tailieunhanh - Modeling of Combustion Systems A Practical Approach 9

Tham khảo tài liệu 'modeling of combustion systems a practical approach 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 1_ Introduction to Modeling Chapter Overview We begin this chapter by looking at various model categories and associated kinds of experiments. We then survey various analytical methods such as qualitative analysis and dimensional analysis and introduce function shape analysis. Because many times we consider multidimensional data we devote a section to perceiving greater than three dimensions. We then define and discuss basic data classifications . nominal ordinal interval and ratio data. Distinguishing among these data types is important some mathematical operations have no meaning for certain data types. In other cases we must change our analytical methodology. In closing we provide a primer on linear algebra and least squares and some proofs regarding a generalized mean. Model Categories We consider three possible kinds of mathematical models each having two subdivisions Theoretical models - Fundamental - Simulations Semiempirical models - General models with adjustable parameters - Dimensionless models with adjustable parameters Empirical models - Quantitatively empirical - Qualitatively empirical 1 2006 by Taylor Francis Group LLC 2 Modeling of Combustion Systems A Practical Approach Model Validation Validation is the testing of the model with data from the situation of interest. All models must be validated but for different reasons. Theoretical models require validation to define their applicable range. For example the ideal gas law is wrong at high pressures and low temperatures. Newton s second law of motion is wrong at high speeds approaching the velocity of light. But within their spheres of applicability they are highly accurate. Simulations require validation because there may be errors in the computer code ill-conditioned problems improper convergence etc. Semiempirical models require some data to determine values of the adjustable parameters. They cannot even begin without some valid data. But a .