CAPITULO II FUNDAMENTACION TEORICA
II.2. La motivación
II.4.3. Las redes sociales (twitter – facebook)
Two sets of numerical techniques handling computational continuum mechanics dominate the field: the Finite Volume Method (FVM) and the Finite Element Method. Once can clearly show both are based on the same principles and are closely mathematically related. Various variants and generalisations can also be devised, but so far their impact has been limited. Some deserve a mention:
• Discontinuous Galerkin discretisation provides a common framework for the FVM and FEM. It combines the conservative flux formulation which is a basis of the FVM with the elemental shape function and a weak formula-tion of the FEM. One of interesting uses would be a formal higher-order extension beyond second-order integrals. So far, the most important use is the generalisation of mathematical machinery underpinning both methods
• Lattice Gas and Lattice Boltzmann methods claim to simulate the flow equations from basic principles of molecular dynamics instead of using the continuum equations. Clearly, averaging over sufficient number of latice operations will yield the original PDEs and producing the required solution.
Attractions of this method follow from simplifications of latice operations to very primitive accuracy (e.g. 3 velocity levels) and simplifications in complex geometry handling
Numerical Techniques in Aerospace Simulations: Spatial Techniques
• Finite Difference Method (FDM): really appropriate only for structured meshes; no conservation properties. Not used commercially. Important use of FDM is in aero-acoustic simulations, where high-order discretisation is essential (e.g. 6th order in space and 10th order in time). Problems with high-order boundary conditions.
• Finite Volume Method: dominates the fluid simulation arena
• Finite Element Method. No particular reason why it cannot be used; how-ever, the bulk of the numerical method development targeted to FVM. As a result, some techniques and solution methodology not suitable for fluid flow.
I do not know any FEM fluid flow aerospace solvers, but FEM dominates the structural analysis arena
• Discontinuous Galerkin: a formal unification of the FEM and FVM ideas.
Strongly conservative and consistent, but extensions are still impractical
2.3 Finite Volume or Finite Element? 27 (control of matrix properties, solution techniques etc.). Consider it work-in-progress
• Monte Carlo Methods: extensively used in low-density high-speed aerody-namics (Space Shuttle re-entry). Techniques are specialised for high effi-ciency
• Spectral techniques: special purposes only. Extremely efficient and accurate for “box in a box” and cyclic matching simulations, e.g. DNS
Handling Temporal Variation
• Steady state: no temporal discretisation required
• Time domain: bulk of transient flow simulations
• Frequency domain: special purposes. Example: in turbo-machinery simu-lations, it is possible to extract the dominant frequencies. Instead of solving a time-dependent problem, a series of steady simulations is set up, each for a selected frequency (effects of the temporal derivative now convert into a source/sink term). The time-dependent behaviour is recovered from the combination of frequency solutions.
Simplified Flow Solvers in Industrial Use
• It is not always necessary to run a full Navier-Stokes solver to obtain usable results. Also, the simulation time is sometimes critical: approximate result now.
• Panel method. Combination of source, sinks, doublets and vortex el-ements used to assemble a “zero streamline” form which represents the body. Extremely fast and capable of producing indicative solutions with experience.
http://www.engapplets.vt.edu/fluids/vpm/
• Potential Flow Solvers. Incompressible formulation considered too ba-sic. However, the compressible potential formulation, or even a transient compressible potential can be very useful. The main effect missing in the simplified form is the viscosity effect in the boundary layer: effective change of shape for the potential region. Potential flow solver can be used to ac-celerate the solution to steady-state for more complex solver: initialisation of the solution
• Potential Flow with Boundary Layer Correction. Here, a combina-tion of the compressible potential and boundary layer correccombina-tion takes into account the near-wall effect: the geometry is corrected for displacement thickness in the boundary layer
• Euler Flow Solver. Neglects the viscous effects but the compressibility physics can be handled in full.
