Numerical studies of specific features of the transonic flow reconstruction on a hammerhead model

The results of the numerical studies of transonic flow reconstruction occurring with an increase in the free stream Mach number on a hammerhead cone-cylinder body with a small break angle in the generatrix are presented. A turbulent flow regime is considered. The Reynolds equations with different turbulence models are used. The numerical results are compared to the experimental data and the results of the calculation using the Euler model.     

Studies of shock/turbulent shear layer interaction using Large-Eddy Simulation

Shock/shear/turbulence interactions are simulated using Large-Eddy Simulation (LES) with a new localized subgrid closure approach. Both normal and oblique shocks interactions with turbulence are considered. The LES methodology adopted here combines a hybrid numerical scheme that switches automatically and locally between a shock-capturing scheme and a low-dissipation high-order central scheme.The fundamental role of the diffusion of turbulent kinetic energy by pressure fluctuations in the problem of normal shock/isotropic turbulence interaction is stressed in the DNS study, and accounted for in the closure model. The study of the interaction between two oblique shocks and a turbulent shear layer shows that the turbulence evolution is mostly affected by two competing phenomena. An amplification of the turbulent levels occurs downstream of the interaction, and the mixing layer growth rate is significantly increased. However, the integrated production of turbulent energy across the mixing layer is reduced, and the increase in mixing is found to be localized in space, the turbulent statistics quickly relaxing to their undisturbed levels. Furthermore, the increase in vorticity from the compression of the mixing layer remains small, unaffected by the presence of turbulent and coherent structures.     

Numerical study of the flow over shallow cavities

This paper reports on a series of numerical simulations of both laminar and turbulent flows over shallow cavities. For the turbulent case the influences of the following parameters were considered: (i) cavity aspect ratios, (ii) turbulence level of the oncoming flow, and (iii) Reynolds number. Several important results and conclusions are reported. We have found that for the turbulent case the external flow touches the floor of the cavity, and this depends on a specific value of each of these parameters. This condition has an important impact upon convective effects inside the cavity. The mathematical model corresponds to the incompressible, Reynolds-averaged, Navier-Stokes equations plus a high-Reynolds κ-ε model of turbulence, and the numerical computation is performed using the SIMPLER algorithm.     

Turbulence modeling for two-dimensional water hammer simulations in the low Reynolds number range

Modeling turbulence in two-dimensional water hammer simulations is considered in the present study. The Baldwin–Lomax turbulence model is implemented, both in quasi-steady and frozen forms. Numerical simulations using both forms agree well with experimental data for lower Reynolds numbers (Re = 5600) and the attenuation of the transient is adequately captured. However, for higher Reynolds numbers (Re = 15,800), the frozen form overpredicts the attenuation of the transient. Moreover, it is shown that switching the turbulence model off altogether and applying a quasi-laminar approximation results in good agreement with experimental data for the lower Reynolds number case (Re = 5600) while underpredicting the attenuation of the transient for the higher Reynolds number case (Re = 15,800).     

Assessment of multiscale resolution for hybrid turbulence model in unsteady separated transonic flows

This paper presents results of a computational study conducted to assess the multi-scale resolution capabilities of a hybrid two-equation turbulence model in predicting unsteady separated high speed flows. Numerical solutions are obtained using a third order Roe scheme and the SST (shear-stress-transport) two-equation-based hybrid turbulence model for three-dimensional transonic flow over an open cavity. A detailed assessment of the effects of the computational grid and the hybrid turbulence model coefficient is presented for the unsteady flow field. Computed results are presented for both the resolved and the modeled turbulent kinetic energy (TKE) and for the predicted sound pressure level (SPL) spectra, which are compared to available experimental data and large Eddy simulation (LES) results. The comparison shows that the predicted SPL spectra agree well with the experimental results over a frequency range up to 2500 Hz, and that hybrid turbulence effectively models the shorter wavelengths. The results demonstrate improved agreement with experimental SPL spectra with increased grid resolution and a reduced hybrid turbulence model coefficient. In addition, they show that energy dissipation of the unresolved scales is over-predicted at low resolutions and that the hybrid coefficient influences the grid resolution requirements.     

Numerical modelling of laminar-turbulent transition in the boundary layers under the influence of low free-stream turbulence intensities

Predictions of laminar-turbulent transition in the two-dimensional and axisymmetric boundary layers under the influence of low free-stream turbulence levels are presented. A ‘near-wall’ version of the k- turbulence model is used for simulation of turbulent transport. The calculations are based on Patankar and Spalding's finite difference algorithm. It is known that for high free-stream turbulence levels, the k- model simulates the transition well but it fails for low ones. In the present work, calculations are successfully, made for low turbulence levels using Abu-Ghannam and Shaw's correlation for determination of the flow transition point and Dhawan and Narasimha's intermittency factor in the transition zone. The examples include various levels of free-stream turbulence as well as a variety of boundary layers on a rotary ellipsoid. The numerical results are compared with experimental data and the agreement is good.     

