Decay Of Kinetic Energy Research Articles

Low-Noise Synthetic Turbulence Tailored to Lateral Periodic Boundary Conditions

The present work is dedicated to turbulence synthesis tailored to lateral periodic boundary conditions for direct noise computations through compressible large eddy simulations. Synthetic turbulence can be essential for aeroacoustic applications when computing airfoil turbulent inflow noise or for accurately capturing the behavior of boundary layers. This behavior determines both trailing edge noise and complex flow structures such as laminar separation bubbles. For airfoil simulation purposes, spanwise periodic boundary conditions are usually considered. If synthetic perturbations are injected without observing the periodicity rule, strong spurious pressure waves are emitted and pollute the entire computational domain. In this work, the random Fourier modes method for turbulence generation is adapted in order to respect the spanwise periodicity constraint right at the computational domain inlet. This approach does not affect the turbulence properties such as the spectral shape and the turbulent kinetic energy decay. Since the emphasis is put on the generation and convection of the turbulence, only the turbulence convection region between the inlet and the airfoil is considered in this paper, without the airfoil. Two geometrical configurations are tested: the first one is a simple box with a constant mesh size, and the second one concentrates the fine cells on the area in front of the airfoil. In the second configuration, the computational cost is reduced by up to 25%, but more spurious noise is present because of interpolation areas between different grids using the Chimera method. Finally, the results’ reproducibility is assessed using different turbulence realizations.

Gulf Stream Mean and Eddy Kinetic Energy: Three‐Dimensional Estimates From Underwater Glider Observations

AbstractThe strong, meandering, and eddy‐shedding Gulf Stream is a large oceanic reservoir of both mean and eddy kinetic energy in the northwestern Atlantic. Since 2015, underwater gliders equipped with Doppler current profilers have collected over 20,000 absolute velocity profiles in and near the Gulf Stream along the US East Coast. Those observations are used to make three‐dimensional estimates of mean and eddy kinetic energy, substantially expanding the geographic coverage of prior estimates of subsurface kinetic energy in the Gulf Stream. Glider observations are combined via weighted least squares fitting with anisotropic and inhomogeneous length scales to reflect both circulation and sampling density; this averaging technique can be applied to other quantities measured by the gliders. Mean and eddy kinetic energy decay approximately exponentially away from the surface. Vertical decay scales are longest within the high‐speed core of the Gulf Stream and somewhat shorter on the flanks of the Gulf Stream.

Numerical Modeling of Freestream Turbulence Decay Using Different Commercial Computational Fluid Dynamics Codes

Abstract This work models the spatial decay of freestream turbulence using three different commercial computational fluid dynamics (CFD) codes: Fluent, star-ccm+, and cfx. The two-equation shear stress transport k–ω (SST-k–ω) steady Reynolds-averaged-Navier–Stokes (RANS) model was used, within each of these three different commercial codes, and the modeling variations were analyzed. Comparison of the results from the SST-k–ω model with experiments and large eddy simulation (LES) (carried out using star-ccm+) were also made, which reveal that all the commercial CFD codes demonstrate either a higher or slower rate of spatial turbulent kinetic energy (TKE) decay. Attempts were then made to unify the resultant modeling approach between these three CFD tools, by careful manipulation of the inlet boundary conditions and subsequent fine-tuning of the SST-k–ω model constant (β∞∗). The results obtained not only displayed uniformity among the three CFD codes but also demonstrated a much better agreement to the experiments and the LES results. Thereafter, the optimized model coefficient (β∞∗) was integrated with the three-equation k–kl–ω transition model to examine its applicability in modeling a turbulent boundary layer flow over a flat plate with low incoming turbulence. The results showed good agreement with the theoretical boundary layer correlations, with correct prediction of the transition location. The findings from this study can be used as a suitable modeling method to accurately model the effects of freestream turbulence on bluff-body and boundary layer flows.