Chapter 3
CFD in Automotive Applications
CFD Methodology
• Numerous automotive components involve fluid flow and require optimi-sation. This opens a wide area of potential of CFD use in automotive industry
• CFD approaches the problem of fluid flow from fundamental equations:
no problem-specific or industry-specific simplification
• A critical step involves complex geometry handling: it is essential to capture real geometrical features of the engineering component under con-sideration
• Traditional applications involve incompressible turbulent flow of Newtonian fluids
• While most people think of automotive CFD in terms of external aerody-namics simulations, reality of industrial CFD use is significantly different
Automotive CFD Today
• In numbers of users in automotive companies, CFD today is second only to CAD packages
• In some areas, CFD replaces experiments
– Engine coolant jackets
– Under-hood thermal management – Passenger compartment comfort
• In comparison with CFD, experimental studies are expensive, carry limited information and it is difficult to achieve sufficient turn-over
• The biggest obstacle is validation: can CFD results be trusted?
• In other areas, CFD is insufficiently accurate for complete design studies
CFD in Automotive Applications 31 – Required accuracy is beyond the current state of physical modelling
(especially turbulence modelling)
– Simulation cost is prohibitive or turn-around is too slow
– Flow physics is too complex: incomplete modelling or insufficient un-derstanding of detailed physical processes
– In some cases, combined 1-D/3-D studies capture the physics without resorting to complete 3-D study
• Examples:
– Prediction of the lift and drag coefficient on a car body – In-cylinder simulations in an internal combustion engine
– Complete internal combustion engine system: air intake, turbo-charger, engine ports and valves, in-cylinder flow, exhaust and gas after-treatment
• CFD can still contribute: parametric study (trends), reduced experimental work etc.
• Numerical modelling is particularly useful in understanding the flow or looking for qualitative improvements: e.g. optimisation of vehicle soiling pattern on windows
Examples of External Aerodynamics Simulations
CFD in Automotive Applications 33
• CFD is used across the industry, at various levels of sophistication
• Impact of simulations and reliance on numerical methods is greatest in areas that were not studied in detail beforehand
• Considerable use in cases where it is difficult to quantify the results in simple terms like the lift and drag coefficient
– Flow organisation, stability and optimisation
– Detailed look at the flow field, especially in complex geometry
– Optimisation of secondary effects: fuel-air mixture preparation
CFD Capabilities in 1980s: Early Adoption in Aerospace Industry
• Historically, early efforts in CFD involve simplified equations and simula-tions relevant for aerospace industry
• Experience in achieving best results with limited computational resources:
attention given to solution acceleration techniques
• Application-specific physical models
– Linearised potential equations, Hess and Smith, Douglas Aircraft 1966 – 3-D panel codes developed by Boeing, Lockheed, Douglas and others
in 1968
– Specific turbulence models for aerospace flows, e.g. Baldwin-Lomax – Coupled boundary layer-potential flow solver, Euler flow solver
• Capabilities beyond steady-state compressible flow were very limited
CFD in Automotive Applications 35
Early Automotive CFD Simulations
• First efforts aimed at simplified external aerodynamics (1985-1988)
• . . . but airfoil assumptions are not necessarily applicable
• Joint numerical and experimental studies: validation of numerical tech-niques and simulation tools, qualitative results, analysis of flow patterns and similar
• It is quickly recognised that the needs of automotive industry and (poten-tial) capabilities of CFD solvers are well beyond contemporary experimental work
• Focus of early numerical work is on performance-critical components: in-ternal combustion engines and exin-ternal aerodynamics
• Geometry and flow conditions are simplified to help with simulation set-up Example: Intake Valve and Manifold
• 2-D steady-state incompressible turbulent fluid flow
• Axi-symmetric geometry with a straight intake manifold and fixed valve lift
• Simulation by Peri´c, Imperial College London 1985
Automotive of CFD in 1990s: Expanding Computer Power and Vali-dated Models
• Numerical modelling is moving towards product design
– Improvements in computer performance: reduced hardware cost, Moore’s law
– Improved physical modelling and numerics: fundamental problems are with flow, turbulence and discretisation are resolved
– Sufficient validation and experience accumulated over 10 years
CFD in Automotive Applications 37
• Notable improvement in geometrical handling: realistic 3-D geometry
• Graphical post-processing tools and animations: easier solution analysis
• Mesh generation for complex geometry is a bottle-neck: need better tools
Expansion of Automotive CFD
• Increase in computer performance drives the expansion of CFD into new areas by reducing simulation turn-over time
• Massively parallel computers provide the equivalent largest supercomputers at prices affordable in industrial environment (1000s of CPUs)
Physical Modelling
• New physical models quickly find their use, e.g. free surface flows
• Looking at more complex systems in transient mode and in 3-D: simulation of a multi-cylinder engine, with dynamic effects in the intake and exhaust system
• Computing power brings in new areas of simulation and physical modelling paradigms. Example: Large Eddy Simulation (LES) of turbulent flows Integration into a CAE Environment
• Computer-Aided Design software is the basis of automotive industry
• Historically, mesh generation and CFD software are developed separately and outside of CAD environment, but the work flow is CAD based!
