Large-Eddy Simulation of a Two-Phase Plane Mixing-Layer

ERCOFTAC Series, 2011

quality of LES. The development of computational resources and the corresponding tendency to apply LES-methodologies to turbulent flow problems of significant complexity, such as arise in various applications in technology and in many natural flows, makes the issue of assessing and optimizing the quality of LES predictions a timely challenge. Different error sources are present in LES, which are mainly related to physical modeling (especially as regards subgrid scales), to numerical discretization techniques, to boundary-condition treatment, and to grid resolution and design. These errors may interact in a complex non-linear manner, eventually leading to unpredictable and unexpected effects on LES results.

ERCOFTAC series, 2001

Aims and Scope of the Series ERCOFTAC (European Research Community on Flow, Turbulence and Combustion) was founded as an international association with scientific objectives in 1988. ERCOFTAC strongly promotes joint efforts of European research institutes and industries that are active in the field of flow, turbulence and combustion, in order to enhance the exchange of technical and scientific information on fundamental and applied research and design. Each year, ERCOFTAC organizes several meetings in the form of workshops, conferences and summerschools, where ERCOFTAC members and other researchers meet and exchange information. The ERCOFTAC Series will publish the proceedings of ERCOFTAC meetings, which cover all aspects of fluid mechanics. The series will comprise proceedings of conferences and workshops, and of textbooks presenting the material taught at summerschools. The series covers the entire domain of fluid mechanics, which includes physical modelling, computational fluid dynamics including grid generation and turbulence modelling, measuring-techniques, flow visualization as applied to industrial flows, aerodynamics, combustion, geophysical and environmental flows, hydraulics, multiphase flows, non-Newtonian flows, astrophysical flows, laminar, turbulent and transitional flows. The titles published in this series are listed at the end of this volume.

22nd Australasian Fluid Mechanics Conference AFMC2020, Brisbane, Australia, 7-10 December 2020, 2020

The Proceedings of the 22nd Australasian Fluid Mechanics Conference AFMC2020 focuses on many aspects of fluid mechanics and their applications, especially in terms of diversity, challenges, ecology, and public health relevant to the 21st century. The event organisation aimed to facilitate the sharing of information among biomedical, chemical, civil, environmental, mechanical, mining, nuclear and water engineers, mathematicians and scientists coming from different regions, universities, industries and backgrounds, including developed and developing countries, and students, young and senior professionals. After reviewing the challenges associated with fluid mechanics in terms of diversity, challenges, ecology, public health, socio-economics into the 21st century, the proceedings peer-review process is detailed. The proceedings contents are listed, as well as the AFMC2020 organisation. At the end, the reviewers are acknowledged.

Journal of Turbulence, 2012

Fluid Mechanics and Its Applications, 2002

The purpose of this series is to focus on subjects in which fluid mechanics plays a fundamental role. As well as the more traditional applications of aeronautics, hydraulics, heat and mass transfer etc., books will be published dealing with topics which are currently in a state of rapid development, such as turbulence, suspensions and multi phase fluids, super and hypersonic flows and numerical modelling techniques.

Flow dynamics is a basic research field that deals with physical phenomena appearing in wide spatial and temporal scales. Also, it involves various applications including keys to solve serious problems in this century --about environment, energy, safety, biology, transportation, etc. The "International COE (Center of Excellence) of Flow Dynamics," Tohoku University, is selected as a 21st Century COE program, Ministry of Education,Culture,Sports,Science and Technology. This international conference would provide unique opportunities for promoting discussions and information exchange on this attractive subject.

