Status and future directions for turbulence modelling

Progress in the development of a hierarchy of turbulence models for Reynolds-averaged Navier-Stokes codes used in aerodynamic applications is discussed. Although steady progress is demonstrated, transfer of the modelling technology has not kept pace with the development and demands of the CFD tools. An examination of the process of model development leads to recommendations for a better process involving close coordination between modellers, CFD developers and application engineers. In instances where the process is changed and cooperation enhanced, timely transfer is realized. A turbulence modelling information database is proposed to refine the process and open it to greater participation among modelling and CFD practitioners. The citations in this paper are not in our usual format     

Introduction. Computational aerodynamics

The wide range of uses of computational fluid dynamics (CFD) for aircraft design is discussed along with its role in dealing with the environmental impact of flight. Enabling technologies, such as grid generation and turbulence models, are also considered along with flow/turbulence control. The large eddy simulation, Reynolds-averaged Navier-Stokes and hybrid turbulence modelling approaches are contrasted. The CFD prediction of numerous jet configurations occurring in aerospace are discussed along with aeroelasticity for aeroengine and external aerodynamics, design optimization, unsteady flow modelling and aeroengine internal and external flows. It is concluded that there is a lack of detailed measurements (for both canonical and complex geometry flows) to provide validation and even, in some cases, basic understanding of flow physics. Not surprisingly, turbulence modelling is still the weak link along with, as ever, a pressing need for improved (in terms of robustness, speed and accuracy) solver technology, grid generation and geometry handling. Hence, CFD, as a truly predictive and creative design tool, seems a long way off. Meanwhile, extreme practitioner expertise is still required and the triad of computation, measurement and analytic solution must be judiciously used.     

旋转式压缩机气流噪声研究综述和展望

回顾了旋转式压缩机气流噪声理论与应用的国内外研究现状。对气流噪声研究情况进行分类评述：储液器内气流噪声研究，涉及到计算方法和试验设计分析；排气阀的研究，包括流固耦合分析模型和可视化试验；消声器的研究，包括声学理论分析、试验技术和降噪改进方法；压缩机腔体内气流噪声研究，主要集中在声源识别，简化的集总参数模型和基于CFD的声学分析等3个方面。最后讨论了目前研究存在的一些问题和今后的研究方向。     

Direct numerical simulations for assessment of gas-solid drag models in two-dimensional random arrays of particles

The momentum exchange between the phases plays a vital role in modelling of gas–solid flows and it is mathematically described by drag models. However, no consensus exists on which drag model gives the most accurate prediction of the drag force, and, despite the increase in available computing power, the same drag models are used in two-dimensional and three-dimensional simulations. In this study, direct numerical simulations of gas flow through multiple random configurations of static monodisperse particles are performed. The variations of solid volume fraction and particle Reynolds number are in the ranges of 0.05–0.4 and 13.7–136.9, respectively. The drag force exerted on particles is calculated and properly averaged. Based on the simulation results, thirteen drag models are compared and correction factors are introduced using the stochastic gradient descent algorithm. The correction factors provide a simple adjustment for the models to be used in 2D modelling.     

Universal predictability of mobility patterns in cities

Despite the long history of modelling human mobility, we continue to lack a highly accurate approach with low data requirements for predicting mobility patterns in cities. Here, we present a population-weighted opportunities model without any adjustable parameters to capture the underlying driving force accounting for human mobility patterns at the city scale. We use various mobility data collected from a number of cities with different characteristics to demonstrate the predictive power of our model. We find that insofar as the spatial distribution of population is available, our model offers universal prediction of mobility patterns in good agreement with real observations, including distance distribution, destination travel constraints and flux. By contrast, the models that succeed in modelling mobility patterns in countries are not applicable in cities, which suggests that there is a diversity of human mobility at different spatial scales. Our model has potential applications in many fields relevant to mobility behaviour in cities, without relying on previous mobility measurements.     

