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ENGSCI 344 City ENGINEERING SCIENCE Modelling

创建日期：2024-04-16 18:07:28

所属分类：经济Economics

标签： ENGSCI 344

City ENGINEERING SCIENCE Modelling

City ENGINEERING SCIENCE Modelling and Simulation in Computational Mechanics

(Time Allowed: TWO hours) NOTE: Answer ALL questions. Total marks: 120 ENGSCI 344 Page 2 of 6 Question 1 Computational Design (30 marks) As a computational analyst you have been contracted to analyse the aerodynamic behaviour of a scaled-up, heavy-lift version of a successful smaller rocket, which can be used for commercial launching of satellites into space. You need to determine the aerodynamic drag coefficient during both early-stage subsonic flight (shortly after lift-off), and at Max Q (maximum aerodynamic load). The client has provided you with CAD data of the rocket geometry (constant diameter cylinder with a pointed tip) and altitude vs velocity data for its flight trajectory. (a) Define THREE additional types of information that you would need to request from the client or obtain independently to enable your computational design to be completed. (3 marks) (b) Define TWO relevant non-dimensional parameters that could be used to determine whether the flight velocity at Max-Q is sub-sonic or super-sonic and whether flow near to the surface of the rocket is likely to be lamina or turbulent. (4 marks) (c) Define TWO important constitutive properties of the air that would be needed for your computational model and describe possible sources of this information. (4 marks) (d) Would it be better to use a frame of reference with the rocket static and the air moving, or the air static and the rocket moving? Justify your answer. (3 marks) (e) Sketch a suitable domain shape for the computational model(s) and describe the process you would use during your modelling to determine the required domain size and shape. Would this be likely to be different for the early-stage and Max Q cases and, if so, which is likely to be larger and why? (6 marks) (f) Define suitable boundary conditions for your domain shape chosen in Part (e). (4 marks) (g) Briefly describe and sketch TWO simple benchmark cases that could be used to verify your modelling approach prior to implementing your full model(s). (6 marks) ENGSCI 344 Page 3 of 6 Question 2 Geometry/Import, Materials, Boundary Conditions/Loads (30 marks) (a) Briefly describe THREE situations where it would be beneficial to import existing geometry rather than generate the geometry in a pre-processor. (6 marks) (b) If you had a choice of importing geometry data from a Parasolid or Stereolithography file which type would you choose? Justify why, including describing TWO advantages of your choice. (5 marks) (c) Define TWO benefits of using scripting to create geometry in a pre-processor. (4 marks) (d) You are to model the response of an aluminium alloy in two different scenarios. The first is in the roofing structure of a warehouse, the second is in a car which crashes at high speed. Briefly, discuss the differences between the two material models you might choose for the aluminium in these two scenarios, mentioning which would be more difficult to cope with from a computational modelling point of view, and why. (5 marks) (e) Give THREE different boundary conditions which might arise in a computational flow model, and give one practical example of an occurrence of each of these boundary conditions. (6 marks) (f) What is a Dirichlet boundary condition? What is a Neumann boundary condition? Give an example of each. (4 marks) ENGSCI 344 Page 4 of 6 Question 3 Mesh Generation, Solving, Post-processing (30 marks) (a) You are developing a model of fluid flow over a solid object. Briefly, discuss how you would use inflation layers, mentioning what they are, their typical geometry, why that geometry, and why they might be useful. (6 marks) (b) (i) Give ONE advantage and ONE disadvantage each for a structured mesh and an unstructured mesh. (4 marks) (ii) You are to model the concrete structure shown below, which contains a cylindrical hole and is loaded and supported around its outer surface. Briefly, discuss whether you would use a structured mesh, an unstructured mesh, or some combination of both. Give reasons for your choice. (6 marks) (c) Briefly, what is Numerical Diffusion? (Do not use equations in your explanation; draw a picture.) (4 marks) (d) When post-processing a computational fluid dynamics solution, give one example for each of an Integral, Scalar, Vector and Tensor result quantity. (4 marks) (e) Briefly describe and sketch an example of a situation for a structural Finite Element Analysis problem where the use of averaged contours may lead to errors in interpreting stress results. Describe what information plotting nodal differences in the results would provide. (6 marks) ENGSCI 344 Page 5 of 6 Question 4 Verification & Validation (30 marks) (a) You have just run a computational structural mechanics simulation. State two very simple checks you could carry out on the output which could be used to verify that the solution is correct, or at least not obviously wrong. (2 marks) (b) Define the following, and give one example of each (or an explanation as to why it occurs): (i) Discretisation error (ii) Solution error (8 marks) (c) You are asked to model the stresses in a metallic component, supported at one end and loaded in tension at the other end, as sketched below. The details of the fixation and loading are well-known and are modelled with sufficient accuracy (the left-hand end is modelled using a frictionless support). The details of the geometry at the sharp corner at A are not known to a high degree of accuracy. The exact theoretical solution predicts that the stress at a perfectly sharp re-entrant corner of an elastic plate, as at point A, is infinite. Your team leader wants you to analyse this problem using a computer simulation, and give advice on what magnitude of load is allowable so as to prevent failure of the plate at the fixed end. Discuss what you might do, answering the following questions: (i) What is a stress singularity? (ii) What would the effect of mesh convergence be at a stress singularity? (iii) Do stress singularities exists in the real physical world of loaded metallic plates? (iv) What is a stress concentration? (v) How would you turn a point of stress singularity into a point of stress concentration? (vi) How do you think the operation described in (v) to the point A might affect the stresses at the supported end? (10 marks) A Applied load Frictionless support ENGSCI 344 Page 6 of 6 (d) Briefly describe what is meant by calibration of a numerical model, and describe why calibration on its own is not enough to ensure the accuracy of a model. (5 marks) (e) Define what is meant by Unit and Benchmark problems for validating a computational model. Which one of these is likely to be the most complicated problem? (5 marks)

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