A three-dimensional numerical study of turbulence in homogeneous fluids

Results are reported from computations of homogeneous, nearly isotropic turbulence using a low resolution three-dimensional numerical model with subgrid-scale closure. Both the nonlinear eddy viscosity closure of Smagorinsky and a modified second-order closure involving solution of a prognostic equation for the subgrid-scale kinetic energy are tested in a 20³ grid-point model. A higher resolution 32³ model is exercised to examine the effects of changes in model constants and in grid-point resolution. It is shown, based on comparisons of the turbulence energy spectra, that calculations using the nonlinear eddy viscosity formulation are extremely sensitive to variations in the constant. It is also concluded that little is to be gained from the use of second-order closure in problems where stratification is unimportant. This is not inconsistent with results from a previous study by the authors of thermal convection in the planetary boundary layer. From that study it was concluded that some form of second-order closure is essential in stratified turbulence calculations.     

A new second-order closure model for rough-wall turbulent flows using the Brinkman equation

A second-order turbulence closure is developed for the new rough-wall layer modeling approach using the Brinkman equation for turbulent flows over rough walls. In the proposed approach, we model the fluid dynamics of the volume averaged flow in the near-wall rough layer by using the Brinkman equation. The porosity can be calculated based on the volumetric characteristics of the roughness and the permeability is modeled. Interface stress jump conditions including the Reynolds stress components are also considered. The Reynolds-averaged Navier-Stokes equations are solved numerically above the near-wall rough layer, while a second-order turbulence closure is employed in all regions. The rough-wall second-order closure is developed by adopting an existing smooth-wall model. The computational results, including the skin friction coefficient, the log-law mean velocity, the roughness function, the Reynolds stresses, and the turbulent kinetic energy, are presented and compared with those obtained by using a previously developed two-equation turbulence closure. The results show that the new rough-wall layer modeling approach with the second-order turbulence closure model satisfactorily predicted the skin friction coefficient, the log-law mean velocity, the roughness function, and the Reynolds shear stress. However, the results for the Reynolds normal stresses are different from the measured data in the inner 20-60% of the boundary layer due to the interface stress jump conditions employed in the present rough-wall layer modeling approach.     

Improved parameterisation for the numerical modelling of air pollution within an urban street canyon

Numerical modelling for application to wind flow and dispersion in urban environments has noticeably progressed in recent years, to currently represent a widely used tool for simulating mechanical processes governing air pollution in complex geometries. In particular, Computational Fluid Dynamic (CFD) techniques based on RANS (Reynolds-Averaged Navier–Stokes equations) models, are extensively used to produce detailed simulations of the wind flow and turbulence in the urban canopy. However, several studies have indicated that RANS models, and in particular the widely used standard k–? turbulence model, are sensitive to the particular form of inlet profiles for turbulence and velocity. In the present study, simulations of the wind flow and dispersion within an idealised street canyon were carried out using the standard k–? turbulence model provided by the commercial software FLUENT. The aim of this study was to improve the standard k–? model performance by modifying the model parameters according to the chosen form of inlet profiles for velocity and turbulence. Capability of the model to reproduce real wind flow fields, turbulence and concentration patterns was evaluated by comparing the model results against recently published wind tunnel data. Results for turbulent kinetic energy and concentration showed that the redefinition of the default dispersive parameters can significantly enhance the model performance. The newly proposed parameterisations of the standard k–? turbulence model can be readily implemented within commercial CFD software packages, offering a reliable modelling tool for application to urban air pollution and other environmental studies.     

Application of the Boltzmann kinetic equation to the eddy problems

The main purpose of this work is to investigate the feasibility of applying a kinetic approach to the problem of modeling turbulent and unstable flows. First, initial value problems with the Taylor–Green (TG) type and isotropic velocity conditions for compressible flow in two-dimensional (2D) and three-dimensional (3D) periodic domains are considered. Further, 3D direct numerical simulation of decaying isotropic turbulence is performed. Macroscopic flow quantities of interest are examined. The simulation is based on the direct numerical solution of the Boltzmann kinetic equation using an explicit–implicit scheme for the relaxation stage. Comparison with the solution of the Bhatnagar–Gross–Krook (BGK) model equation obtained by using an implicit scheme is carried out for the decaying isotropic turbulence problem and demonstrates a small difference. For the TG initial condition results show a fragmentation of the large initial eddies and subsequently the full damping of the system. Numerical data are close to the analytic solution of TG problem. A dependence of the kinetic energy on the wave number is obtained by means of the Fourier expansion of velocity components. A power-law exponent for the kinetic energy spectrum tends to the theoretical value “−3” for 2D turbulence in 2D case and to the famous Kolmogorov value “−5/3” in 3D case.     

