Fluid Mechanics (Mechanical) 4 (MECE10004)
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A general form of the Navier-Stokes equation is derived with a focus on the physical interpretation of the mathematical model. This equation is used to derive simplified models for bidimensional incompressible flows, including potential flow and boundary layer flow. The fundamentals of turbulent flow, including basic turbulent statistics, are presented.
The following list of lectures is only indicative and should be considered an example of delivery of the course. Introduction and Math RecapL1. Introduction to the course. L2. Mathematical methods for fluid mechanics: revision of vector total and partial derivatives, application to fluid mechanics, introduction to Einstein notation and application to differential operations, revision of vector calculus (gradient, divergence, Stokes and Green s theorem), complex variable calculus and Fourier and Laplace transforms.Governing Equations of Fluids L3. Derivation of the continuity equation.L4. Definition of the stresses and of the strain rate tensor; derivation of the momentum Cauchy equation.L5. Constitutive equation for Newtonian fluids, derivation of the Navier-Stokes equation.L6. Exact and integral solutions of the Navier-Stokes equation. L7. Derivation of the nondimensional form of the Navier-Stokes equation.Potential flowL8. The basics of potential flow: introduction of vorticity and the velocity potential and derivation of the conservation laws governing incompressible irrotational flow, including Bernoulli's law.L9. The building blocks of potential flow: introduction to the elementary solutions to the Laplace equation, the principle of linear superposition and application to explain applied fluid dynamics problems.L10. Forces on objects in potential flow: flow past a rotating circle, the Magnus effect and the d'Alembert's paradox, Kelvin s circulation theorem and Kutta-Joukowsky s theorem.L11. How to reconcile potential flow with rotational flow: the link between circulation and vorticity, bound circulation and free vortices. L12. Introduction to thin airfoil theory: key assumptions and basic results. Turbulent FlowL13. Phenomenology of turbulent flow, Reynolds-averaged Navier-Stokes equation.L14. Reynolds stress tensor, wall scales, Boussinesq hypothesis, turbulent viscosity.L15. Derivation of the universal law of the wall and taxonomy of wall bounded flow.L16. Moody diagram, k-type and d-type roughness.Boundary LayerL17. Phenomenology and taxonomy of boundary layer flow, von Karman integral of the boundary layer and definition of the displacement and momentum thickness.L18. Derivation of the boundary layer equations, summary of results of the Blasius solution of the laminar boundary layer equations, and summary of results of the solutions of the power law for turbulent flow.Turbulent StatisticsL19. The statistical approach: ensemble, moments, stationarity and homogeneity.L20. Correlations, integral scale, spectra, Kolmogorov s scales.Tutorial classesT1. Mathematics revisionT2. Navier-Stokes equationT3. Navier-Stokes equationT4. Potential flowT5. Potential flowT6. Mock examT7. Turbulent flowT8. Turbulent flowT9. Boundary layerT10. Turbulent statisticsAHEP outcomes: SM1m, SM2m, SM3m, SM5m, SM6m, EA1m, EA2m, P1, G1, G2.
Written Exam 100%, Coursework 0%, Practical Exam 0%
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