Direct numerical simulation is used to study a turbulent plane wall-jet including the mixing of a passive scalar. The Reynolds and Mach numbers at the inlet are Re=2000 and M=0.5, respectively, and a constant coflow of 10% of the inlet jet velocity is used. The passive scalar is added at the inlet enabling an investigation of the wall-jet mixing. The self-similarity of the inner and outer shear layers is studied by applying inner and outer scaling. The characteristics of the wall-jet are compared to what is reported for other canonical shear flows. In the inner part, the wall-jet is found to closely resemble a zero pressure gradient boundary layer, and the outer layer is found to resemble a free plane jet. The downstream growth rate of the scalar is approximately equal to that of the streamwise velocity in terms of the growth rate of the half-widths. The scalar fluxes in the streamwise and wall-normal direction are found to be of comparable magnitude. The scalar mixing situation is further studied by evaluating the scalar dissipation rate and the mechanical to mixing time scale ratio.
Direct numerical simulations of plane turbulent nonisothermal wall jets are performed and compared to the isothermal case. This study concerns a cold jet in a warm coflow with an ambient to jet density ratio of ρa/ρj = 0.4, and a warm jet in a cold coflow with a density ratio of ρa/ρj = 1.7. The coflow and wall temperature are equal and a temperature dependent viscosity according to Sutherland’s law is used. The inlet Reynolds and Mach numbers are equal in all these cases. The influence of the varying temperature on the development and jet growth is studied as well as turbulence and scalar statistics. The varying density affects the turbulence structures of the jets. Smaller turbulence scales are present in the warm jet than in the isothermal and cold jet and consequently the scale separation between the inner and outer shear layer is larger. In addition, a cold jet in a warm coflow at a higher inlet Reynolds number was also simulated. Although the domain length is somewhat limited, the growth rate and the turbulence statistics indicate approximate self-similarity in the fully turbulent region. The use of van Driest scaling leads to a collapse of all mean velocity profiles in the near-wall region. Taking into account the varying density by using semilocal scaling of turbulent stresses and fluctuations does not completely eliminate differences, indicating the influence of mean density variations on normalized turbulence statistics. Temperature and passive scalar dissipation rates and time scales have been computed since these are important for combustion models. Except for very near the wall, the dissipation time scales are rather similar in all cases and fairly constant in the outer region.
In this study, we investigate the flow and aeroacoustics of twin square (i.e., aspect ratio of 1.0) jets by implicit large-eddy simulations (LESs) under a nozzle pressure ratio of 3.0 and a temperature ratio of 1.0 conditions. A second-order central scheme coupled with a modified Jameson's artificial dissipation is used to resolve acoustics as well as to capture discontinuous solutions, e.g., shock waves. The flow boundary layer inside of the nozzle is tripped, using a small step in the convergent section of the nozzle. The time-averaged axial velocity and turbulent kinetic energy of LES with boundary layer tripping approaches better to particle image velocimetry experimental data than the LES without turbulence tripping case. A two-point space–time cross-correlation analysis suggests that the twin jets are screeching and are coupled to each other in a symmetrical flapping mode. Intense pressure fluctuations and standing waves are observed between the jets. Spectral proper orthogonal decomposition (SPOD) confirms the determined mode and the relevant wave propagation. The upstream propagating mode associated with the shock-cell structures is confined inside jets. Far-field noise obtained by solving Ffowcs Williams and Hawkings equation is in good agreement with the measured acoustic data. The symmetrical flapping mode of twin jets yields different levels of the screech tone depending on observation planes. The tonalities—the fundamental tone, second and third harmonics—appear clearly in the far-field, showing different contributions at angles corresponding to the directivities revealed by SPOD.
We investigate the behavior of a fluid near the critical point by using numerical simulations of weakly compressible three-dimensional isotropic turbulence. Much has been done for a turbulent flow with an ideal gas. The primary focus of this work is to analyze fluctuations of thermodynamic variables (pressure, density, and temperature) when a non-ideal Equation Of State (EOS) is considered. In order to do so, a hybrid lattice Boltzmann scheme is applied to solve the momentum and energy equations. Previously unreported phenomena are revealed as the temperature approaches the critical point. Fluctuations in pressure, density, and temperature increase, followed by changes in their respective probability density functions. Due to the non-linearity of the EOS, it is seen that variances of density and temperature and their respective covariance are equally important close to the critical point. Unlike the ideal EOS case, significant differences in the thermodynamic properties are also observed when the Reynolds number is increased. We also address issues related to the spectral behavior and scaling of density, pressure, temperature, and kinetic energy.
We investigate the behavior of a uid near the critical point by using numerical simulations of weakly compressible three-dimensional isotropic turbulence. Much has been done for a turbulent ow with an ideal gas. The primary focus of this work is to analyze uctuations of thermodynamic variables (pressure, density and temperature) when a non-ideal Equation Of State (EOS) is considered. In order to do so, a hybrid lattice Boltzmann scheme is applied to solve the momentum and energy equations. Previously unreported phenomena are revealed as the temperature approaches the critical point. These phenomena include increased uctuations in pressure, density and temperature, followed by changes in their respective probability density functions (PDFs). Unlike the ideal EOS case, signicant dierences in the thermodynamic properties are also observed when the Reynolds number is increased. We also address issues related to the spectral behavior and scaling of density, pressure, temperature and kinetic energy.
One recent focus of experimental studies of turbulence in high Reynolds number wall-bounded flows has been the scaling of the root mean square of the fluctuating streamwise velocity, but progress has largely been impaired by spatial resolution effects of hot-wire sensors. For the near-wall peak, recent results seem to have clarified the controversy; however, one of the remaining issues in this respect is the emergence of a second (so-called outer) peak at high Reynolds numbers. The present letter introduces a new scaling of the local turbulence intensity profile, based on the diagnostic plot by Alfredsson and Orlu [Eur. J. Mech. B/Fluids 42, 403 (2010)], which predicts the location and amplitude of the "outer" peak and suggests its presence as a question of sufficiently large scale separation.
