An implicit high-order spectral difference approach for large eddy simulation

The filtered fluid dynamic equations are discretized in space by a high-order spectral difference (SD) method coupled with large eddy simulation (LES) approach. The subgrid-scale stress tensor is modelled by the wall-adapting local eddy-viscosity model (WALE). We solve the unsteady equations by advancing in time using a second-order backward difference formulae (BDF2) scheme. The nonlinear algebraic system arising from the time discretization is solved with the nonlinear lower–upper symmetric Gauss–Seidel (LU-SGS) algorithm. In order to study the sensitivity of the method, first, the implicit solver is used to compute the two-dimensional (2D) laminar flow around a NACA0012 airfoil at Re = 5 × 10⁵ with zero angle of attack. Afterwards, the accuracy and the reliability of the solver are tested by solving the 2D “turbulent” flow around a square cylinder at Re = 10⁴ and Re =  2.2 × 10⁴. The results show a good agreement with the experimental data and the reference solutions.     

Optimal time advancing dispersion relation preserving schemes

In this paper we examine the constrained optimization of explicit Runge–Kutta (RK) schemes coupled with central spatial discretization schemes to solve the one-dimensional convection equation. The constraints are defined with respect to the correct error propagation equation which goes beyond the traditional von Neumann analysis   developed in Sengupta et al. [T.K. Sengupta, A. Dipankar, P. Sagaut, Error dynamics: beyond von Neumann analysis, J. Comput. Phys. 226 (2007) 1211–1218]. The efficiency of these optimal schemes is demonstrated for the one-dimensional convection problem and also by solving the Navier–Stokes equations for a two-dimensional lid-driven cavity (LDC) problem. For the LDC problem, results for Re=1000$\mathit{Re}=1000$ are compared with results using spectral methods in Botella and Peyret [O. Botella, R. Peyret, Benchmark spectral results on the lid-driven cavity flow, Comput. Fluids 27 (1998) 421–433] to calibrate the method in solving the steady state problem. We also report the results of the same flow at Re=10,000$\mathit{Re}=10\text{,}000$ and compare them with some recent results to establish the correctness and accuracy of the scheme for solving unsteady flow problems. Finally, we also compare our results for a wave-packet propagation problem with another method developed for computational aeroacoustics.     

Large Eddy Simulation composition equations for single-phase and two-phase fully multicomponent flows

The Large Eddy Simulation (LES) equations for multicomponent (MC) fuel single-phase (SP) flow and two-phase (TP) flow with phase change are derived from the Direct Numerical Simulation (DNS) equations by filtering the DNS equations using a top-hat filter. Additional to the equations solved for single-component (SC) fuels, composition equations enter the formulation. The species composition is represented through a Probability Distribution Function (PDF), and DNS equations for the PDF moments are solved to find the composition. The TP filtered equations contain three categories of subgrid-scale (SGS) terms: (1) SGS–flux terms, (2) filtered source terms (FSTs) and (3) terms representing the ‘LES assumptions’. For SP flows no FSTs exist. The SGS terms in the LES equations must be either shown negligible or modeled. It is shown that for the composition equations, two equivalent forms of the DNS equations lead to two non-equivalent forms of the LES equations. Criteria are proposed to select the form best suited for LES. These criteria are used in conjunction with evaluations based on a DNS database portraying mixing and phase change, and lead to choosing one of the LES forms which satisfies all criteria. It is shown that the LES assumptions lead to additional SGS terms which require modeling. Further considerations are made for reactive flows.     

Experimental evidence of extreme inhomogeneity of multifractal dissipation

Using data of laboratory experiments on scalar dissipation in turbulent flows [Antonia and Sreenivasan, Phys. Fluids 20 (1977) 1800; Prasad, Meneveau, and Sreenivasan, Phys. Rev. Lett. 61 (1988) 74] it is shown that a morphological phase transition to extreme inhomogeneity occurs in the passive scalar dissipation fields.     

