Use Of Direct Numerical Simulation Research Articles

Lagrangian investigation of the correlation of helicity with coherent flow characteristics for turbulent transport

The correlation between helicity and turbulent transport in turbulent flows is probed with the use of direct numerical simulation and Lagrangian scalar tracking. Channel flow and plane Couette flow at friction Reynolds number 300 and Lagrangian data along the trajectories of fluid particles and passive particles with Schmidt numbers 0.7 and 6 are used. The goal is to identify characteristics of the flow that enhance turbulent transport from the wall, and how flow regions that exhibit these characteristics are related to helicity. The relationship between vorticity and relative helicity along particle trajectories is probed, and the relationship between the distribution of helicity conditioned on Reynolds stress quadrants is also evaluated. More importantly, the correlation between relative helicity density and the alignment of vorticity with velocity vectors and eigenvectors of the rate of strain tensor is presented. Separate computations for particles that disperse the farthest into the flow field and those that disperse the least are conducted to determine the flow structures that contribute to turbulent dispersion. The joint distribution of helicity and vertical velocity, and helicity and vertical vorticity depends on the location of particle release and the Schmidt number. The trajectories of particles that disperse the least are characterized by a correlation between the absolute value of the relative helicity density and the absolute value of the cosine between the vorticity vector and the eigenvectors of the rate of strain tensor, while the value of this correlation approaches zero for the particles that disperse the most.

Comprehensive simulations of boiling with a resolved microlayer: validation and sensitivity study

The dynamics of the microlayer beneath a growing bubble in nucleate boiling significantly impacts the heat-transfer characteristics of the process. The minute thickness of the microlayer motivates the use of direct numerical simulation (DNS) to model its behaviour if empirical models are to be avoided. In this work, we develop a computational strategy for utilising DNS to model nucleate boiling by resolving explicitly the microlayer, directly coupling, in a stable manner, the mass, momentum and energy conservation equations with the conjugate heat transfer between the solid and fluid domains. To this end, closure models for the treatment of interfacial heat transfer and the dynamic contact angle are introduced and substantiated. The computational procedure is validated against relevant experimental data recently measured at the Massachusetts Institute of Technology; it is shown that the main observed growth features and surface heat-transfer characteristics are well reproduced using our model. We go on to perform a sensitivity study of the dependence of the initial microlayer thickness distribution on the applied superheat and fluid properties. The results indicate that an equation derived from lubrication theory captures the observed trends well. Finally, a first demonstration of DNS of boiling with an explicitly resolved microlayer in three-dimensional Cartesian coordinates is presented in one of the appendices.

Information production in homogeneous isotropic turbulence.

We study the Reynolds number scaling of the Kolmogorov-Sinai entropy and attractor dimension for three-dimensional homogeneous isotropic turbulence through the use of direct numerical simulation. To do so, we obtain Lyapunov spectra for a range of different Reynolds numbers by following the divergence of a large number of orthogonal fluid trajectories. We find that the attractor dimension grows with the Reynolds number as Re^{2.35} with this exponent being larger than predicted by either dimensional arguments or intermittency models. The distribution of Lyapunov exponents is found to be finite around λ≈0 contrary to a possible divergence suggested by Ruelle. The relevance of the Kolmogorov-Sinai entropy and Lyapunov spectra in comparing complex physical systems is discussed.

Effect of external turbulence on the short-wavelength instability of a counter-rotating vortex pair

The effect of background turbulence on the evolution and instability of a counter-rotating vortex pair is investigated via the use of direct numerical simulation at a circulation Reynolds number of 2400. The ambient turbulence is modelled as decaying homogeneous isotropic turbulence with the initial levels of turbulence intensity (Tu) varied from 0.0% to 10.0%. The major effect of the external turbulence during the early-time development is that it reduces the vortex separation distance, leading to the mutual interaction of the two vortices. The onset to transition is also found to occur earlier. For a low-level turbulence intensity (Tu ≤ 6.25%), the vortex pair breaks down to turbulence due to the short-wavelength elliptic instability, whose characteristic is qualitatively similar to that in a quiescent background despite exhibiting a shorter wavelength. Increasing the turbulence intensity results in a decrease in the growth rate of the elliptic mode. The long-wavelength Crow mode dominates the breakdown process of the flow once Tu ≥ 7.5%. The Crow instability gives rise to the vortex disconnection and reconnection, resulting in the transformation of the vortex pair into a vortex ring.