The present paper focuses on the linear spatial instability of a viscous two-dimensional liquid sheet bounded by two identical viscous gas streams. The Orr–Sommerfeld differential equations and the boundary conditions of the flow configuration are numerically solved using Chebyshev series expansions and the collocation method. The strong dependence of the instability parameters on the velocity profiles is proven by using both quadratic and error functions to define the base flow in the liquid sheet and the gas shear layer. The sensitivity of the spatial instability growth rate to changes in the dimensionless parameters of the problem is assessed. Regarding the liquid sheet Reynolds number, it has been observed that, when this parameter increases, both the most unstable growth rate and the corresponding wavenumber decrease, whereas the cutoff wavenumber increases. The results of this analysis are compared with temporal theory through Gaster transformation. The effects liquid and gas viscosity have on instability are studied by comparing the instability curves given by the presented model with those from an inviscid liquid sheet and a viscous liquid sheet in an inviscid gaseous medium. The model presented in this paper features a variation in the cutoff wavenumber with all the governing parameters of the problem, whereas that provided by cases that account for an inviscid surrounding gas depends only on the liquid sheet Weber number and the ratio of gas to liquid densities. Results provided by the presented model have been experimentally validated and show that quadratic profiles have a greater capacity to predict the disturbance wavelength.
Thixo-elasto-viscoplastic (TEVP) fluids are very complex fluids. In addition to elasticity and viscoplasticity, they exhibit thixotropy, i.e., time-dependent rheology due to breakdown and recovery of internal structures at different length- and timescales. General and consistent methods for a priori flow prediction of TEVP fluids based on rheological characteristics are yet to be developed. We report a combined study of the rheology and flow of 18 samples of different TEVP fluids (three yogurts and three concentrations of Laponite and Carbopol, respectively, in water in both the unstirred and a stirred state). The rheology is determined both with standard protocols and with an ex situ protocol aiming at reproducing the shear history of the fluid in the flow. Micrometer resolution flow measurements in a millimeter scale rectangular duct are performed with Doppler Optical Coherence Tomography (D-OCT). As expected, the results show the existence of a plug flow region for samples with sufficiently high yield stress. At low flow rates, the plug extends almost all the way to the wall and the extent of the plug decreases not only with increased flow rate but also with increased thixotropy. The ex situ rheology protocol enables estimation of the shear rate and shear stress close to the wall, making it possible to identify two scaling laws that relates four different non-dimensional groups quantifying the key properties wall-shear stress and slip velocity. The scaling laws are suggested as an ansatz for a priori prediction of the near-wall flow of TEVP fluids based on shear flow-curves obtained with a rheometer.
Given the recent acceptance of the central role of airborne transmission for SARS-CoV-2, increased attention has been paid to the dispersion of respiratory droplets in different scenarios. Studies including numerical simulations have been conducted on methods for breaking the chains of transmission. Here, we present the first such study on the impact of body position while coughing on the dispersion of respiratory droplets. Four scenarios are examined, including normal standing, bending the head at different angles, coughing into the elbow in still air, and a gentle breeze from the front and behind. The model showed that an uncovered cough is dangerous and causes many droplets to enter the environment, posing a cross-contamination threat to the others. Droplets with an initial diameter smaller than 62.5 mu m remain suspended in windless air for more than 3 min. In the presence of wind, these droplets move with the wind flow and may travel long distances greater than 3.5 m. The model showed that covering the mouth with the elbow while coughing is clearly the best strategy for reducing airborne transmission of exhaled pathogens. About 62% of the initial number of droplets deposit on the cougher's elbow immediately after the cough and have no chance of spreading through the air in both windless and windy conditions. Covering the cough in windless or light breeze conditions also causes the upward thermal plume around the body to expel many small droplets.
A semi-conservative, stable, interphase-capturing numerical scheme for shock propagation in heterogeneous systems is applied to the problem of shock propagation in liquid-gas systems. The scheme is based on the volume-fraction formulation of the equations of motion for liquid and gas phases with separate equations of state. The semi-conservative formulation of the governing equations ensures the absence of spurious pressure oscillations at the material interphases between liquid and gas. Interaction of a planar shock in water with a single spherical bubble as well as twin adjacent bubbles is investigated. Several stages of the interaction process are considered, including focusing of the transmitted shock within the deformed bubble, creation of a water-hammer shock as well as generation of high-speed liquid jet in the later stages of the process.
A supersonic jet of Mach number M = 4.5 in air is produced experimentally at the apex of a miniature 150 x 50 x 5 mm converging section with a 2 x 5 mm opening by the principle of blast wave amplification through focusing. An initial plane blast wave of M = 2.4 in the convergence section is generated by the exploding wire technique. The profile of the convergence section is specially tailored to smoothly transform a plane blast wave into a perfectly cylindrical arc, imploding at the apex of the section. The cylindrical form of the imploding shock delivers maximum shock amplification in the two-dimensional test section and maximum subsequent jet flow velocity behind the shock front. Blast wave propagation in the convergence chamber as well as jet generation through a 2 mm opening at the apex into the adjacent exhaust chamber is optically captured by a high-speed camera using the shadowgraph method. Visualizing the flow provided a distinct advantage not only for obtaining detailed information on the flow characteristics but also for validating the numerical scheme which further enhanced the analysis. Experimental images together with the numerical analysis deliver detailed information on the blast wave propagation and focusing as well as subsequent jet initiation and development. One of the main advantages of the described method apart from being simple and robust is the effective focusing of low initial input energy levels of just around 500 Joules, resulting in production of supersonic jets in a small confined chamber.