Evaluation of assumed-PDF methods in two-phase flows using direct numerical simulation

The hypothesis of uncorrelated temperature (T) and vapor-fuel mass fraction (Y_v), frequently made when modeling reaction rates using assumed-PDF models, is examined utilizing transitional databases from direct numerical simulation (DNS) of three-dimensional mixing-layers two-phase (TP) flows with evaporation. Because the databases do not contain chemical reaction, which would further correlate variables, finding here a correlation between T and Y_v is sufficient for invalidating reaction rate modeling of the joint (T, Y_v) probability distribution function (PDF) as a product of the marginal PDFs. The databases comprise four multicomponent fuels, two mass loadings and two free-stream gas temperatures. For comparison, databases for single-phase (SP) flows are also analyzed at two initial Reynolds numbers. The examination is conducted in the mixing layer excluding the free streams and in a more restricted part of the mixing layer constituting its core. The analysis is performed at the DNS and large eddy simulation (LES) scales, and subgrid scale (SGS). To obtain the LES database, the DNS database is filtered, and an evaluation of the examined correlation at the LES and SGS scales is made at two filter sizes. At the DNS scale, T and Y_v are practically uncorrelated for SP flows, showing the weak influence of the perfect-gas equation of state, whereas for TP flows the correlation is strong and increases with mass loading indicating the powerful effect of the phase change. At the LES scale, the findings emulate those at the DNS scale. The fluctuations of the SGS scale are uncorrelated for SP flows, but the product of the marginal PDFs is different from the joint PDF. For TP flows, the fluctuations are correlated and the correlation increases with temperature, casting doubt on current assumed PDFs used to model chemistry in reacting sprays. These results are independent of filter size. The joint PDFs for TP and SP fluctuations are successfully modeled.     

Investigating asymptotic suction boundary layers using a one-dimensional stochastic turbulence model

The turbulent asymptotic suction boundary layer is studied using a one-dimensional turbulence (ODT) model. ODT is a fully resolved, unsteady stochastic simulation technique. While flow properties reside on a one-dimensional domain, turbulent advection is represented using mapping events whose occurrences are governed by a random process. Due to its reduced spatial dimensionality, ODT achieves major cost reductions compared to three-dimensional (3D) simulations. A comparison to recent direct numerical simulation (DNS) data at moderate Reynolds number (Re = u_∞ / v₀ = 333, where u_∞ and v₀ are the free stream and suction velocity, respectively) suggests that the ODT model is capable of reproducing several velocity statistics, i.e. mean velocity and turbulent kinetic energy budgets, while peak turbulent stresses are under-estimated by ODT. Variation of the Reynolds number in the range Re ∈ [333,400,500,1000] shows that ODT can reproduce various trends observed as a result of increased suction in turbulent asymptotic suction boundary layers, i.e. the reduction of Reynolds stresses and enhanced skin friction. While up to Re = 500 our results can be directly compared to recent LES data, the simulation at Re = 1000 is currently not feasible through full 3D simulations, hence ODT may assist the design of future DNS or LES simulations at larger Reynolds numbers.     

Double-component convection due to different boundary conditions in an infinite slot diversely oriented to the gravity

Onset of small-amplitude oscillatory and both small- and finite-amplitude steady double-component convection arising due to component different boundary conditions in an infinite slot is studied for various slot orientations to the gravity. The main focus is on two compensating background gradients of the components. The physical mechanisms underlying steady and oscillatory convection are analyzed from the perspective of a universally consistent understanding of the effects of different boundary conditions. In a horizontal slot with inviscid fluid addressed by Welander [P. Welander, Tellus Ser. A 41 (1989) 66], oscillatory convection sets in with the most unstable wave number and oscillation frequency being zero. Exact expressions for the critical fixed-value background gradient and the respective group velocity at zero wave number are derived from the long-wavelength expansion both for the horizontal slot with independently varying background gradients and for the inclined slot with the compensating gradients. In the horizontal slot with viscous fluid, the dissipation of along-slot perturbation-cell motion reduces efficiency of the oscillatory instability feedback and thus prevents the most unstable wavelength from being infinite. Based on this interpretation, the oscillatory instability of a three-dimensional (3D) nature is predicted for an interval of long two-dimensional (2D) wavelengths in an inclined slot, and such 3D instability is indeed shown to arise. Related general conditions for three-dimensionality of most unstable disturbances are also formulated. As the slot orientation changes from the horizontal by angle θ (?π/2), the oscillatory 2D marginal-stability boundaries in inviscid and viscous fluid are expected to eventually transform into respective steady ones. Oscillatory instability in the vertical slot with viscous fluid, first reported by Tsitverblit [N. Tsitverblit, Phys. Rev. E 62 (2000) R7591], is of a quasi-steady nature. Its (new) mechanism is identified. It is underlain by differential gradient diffusion. As the horizontal slot at θ = π, addressed by Tsitverblit [N. Tsitverblit, Phys. Fluids 9 (1997) 2458], changes its orientation to vertical, the wave number interval of linear steady instability shrinks to the vicinity of the most unstable zero wave number and vanishes. Consistently with the basic nature of finite-amplitude steady convection being the same in the horizontal and vertical slots, the respective convective flows are continuously transformed into each other. The dissimilarity between the nature of finite-amplitude steady convective flows in the horizontal slot with θ = 0, revealed by Tsitverblit [N. Tsitverblit, Phys. Lett. A 329 (2004) 445], and that in the vertical slot is shown to eventually give rise to a region of hysteresis in θ ∈ (0, π/2).     