• Current trend looks to seamlessly include CFD capabilities in CAD Summary: Automotive CFD Today
• CFD is successfully used across automotive product development
• Initial “landing target” of external aerodynamics and in-cylinder engine simulation still not reached (!) – sufficient accuracy difficult to achieve Lessons Learned
• The success of CFD in automotive simulation is based on providing indus-try needs rather than choosing problems we may simulate: find a critical broken process and offer a solution
• Numerical simulation tools will be adopted only when they fit the product development process: robust, accurate and validated solver, rapid turn-over
• Experimental and numerical work complement each other even if sufficient accuracy for predictive simulations cannot be achieved
– Validation of simulation results ↔ understanding experimental set-up – Parametric studies: speeding up experimental turn-over
• True impact of simulation tools is beyond the obvious uses: industry will drive the research effort to answer its needs
Part II
The Finite Volume Method
Chapter 4
Mesh Handling
4.1 Introduction
When presenting a continuum mechanics problem for computer simulation, one needs to establish not only the mathematical model but also the computational domain. While the choice of physics is relatively general, numerical description of the domain of interest is considerably more complex. Looking at the area of external aerodynamics in aerospace, compressible Navier-Stokes equations for an ideal gas with typically suffice, while the wealth of geometrical shapes defies even basic classification.
In most cases, shape of the spatial domain is of primary interest: capturing it in all relevant detail is essential. In transient simulations, handling the temporal axis is considerably simpler. Due to uni-directional nature of interaction, it is sufficient to split the time interval into a finite number of time-steps and march the solution forward in time.
It quickly becomes clear that fidelity of geometrical description of an engi-neering object plays an important role. For example, in a heat exchanger, it is necessary to capture active surface area with some precision in order to correctly calculate the total heat transfer. At the same time, it is a question of engineering judgement to decide which geometrical features are important for the result and which may be omitted.
A computational mesh splits the space into a finite number of elements (cells, control volumes or similar), bounded by faces and supported by points. Compu-tational locations are located in the cells or on the points in a regular manner.
The idea of mesh support is to discretise the governing equations over each cell and handle cell-to-cell interaction. Some mesh validity criteria follow directly from the above:
• Computational cells should not overlap;
• Computational cells should completely fill the domain of interest.
Every discretisation method bring its own mesh validity criteria and measures of mesh quality. In general terms, a mesh that visually pleasing is also likely to support a quality solution. Our second concern is the interaction between the mesh resolution and (known or implied) solution characteristics. Features such as shocks, boundary layers and mixing planes require higher resolution that a
“far field” section of the domain. Construction of a quality mesh is usually a question of experience and use of quality mesh generation tools. An ideal mesh would be the one uniformly distributing the discretisation error in the solution volume and producing “user-independent” (or, more precisely, user-experience-independent) result. The quest for fast and robust automatic mesh generators iteratively sensitised to the solution is still ongoing.