Many fluid flows, such as bluff body wakes, exhibit stable self-sustained oscillations for a wide range of parameters. Here we study the effect of weak noise on such flows. In the presence of noise, a flow with self-sustained oscillations is characterized not only by its period, but also by the quality factor. This measure gives an estimation of the number of oscillations over which periodicity is maintained. Using a recent theory [P. Gaspard, J. Stat. Phys. 106, 57 (2002)], we report on two observations. First, for weak noise the quality factor can be approximated using a linear Floquet analysis of the deterministic system; its size is inversely proportional to the inner-product between first direct and adjoint Floquet vectors. Second, the quality factor can readily be observed from the spectrum of evolution operators. This has consequences for Koopman/Dynamic mode decomposition analyses, which extract coherent structures associated with different frequencies from numerical or experimental flows. In particular, the presence of noise induces a damping on the eigenvalues, which increases quadratically with the frequency and linearly with the noise amplitude. (C) 2014 AIP Publishing LLC.
The stabilizing effect of finite amplitude streaks on the linear growth of unstable perturbations [Tollmien-Schlichting (TS) and oblique waves] is numerically investigated by means of the nonlinear parabolized stability equations. We have found that for stabilization of a TS-wave, there exists an optimal spanwise spacing of the streaks. These streaks reach their maximum amplitudes close to the first neutral point of the TS-wave and induce the largest distortion of the mean flow in the unstable region of the TS-wave. For such a distribution, the required streak amplitude for complete stabilization of a given TS-wave is considerably lower than for beta=0.45, which is the optimal for streak growth and used in previous studies. We have also observed a damping effect of streaks on the growth rate of oblique waves in Blasius boundary layer and for TS-waves in Falkner-Skan boundary layers.
This paper presents a self-consistent model of electrohydrodynamic (EHD) laminar plumes produced by electron injection from ultra-sharp needle tips in cyclohexane. Since the density of electrons injected into the liquid is well described by the Fowler-Nordheim field emission theory, the injection law is not assumed. Furthermore, the generation of electrons in cyclohexane and their conversion into negative ions is included in the analysis. Detailed steady-state characteristics of EHD plumes under weak injection and space-charge limited injection are studied. It is found that the plume characteristics far from both electrodes and under weak injection can be accurately described with an asymptotic simplified solution proposed by Vazquez et al. ["Dynamics of electrohydrodynamic laminar plumes: Scaling analysis and integral model," Phys. Fluids 12, 2809 (2000)] when the correct longitudinal electric field distribution and liquid velocity radial profile are used as input. However, this asymptotic solution deviates from the self-consistently calculated plume parameters under space-charge limited injection since it neglects the radial variations of the electric field produced by a high-density charged core. In addition, no significant differences in the model estimates of the plume are found when the simulations are obtained either with the finite element method or with a diffusion-free particle method. It is shown that the model also enables the calculation of the current-voltage characteristic of EHD laminar plumes produced by electron field emission, with good agreement with measured values reported in the literature.
We analyze the effects of different types and positions of actuators and sensors on controllers' performance and robustness in the linearized 2D Blasius boundary layer. The investigation is carried out using direct numerical simulations (DNS). To facilitate controller design, we find reduced-order models from the DNS data using a system identification procedure called the Eigensystem Realization Algorithm. Due to the highly convective nature of the boundary layer and corresponding time delays, the relative position of the actuator and sensor has a strong influence on the closed-loop dynamics. We address this issue by considering two different configurations. When the sensor is upstream of the actuator, corresponding to disturbance-feedforward control, good performance is observed, as in previous work. However, feedforward control can be degraded by additional disturbances or uncertainties in the plant model, and we demonstrate this. We then examine feedback controllers in which the sensor is a short distance downstream of the actuator. Sensors farther downstream of the actuator cause inherent time delays that limit achievable performance. The performance of the resulting feedback controllers depends strongly on the form of actuation introduced, the quantities sensed, and the observability of the structures deformed by the controller's action. These aspects are addressed by varying the spatial distribution of actuator and sensor. We find an actuator-sensor pair that is well-suited for feedback control, and demonstrate that it has good performance and robustness, even in the presence of unmodeled disturbances.
The force acting on a spinning sphere moving in a rarefied gas is calculated. It is found to have three contributions with different directions. The transversal contribution is of opposite direction compared to the so-called Magnus force normally exerted on a sphere by a dense gas. It is given by F=-alpha(tau)xi2/3piR(3)mnomegaxv, where alpha(tau) is the accommodation coefficient of tangential momentum, R is the radius of the sphere, m is the mass of a gas molecule, n is the number density of the surrounding gas, omega is the angular velocity, and v is the velocity of the center of the sphere relative to the gas. The dimensionless factor xi is close to unity, but depends on omega and kappa, the heat conductivity of the body.
Extensive combined experimental and theoretical investigations of the linear evolution of three-dimensional (3D) Tollmien-Schlichting (TS) instability modes of 3D boundary layers developing on a swept airfoil section have been carried out. The flow under consideration is the boundary layer over an airfoil at 350 sweep and an angle of attack of +1.5 degrees. At these conditions, TS instability is found to be the predominant one. Perturbations with different frequencies and spanwise wavenumbers are generated in a controlled way using a row of elastic membranes. All experimental results are deeply processed and compared with results of calculations based on theoretical approaches. Very good quantitative agreement of all measured and calculated stability characteristics of swept-wing boundary layers is achieved.