A three-dimensional passage flow analysis method aimed at centrifugal impellers

A partially parabolic procedure is developed to analyze three-dimensional viscous flows through curved ducts of arbitrary cross-section. The procedure, eventually aimed at centrifugal impeller analysis, incorporates a finite-volume method using a strong conservation form of the parabolized Navier-Stokes equations written in arbitrary curvilinear coordinates. Cartesian velocity components and pressure are used as dependent variables. A solution is achieved through pressure corrections which influence velocity semi-implicity. The basic physical elements associated with centrifugal impellers are considered. Laminar flow through 90° bent square duct, turbulent flow in low-aspect-ratio diffusers and subsonic compressible flow through an accelerating rectangular elbow are calculated. Turbulence is accounted for using the k − ε turbulence model. Good correlation between the predictions and experimental data was achieved.     

三相鼓泡床反应器中固体浓度分布与数值模拟

在气、液两相为连续相固相为颗粒流(granular)的基础上进行模拟,建立了描述三相浆态鼓泡床中湍流流动的模型,在模型中考虑了气相在穿过液相中所形成的气泡直径以及固体颗粒大小对系统的影响,同时对任意两相之间的连续性方程和动量方程进行耦合。以三相浆态鼓泡床固体浓度分布为例进行数值模拟,模拟值与实验值吻合较好,表明模型可靠,模拟方法正确,为研究三相浆态床流态特征提供了一种便捷的方法,也为三相浆态床反应器的设计、开发、放大开辟了一条新的道路。     

A Functional Approach to the Visual Simulation of Gaseous Turbulence

This paper presents a functional method for the visual simulation of 2-D or 3-D turbulent gaseous motion by using time-varying fractals. The used function incorporates results from the “spectral theory of turbulence”, thereby providing a physics-based approach adapted to the needs of computer graphics. The involved turbulence function is band-limited, continuous, differentiable, anisotrop, and smooth, provides different fractal dimensions along each axis, may be evaluated locally with different parameters, and requires only minimal storage space, thus supporting an implementation on large parallel processing networks with small nodes. Inhomogeneity in the form of local disturbances of the turbulence field may also be easily considered. The parameters used to describe turbulent motion are rather intuitive, so that they may be utilized easily by users. Examples for modeling different types of clouds and fire are given.     

On the realizability of reynolds stress turbulence closures

The realizability of Reynolds stress models in homogeneous turbulence is critically assessed from a theoretical standpoint. It is proven that a well known second-order closure model formulated using the strong realizability constraints of Schumann (1977) and Lumley (1978) is, in fact, not a realizable model. The problem arises from the failure to properly satisfy the necessary positive second time derivative constraint when a principal Reynolds stress vanishes-a flaw that becomes apparent when the nonanalytic terms in the model are made single-valued as required on physical grounds. More importantly, arguments are advanced which suggest that it is impossible to identically satisfy the strong from of realizability in any version of the present generation of second-order closures. On the other hand, models properly formulated to satisfy the weak form of realizability—wherein states of one or two component turbulence are made inaccessible in finite time via the imposition of a positive first derivative condition—are found to be realizable. However, unlike the simpler and more commonly used second-order closures, these models can be ill-behaved near the extreme limits of realizable turbulence due to the way that higher-degree nonlinearities are often unnecessarily introduced to satisfy realizability. Illustrative computations of homogeneous shear flow are presented to demonstrate these points which can have important implications for turbulence modeling.     

Using random forests to diagnose aviation turbulence

Atmospheric turbulence poses a significant hazard to aviation, with severe encounters costing airlines millions of dollars per year in compensation, aircraft damage, and delays due to required post-event inspections and repairs. Moreover, attempts to avoid turbulent airspace cause flight delays and en route deviations that increase air traffic controller workload, disrupt schedules of air crews and passengers and use extra fuel. For these reasons, the Federal Aviation Administration and the National Aeronautics and Space Administration have funded the development of automated turbulence detection, diagnosis and forecasting products. This paper describes a methodology for fusing data from diverse sources and producing a real-time diagnosis of turbulence associated with thunderstorms, a significant cause of weather delays and turbulence encounters that is not well-addressed by current turbulence forecasts. The data fusion algorithm is trained using a retrospective dataset that includes objective turbulence reports from commercial aircraft and collocated predictor data. It is evaluated on an independent test set using several performance metrics including receiver operating characteristic curves, which are used for FAA turbulence product evaluations prior to their deployment. A prototype implementation fuses data from Doppler radar, geostationary satellites, a lightning detection network and a numerical weather prediction model to produce deterministic and probabilistic turbulence assessments suitable for use by air traffic managers, dispatchers and pilots. The algorithm is scheduled to be operationally implemented at the National Weather Service’s Aviation Weather Center in 2014.     