Comparison of CFD analysis to empirical data in a commercial vortex tube

This paper presents a comparison between the performance predicted by a computational fluid dynamic (CFD) model and experimental measurements taken using a commercially available vortex tube. Specifically, the measured exit temperatures into and out of the vortex tube are compared with the CFD model. The data and the model are both verified using global mass and energy balances. The CFD model is a two-dimensional (2D) steady axisymmetric model (with swirl) that utilizes both the standard and renormalization group (RNG) k-epsilon turbulence models. While CFD has been used previously to understand the fluid behavior internal to the vortex tube, it has not been applied as a predictive model of the vortex tube in order to develop a design tool that can be used with confidence over a range of operating conditions and geometries. The objective of this paper is the demonstration of the successful use of CFD in this regard, thereby providing a powerful tool that can be used to optimize vortex tube design as well as assess its utility in the context of new applications.     

Towards a virtual lung: multi-scale, multi-physics modelling of the pulmonary system

The essential function of the lung, gas exchange, is dependent on adequate matching of ventilation and perfusion, where air and blood are delivered through complex branching systems exposed to regionally varying transpulmonary and transmural pressures. Structure and function in the lung are intimately related, yet computational models in pulmonary physiology usually simplify or neglect structure. The geometries of the airway and vascular systems and their interaction with parenchymal tissue have an important bearing on regional distributions of air and blood, and therefore on whole lung gas exchange, but this has not yet been addressed by modelling studies. Models for gas exchange have typically incorporated considerable detail at the level of chemical reactions, with little thought for the influence of structure. To date, relatively little attention has been paid to modelling at the cellular or subcellular level in the lung, or to linking information from the protein structure/interaction and cellular levels to the operation of the whole lung. We review previous work in developing anatomically based models of the lung, airways, parenchyma and pulmonary vasculature, and some functional studies in which these models have been used. Models for gas exchange at several spatial scales are briefly reviewed, and the challenges and benefits from modelling cellular function in the lung are discussed.     

Theoretical modelling of laminated composite plates

Formulation of appropriate governing equations, simpler than the three-dimensional equations of elasticity yet capable of predicting, fairly accurately, all important response parameters such as stress and strain, is attempted in modelling a structural component. Several theoretical models are available in the literature for the analyses of plates. The emergence of fibre-reinforced plastics as an attractive form of structural construction, added a new complexity to the modelling considerations of laminates by requiring the estimation of the interlaminar stresses and strains. In this paper, modelling considerations of laminated composite plates are discussed. The classical laminated plate theory and higher-order shear deformation models are reviewed to bring out their interlaminar stress predictive capabilities, and some new modelling possibilities are indicated. This work has been supported by the Aeronautics Research and Development Board, Ministry of Defence, Government of India.     

Computational fluid dynamics for turbomachinery internal air systems

Considerable progress in development and application of computational fluid dynamics (CFD) for aeroengine internal flow systems has been made in recent years. CFD is regularly used in industry for assessment of air systems, and the performance of CFD for basic axisymmetric rotor/rotor and stator/rotor disc cavities with radial throughflow is largely understood and documented. Incorporation of three-dimensional geometrical features and calculation of unsteady flows are becoming commonplace. Automation of CFD, coupling with thermal models of the solid components, and extension of CFD models to include both air system and main gas path flows are current areas of development. CFD is also being used as a research tool to investigate a number of flow phenomena that are not yet fully understood. These include buoyancy-affected flows in rotating cavities, rim seal flows and mixed air/oil flows. Large eddy simulation has shown considerable promise for the buoyancy-driven flows and its use for air system flows is expected to expand in the future.     