On the effect of an anisotropy-resolving subgrid-scale model on large eddy simulation predictions of turbulent open channel flow with wall roughness

A large eddy simulation (LES) was conducted of turbulent flow in a channel with a rough wall on one side and a free surface on the other by adopting an anisotropy-resolving subgrid-scale (SGS) model. A shear Reynolds number of Re_τ = 395 was used based on the mean friction velocity and channel height. To investigate the grid dependency of the LES results caused by the SGS model, three grid resolutions were tested under the same definition of a roughness shape by using the immersed boundary method. The results obtained were compared with direct numerical simulation data with and without the wall roughness and those without the extra anisotropic term. The primary focus was on how the present anisotropic SGS model with coarser grid resolutions can properly provide the effects of roughness on the mean velocity and turbulent stresses, leading to a considerable reduction of the computational cost of LES.     

Large eddy simulation of orientation and rotation of ellipsoidal particles in isotropic turbulent flows

The rotational motion and orientational distribution of ellipsoidal particles in turbulent flows are of significance in environmental and engineering applications. Whereas the translational motion of an ellipsoidal particle is controlled by the turbulent motions at large scales, its rotational motion is determined by the fluid velocity gradient tensor at small scales, which raises a challenge when predicting the rotational dispersion of ellipsoidal particles using large eddy simulation (LES) method due to the lack of subgrid scale (SGS) fluid motions. We report the effects of the SGS fluid motions on the orientational and rotational statistics, such as the alignment between the long axis of ellipsoidal particles and the vorticity, the mean rotational energy at various aspect ratios against those obtained with direct numerical simulation (DNS) and filtered DNS. The performances of a stochastic differential equation (SDE) model for the SGS velocity gradient seen by the particles and the approximate deconvolution method (ADM) for LES are investigated. It is found that the missing SGS fluid motions in LES flow fields have significant effects on the rotational statistics of ellipsoidal particles. Alignment between the particles and the vorticity is weakened; and the rotational energy of the particles is reduced in LES. The SGS-SDE model leads to a large error in predicting the alignment between the particles and the vorticity and over-predicts the rotational energy of rod-like particles. The ADM significantly improves the rotational energy prediction of particles in LES.     

A new mixed subgrid-scale model for large eddy simulation of turbulent drag-reducing flows of viscoelastic fluids

A mixed subgrid-scale(SGS) model based on coherent structures and temporal approximate deconvolution(MCT) is proposed for turbulent drag-reducing flows of viscoelastic fluids. The main idea of the MCT SGS model is to perform spatial filtering for the momentum equation and temporal filtering for the conformation tensor transport equation of turbulent flow of viscoelastic fluid, respectively. The MCT model is suitable for large eddy simulation(LES) of turbulent dragreducing flows of viscoelastic fluids in engineering applications since the model parameters can be easily obtained. The LES of forced homogeneous isotropic turbulence(FHIT) with polymer additives and turbulent channel flow with surfactant additives based on MCT SGS model shows excellent agreements with direct numerical simulation(DNS) results. Compared with the LES results using the temporal approximate deconvolution model(TADM) for FHIT with polymer additives, this mixed SGS model MCT behaves better, regarding the enhancement of calculating parameters such as the Reynolds number.For scientific and engineering research, turbulent flows at high Reynolds numbers are expected, so the MCT model can be a more suitable model for the LES of turbulent drag-reducing flows of viscoelastic fluid with polymer or surfactant additives.     