Extensive combined experimental and theoretical investigations of the linear evolution of unsteady (in general) Cross-Flow (CF) and three-dimensional (3D) Tollmien-Schlichting (TS) instability modes of 3D boundary layers developing on a swept airfoil section have been carried out. CF-instability characteristics are investigated in detail at an angle of attack of -5 degrees when this kind of instability dominates in the laminar-turbulent transition process, while the 3D TS-instability characteristics are studied at an angle of attack of +1.5 degrees when this kind of instability is predominant in the transition process. All experimental results are deeply processed and compared with results of calculations based on several theoretical approaches. For the first time, very good quantitative agreement of all measured and calculated stability characteristics of swept-wing boundary layers is achieved both for unsteady CF- and 3D TS-instability modes for the case of a boundary layer developing on a real swept airfoil. The first part of the present study (this paper) is devoted to the description of the case of CF-dominated transition, while the TS-dominated case will be described in detail in a subsequent second part of this investigation.
Radiation transport plays an important role in stellar atmospheres, but the effects of turbulence are being obscured by other effects such as stratification. Using radiative hydrodynamic simulations of forced turbulence, we determine the decay rates of sinusoidal large-scale temperature perturbations of different wavenumbers in the optically thick and thin regimes. Increasing the wavenumber increases the rate of decay in both regimes, but this effect is much weaker than for the usual turbulent diffusion of passive scalars, where the increase is quadratic for small wavenumbers. The turbulent decay is well described by an enhanced Newtonian cooling process in the optically thin limit, which is found to show a weak increase proportional to the square root of the wavenumber. In the optically thick limit, the increase in turbulent decay is somewhat steeper for wavenumbers below the energy-carrying wavenumber of the turbulence, but levels off toward larger wavenumbers. In the presence of turbulence, the typical cooling time is comparable to the turbulent turnover time. We observe that the temperature takes a long time to reach equilibrium in both the optically thin and thick cases, but in the former, the temperature retains smaller scale structures for longer.
The objective of this paper is to show that the interaction of streamwise velocity streaks of finite length can lead to turbulent breakdown in the flat-plate boundary layer flow. The work is motivated by previous numerical and experimental studies of transitional flows where the high-frequency oscillations leading to turbulence are seen to form in the region of strongest shear induced by streaks in relative motion. Therefore, a model for the interaction of steady and unsteady (i.e., slowly moving in the spanwise direction) spanwise periodic streaks is proposed. The interaction of two subsequent streaks is investigated for varying collision parameters. In particular, the relative spanwise position and angle are considered. The results show that the interaction is able to produce both a symmetric and asymmetric breakdown without the need for additional random noise from the main stream. Velocity structures characteristic of both scenarios are analyzed. Hairpin and A vortices are found in the case of symmetric collision between a low-speed region and an incoming high-speed streak, when a region of strong wall-normal shear is induced. Alternatively, when the incoming high-momentum fluid is misaligned with the low-speed streak in front, single quasi-streamwise vortices are identified. Despite the different symmetry at the breakdown, the detrimental interaction involves for both cases the tail of a low-speed region and the head of a high-speed streak. Further, the breakdown appears in both scenarios as an instability of three-dimensional shear layers formed between the two streaks. The streak interaction scenario is suggested to be of relevance for turbulence production in wall-bounded flows.
The intent of the present paper is to study the receptivity of a zero pressure gradient boundary layer to free-stream disturbances with the aim to isolate the essential features involved in the generation of streamwise streaks. A weakly nonlinear formulation based on a perturbation expansion in the amplitude of the disturbance truncated at second order is used. It is shown that the perturbation model provide an efficient tool able to disentangle the sequence of events in the receptivity process. Two types of solutions are investigated: the first case amounts to the receptivity to oblique waves generated by a wave-like external forcing term oscillating in the free stream, the second the receptivity to free-stream turbulence-like disturbances, represented as a superposition of modes of the continuous spectrum of the Orr-Sommerfeld and Squire operators. A scaling property of the governing equations with the Reynolds number is also shown to be valid. The relation between this nonlinear receptivity process and previously investigated linear ones is also discussed.
We report experiments on control of thermocapillary instabilities at high temperature differences, in an annular geometry. Previous studies [Phys. Fluids 14, 3039 (2002)] showed that a reasonable control of oscillatory instability could be achieved by optimizing a local heating feedback process. We conducted experiments with a basic flow converging from periphery to center. This constitutes a more unstable configuration than previously, and enables appearance of higher-order instabilities and chaos. Applying successfully local feedback control to the periodic state close to the threshold, we extend the process to higher temperature differences, where nonlinear as well as proportional/derivative control laws are necessary to obtain a significant decrease of the temperature fluctuations. Finally, proportional control allows us to synchronize a chaotic state, to a periodic one.
The hydrodynamic interaction of two neutrally buoyant porous aggregates is investigated under creeping flow conditions for the case where the undisturbed velocity of the surrounding flow field is a linear function of position. In this framework, the relative velocity between two aggregates is given by the deformation of the undisturbed flow expressed through the rate of strain and the angular velocity of the flow field, and by two flow-independent hydrodynamic functions, typically referred to as A and B, which account for the disturbance of the flow field due to the presence of the particles [G. K. Batchelor and J. T. Green, J. Fluid Mech. 56, 375 (1972)]. In the present paper, the analysis of thehydrodynamic interaction that is known for the case of two impermeable, solid particles is extended to the case of porous aggregates by applying Brinkman's equation to describe the flow within the aggregates. A reflection scheme is applied to calculate A and B and the obtained expressions are applied to interpret the orthokinetic aggregation ofaggregates in diluted suspensions, where the collision frequency is computed using the method of relative trajectories of a pair of aggregates.