Adjoint optimal control problems for the RANS system

Adjoint optimal control in computational fluid dynamics has become increasingly popular recently because of its use in several engineering and research studies. However the optimal control of turbulent flows without the use of Direct Numerical Simulation is still an open problem and various methods have been proposed based on different approaches. In this work we study optimal control problems for a turbulent flow modeled with a Reynolds-Averaged Navier-Stokes system. The adjoint system is obtained through the use of a Lagrangian multiplier method by setting as objective of the control a velocity matching profile or an increase or decrease in the turbulent kinetic energy. The optimality system is solved with an in-house finite element code and numerical results are reported in order to show the validity of this approach.

Systematic Analysis Strategies for the Development of Combustion Models from DNS: A Review

Direct numerical simulation (DNS) of turbulent combustion is a research area becoming ever more important and has been established as a powerful tool in combustion science to complement theory and experiment. The rapid advancement of supercomputing has lately enabled a series of interesting DNS studies with some practical relevance. This advent along with the severe lack of experimental data sets with a high degree of data completeness motivates the use of DNS for combustion modeling. Simultaneously, enormous progress is made in the utilization of DNS data as a valuable resource to develop and validate combustion models from DNS data. In this paper, several promising and useful analysis techniques are identified and reviewed. Their usefulness is demonstrated on the basis of selected modeling studies, which comprise examples of various commonly employed modeling frameworks, and which integrate DNS in a systematic way into the process of model development and validation. It is expected that the modeling routes outlined here can be used to address currently open modeling questions and to advance the fidelity of existing models.

Advancing predictive models for particulate formation in turbulent flames via massively parallel direct numerical simulations.

Combustion of fossil fuels is likely to continue for the near future due to the growing trends in energy consumption worldwide. The increase in efficiency and the reduction of pollutant emissions from combustion devices are pivotal to achieving meaningful levels of carbon abatement as part of the ongoing climate change efforts. Computational fluid dynamics featuring adequate combustion models will play an increasingly important role in the design of more efficient and cleaner industrial burners, internal combustion engines, and combustors for stationary power generation and aircraft propulsion. Today, turbulent combustion modelling is hindered severely by the lack of data that are accurate and sufficiently complete to assess and remedy model deficiencies effectively. In particular, the formation of pollutants is a complex, nonlinear and multi-scale process characterized by the interaction of molecular and turbulent mixing with a multitude of chemical reactions with disparate time scales. The use of direct numerical simulation (DNS) featuring a state of the art description of the underlying chemistry and physical processes has contributed greatly to combustion model development in recent years. In this paper, the analysis of the intricate evolution of soot formation in turbulent flames demonstrates how DNS databases are used to illuminate relevant physico-chemical mechanisms and to identify modelling needs.

Reply to “Comments on ‘Direct Numerical Simulation of the Turbulent Ekman Layer: Evaluation of Closure Models’”

In this note, we respond to J. C. Bergmann’s comments (Bergmann 2014) regarding our recent article assessing Ekman-layer turbulence closure models using direct numerical simulation (DNS) results. As Bergmann notes in his introduction, many of the comments that he provides are not specifically related to our paper. While many of these issues are of interest for understanding the dynamicsoftheatmosphericboundarylayer(ABL),wewill limit our responses primarily to those issues that directly relate to the objectives and the results of our paper. In the following reply, we first discuss of the applicabilityoftheneutral,turbulentEkmanlayerasamodelfor the ABL, and we then address some fundamental objections that Bergmann raises to the use of DNS. We also address Bergmann’s other concerns regarding turbulence models, momentum balance, and vertical exchange and eddy viscosity modeling assumptions.

Computational fluid dynamics as a modern tool for engineering characterization of bioreactors

Since design, construction and evaluation of bioreactors for large-scale production is costly and time consuming, computational methods may give some insights into the fluid mechanics within bioreactors. Thus, critical limiting factors, such as insufficient mixing as well as inhomogeneous nutrient and oxygen mass transfer, may be identified early in the design process. Although advanced experimental techniques such as laser Doppler anemometry and particle image velocimetry are also reliable, they are too time consuming to characterize the complete flow pattern in industrial scales and rely on optical accessibility. Therefore, the knowledge of flow characteristics provided by computational fluid dynamics (CFD) is indispensable for the rational design of bioreactors. Based on previously published reviews, the present work summarizes the latest publications on the usage of CFD to characterize and scale-up bioreactors used in biotechnological processes. Selected models that are used to predict the fluid flow pattern and key engineering parameters of commonly used bioreactors are described. Related issues, such as grid dependency of CFD results and the requirement for experimental verification are also addressed. Finally, an overview of proposed but not yet feasible CFD applications is presented, including fluid–structure interaction, the use of direct numerical simulation and the coupling fluid flow and chemical reactions.