Analysis of turbulent kinetic energy decay power law in atmospheric boundary layer models

The transitional periods that take place in the atmospheric boundary layer are challenging to model due to their non-stationary nature. Large-eddy simulation (LES) models have proven to be sufficiently accurate for modeling the evening transitions, and now a possibility to adapt turbulent kinetic energy (TKE) closure models for calculations in single-column models appears to be very plausible. In this study, evening transition modeling is analysed with emphasis on the pattern of a TKE decay which follows the power law. E(t) α t −αThe effects of different parameters on the results of the simulations are explored, along with the geostrophic wind effect on the model. It is shown that the model presented here behaves in a manner similar to that of a LES model, thus showing that the above adaptation is possible and worth being investigated further.

Direct numerical simulation study on the mechanisms of the magnetic field influencing the turbulence in compressible magnetohydrodynamic flow

The magnetohydrodynamic (MHD) control has great potential in the applications of hypersonic vehicles. Typically, the MHD flowfield in these applications is low magnetic Reynolds (Rem ) compressible turbulent flow, which is different from that without magnetic field and within the high Rem range. This paper investigated the low Rem compressible MHD isotropic turbulence in different Taylor-scale Reynolds numbers and interaction parameters via the Direct Numerical Simulation (DNS), and the influence of the magnetic field on the turbulence is researched. Results indicate that the normal Reynolds stress decreases in the direction perpendicular to the magnetic field. Moreover, the eddies are stretched in the direction parallel to the magnetic field. Besides, the Joule dissipation quicken the decay of the turbulent kinetic energy, and occurs mainly in large scale vortex. Based on the DNS data, the correlation between fluctuating electric intensity and velocity is studied. Results indicate that the electric intensity agrees well with the first-order approximate solution of the electric potential equation. Accordingly, an improved closure model of the correlation terms is established, where a coefficient related to the local turbulent Mach number is proposed. Comparisons with the DNS results reveal that the proposed model could correctly predict the correlation terms.

Improved δ-SPH Scheme with Automatic and Adaptive Numerical Dissipation

In this work we present a δ-Smoothed Particle Hydrodynamics (SPH) scheme for weakly compressible flows with automatic adaptive numerical dissipation. The resulting scheme is a meshless self-adaptive method, in which the introduced artificial dissipation is designed to increase the dissipation in zones where the flow is under-resolved by the numerical scheme, and to decrease it where dissipation is not required. The accuracy and robustness of the proposed methodology is tested by solving several numerical examples. Using the proposed scheme, we are able to recover the theoretical decay of kinetic energy, even where the flow is under-resolved in very coarse particle discretizations. Moreover, compared with the original δ-SPH scheme, the proposed method reduces the number of problem-dependent parameters.

Induction heating of dispersed metallic particles in a turbulent flow

Inductively-heated solid particles dispersed within a decaying isotropic turbulent carrier gas are investigated via Direct Numerical Simulations (DNS). The multiphase simulations account for the compressibility and temperature-dependent viscosity effects of the carrier gas. We develop a semi-empirical model for solid particle heating through hysteresis and Joules mechanisms as these dispersed particles are inductively heated by an external high-frequency alternating magnetic field. The present study focuses on the characteristic time scales of the induction heating and thermal transport of the gas and their modulating effects on the turbulence. We show that the growth of the Kolmogorov length scale is due to a simultaneous increase in viscosity and decrease in the dissipation rate. The temperature-dependent viscosity of the gas leads to a faster decay of the gas turbulent kinetic energy, mainly due to a decrease of energy at intermediate wavenumbers. The evolution of the gas and particle thermal fluctuations are inversely correlated based on the relative thermodynamic timescales. By investigating the change in the temperature spectrum, two regimes could be identified. A first regime arises as the thermal fluctuations increase in time and is defined by a monotonic increase of thermal energy in the low wavenumber range; as the thermal fluctuations decrease in the second regime, the decay occurs over the entire spectrum. Furthermore, aggressive heating set by lower induction heating timescales results in a decrease in particle clustering whereas the particle thermal response time did not show any effect.