We study the effect of droplet coalescence on turbulent wall-bounded flows by means of direct numerical simulations. In particular, the volume-of-fluid and front-tracking methods are used to simulate turbulent channel flows containing coalescing and non-coalescing droplets, respectively. We find that coalescing droplets have a negligible effect on the drag, whereas the non-coalescing ones steadily increase drag as the volume fraction of the dispersed phase increases: indeed, at 10% volume fraction, the non-coalescing droplets show a 30% increase in drag, whereas the coalescing droplets show less than 4% increase. We explain this by looking at the wall-normal location of droplets in the channel and show that non-coalescing droplets enter the viscous sublayer, generating an interfacial shear stress, which reduces the budget for viscous stress in the channel. On the other hand, coalescing droplets migrate toward the bulk of the channel forming large aggregates, which hardly affect the viscous shear stress while damping the Reynolds shear stress. We prove this by relating the mean viscous shear stress integrated in the wall-normal direction to the centerline velocity.
In this paper we present simulations of dynamic wetting far from equilibrium based on phase field theory. In direct simulations of recent experiments [J. C. Bird, S. Mandre, and H. A. Stone, Phys. Rev. Lett. 100, 234501 (2008)], we show that in order to correctly capture the dynamics of rapid wetting, it is crucial to account for nonequilibrium at the contact line, where the gas, liquid, and solid meet. A term in the boundary condition at the solid surface that naturally arises in the phase field theory is interpreted as allowing for the establishment of a local structure in the immediate vicinity of the contact line. A direct qualitative and quantitative match with experimental data of spontaneously wetting liquid droplets is shown.
Turbulent flow through 90 degrees pipe bends, for four different curvatures, has been investigated using large eddy simulations. In particular, the origin of the so-called swirl switching phenomenon, which is a large scale oscillation of the flow after the bend, has been studied for different bend curvature ratios. A classification of the phenomenon into a high and a low frequency switching, with two distinct physical origins, is proposed. While the high frequency switching stems from modes formed at the bend, and becomes increasingly important for sharp curvatures, the low frequency switching originates from very-large-scale motions created in the upstream pipe flow.
A computational study based on well-resolved large-eddy simulations is performed to study the skin friction modification by a large-eddy breakup device (LEBU) in a zero-pressure-gradient turbulent boundary layer. The LEBU was modeled using an immersed boundary method. It is observed that the presence of the device leads to the generation of wake vortices, which propagate downstream from the LEBU and toward the wall. A skin friction decomposition procedure is utilized to study different physical mechanisms of the observed skin friction reduction. From the skin friction decomposition, it is found that the skin friction reduction can be characterized by three universal regions of different changes for the skin friction contributions. The first region is predominantly associated with the formation of the wake vortices and the reduction of Reynolds shear stress. In the second region, the mean streamwise velocity fields show that a region of velocity deficit formed downstream of the LEBU propagates toward the wall and leads to turbulence reduction due to wake wall interactions, which also induces a local maximum skin friction reduction. In the third region, the dissipation of wake vortices leads to the regeneration of Reynolds shear stress. A quadrant analysis of the Reynolds shear stress contribution reveals that the LEBU increases the Q2 and Q4 contributions and attenuates the Q1 and Q3 contributions in the first region, followed by an onset of Reynolds shear stress further downstream.
The interaction of several instabilities and the influence of free-stream turbulence on laminar-turbulent transition on a 20% thick wind-turbine blade section with a laminar separation bubble (LSB) are investigated with wall-resolved large-eddy simulations (LES). Turbulence intensities (TI) of 0%, 2.2%, 4.5%, 8.6%, and 15.6% at chord Reynolds number 100,000 are considered. Linear receptivity occurs for the most energetic disturbances; high-frequency perturbations are excited via non-linear mechanisms for TI≥8.6%. Unstable Tollmien–Schlichting (TS) waves appear in the inflectional flow region for TI≤4.5%, shifting to inviscid Kelvin–Helmholtz (KH) modes upon separation and forming spanwise rolls. Sub-harmonic secondary instability occurs for TI=0%, with rolls intertwining before transition. Streaks spanwise modulate the rolls and increase their growth rates with TI for TI≤4.5%, reducing separation and shifting transition upstream. The TI=4.5% case presents the highest perturbations, leading to the smallest LSB and most upstream transition. Earlier inception of TS/KH modes occurs on low-speed streaks, inducing premature transition. However, for TI=8.6%, the effect of the streaks is to stabilize the attached mean flow and front part of the LSB. This occurs due to the near-wall momentum deficit alleviation, leading to the transition delay and larger LSB than TI=4.5%. This also suppresses separation and completely stabilizes TS/KH modes for TI=15.6%. Linear stability theory predicts well the modal evolution for TI≤8.6%. Optimal perturbation analysis accurately computes the streak development upstream of the inflectional flow region but indicates higher amplification than LES downstream due to the capture of low-frequency, oblique modal instabilities from the LSB. Only low-amplitude [ O(1%)] streaks displayed exponential growth in the LES since non-linearity precludes the appearance of these modes.
The Chew–Goldberger–Low equations are used to study the effect of pressure anisotropy on Z‐pinches operating in the collisionless regime. The limitations on the form of accessible equilibria are investigated. The effect on the m=0 instability is asessed both by means of the energy principle and by direct solution of the eigenvalue equation for a variety of anisotropicequilibria. The results indicate that in the small Larmor radius limit pressure anisotropy offers a rather slight enhancement of the linear stability of the Z‐pinch.
A complete original study of the linear temporal instability analysis of two viscous and immiscible fluids enclosed in a rigid cylinder rotating about its axis and separated by a cylindrical interface is performed for the case of higher density fluid located in the annulus. The results of the present contribution fill the lack of an overall assessment of the system behavior due to the increase of both the analytical difficulties and the number of the governing parameters when the several physical effects are all included. The analysis is carried out numerically by discretizing the equations of the evolution of disturbances separately in the two phases formulated in a rotating reference frame. Normal mode analysis leads to a generalized eigenvalue problem which is solved by means of a Chebyshev collocation spectral method. The investigation of the preferred modes of instability is carried out over wide ranges of the parameters space. The behavior of the system is physically discussed and is compared to inviscid asymptotic limits and to viscous approximate solutions of the previous literature.