桥梁气动力CFD模拟中湍流模型的应用现状

近年来,计算流体动力学(CFD)在桥梁风工程中得到了越来越多的尝试与应用。CFD的应用不仅仅是顺应了计算机硬件浮点运算速度的快速发展,而且在处理复杂问题、时间及经济成本方面与风洞试验相比具有巨大的优越性。但是,这一优越性是建立在CFD求解结果具有实用精度的假设前提下的。该文综述了桥梁气动力CFD数值模拟中湍流问题的起源、各类湍流模型的本质特征及其适用范围与局限性。在此基础上,广泛调研了CFD在国内外桥梁气动力数值模拟中的应用,分别按静气动力与气弹两大类问题统计分析了目前CFD模拟与风洞试验结果之间的差距。结果表明,对于静气动力问题,CFD模拟的误差普遍在10%~40%之间;对于气弹问题,CFD模拟的误差普遍介于20%~300%。这一现实表明,以目前的水平,CFD尚无法独立于风洞试验而对桥梁气弹问题给出可靠的评估。要充分发挥计算流体动力学的优势,则必须结合湍流理论,加强各种湍流模型在各类桥梁气动问题中的应用基础研究。     

A crystal plasticity based methodology for fatigue crack initiation life prediction in polycrystalline copper

Fatigue failure is the dominant mechanism that governs the failure of components and structures in many engineering applications. In conventional engineering applications due to the design specifications, a significant proportion of the fatigue life is spent in the crack initiation phase. In spite of the large number of works addressing fatigue life modelling, the problem of modelling crack initiation life still remains a major challenge in the scientific and engineering community. In the present work, we present a methodology for estimating fatigue crack initiation life using macroscale loading conditions and the microstructural phenomenon causing crack initiation. Microstructure sensitive modelling is used for predicting potential crack initiation life by employing randomly generated representative microstructures. The microstructural parameters contributing to crack initiation life are identified and accounted for by computing lattice level energy dissipation during fatigue crack initiation. This model is coupled with experimental results to improve the predictive capabilities and identification of potentially damaging weak points in the microstructures. The estimated values for crack initiation life were found to be in good agreement with the experimentally observed values of initiation life. The results have shown that this kind of approach could be successfully used to predict crack initiation life in polycrystalline materials. This work successfully provides an approach for estimating crack initiation life based upon numerical computations accounting for the microstructural phenomenon.     

Critical wind velocity for arresting upwind gas and smoke dispersion induced by near-wall fire in a road tunnel

In case of a tunnel fire, toxic gas and smoke particles released are the most fatal contaminations. It is important to supply fresh air from the upwind side to provide a clean and safe environment upstream from the fire source for people evacuation. Thus, the critical longitudinal wind velocity for arresting fire induced upwind gas and smoke dispersion is a key criteria for tunnel safety design. Former studies and thus, the models built for estimating the critical wind velocity are all arbitrarily assuming that the fire takes place at the centre of the tunnel. However, in many real cases in road tunnels, the fire originates near the sidewall. The critical velocity of a near-wall fire should be different with that of a free-standing central fire due to their different plume entrainment process. Theoretical analysis and CFD simulation were performed in this paper to estimate the critical velocity for the fire near the sidewall. Results showed that when fire originates near the sidewall, it needs larger critical velocity to arrest the upwind gas and smoke dispersion than when fire at the centre. The ratio of critical velocity of a near-wall fire to that of a central fire was ideally estimated to be 1.26 by theoretical analysis. Results by CFD modelling showed that the ratio decreased with the increase of the fire size till near to unity. The ratio by CFD modelling was about 1.18 for a 500kW small fire, being near to and a bit lower than the theoretically estimated value of 1.26. However, the former models, including those of Thomas (1958, 1968), Dangizer and Kenndey (1982), Oka and Atkinson (1995), Wu and Barker (2000) and Kunsch (1999, 2002), underestimated the critical velocity needed for a fire near the tunnel sidewall.     