Flow characteristics of back supported V-cone flowmeter (wafer cone) using PIV

The present experimental study has been carried out to evaluate the performance and flow characteristics of the Wafer cone flowmeter using Particle Image Velocimetry (PIV). Two equivalent diameters (β) of 0.62 and 0.72 with combination of two vertex angles (ϕ) namely 30°and 45°are used for the evaluation of the performance of the flowmeter in the range of Reynolds number of 3 × 103 to 8.19 × 104. The investigation shows that the coefficient of discharge seems to be independent of β-value with the increase in vertex angle. Further, the appropriate location of the downstream pressure tap is also estimated for the cone configuration of β = 0.62 and ϕ = 30°. It is observed that the downstream pressure tap location of 0.8D distance gives a higher value of discharge coefficient compared to 0.0D distance with the error being also lower marginally. PIV data has been analysed for the cone configuration of β = 0.62 and ϕ = 30°at four Reynolds numbers of 3028, 6057, 52755 and 74488 in terms of axial velocity and turbulent intensity. The measurements reveal an interesting phenomenon in terms of the rapid decay of turbulent kinetic energy on the downstream of the cone. This may be due to the interference of the cone wake with the support wake resulting in fast decay. This unique phenomenon leads to the reduction in the requirement of the downstream straight length for the Wafer cone flow meter, unlike other obstruction type flowmeters.

Effects of Mesoscale Surface Heterogeneity on the Afternoon and Early Evening Transition of the Atmospheric Boundary Layer

Large-eddy simulation is used to examine the afternoon and early evening transition of the atmospheric boundary layer (ABL) over heterogeneous surfaces with respect to the decay of the turbulence kinetic energy (TKE). The heterogeneous surface sensible heat flux is prescribed based on the inverse transform of the Fourier spectrum whose slope is controlled to behave as $$ \kappa^{0} $$, $$ \kappa^{ - 1} $$, $$ \kappa^{ - 2} $$, and $$ \kappa^{ - 3} $$ (where $$ \kappa $$ is the wavenumber) in the wavelength range from 18 to 0.2 km. The $$ \kappa^{0} $$ slope spectrum corresponds to a randomly homogeneous field of surface flux, which is implicitly assumed in the grid cells of most large-scale models. The spectral slopes of negative exponents represent heterogeneous surface fields with a larger negative exponent describing stronger mesoscale heterogeneity. The results for a homogeneous surface flux are consistent with that of previous studies in which, during the transition period, the decay of the volume-averaged TKE normalized with the convective velocity scale follows the power law $$ \tau^{ - n} $$ (where $$ \tau $$ is time normalized by the eddy turnover time scale) for exponents n = 1, 2, and 6. While the $$ \tau^{ - 6} $$ portion still remains over the surface with weak mesoscale heterogeneity, the $$ \tau^{ - 6} $$ portion of the spectrum is replaced with a $$ \tau^{ - 2/3} $$ portion over moderate heterogeneity, and the $$ \tau^{ - 2} $$ and $$ \tau^{ - 6} $$ portions are replaced with $$ \tau^{ - 2/3} $$ and $$ \tau^{ - 1} $$ portions of the spectrum over strong heterogeneity, resulting from the surface-heterogeneity-induced horizontal flow persisting after sunset. In fact, mesoscale features across the ABL become more apparent with the reduced number of turbulent eddies in the evening.

Exergy analysis of supersonic steam jet condensed into subcooled water

Exergy analysis of supersonic steam jet condensed into subcooled water was conducted via a numerical method. A thermal phase-change model was employed by Ansys, and considering turbulence interaction and turbulent dispersion force, three-dimensional simulations were conducted to simulate supersonic steam jet at different test conditions. Results indicated that the exergy flow of steam jet was mainly affected by water temperature and inlet steam pressure. The total physical exergy flow decayed monotonically due to the significant irreversible losses caused by heat and momentum transfer. For under-expanded supersonic steam jet, the peak distributions of steam kinetic exergy flow were obtained. The peak distributions of the water enthalpy exergy flow were also obtained at low water temperatures (293.15 K and 303.15 K). In addition, water temperature was found to be the main factor in the damping-energy properties of the supersonic steam jet. The damping-energy ratio and decay rate of the time-averaged kinetic energy decreased with the increase in water temperature, and a correlation was proposed to predict the time-averaged kinetic energy decay ratio.