In this Letter we show by numerical simulation that streamwise streaks of sufficiently large amplitude are able to stabilize Tollmien-Schlichting waves in zero pressure gradient boundary layers at least up to Re=1000. This stabilization is due to the spanwise averaged part of the nonlinear basic flow distortion induced by the streaks and occurs for streak amplitudes lower than the critical threshold beyond which secondary inflectional instability is observed. A new control strategy is implemented using optimal perturbations in order to generate the streaks.
The nonlinear stability of laminar sinuously bent streaks is studied for the plane Couette flow at Re = 500 in a nearly minimal box and for the Blasius boundary layer at Re(delta)(*)=700. The initial perturbations are nonlinearly saturated streamwise streaks of amplitude A(U) perturbed with sinuous perturbations of amplitude A(W). The local boundary of the basin of attraction of the linearly stable laminar flow is computed by bisection and projected in the A(U) - A(W) plane providing a well defined critical curve. Different streak transition scenarios are seen to correspond to different regions of the critical curve. The modal instability of the streaks is responsible for transition for A(U) = 25%-27% for the considered flows, where sinuous perturbations of amplitude below A(W) approximate to 1%-2% are sufficient to counteract the streak viscous dissipation and induce breakdown. The critical amplitude of the sinuous perturbations increases when the streamwise streak amplitude is decreased. With secondary perturbations amplitude A(W) approximate to 4%, breakdown is induced on stable streamwise streaks with A(U) approximate to 13%, following the secondary transient growth scenario first examined by Schoppa and Hussain [J. Fluid Mech. 453, 57 (2002)]. A cross-over, where the critical amplitude of the sinuous perturbation becomes larger than the amplitude of streamwise streaks, is observed for streaks of small amplitude A(U) < 5%-6%. In this case, the transition is induced by an initial transient amplification of streamwise vortices, forced by the decaying sinuous mode. This is followed by the growth of the streaks and final breakdown. The shape of the critical A(U) - A(W) curve is very similar for Couette and boundary layer flows and seems to be relatively insensitive to the nature of the edge states on the basin boundary. The shape of this critical curve indicates that the stability of streamwise streaks should always be assessed in terms of both the streak amplitude and the amplitude of spanwise velocity perturbations.
The optimal growth of perturbations to transiently growing streaks is studied in Poiseuille flow. Basic flows are generated by direct numerical simulation giving primary optimal spanwise periodic vortices of finite amplitude as the initial condition. They evolve into finite amplitude primary transiently growing streaks. Linear secondary optimal energy growth supported by these primary flows are computed using an adjoint technique which takes into full account the unsteadiness of the basic flows. Qualitative differences between primary and secondary optimal growths are found only when the primary streaks are locally unstable. For locally stable primary streaks, the secondary optimal growth has the same scalings with Reynolds number R as the primary optimal growth and the maximum growth is attained by streamwise uniform vortices, suggesting that the primary and secondary optimal growth are based on the same physical mechanisms. When the primary streaks are locally unstable the secondary optimal growth of unstable wavenumbers scale differently with R and the maximum growth is attained for streamwise nonuniform sinuous perturbations, indicating the prevalence of the inflectional instability mechanism.
We study the transport of reactive solute in a three-phase system (water-solid matrix-colloids) in natural porous media. Semianalytical (integral) solutions are derived for the first time, which can be used for computing expected concentration, mass flux, or discharge for the dissolved as well as for colloid-bounded tracer. The results are based on a few simplifying assumptions: advection-dominated transport, linear mass transfer reactions, and steady-state colloidal concentration. Derived semianalytical expressions capture the main features of colloid-facilitated transport (the reversible-equilibrium and irreversible-kinetic sorption of tracers on colloids), and are applicable for the general class of linear sorption processes on the porous matrix. Derived solutions account for spatial variability of flow and sorption parameters, which is relevant for field-scale applications. We apply the theoretical results to the transport of neptunium and plutonium, using flow and transport data from the alluvial aquifer near Yucca Mountain, Nevada. Based on the zeroth and first temporal moment, dimensionless indicators are proposed for assessing the potential impact of colloid-facilitated tracer transport in aquifers. Generic sensitivity curves show the importance of tracer-colloid kinetic rates. Even very low irreversible rates (which will generally be difficult to determine in the laboratory) may yield observable effects for sufficiently long transport times. The obtained results can be used for assessing the significance of colloid-facilitated tracer transport under field conditions, as well as for setting further constraints on relevant parameters which need to be estimated in the field.
The impact of a solid sphere on a liquid surface has challenged researchers for centuries and remains of interest today. Recently, Duez [Nat. Phys. 3, 180 (2007)] published experimental results of the splash generated when a solid sphere enters water. Interestingly, the microscopic properties of the solid surface control the nature of the macroscopic behavior of the splash. So by a change in the surface chemistry of the solid sphere, a big splash can be turned into an inconspicuous disappearance and vice versa. This problem was investigated by numerical simulations based on the Navier-Stokes equations coupled with the Cahn-Hilliard equations. This system allows us to simulate the motion of an air-water interface as a solid sphere impacts the liquid pond. The inclusion of the surface energies of the solid surface in the formulation gives a reasonably quantitative description of the dynamic wetting. Numerical results with different wetting properties and impact speed are presented and directly compared with the recent experimental results from Duez.