J054026 乱流場における運動量と熱輸送の非相似性に及ぼすスパン方向渦度の影響

The influence of transverse vorticity on the dissimilarity between turbulent heat flux and Reynolds stress was investigated by use of direct numerical simulation for two-dimensional channel flow. It is shown that the negative correlation R between wall-normal velocity and pressure gradient fluctuation has an important effect on the dissimilarity. The correlation R would be strongly related to the transverse clockwise vortex in the turbulent flow field. The numerical results show that the correlation R increases and the strength of dissimilarity 5 (turbulent heat flux minus Reynolds stress) decreases as the transverse vorticity shifts to positive The dissimilarity would be mainly caused by the reduction of Reynolds stress near the vortex region, where the velocity fluctuation in the flow direction is accelerated (or decelerated) during fluid particle motion on the ejection (or sweep) side due to the pressure gradient. When an external force is imposed to reinforce the clock-wise vortex, the turbulent Prandtl number Prt is calculated. The numerical results show that Prt is remarkable reduced in the region where the clock-wise vorticity is strengthened.

J056013 ミニマル平面クエット流におけるホモクリニック軌道([J05601]乱流における運動量,熱,物質の輸送現象(1))

The homoclinic orbit from/to the unstable periodic orbit found by Kawahara and Kida (2001) in minimal plane Couette flow is numerically computed by use of direct numerical simulation and multiple shooting method which allow us to perform the long-time integration of the Navier-Stokes equation. This homoclinic orbit yields the infinite number of transversal intersections between the unstable and stable manifolds of the periodic orbit in a Poincare section, leading to chaotic dynamics described mathematically by Smale's horseshoe map. Along the homoclinic orbit vortical structures and the associated energy dissipation are observed to be highly localized on the crest or valley of a velocity streak, in contrast to the familiar near-wall regeneration cycle.

Effect of Prandtl number on the turbulent thermal field in annular pipe flow

The effect of Prandtl number on the turbulent thermal statistics in fully developed annular pipe flow, with isoflux boundary conditions, is investigated by use of direct numerical simulation, for two values of Reynolds number. The Prandtl number has marked influence on the thermal field. With decreasing Pr, the conductive sublayer at both walls spreads from the walls to the core region, while the root mean square of temperature fluctuations and the turbulent heat fluxes are reduced near both walls. Asymptotic behaviours of these quantities are analyzed.

Numerical predictions of turbulent heat transfer for air flow in rotating pipe

Heat transfer in fully developed turbulent pipe flow with isoflux condition imposed at the wall is investigated numerically by use of direct numerical simulation (DNS) and large eddy simulation (LES) for various rotation rates ( 0 ⩽ N ⩽ 7 ) at a Reynolds number equal to 5500. To validate the present computations, predictions are compared to the results reported in the archival literature, and found to agree fairly well with them. With increasing rotation number, the temperature fluctuations decrease near the wall and are enhanced in the core region. The pipe rotation induces a reduction of the streamwise turbulent heat flux and an obvious augmentation of the azimuthal one, especially near the wall. Thus, heat transfer between fluid and wall is reduced. For higher rotation numbers ( N > 3 ) , the flow and the scalar transport become nearly insensitive to N. Joint probability density functions sketch the correlation between flow and thermal fields. Visualization of the temperature field exhibits the stabilizing effects of the centrifugal forces.

Towards a multi-scale approach of two-phase flow modeling in the context of DNB modeling

In this article, we present how Direct Numerical Simulation (DNS) is being used in the context of Departure from Nucleate Boiling (DNB) modeling. Two particular applications are analyzed: wall boiling and bubble column flow. An analysis of the relevant length scales involved shows that true DNS, where all the length scales are resolved, is necessarily restricted to flow configurations where one or a few bubbles are involved. In the context of DNB modeling, DNS can thus be used to study (i) the dynamics of the growth of a few bubbles with their eventual spreading and (ii) bubble column flows to predict the void fraction field in the near wall region. To account for collective effects in bubbly flows, we show that it is necessary to develop a new approach where the large turbulence structures and large interface deformations are captured whereas the smallest scales are modeled; this is the Interface and Subgrid Scale (ISS) method. The DNS and ISS methods are presented and preliminary results on the use of DNS for larger scales models are presented.

Use of direct numerical simulation (DNS) data to investigate spatial resolution issues in measurements of wall-bounded turbulence

The effect of limited spatial resolution for hot-wire anemometry (HWA) is investigated by analysing the two-dimensional energy spectra from direct numerical simulation (DNS) of turbulent channel flow at Reτ ≈ 950. Various spanwise filter lengths are applied to the streamwise velocity components in order to mimic the limited spatial resolution of a single-normal hot-wire experiment. Clear attenuation of the small-scale DNS energy is observed as the filter length is increased and good agreement is noted between the missing energy from filtered DNS and that from hot-wire experiments over a range of sensing lengths. The missing energy in the near-wall region is shown to be highly anisotropic in nature, thus bringing into question existing correction schemes that rely on small-scale isotropic flow assumptions. An empirical model of the missing streamwise component energy spectra is formulated, as a function of wire length, and is shown to be useful as a new correction function for the missing energy and streamwise turbulence intensity at the near-wall energetic peak.