Performance of high velocity stream heat exchangers subjected to external heat transfer

Performance is analyzed for kinetic energy variation in high velocity stream heat exchangers that are subjected to external heat transfer. Analytical solutions are obtained using the method of inverse operators. They are verified against the reported expressions in the appropriate limits for constant kinetic energy system as well as for perfectly insulated conditions. Kinetic energy decay in hot stream enhances performance that exceeds the conventional heat exchanger effectiveness. For kinetic-to-thermal energy ratio and dimensionless characteristic length constant each equaling unity on the hot side, the terminal effectiveness under balanced operation is 136% for counter-flow arrangement and 82% for parallel-flow in the absence of external heat load. On the contrary, decay on the cold side lowers performance. For unbalanced flow, kinetic energy change in the higher heat capacity rate fluid has a lesser impact on the effectiveness. Thermal interaction with the ambient generally has a deleterious effect on the hot stream effectiveness of the cryogenic system. However, the performance improves under certain conditions such that the rise in fluid temperature caused by kinetic energy deterioration promotes heat loss to the surroundings.

Rate of decay of turbulent kinetic energy in abruptly stabilized Ekman boundary layers

In the late afternoon, the surface temperature drops below air temperature and the lower atmosphere's density stratification becomes stable. A simple model that predicts the rate at which turbulence kinetic energy and mixing decrease after the onset of stable stratification is presented.

Scaling the Decay of Turbulence Kinetic Energy in the Free-Convective Boundary Layer

We investigate the scaling for decaying turbulence kinetic energy (TKE) in the free-convective boundary layer, from the time the surface heat flux starts decaying, until a few hours after it has vanished. We conduct a set of large-eddy simulation experiments, consider various initial convective situations, and prescribe realistic decays of the surface heat flux over a wide range of time scales. We find that the TKE time evolution is dictated by the decaying magnitude of the surface heat flux up to 0.7 tau approximately, where tau is the prescribed duration from maximum to zero surface heat flux. During the time period starting at zero surface heat flux, we search for potential power-law scaling by examining the log–log presentation of TKE as a function of time. First, we find that the description of the decay highly depends on whether the time origin is defined as the time when the surface heat flux starts decaying (traditional scaling framework), or the time when it vanishes (proposed new scaling framework). Second, when varying tau , the results plotted in the traditional scaling framework indicate variations in the power-law decay rates over several orders of magnitude. In the new scaling framework, however, we find a unique decay exponent in the order of 1, independent of the initial convective condition, and independent of tau , giving support for the proposed scaling framework.

Direct numerical simulation and Reynolds-averaged Navier-Stokes modeling of the sudden viscous dissipation for multicomponent turbulence.

Simulations of a turbulent multicomponent fluid mixture undergoing isotropic deformations are carried out to investigate the sudden viscous dissipation. This dissipative mechanism was originally demonstrated using simulations of an incompressible single-component fluid [S. Davidovits and N. J. Fisch, Phys. Rev. Lett. 116, 105004 (2016)10.1103/PhysRevLett.116.105004]. By accounting for the convective and diffusive transfer of various species, the current work aims to increase the physical fidelity of previous simulations and their relevance to inertial confinement fusion applications. Direct numerical simulations of the compressed fluid show that the sudden viscous dissipation of turbulent kinetic energy is unchanged from the single-component scenario. More importantly, the simulations demonstrate that the mass fraction variance and covariance for the various species also exhibit a sudden viscous decay. Reynolds-averaged Navier-Stokes simulations were carried out using the k-l model to assess its ability to reproduce the sudden viscous dissipation. Results show that the standard k-l formulation does not capture the sudden decay of turbulent kinetic energy, mass-fraction variance, and mass-fraction covariance for simulations with various compression and expansion rates, or different exponents for the power-law model of viscosity. A new formulation of the k-l model that is based on previous improvements to the k-ε family of models is proposed, which leads to consistently good agreement with the direct numerical simulations for all the isotropic deformations under consideration.