Subcritical transition to turbulence requires finite-amplitude perturbations. Using a nonlinear optimisation technique in a periodic computational domain, we identify the perturbations of plane Couette flow transitioning with least initial kinetic energy for Re <= 3000. We suggest a new scaling law E-c = O(Re-2.7) for the energy threshold vs. the Reynolds number, in quantitative agreement with experimental estimates for pipe flow. The route to turbulence associated with such spatially localised perturbations is analysed in detail for Re = 1500. Several known mechanisms are found to occur one after the other: Orr mechanism, oblique wave interaction, lift-up, streak bending, streak breakdown, and spanwise spreading. The phenomenon of streak breakdown is analysed in terms of leading finite-time Lyapunov exponents of the associated edge trajectory.
A dynamical system description of the transition process in shear flows with no linear instability starts with knowledge of exact coherent solutions, among them traveling waves (TWs) and relative periodic orbits (RPOs). We describe a numerical method to find such solutions in pipe flow and apply it in the vicinity of a Hopf bifurcation from a TW which looks to be especially relevant for transition. The dominant structural feature of the RPO solution is the presence of weakly modulated streaks. This RPO, like the TW from which it bifurcates, sits on the laminar-turbulent boundary separating initial conditions which lead to turbulence from those which immediately relaminarize.
The dynamics at the threshold of transition in plane Couette flow is Investigated numerically in a large spatial domain for a certain type of localized initial perturbation, for Re between 350 and 1000 The corresponding edge state is all unsteady spotlike Structure, localized in both streamwise and spanwise directions, which neither grows nor decays in size. We show that the localized nature of the edge state is numerically robust. and IS not Influenced by the size of the computational domain The edge trajectory appeals to transiently visit localized steady states This suggests that basic spatiotemporally intermittent features of transition to turbulence. such as the growth Of it turbulent spot, call be described as a dynamical system.
The dynamics of a swirl-stabilized premixed flame is studied using large eddy simulation (LES). A filtered flamelet model is used to account for the subgrid combustion. The model provides a consistent and robust reaction-diffusion expression for simulating the propagation of turbulent premixed flames correctly. The numerical results were found to be relatively insensitive to small changes in the inflow boundary conditions and to the numerical mesh employed. Furthermore, the results were found to agree well with the available experimental data both for velocity and scalar fields. In addition, unsteady flame features [i.e., precessing vortex core (PVC)] were identified and compared with experimental data. The agreement between LES results and experimental data, in terms of flame dynamics, was also good. Increasing swirl did not affect the flame strongly but a decrease of swirl number was shown to change the flame shape and suppress the PVC. The PVC and flame dynamics were studied using proper orthogonal decomposition (POD) allowing us to identify and isolate the PVC from smaller-scale turbulence. The POD results indicate that the PVC corresponds to a helical wave consisting of two counter-rotating helices. A dynamical reduced model was also derived do describe the flame response to the PVC.
We derive an effective equation of motion for the orientational dynamics of a neutrally buoyant spheroid suspended in a simple shear flow, valid for arbitrary particle aspect ratios and to linear order in the shear Reynolds number. We show how inertial effects lift the degeneracy of the Jeffery orbits and determine the stabilities of the log-rolling and tumbling orbits at infinitesimal shear Reynolds numbers. For prolate spheroids, we find stable tumbling in the shear plane and log-rolling is unstable. For oblate spheroids, by contrast, log-rolling is stable and tumbling is unstable provided that the particle is not too disk-like (moderate asphericity). For very flat oblate spheroids, both log-rolling and tumbling are stable, separated by an unstable limit cycle.
The present work presents a number of parallel and spatially developing simulations of boundary layers to address the question of whether hairpin vortices are a dominant feature of near-wall turbulence, and which role they play during transition. In the first part, the parent-offspring regeneration mechanism is investigated in parallel (temporal) simulations of a single hairpin vortex introduced in a mean shear flow corresponding to either turbulent channels or boundary layers (Re-tau less than or similar to 590). The effect of a turbulent background superimposed on the mean flow is considered by using an eddy viscosity computed from resolved simulations. Tracking the vortical structure downstream, it is found that secondary hairpins are only created shortly after initialization, with all rotational structures decaying for later times. For hairpins in a clean (laminar) environment, the decay is relatively slow, while hairpins in weak turbulent environments (10% of nu(t)) dissipate after a couple of eddy turnover times. In the second part, the role of hairpin vortices in laminar-turbulent transition is studied using simulations of spatial boundary layers tripped by hairpin vortices. These vortices are generated by means of specific volumetric forces representing an ejection event, creating a synthetic turbulent boundary layer initially dominated by hairpin-like vortices. These hairpins are advected towards the wake region of the boundary layer, while a sinusoidal instability of the streaks near the wall results in rapid development of a turbulent boundary layer. For Re-theta > 400, the boundary layer is fully developed, with no evidence of hairpin vortices reaching into the wall region. The results from both the parallel and spatial simulations strongly suggest that the regeneration process is rather short-lived and may not sustain once a turbulent background is developed. From the transitional flow simulations, it is conjectured that the forest of hairpins reported in former direct numerical simulation studies is reminiscent of the transitional boundary layer and may not be connected to some aspects of the dynamics of the fully developed wall-bounded turbulence.
Physics-informed neural networks (PINNs) are successful machine-learning methods for the solution and identification of partial differential equations. We employ PINNs for solving the Reynolds-averaged Navier-Stokes equations for incompressible turbulent flows without any specific model or assumption for turbulence and by taking only the data on the domain boundaries. We first show the applicability of PINNs for solving the Navier-Stokes equations for laminar flows by solving the Falkner-Skan boundary layer. We then apply PINNs for the simulation of four turbulent flow cases, i.e., zero-pressure-gradient boundary layer, adverse-pressure-gradient boundary layer, and turbulent flows over a NACA4412 airfoil and the periodic hill. Our results show the excellent applicability of PINNs for laminar flows with strong pressure gradients, where predictions with less than 1% error can be obtained. For turbulent flows, we also obtain very good accuracy on simulation results even for the Reynolds-stress components.
