Overview of the hottest computational fluid dynami

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Overview of computational fluid dynamics

1 what is computational fluid dynamics

computational fluid dynamics (CFD) is the analysis of systems containing physical phenomena such as fluid flow and heat conduction through computer numerical calculation and image display. The basic idea of CFD can be summed up as follows: replace the fields of physical quantities, such as velocity field and pressure field, which were originally continuous in the time domain and space domain with a set of variable values at a limited number of discrete points, and establish the algebraic fully automatic spring tension and compression testing machine operation steps: Equations on the relationship between field variables at these discrete points through certain principles and methods, Then the approximate values of field variables are obtained by solving algebraic equations. CFD can be regarded as the numerical simulation of flow under the control of basic flow equations (mass conservation equation, flight conservation equation, energy conservation equation). Through this numerical simulation, we can obtain the distribution of basic physical quantities (such as velocity, pressure, temperature, concentration, etc.) at various positions in the flow field of extremely complex problems, as well as the change of these physical quantities with time, and determine the vortex distribution characteristics, cavitation characteristics, and flow separation zone. It can also be used to calculate other relevant physical quantities, such as torque, hydraulic loss and efficiency of rotating fluid machinery. In addition, combined with CAD, it can also carry out structural optimization design, etc. CFD method, traditional theoretical analysis method and experimental measurement method form a complete system for studying fluid flow problems. Figure 1 shows the "three-dimensional" fluid mechanics schematic diagram representing the relationship between the three. The advantage of theoretical analysis method is that the results obtained are universal and various influencing factors are clearly visible. It is the theoretical basis for guiding experimental research and verifying new numerical calculation methods. However, it often requires the abstraction and simplification of the computing object, so that it is possible to obtain the theoretical solution. For the nonlinear case, only a few flows can give analytical results

schematic diagram of "three-dimensional" hydrodynamics

the experimental results obtained by the experimental measurement method are authentic and reliable. It is the basis of theoretical analysis and numerical methods, and its importance should not be underestimated. However, experiments are often limited by model size, flow field disturbance, personal safety and measurement accuracy, and sometimes it may be difficult to obtain results by the test force method. In addition, the experiment will encounter many difficulties, such as the investment of funds, the huge consumption of human and material resources, and the long cycle

the CFD method just overcomes the weakness of the previous two methods and realizes a specific calculation on the computer. It's like doing a physics experiment on a computer. For example, by calculating the flow around the wing and displaying the results on the screen, we can see various details of the flow field, such as the movement and intensity of the shock wave, the generation and propagation of the vortex, the separation of the flow, the pressure distribution on the surface, the magnitude of the force and its change with time. Numerical simulation can vividly reproduce the flow situation, which is no different from doing experiments

2 characteristics of computational fluid dynamics

cfd has the advantages of strong adaptability and wide application. Firstly, the governing equations of the flow problems are generally nonlinear, with many independent variables, and the geometry and boundary conditions of the computational domain are complex, so it is difficult to obtain analytical solutions. However, it is possible to find numerical solutions that meet the needs of engineering by using CFD method; Secondly, the computer can be used to carry out various numerical tests, for example, selecting different flow parameters to carry out various effectiveness and sensitivity tests in the physical equation, so as to compare the schemes. Moreover, it is not limited by the physical model and experimental model. It saves money and time, has more flexibility, can give detailed and complete data, and is easy to simulate the real conditions such as special size, high temperature, toxic, flammable and the ideal conditions that can only be approached but can not be achieved in the experiment. CFD also has some limitations. Firstly, the numerical solution is a discrete approximate calculation method, which depends on the discrete finite mathematical model which is physically reasonable, mathematically applicable and suitable for calculation on the computer, and the final result can not provide any form of analytical expression, but the numerical solution on a finite number of discrete points, with certain calculation error; Second, unlike the physical model experiment, which can give a qualitative description of the flow phenomenon at the beginning, it often needs to provide some flow parameters by the prototype observation or physical model experiment, and needs to verify the established mathematical model; Third, the compilation of the program and the collection, reproduction and correct use of data depend on experience and skills to a great extent. In addition, the numerical processing methods may lead to the unreal results, such as numerical viscosity, frequency dispersion and other pseudo physical effects. Of course, some shortcomings or limitations can be overcome or compensated in some way, which will be introduced in this book. In addition, CFD involves a large number of numerical calculations, so higher computer hardware and software configuration is often required

cfd has its own principles, methods and characteristics. Numerical calculation, theoretical analysis and experimental observation are interrelated and promote each other, but they cannot be completely replaced. Each of them has its own application occasions. In practical work, we should pay attention to the organic combination of the three and strive to learn from each other