Vorticity,backscatter and counter-gradient transport predictions using two-level simulation of turbulent flows

The two-level simulation (TLS) method evolves both the large-and the small-scale fields in a two-scale approach and has shown good predictive capabilities in both isotropic and wall-bounded high Reynolds number (Re) turbulent flows in the past. Sensitivity and ability of this modelling approach to predict fundamental features (such as backscatter, counter-gradient turbulent transport, small-scale vorticity, etc.) seen in high Re turbulent flows is assessed here by using two direct numerical simulation (DNS) datasets corresponding to a forced isotropic turbulence at Taylor’s microscale-based Reynolds number Re_λ ≈ 433 and a fully developed turbulent flow in a periodic channel at friction Reynolds number Re_τ ≈ 1000. It is shown that TLS captures the dynamics of local co-/counter-gradient transport and backscatter at the requisite scales of interest. These observations are further confirmed through a posteriori investigation of the flow in a periodic channel at Re_τ = 2000. The results reveal that the TLS method can capture both the large- and the small-scale flow physics in a consistent manner, and at a reduced overall cost when compared to the estimated DNS or wall-resolved LES cost.     

The effect of subgrid-scale models on the entrainment of a passive scalar in a turbulent planar jet

Classical large-eddy simulation (LES) modelling assumes that the passive subgrid-scale (SGS) models do not influence large-scale quantities, even though there is now ample evidence of this in many flows. In this work, direct numerical simulation (DNS) and large-eddy simulations of turbulent planar jets at Reynolds number Re_H = 6000 including a passive scalar with Schmidt number Sc = 0.7 are used to study the effect of several SGS models on the flow integral quantities e.g. velocity and scalar jet spreading rates. The models analysed are theSmagorinsky, dynamic Smagorinsky, shear-improved Smagorinsky and the Vreman. Detailed analysis of the thin layer bounding the turbulent and non-turbulent regions – the so-called turbulent/non-turbulent interface (TNTI) – shows that this region raises new challenges for classical SGS models. The small scales are far from equilibrium and contain a high fraction of the total kinetic energy and scalar variance, but the situation is worse for the scalar than for the velocity field. Both a-priori and a-posteriori (LES) tests show that the dynamic Smagorinsky and shear-improved models give the best results because they are able to accurately capture the correct statistics of the velocity and passive scalar fluctuations near the TNTI. The results also suggest the existence of a critical resolution Δ_x, of the order of the Taylor scale λ, which is needed for the scalar field. Coarser passive scalar LES i.e. Δ_x ≥ λ results in dramatic changes in the integral quantities. This fact is explained by the dynamics of the small scales near the jet interface.     

不可压反应流动直接模拟和亚网格模型的检验

本文用谱方法对三维槽道不可压湍流反应流动进行了直接模拟,用直接模拟数据对大涡模拟亚网格质量流和燃烧模型进行了检验,结果发现,引入壁面阻尼修正的模型与精确值的符合比较好.     

Minimum state for high Reynolds and Péclet number turbulent flows

Direct numerical simulations (DNS) or experiments for the very high Reynolds (Re) and Péclet (Pe) number flows commonly exceed the resolution possible even when use is made of the most advanced computer capability or most sophisticated diagnostics and physical capabilities of advanced laboratory facilities. In practice use is made of statistical flow data bases developed at the highest Re and Pe levels achievable within the currently available facility limitations. In addition, there is presently no metric to indicate whether and how much of the fully resolved physics of the flow of interest has been captured within the facilities available. In this Letter the authors develop the necessary metric criteria for homogeneous, isotropic and shear layer flows. It is based on establishing a smaller subset of the total range of dynamic scale interactions that will still faithfully reproduce all of the essential, significant, influences of the larger range of scale interactions. The work identifies a minimum significant Re and Pe level that must be obtained by DNS or experiment in order to capture all of the significant dynamic influences in data which is then scaleable to flows of interest. Hereafter this is called the minimum state. Determination of the minimum state is based on finding a minimum scale separation for the energy-containing scales of the flow and scalar fields sufficient to prevent contamination by interaction with the (non-universal) velocity dissipation and scalar diffusivity inertial range scale limits.     

Multi-scale properties of large eddy simulations: correlations between resolved-scale velocity-field increments and subgrid-scale quantities

We provide analytical and numerical results concerning multi-scale correlations between the resolved velocity field and the subgrid-scale (SGS) stress-tensor in large eddy simulations (LES). Following previous studies for Navier–Stokes equations, we derive the exact hierarchy of LES equations governing the spatio-temporal evolution of velocity structure functions of any order. The aim is to assess the influence of the subgrid model on the inertial range intermittency. We provide a series of predictions, within the multifractal theory, for the scaling of correlation involving the SGS stress and we compare them against numerical results from high-resolution Smagorinsky LES and from a-priori filtered data generated from direct numerical simulations (DNS). We find that LES data generally agree very well with filtered DNS results and with the multifractal prediction for all leading terms in the balance equations. Discrepancies are measured for some of the sub-leading terms involving cross-correlation between resolved velocity increments and the SGS tensor or the SGS energy transfer, suggesting that there must be room to improve the SGS modelisation to further extend the inertial range properties for any fixed LES resolution.     