Flashing liquid jets and two-phase droplet dispersion II. Comparison and validation of droplet size and rainout formulations

Loss of containment often results in flashing releases of hazardous chemicals into the atmosphere. Rainout of these chemicals reduces airborne concentrations, but can also lead to extended cloud duration because of re-evaporation of the rained-out liquid. Therefore, for hazard assessment one must use models which accurately predict both the amount of rainout and its rate of re-evaporation. However, the findings of a literature survey reveal weaknesses in the state-of-the-art for modelling the sub-processes of droplet atomisation, atmospheric expansion, two-phase dispersion, rainout, pool formation and re-evaporation. A recent joint industry project has implemented recommendations from this survey, deriving from scaled water experiments droplet size correlations for conditions ranging from negative to high superheat. This experimental programme is reported in more detail in a separate companion paper. As a whole these correlations describe a tri-linear function of droplet size (expressed as Sauter mean diameter) as a function of superheat. This function describes the regimes of non-flashing, the transition between non-flashing and flashing, and fully flashing. The new correlations have been compared with previous correlations recommended by the Dutch Yellow Book and CCPS Books. The correlations are validated against published experiments including the STEP experiments (flashing propane jets), experiments by the Von Karman Institute (flashing R134-A jets), and water and butane experiments carried out by Ecole des Mines and INERIS. The rainout calculations by the dispersion model have been validated against a subset of the CCPS experiments (flashing jets of water, CFC-11, chlorine, cyclohexane, monomethylamine).     

Flashing liquid jets and two-phase droplet dispersion I. Experiments for derivation of droplet atomisation correlations

The large-scale release of a liquid contained at upstream conditions above its local atmospheric boiling point is a scenario often given consideration in process industry risk analysis. Current-hazard quantification software often employs simplistic equilibrium two-phase approaches. Scaled water experiments have been carried out measuring droplet velocity and droplet size distributions for a range of exit orifice aspect ratios (L/d) and conditions representing low to high superheat. 2D Phase-Doppler Anemometry has been utilised to characterise droplet kinematics and spray quality. Droplet size correlations have been developed for non-flashing, the transition between non-flashing and flashing, and fully flashing jets. Using high-speed shadowography, transition between regimes is defined in terms of criteria identified in the external flow structure. An overview companion paper provides a wider overview of the problem and reports implementation of these correlations into consequence models and subsequent validation. The fluid utilised throughout is water, hence droplet correlations are developed in non-dimensional form to allow extrapolation to other fluids through similarity scaling, although verification of model performance for other fluids is required in future studies. Data is reduced via non-dimensionalisation in terms of the Weber number and Jakob number, essentially representing the fluid mechanics and thermodynamics of the system, respectively. A droplet-size distribution correlation has also been developed, conveniently presented as a volume undersize distribution based on the Rosin-Rammler distribution. Separate correlations are provided for sub-cooled mechanical break-up and fully flashing jets. This form of correlation facilitates rapid estimates of likely mass rainout quantities, as well as full distribution information for more rigorous two-phase thermodynamic modelling in the future.     

Efficient CFD Simulation Model for a Planetary Gearbox

Planetary gears are used to transmit power at high gear ratios in limited space. Typical applications are drive trains in the automotive industry, e.?g. in cars, trucks and buses. The oil distribution in planetary gearboxes is difficult to predict. There is only basic knowledge about lubrication designs with effective oil distribution and high efficiency. Advanced methods are very helpful in improving the design of planetary gearboxes in respect of their lubrication.In recent years, CFD (computational fluid dynamics) has become a valuable tool for simulating the oil distribution in gearboxes. By comparison with experimental and empirical methods, CFD provides oil distribution simulation results and can be applied to arbitrary geometries. However, CFD simulations tend to require comparatively high computing time and capacities. Therefore, efficient CFD simulation models are required, especially for complex gearbox topologies.Within the framework of this study, a finite volume CFD model of a dip-lubricated planetary test gearbox has been developed. It includes the modelling of all gear meshes and bearings and has a very high level of detail. The element number was reduced as far as reasonable possible, resulting in little computing time with regard to the modeling depth. Moreover, the computational effort was further reduced by considering the bearings to be static. Through use of the developed simulation model, the influence of different parameters was investigated. This work will help to improve the lubrication design of planetary gearboxes.     