3 application field of computational fluid dynamics

in recent ten years, CFD has made great progress, replacing some approximate calculation methods and graphic methods in classical fluid mechanics: some typical teaching experiments in the past, such as Reynolds experiment, can now be realized on the computer with the help of CFD. All problems involving fluid flow, heat exchange, molecular transport and other phenomena can be analyzed and simulated by computational fluid dynamics. CFD plays a role not only as a research tool, but also as a design tool in the fields of hydraulic engineering, civil engineering, environmental engineering, food engineering, marine structure engineering, industrial manufacturing and so on. Typical applications and related engineering problems include:

. Hydraulic turbine Fluid flow inside fluid machinery such as fans and pumps

. Design of aircraft and space shuttles

. Influence of automobile streamline shape on performance

. Calculation of flood and estuarine tidal current

. Influence of wind load on stability and structural performance of high-rise buildings

. Analysis of greenhouse and indoor air flow and environment

. Cooling of electronic components

. Performance analysis of heat exchanger and shape of heat exchanger sheet In the past, the treatment of these problems mainly relied on basic theoretical analysis and a large number of physical model experiments, but now most of them are analyzed and solved by CFD. CFD technology has now developed to the extent that it can fully analyze complex problems such as three-dimensional viscous turbulence and vortex motion

4 the branch of computational fluid dynamics

after more than 40 years of development, CFD has appeared a variety of numerical solutions. The difference between these methods lies in the discretization of the governing equations. According to different discretization principles, CFD can be generally divided into three branches:

. Finite difference method (FDM)

. Finite element method (FEM)

. Finite volume method (FVM, a special optical instrument developed by finite volume for checking the notch processing quality of Charpy V-shaped and U-shaped impact samples)

finite difference method is the earliest and most classical CFD method, The model of the resin is selected according to the melt activity rate (MFR) of the resin. The solution domain is divided into difference lattices, and the continuous solution domain is replaced by a finite number of lattice nodes. Then the derivative of the partial differential equation is replaced by a difference quotient, and the difference equations containing finite Unknowns at discrete points are derived. The solution of differential equations is the numerical approximate solution of the definite solution problem of differential equations. It is an approximate numerical solution that directly changes differential problems into algebraic problems. This method is developed earlier and more mature, and is mostly used to solve hyperbolic and parabolic problems. The methods developed on this basis include pic (particle in cell) method, MAC (marker and cell) method, and the finite element method proposed by chenjingren, a Chinese American scholar. The finite element method is a numerical solution that has been applied since the 1980s. It absorbs the core of discrete processing in the finite difference method and adopts a reasonable method of selecting the approximation function to integrate the region in the variational calculation. The finite element method is not widely used because its solution speed is slower than that of the finite difference method and the finite volume method. Limited oil supply of oil pump! On the basis of the maximum flow element method, it is not necessary to reach the load. Ebbia et al. Proposed the boundary element method and the mixed element method

the finite volume method divides the calculation area into a series of control volumes, and integrates the differential equation to be solved with each control volume to obtain a discrete equation. The key of the finite volume method is that in the process of deriving the discrete equation, it is necessary to make some form of assumptions about the distribution of the solved function itself and its derivatives on the interface. The discrete equation derived by the finite volume method can ensure that it has conservation characteristics, and the physical meaning of the coefficients of the discrete equation is clear, and the amount of calculation is relatively small. In 1980, tanker comprehensively expounded the finite volume method in his monograph numerical heat transfer and fluidflow. Since then, this method has been widely used, which is the most widely used CFD method at present. Of course, the research and extension of this method are also ongoing, such as ow's extended finite volume method for arbitrary polygon unstructured lattices. (end)

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