不确定环境下的软管-锥套建模及控制研究

提出了一种能有效适应不确定性环境的锥套稳定控制方法。在对软管-锥套非线性动力学模型线性化及降阶处理的基础上,将大气紊流对软管-锥套的扰动视为随机扰动,并把这种扰动作为参数与软管-锥套系统降阶模型中的状态合并成增广的系统状态量,采用卡尔曼滤波方法对系统状态量进行实时估计,并设计LQG控制器,实现对锥套的稳定控制。仿真结果表明,该方法能实时跟踪大气紊流的变化,且具有较好的抗大气紊流干扰的能力,能保证锥套的稳定。     

Lattice BGK direct numerical simulation of fully developed turbulence in incompressible plane channel flow

Over the last decade, lattice Boltzmann methods have proven to be reliable and efficient tools for the numerical simulation of complex flows. The specifics of such methods as turbulence solvers, however, are not yet completely documented. This paper provides results of direct numerical simulations (DNS), by a lattice Boltzmann scheme, of fully developed, incompressible, pressure-driven turbulence between two parallel plates. These are validated against results from simulations using a standard Chebyshev pseudo-spectral method. Detailed comparisons, in terms of classical one-point turbulence statistics at moderate Reynolds number, with both numerical and experimental data show remarkable agreement.

Consequently, the choice of numerical method has, in sufficiently resolved DNS computations, no dominant effect at least on simple statistical quantities such as mean flow and Reynolds stresses. Since only the method-independent statistics can be credible, the choice of numerical method for DNS should be determined mainly through considerations of computational efficiency. The expected practical advantages of the lattice Boltzmann method, for instance against pseudo-spectral methods, are found to be significant even for the simple geometry and the moderate Reynolds number considered here. This permits the conclusion that the lattice Boltzmann approach is a promising DNS tool for incompressible turbulence.     

Verification of RANS solvers with manufactured solutions

This paper discusses code verification of Reynolds-Averaged Navier Stokes (RANS) solvers with the method of manufactured solutions (MMS). Examples of manufactured solutions (MSs) for a two-dimensional, steady, wall-bounded, incompressible, turbulent flow are presented including the specification of the turbulence quantities incorporated in several popular eddy-viscosity turbulence models. A wall-function approach for the MMS is also described. The flexiblity and usefulness of the MS is illustrated with calculations performed in three different exercises: the calculation of the flow field using the manufactured eddy-viscosity; the calculation of the eddy-viscosity using the manufactured velocity field; the calculation of the complete flow field coupling flow and turbulence variables. The results show that the numerical performance of the flow solvers is model dependent and that the solution of the complete problem may exhibit different orders of accuracy than in the exercises with no coupling between the flow and turbulence variables.     

Nonlinear aircraft sensor fault reconstruction in the presence of disturbances validated by real flight data

This paper proposes an approach for Inertial Measurement Unit sensor fault reconstruction by exploiting a ground speed-based kinematic model of the aircraft flying in a rotating earth reference system. Two strategies for the validation of sensor fault reconstruction are presented: closed-loop validation and open-loop validation. Both strategies use the same kinematic model and a newly-developed Adaptive Two-Stage Extended Kalman Filter to estimate the states and faults of the aircraft. Simulation results demonstrate the effectiveness of the proposed approach compared to an approach using an airspeed-based kinematic model. Furthermore, the major contribution is that the proposed approach is validated using real flight test data including the presence of external disturbances such as turbulence. Three flight scenarios are selected to test the performance of the proposed approach. It is shown that the proposed approach is robust to model uncertainties, unmodeled dynamics and disturbances such as time-varying wind and turbulence. Therefore, the proposed approach can be incorporated into aircraft Fault Detection and Isolation systems to enhance the performance of the aircraft.     

Depth Averaged Modelling of Turbulent Shallow Water Flow with Wet-Dry Fronts

Depth averaged models are widely used in engineering practice in order to model environmental flows in river and coastal regions, as well as shallow flows in hydraulic structures. This paper deals with depth averaged turbulence modelling. The most important and widely used depth averaged turbulence models are reviewed and discussed, and a depth averaged algebraic stress model is presented. A finite volume model for solving the depth averaged shallow water equations coupled with several turbulence models is described with special attention to the modelling of wet-dry fronts. In order to asses the performance of the model, several flows are modelled and the numerical results are compared with experimental data.