Shock Waves, 1999

Advances in Heat Transfer, 1994

LARGE-EDDY SIMULATION: MODELS AND APPLICATIONS 327 1. For directions normal to solid walls (y in this case), Grotzbach suggests that the viscous sublayer should be resolved by at least three grid points. Now, the sublayer thickness is Y: y v = uu, Thus, by assuming y: = 11 and using Eq. (1 1) for the friction velocity u,, this condition can be expressed as Of course, if the computational grid is selectively refined near the walls, a somewhat larger value of A y can be used in the bulk flow region. 2. As for the streamwise direction x , the Kolmogorov length scale, Eq. (5a), can be written (Landau and Lifschitz, 1959) as in which E is the turbulence energy-dissipation rate. Grotzbach assumes that the mesh size along x can be somewhat larger than this scale: A x 5 (M)(Now, since the mesh spacing along x cannot depend on the distance from walls, the constraint on A x is actually imposed by the highest value attained by E along the cross-stream direction. According to the theory of equilibrium boundary layers (Hinze, 1975) and to experimental data (Laufer, 1950, 1954), this occurs at the edge of the viscous sublayer (y = y,) and is 4 E,, = (2-3)-, Y v the exact value depending on the Reynolds number of the flow. By using Eqs. (11) and (14) for u, and y v , we may write Eq. (18) as follows: Re: ' ' s4 E,, = (1.50-2.25)10-'~'-328 MICHELE CIOFALO From Eqs. (17) and (19) the following condition is obtained for A x : A x-I (23-46)Rer7/'. 6 It is noteworthy that the constraints on A x , Eq. (201, and on Ay, Eq. (151, are comparable, although they were derived from quite different approaches. This is a consequence of turbulence being nearly isotropic at the smallest scales. 3. Finally, the spanwise direction z can be treated as the streamwise direction x if the computational box is bounded laterally by periodicity planes, and as the cross-stream direction y if it is bounded by solid walls. In the former case, the spanwise meshing must satisfy Az-5 (23-46)Re;7/8. s Conditions (15)) (201, and (21) may be summarized, choosing intermediate values for the constants, as A x Ay Az-= 2-=-< 35Rei7l8 6 6 6-Hence, the minimum total number of grid points is for L, = 46, L, = L, = 26. Equation (23) gives a dependence of Np on Re, even more sensitive than Eq. (81, but specifies a small proportionality factor. As regards the time step, criterion (7) should be complemented by the Courant criterion. In fact, although this is a necessary stability requirement only when explicit time-stepping methods are used, it is generally considered as a more widely applicable accuracy requirement for complex flows. It may be written here as Ax U At <-, which, taking Eq. (22) into account, becomes rS2 A t < 35v This last criterion describes a more sensitive dependence of A t on Re, than does Eq. (71, but actually becomes more stringent only at very large LARGE-EDDY SIMULATION: MODELS AND APPLICATIONS 329 Reynolds numbers. Up to Re, 2: 10" it is automatically satisfied provided that criterion (7) is respected. Thus, the time step can be chosen to be s2 A t = const *-V in which the constant is of the order of 1 (in the following, the value 0.5 will be conservatively assumed). In a simulation involving n LETOTs, Eqs. (12) and (26) imply for the number of time steps The values of Np and Nt given by Eqs. (23) and (271, respectively, for the direct simulation of a plane-channel turbulent flow over n = 10 LETOTs, are summarized in Table I (columns 2 and 3) as functions of the Reynolds number Re, in the range 103-104 (column 1). The same table reports in column 4 corresponding estimates of the storage that would be required if the Harwell-FLOW3D code (Burns et al., 1988, 1989) were used. It is expressed in megawords, i.e., millions of real 8-byte locations, and is computed on the basis of about 80 words per grid point. Finally, estimates of the required CPU time on a Cray-2 computer for the same code are reported in column 5. They are computed by assuming the CPU time to be proportional to Np"I3 and to N,, and to be about 1 second per time step for a grid having lo4 nodes. All these assumptions are based on the author's previous experience with the Harwell-FLOW3D code. Note that the Cray-2 has 256 megawords (Mwords) of in-core storage; for larger memory requirements, out-of-core storage would have to be used, so that the reported CPU-time estimates should be multiplied even by several TABLE I ESTIMATED MINIMUM STORAGE AND CPU-TIME REQUIREMENTS FOR DIRECT SIMULATION USING HARWELL-FLOW3D ON A CRAY-2 Re, % 4 Storage (Mwords) CPU time