On the Evolution of Thermonuclear Flames on Large Scales

The thermonuclear explosion of a massive white dwarf in a Type Ia supernova explosion is characterized by vastly disparate spatial and temporal scales. The extreme dynamic range inherent to the problem prevents the use of direct numerical simulation and forces modelers to resort to subgrid models to describe physical processes taking place on unresolved scales. We consider the evolution of a model thermonuclear flame in a constant gravitational field on a periodic domain. The gravitational acceleration is aligned with the overall direction of the flame propagation, making the flame surface subject to the Rayleigh-Taylor instability. The flame evolution is followed through an extended initial transient phase well into the steady-state regime. The properties of the evolution of flame surface are examined. We confirm the form of the governing equation of the evolution suggested by Khokhlov (1995). The mechanism of vorticity production and the interaction between vortices and the flame surface are discussed. The results of our investigation provide the bases for revising and extending previous subgrid-scale model.

Turbulent pipe flow of shear-thinning fluids

Direct numerical simulation of the weakly turbulent flow of non-Newtonian fluids is undertaken for two different generalised Newtonian rheology models using a spectral element-Fourier method. Results for a power law (shear-thinning) rheology agree well with experimentally determined logarithmic layer correlations and with other previously published experimental work. As the flow index becomes smaller for the same Reynolds number, the flow deviates further from the Newtonian profile and the results suggest that transition is delayed. Predicted friction factors fall above those in the literature, but below the Newtonian values when a comparison is undertaken on the basis of the Metzner–Reed Reynolds number. Results for a Herschel–Bulkley model (yield stress+shear-thinning) are compared to corresponding experimental measurements and are found to be in very good agreement. Use of direct numerical simulation shows great promise in understanding transition and turbulence in non-Newtonian fluids.

Overall Self-Similar Decay of Two-Dimensional Turbulence

The statistics of two-dimensional decaying turbulence are investigated by the use of direct numerical simulation in a periodic box. A number of cases are systematically compared in which the incompressible Navier-Stokes equation is solved on various resolutions and for various Reynolds numbers starting with random velocity fields of a prescribed energy spectrum. It is observed that the statistics are contaminated rapidly by the periodicity of the flow field which blocks the transfer of velocity fluctuations towards larger scales. At large Reynolds numbers the enstrophy spectrum decays similarly in time throughout the whole wavenumber range and the enstrophy decreases inversely proportionally to time.

Fluid Mechanics in the Driven Cavity

▪ Abstract This review pertains to the body of work dealing with internal recirculating flows generated by the motion of one or more of the containing walls. These flows are not only technologically important, they are of great scientific interest because they display almost all fluid mechanical phenomena in the simplest of geometrical settings. Thus corner eddies, longitudinal vortices, nonuniqueness, transition, and turbulence all occur naturally and can be studied in the same closed geometry. This facilitates the comparison of results from experiment, analysis, and computation over the whole range of Reynolds numbers. Considerable progress has been made in recent years in the understanding of three-dimensional flows and in the study of turbulence. The use of direct numerical simulation appears very promising.

Use of direct numerical simulation to study the effect of Prandtl number on temperature fields

Abstract The influence of Prandtl number on statistical parameters characterizing turbulent transport and the spatial variation of the mean-square of the temperature fluctuations, θ 2 , is described. The system considered is fully developed flow in a channel for which the bottom wall is heated and the top wall is cooled. Results from direct numerical solutions of the Euler balance equations for Pr=0.3, 1, 3, 10 and Lagrangian studies, in a DNS, of the dispersion of heat markers from wall sources for Pr=0.1–2400 are used. The Eulerian results for Pr=10 are new and of particular interest. A time scale τ θ can be defined from the dissipation of k θ = θ 2 /2 , as τ θ = k θ / ϵ θ . This is analogous to the time scale defined from the dissipation of turbulent kinetic energy, τ = k / ϵ . Prandtl number is found to strongly affect τ θ and the correlation, u i θ /( u i 2 ) 1/2 ( θ 2 ) 1/2 . These results can be understood by recognizing that the spectral density function for temperature fluctuations extends over an increasingly larger range of wavenumbers as Pr increases. The observed effect of Pr on τ θ suggests fundamental problems in developing relations for the turbulent diffusivity by a k θ ττ θ approach analogous to the kτ approach used to describe momentum transport. The use of a gradient transport model to represent the turbulent transport of k θ also has fundamental problems.