Comparison of three computational models for predicting pressurization characteristics of cryogenic tank during discharge

In order to select an effective approach to predict the pressurization characteristics of cryogenic tank during rocket launching, three computational models, defined as 0-D, 1-D and CFD models, are used to obtain the pressure evolution and thermal performance of a cryogenic tank during pressurized discharge period. Several pressurization cases are computed by all of the three models to evaluate their predictive abilities and effects, respectively. The comparative study shows that for the case with a diffuser-type injector at the tank inlet, the consistent results by the three models are obtained in the most of period, except that 1-D model has a peak departure prediction of pressure value at the beginning of process. All of the three models can be used to predict the pressurization performance, and their predictive abilities could be validated with one another. The CFD model is the unique suitable model to display the pressurization performance including physical distribution in radial direction especially for the system with no-diffuser-type injector. Based on the analysis, the application selection of three models for different cases is accomplished. The 0-D model is the priority selection for a simple pressure prediction of tank ullage, even for the situation that severe temperature distribution exists in the ullage range. The 1-D model is the optimal selection as considering both the convenience and the time consumption for the constant-pressure cases. But it is not recommended in a constant-inlet flux cases for its distinct predicting deviation at the beginning of the process. When the detailed distributions within the tank are concerned, the CFD model is the unique selection. The results of this paper may be beneficial to the model selection and optimization analysis of a pressurization system.     

A High-Temperature, Thermal Non-equilibrium Equation of State for Ammonia

The engineering applications of ammonia extend far beyond the pressure and temperature ranges for which thermodynamic models currently exist in the literature. Thus, a thermal non-equilibrium thermochemical model was developed to compute the composition and thermodynamic properties of ammonia for an extended temperature and pressure range that includes ionization reactions. Thermal non-equilibrium between electrons and heavy particles was included and is presented for ratios of 1/2, 1, 2 and 3. The fourteen-equation nonlinear system produced under the assumptions of ideal gas and two-temperature local thermodynamic equilibrium was solved numerically using a Newton-Raphson method. The thermochemical model is verified for both the composition and thermodynamic properties by comparisons to existing thermochemical models in the literature. These comparisons verify the model for the available, yet limited, temperature and density ranges. Analysis of the composition and thermodynamic properties as a function of the independent properties confirms the necessity for such a model as part of rigorous computations with computational fluid dynamics (CFD) or magnetohydrodynamics (MHD) computer codes. The model can be easily cast in tabular form to complement the set of conservation equations utilized by such codes.     

More MILP models for hybrid flow shop scheduling problem and its extended problems

With the rapid development of computer technology and related softwares for mathematical models, mathematical modelling of scheduling problems is receiving growing attention from researchers. In this work, the hybrid flow shop scheduling problem with unrelated parallel machines (HFSP-UPM) with the objective aimed to minimise the makespan is studied. According to the characteristics of the HFSP-UPM, eight mixed integer linear programming (MILP) models are formulated in order to obtain optimal solutions based on different modelling ideas. Then, these models are extended to solve HFSP-UPM with sequence-dependent setup times (HFSP-UPM-SDST), no-wait HFSP-UPM (HFSP-UPM-NW) and HFSP-UPM with blocking (HFSP-UPM-B). All the proposed models and the existing model are detailedly compared and evaluated under three aspects namely modelling process, size complexity and computational complexity. Numerical experiments show that MILP models dependent on diverse modelling ideas perform very differently. The model developed based on stage precedence is the best one and should be given preference in future applications. In addition, the proposed models of HFSP-UPM-NW and HFSP-UPM-B improve several best known solutions for the test instances in the existing literature.