The generation of grid turbulence with continuously adjustable intensity and length scales

Studying boundary layer transition and its sensitivity to free-stream turbulence, it is often advantageous to be able to continuously adjust intensity and length scales of the turbulence. In this study, we present a new adjustable static turbulence grid and characterize the turbulence it generates. The biplane grid consists of 7 vertical and 19 horizontal, 1 mm-thick baffle plates with a spacing of 12.5 mm. Four of the vertical and ten of the horizontal baffles can be rotated by 90 $$^\circ$$ around the longitudinal axis to change their angle of attack and effective width, while the whole grid can be shifted by 410 mm in flow direction. Adjusting the baffle plate angle and axial grid displacement allows a variation of the turbulence intensity at the exit of the turbulence generator, while other parameters, such as the integral length scale or the turbulent Reynolds number, remain constant and vice versa. The turbulence intensity at the exit can be set within the range of 1.5–8%. Single and X-wire probes are used to measure the level of isotropy, decay of turbulent kinetic energy as well as characteristic length scales and energy spectra. The experiments are performed in a rectangular duct with a cross section of 100 mm $$\times$$ 250 mm embedded in a closed-loop wind tunnel. Reynolds numbers based on grid spacing vary from 11,000 to 32,500.

Long frontal waves and dynamic scaling in freely evolving equivalent barotropic flow

We present a scaling theory that links the frequency of long frontal waves to the kinetic energy decay rate and inverse transfer of potential energy in freely evolving equivalent barotropic turbulence. The flow energy is predominantly potential, and the streamfunction makes the dominant contribution to potential vorticity (PV) over most of the domain, except near PV fronts of width $O(L_{D})$, where $L_{D}$ is the Rossby deformation length. These fronts bound large vortices within which PV is well-mixed and arranged into a staircase structure. The jets collocated with the fronts support long-wave undulations, which facilitate collisions and mergers between the mixed regions, implicating the frontal dynamics in the growth of potential-energy-containing flow features. Assuming the mixed regions grow self-similarly in time and using the dispersion relation for long frontal waves (Nycander et al., Phys. Fluids A, vol. 5, 1993, pp. 1089–1091) we predict that the total frontal length and kinetic energy decay like $t^{-1/3}$, while the length scale of the staircase vortices grows like $t^{1/3}$. High-resolution simulations confirm our predictions.

Vorticity dynamics of the three-dimensional Taylor-Green vortex problem

The three-dimensional (3D) Taylor-Green Vortex (TGV) flow problem has been used to study turbulence from genesis to eventual decay governed by the 3D Navier-Stokes equation. The evolution of the TGV shows that the solution becomes unstable at very early times and eventually becomes turbulent, but a study of this transition has not been advanced so far. The computations are performed using a high accuracy compact scheme on a uniform grid, with the fourth-order Runge-Kutta time integration method. The vector potential-vorticity (Ψ→,ω→)-formulation of the governing equations is solved in a cubic periodic domain with one complete basic unit of a TGV cell in the interior of the domain at t = 0. The TGV problem allows one to study the vorticity dynamics using highly accurate formulation because of periodic boundary conditions. Simulations performed for different Reynolds numbers and grid resolutions reveal that numerical error in computations induce a period-doubling bifurcation, which leads to new spatial symmetries maintained up to intermediate times, followed by simultaneous stretching and fragmentation of vortices resulting in a decaying turbulent flow. The compensated energy spectrum of the 3D TGV flow displays inertial subrange at t = 9, after which the generated turbulence starts decaying. The power law for turbulent kinetic energy decay is analyzed, and the decay exponent is noted to approach unity as time increases.

