance from the solid body generating the wake. The theory is able to show the existence of self-similarity for the profiles of mean velocity, mean polymer shear stress, averaged polymer chain extension and the conditions for similarity of the turbulent shear stress, and is very well supported by the numerical simulations. Similarly to the case of viscoelastic turbulent planar jets (Guimarães et al., J. Fluid Mech., vol. 899, 2020, p. A11), when the inlet Weissenberg and Deborah numbers are sufficiently large, turbulent viscoelastic wakes exhibit a considerable reduction of the spreading rate and of the normalised Reynolds stresses. However, for very large downstream locations the turbulent viscoelastic wake recovers the classical evolution laws observed for Newtonian turbulent planar wakes.

Evaluation of entropy driven jet symmetry transitions

Here we determine whether entropy drives planar turbulent jets into round turbulent jets. Determining when a jet flow transitions from one symmetry to the next is an important but incompletely resolved problem. The constructal view argues that the transition between symmetries of jet flows is governed by the minimization or maximization of entropy. Here we explore whether entropy increases with the transition of a planar turbulent jet into a round turbulent jet and whether entropy maximization (or minimization) predicts the same location of symmetry transition as velocity matching. We find that entropy considerations presented do not predict this transition.