Spectral line parameters in the (3 ← 0) overtone band of the HI molecule and line-mixing in the band head

The linestrengths, self-pressure broadening and shifting coefficients have been measured for P₃ (10)- R₃ (12) lines in the second overtone band of hydrogen iodide. A dipole moment function in terms of the reduced nuclear displacement x = (R − R_e)/R_e is obtained using rotationless dipole matrix elements determined by the Herman-Wallis analysis of the (1, 2, 3 ← 0) HI bands: μ (x) = 0.4471(5) − 0.0770(2)x + 0.547(3)x² − 1.93(2)x³, in a full agreement with the function proposed previously [J. Mol. Spectrosc. 223 (2004) 67]. A close match is demonstrated of the results of most recent relativistic calculations [Phys. Chem. Chem. Phys. 6 (2004) 3779] with the spectroscopically derived electric dipole parameters for HI. Line-mixing in the band head is observed, the self-pressure shifting and broadening coefficients for the (3 ← 0) band lines are determined.     

Fourier transform emission spectroscopy of the BΣ-XΣ system of CN

The emission spectrum of the B²Σ⁺-X²Σ⁺ system of CN has been observed at high-resolution using a Fourier transform spectrometer. The rotational structure of a large number of bands involving vibrational levels v = 0-15 of both electronic states has been analyzed, and improved spectroscopic constants have been determined by combining the microwave and infrared measurements from previous studies. Improved spectroscopic constants for vibrational levels up to v″ = 18 in the X²Σ⁺ state and v′ = 19 in the B²Σ⁺ state have been determined by combining the measurements of the 16-13, 18-17, 18-18, 19-15, and 19-18 bands of Douglas and Routly [Astrophys. J. Suppl. 1 (1955) 295-318] and 17-14 and 17-16 bands of Ito et al. [J. Chem. Phys. 96 (1992) 4195] with our data. The band constants obtained have been used to estimate equilibrium ground state constants for CN.     

Subgrid modelling for particle-LES by Spectrally Optimised Interpolation (SOI)

This paper focuses on Large-Eddy simulation of particle-laden flow. We present a novel model for the effect of unresolved scales on the particles. The model can be regarded as an extension of the approximate deconvolution method towards higher wavenumbers. The basis of the model is a specific interpolation method which is constructed such that the spectrum seen by the particles attains a model spectrum. Thus, the model is called Spectrally Optimised Interpolation (SOI). The model is developed and tested in the framework of homogeneous isotropic turbulence. A comparison of SOI against ADM [J.G.M. Kuerten, Subgrid modelling in particle-laden channel flow, Phys. Fluids 18 (2006) 025108] shows that in particular in coarse LES, SOI is far more accurate than ADM. The computational costs for SOI are comparable to fourth order interpolation. Possible extensions of the model for general flows are briefly sketched.     

Crystal electric field excitations in ferromagnetic CeTX compounds

A ferromagnetic ground state was identified for the compounds CeCuGe (T_C=10 K), CeCuSi (T_C=15 K) [F. Yang, et al., J. Appl. Phys. 69 (1991) 4705] and CeAuGe (T_C=10 K) [R. Pottgen, J. Magn. Magn. Mater. 152 (1996) 196]. The observed saturation magnetic moment values at low temperatures for all three compounds are considerably less than the theoretically expected value g_JJ=2.14μ_B for the free Ce³⁺ ion involving the entire six-fold J=5/2 multiplet, and thus provide a first indication of partial lifting of the f-electron level degeneracy in these compounds. Specific heat data yield crystal electric field (CEF) excitation energies (Δ_Sch) equivalent to 140 K for CeCuGe, 110 K for CeCuSi and 280 K for CeAuGe. To confirm the presence of CEF excitations directly, we have carried out inelastic neutron scattering (INS) measurements on all three compounds, using the HET spectrometer at ISIS Facility. Here, we present a detailed analysis of the INS spectra of CeCuSi on the basis of a CEF model and the detailed analysis of the INS of the other two compounds will be reported elsewhere.