Laboratory experiments on the temporal decay of homogeneous anisotropic turbulence

We experimentally investigate the temporal decay of homogeneous anisotropic turbulence, monitoring the evolution of velocity fluctuations, dissipation and turbulent length scales over time. We employ an apparatus in which two facing random jet arrays of water pumps generate turbulence with negligible mean flow and shear over a volume that is much larger than the initial characteristic turbulent large scale of the flow. The Reynolds number based on the Taylor microscale for forced turbulence is $Re_{\unicode[STIX]{x1D706}}\approx 580$ and the axial-to-radial ratio of the root mean square velocity fluctuations is $1.22$. Two velocity components are measured by particle image velocimetry at the symmetry plane of the water tank. Measurements are taken for both ‘stationary’ forced turbulence and natural decaying turbulence. For decaying turbulence, power-law fits to the decay of turbulent kinetic energy reveal two regions over time; in the near-field region ($t/t_{L}<10$, $t_{L}$ is the integral time scale of the forced turbulence) a decay exponent $m\approx -2.3$ is found whereas for the far-field region ($t/t_{L}>10$) the value of the decay exponent was found to be affected by turbulence saturation. The near-field exhibits features of non-equilibrium turbulence with constant $L/\unicode[STIX]{x1D706}$ and varying $C_{\unicode[STIX]{x1D716}}$ (dissipation constant). We found a decay exponent $m\approx -1.4$ for the unsaturated regime and $m\approx -1.8$ for the saturated regime, in good agreement with previous numerical and experimental studies. We also observe a fast evolution towards isotropy at small scales, whereas anisotropy at large scales remains in the flow over more than $100t_{L}$. Direct estimates of dissipation are obtained and the decay exponent agrees well with the prediction $m_{\unicode[STIX]{x1D716}}=m-1$ throughout the decay process.

Assessment of numerical methods for fully resolved simulations of particle-laden turbulent flows

During the last decade, many approaches for resolved-particle simulation (RPS) have been developed for numerical studies of finite-size particle-laden turbulent flows. In this paper, three RPS approaches are compared for a particle-laden decaying turbulence case. These methods are, the Volume-of-Fluid Lagrangian method, based on the viscosity penalty method (VoF-Lag); a direct forcing Immersed Boundary Method, based on a regularized delta function approach for the fluid/solid coupling (IBM); and the Bounce Back scheme developed for Lattice Boltzmann method (LBM-BB). The physics and the numerical performances of the methods are analyzed. Modulation of turbulence is observed for all the methods, with a faster decay of turbulent kinetic energy compared to the single-phase case. Lagrangian particle statistics, such as the velocity probability density function and the velocity autocorrelation function, show minor differences among the three methods. However, major differences between the codes are observed in the evolution of the particle kinetic energy. These differences are related to the treatment of the initial condition when the particles are inserted in an initially single-phase turbulence. The averaged particle/fluid slip velocity is also analyzed, showing similar behavior as compared to the results referred in the literature. The computational performances of the different methods differ significantly. The VoF-Lag method appears to be computationally most expensive. Indeed, this method is not adapted to turbulent cases. The IBM and LBM-BB implementations show very good scaling.

An efficient setup for freestream turbulence on transition prediction over aerospace configurations

Inflow turbulence variables play a key role in the performance of correlation-based transition models. In order to consider this important effect, a wing-body configuration in transonic flow is simulated using the γ−Reθ Langtry–Menter transition model. The influences of the freestream turbulence intensity, Tui, and freestream eddy viscosity ratio, μt/μ, over the simulation results are addressed, and an efficient setup for these variables is suggested. Two distinct turbulence conservation boxes, regions in which the turbulence source terms are turned off and in which no turbulence decay occurs, are addressed in the paper. This strategy is an option to the approach of specifying higher values for the freestream turbulence variables and allowing them to decay up to the geometry near field. Discussions on the decay of the turbulent kinetic energy (k) outside of the conservation boxes support the results presented in the paper and provide relevant guidelines regarding the specification of boundary values for turbulence variables.