The light emission from a converging shock wave was investigated experimentally. Results show that the shape of the shock wave close to the center of convergence has a large influence on the amount of emitted light. It was found that a symmetrical polygonal shock front produced more light than an asymmetrical shape. The light emission appears as the shock wave collapses. The full width at half maximum of the light pulse is about 200 ns for all geometrical shapes. It was also found that argon as a test gas produces more light than air. Numerical simulations showed good agreement with experimental results regarding the shape of the shock and the flow field behind the shock. The temperature field from the numerical simulations was investigated and shows that the triple points behind the shock front are hot spots that increase the temperature at the center as they arrive there.
We study tangling clustering instability of inertial particles in a temperature stratified turbulence with small finite correlation time. It is shown that the tangling mechanism in the temperature stratified turbulence strongly increases the degree of compressibility of particle velocity field. This results in the strong decrease of the threshold for the excitation of the tangling clustering instability even for small particles. The tangling clustering instability in the temperature stratified turbulence is essentially different from the inertial clustering instability that occurs in non-stratified isotropic and homogeneous turbulence. While the inertial clustering instability is caused by the centrifugal effect of the turbulent eddies, the mechanism of the tangling clustering instability is related to the temperature fluctuations generated by the tangling of the mean temperature gradient by the velocity fluctuations. Temperature fluctuations produce pressure fluctuations and cause particle accumulations in regions with increased instantaneous pressure. It is shown that the growth rate of the tangling clustering instability is root Re (l(0)/L-T)(2)/(3Ma)(4) times larger than that of the inertial clustering instability, where Re is the Reynolds number, Ma is the Mach number, l(0) is the integral turbulence scale, and L-T is the characteristic scale of the mean temperature variations. It is found that depending on the parameters of the turbulence and the mean temperature gradient there is a preferential particle size at which the particle clustering due to the tangling clustering instability is more effective. The particle number density inside the cluster after the saturation of this instability can be by several orders of magnitude larger than the mean particle number density. It is also demonstrated that the evaporation of droplets drastically changes the tangling clustering instability, e. g., it increases the instability threshold in the droplet radius. The tangling clustering instability is of a great importance, e. g., in atmospheric turbulence with temperature inversions.
We reconstruct the velocity field of incompressible flows given a finite set of measurements. For the spatial approximation, we introduce the Sparse Fourier divergence-free approximation based on a discrete L & nbsp;projection. Within this physics-informed type of statistical learning framework, we adaptively build a sparse set of Fourier basis functions with corresponding coefficients by solving a sequence of minimization problems where the set of basis functions is augmented greedily at each optimization problem. We regularize our minimization problems with the seminorm of the fractional Sobolev space in a Tikhonov fashion. In the Fourier setting, the incompressibility (divergence-free) constraint becomes a finite set of linear algebraic equations. We couple our spatial approximation with the truncated singular-value decomposition of the flow measurements for temporal compression. Our computational framework thus combines supervised and unsupervised learning techniques. We assess the capabilities of our method in various numerical examples arising in fluid mechanics.
Axially rotating turbulent pipe flow is an example where rotation strongly affects the turbulence and thereby the Reynolds stresses and mean flow properties. The present Letter reports new measurements where a rotating pipe flow is used to establish a swirling jet. The measurements in the jet show that at some distance downstream (approximately 6 nozzle diameters) the central part of the jet starts to rotate in the opposite direction as compared to the rotation of the pipe. This effect is explained by the influence of the cross flow Reynolds stress originating in the pipe flow.
Axially rotating turbulent pipe flow is an example in which the rotation strongly affects the turbulence, which then also influences the mean flow properties. For instance, in the fully developed flow as well, the fluid is not in solid body rotation due to the influence of the cross-stream Reynolds stress. The present paper reports new measurements from a rotating pipe flow and the streamwise mean velocity distribution is compared with recent scaling ideas of Oberlack [J. Fluid Mech. 379, 1 (1999)] and good agreement is found. A second part of the paper deals with the initial stages when the flow leaves the pipe and forms a swirling jet. The measurements in the jet show that at some distance downstream (approximately five jet diameters) the central part of the jet actually rotates in the opposite direction as compared to the rotation of the pipe. This effect is explained by the influence of the cross-stream Reynolds shear stress.
Stability of the thermodynamic equilibrium is put forward as a simple test of the validity of dynamic equations, and is applied to perpendicular gyroviscous magnetohydrodynamics (i.e., perpendicular magnetohydrodynamics with gyroviscosity added). This model turns out to be invalid because it predicts exponentially growing Alfvén waves in a spatially homogeneous static equilibrium with scalar pressure.
We study the effect of varying the mass and volume fraction of a suspension of rigid spheres dispersed in a turbulent channel flow. We performed several direct numerical simulations using an immersed boundary method for finite-size particles changing the solid to fluid density ratio R, the mass fraction χ, and the volume fraction φ. We find that varying the density ratio R between 1 and 10 at constant volume fraction does not alter the flow statistics as much as when varying the volume fraction φ at constant R and at constant mass fraction. Interestingly, the increase in overall drag found when varying the volume fraction is considerably higher than that obtained for increasing density ratios at same volume fraction. The main effect at density ratios R of the order of 10 is a strong shear-induced migration towards the centerline of the channel. When the density ratio R is further increased up to 1000, the particle dynamics decouple from that of the fluid. The solid phase behaves as a dense gas and the fluid and solid phase statistics drastically change. In this regime, the collision rate is high and dominated by the normal relative velocity among particles.