Given that E = 16,000 ksi, A = 6 in². Develop a finite-element model in ANSYS™ using top-down modeling in the following steps. Show screen captures of your work. Make sure you use a consistent set of units. (a) Create model geometry using the geometry for key points and lines indicated in the figure above. Present a screen capture of your model. (b) Select an element type and justify your choice? Mesh the model such that is only one-element per line. (c) Show a screen-capture of your meshed model with the applied loads and boundary conditions. (d) Show a screen capture of your material properties and real constants (e) Using the ANSYS™™ Post-processor, determine reaction forces? Show the output from ANSYSTM. (f) Determine the nodal deflections for all the nodes? Create an output table with the nodal deflection values. (g) Determine the axial-stresses in all the members? Create an output table with the axial stress values. (a) Calculate the reaction forces? (b) Calculate the stress in element 1?

The Brayton cycle shown in Figure 1 has reheat and two compressors with a flow rate of 210 kg s-1 of air. Assume this system is being used in Tuscaloosa, AL. The inlet conditions to the first compressor is 1 bar and the inlet temperature would be current temperature of Tuscaloosa in °C (to the nearest whole number value, check current temperature and use it). Both compressors have a pressure ratio of 5:1. The inlet temperature for the second compressor is 40°C. The inlet temperature of first turbine is 970°C. The first turbine drops the pressure to 5 bar and then the air is reheated to927°C before it enters the reheat turbine. There is no pressure drop across the heat exchangers. The approach temperature for the heat exchanger (between state 9 and state 10, as shown in Figure 1) will be last two digits of your CWID (eg. If your CWIDis 12387854, then approach temperature will be 54°C). The isentropic efficiency of both turbines is 92% and that of the compressors is 88%. Use y (ratio of the specific heats) = 1.4 and Cp (specific heat at constant pressure) = 1.005 kJ kg-1 K-1.%3D What is the thermal efficiency of the cycle?

For the above gas turbine (question 1), it has been decided that for efficiency improvement some changes are required. You have been given task of helping the organization, as a consultant. Can you recommend practical changes that can lead to efficiency improvement? One of the researchers at UA's Mechanical Engineering Department, came-up with an idea of integrating above gas turbine with a steam powered cycle, so that end combination would be combined power plant cycle. It was also recommended to use a simple ideal Rankine cycle operating between the pressure limits of 6MPa and 6kPa,for ease of calculations. Steam is heated in a heat exchanger by the exhaust gases toa temperature of 550 degrees C. The exhaust gases leave the heat exchanger at 400K. Use appropriate assumed values, where required. Gas/Steam tables available with you could be used in these questions. Being a consultant, you have been asked to evaluate this approach Can you give details of efficiency improvements by taking above approach? Also give details of numerical method used to calculate improved efficiency?

Submits to ilearn Computational Fluid Dynamics (CFD) is a branch of Fluid Dynamics which is used for numerical engineering to solve and analyse problems in which fluid flows are involved. A static mixer is a device widely used in various industries to blend and homogenize fluid streams. It consists of stationary blades or elements within a pipe, creating a tortuous path for the fluids to mix thoroughly. This mixing process is crucial in applications such as chemical processing, food production, and water treatment, where achieving a consistent blend of different components is essential. In this assignment, water enters both pipes simultaneously but at different temperatures. The first entry has a speed of 2 m/s and a temperature of 3XY K (student ID dependent), while the second entry has a speed of 2 m/s and a temperature of 285 K. The objective of this assignment is to gain proficiency in using CFX to determine the speed and temperature of the water as it exits the static mixer. Additionally, you are tasked with implementing mesh refinement techniques and exploring discretisation schemes that may impact the solution. 2 m/s 3XY K r=2m 0 Pa 2 m/s 285 K Figure 1: Static Mixer with 2 Inlet Pipes and I Outlet Pipe XY is the last two digits of your student ID. For example, if your student ID is 41234567, then temperature at the specified inlet is 3XY=367 K. There is a 50% deduction if these parameters do not match your student ID number./nTo determine if the flow is in the laminar or turbulence regime, Reynold number can be evaluated based on the inlet velocity: Re = pvD/μ where p is the density, μ is the viscosity of the water and D is the diameter. The steps to conducting CFD simulations in ANSYS CFX are a. Import geometry (static.x_t-available in week 8 ilearn page) b. Construct a suitable mesh c. Set up the CFD model that requires the following steps: Setup General: Select solver as a steady state solution • • Models: Turn on energy equations and select viscous model (laminar or turbulence) (1) • Add material properties i.e. water • Assign the boundary conditions, including two inlets and one outlet with the correct boundary conditions according to your student ID. Solution • Methods: Conduct the simulation using the correct flow regime (laminar/turbulent flow) • Solution: Set the relaxation factors and/or residuals (convergence criteria). • Initialisation: Initialise domain-flow field can be initialized with 0 m/s velocity Report files and Report definitions: identify parameters, values, and plots that are required to be reposted. Run calculation: Set-up time step, the maximum number of iterations per time step, number of time steps, and reposting intervals. The total physical time is given in each section. d. Conduct another simulation with a refined mesh. e. Conduct a validation study (suggestion: analytical solution to compare your numerical result) f. Check if the solution converges and physical models are correctly selected. g. Visualise and analyse the results. A professional report in conference proceeding format should be prepared using the provided template (refer to MECH3004_assignment2_template.docx) and address the following within your report. The page limit for this report is 10 pages. The choice to adopt the conference proceeding format is strategic, aiming at effective communication of your findings. This format not only facilitates a structured presentation of your research but also ensures that your work reaches a broader audience. The dissemination of information through conference proceedings allows for knowledge exchange and engagement with peers, experts, and professionals in the field./nYour professional report can be structured with the following headings: 1. Problem Description & Introduction (5%) Introduction with references. 2. Governing equations, boundary conditions and assumption (20%) Report on the boundary conditions. Are your boundaries placed at the correct location? Any simplification approach you use for this problem and is it valid? Use figure to report. 3. Validation (5%) Discuss how you have validated. How valid are they? 4. General results (30%) Discuss some of the flow features you have found in your analysis. Discuss the mixing and the temperature distribution. Consider using streamline plot, velocity vector, velocity contour, temperature contour, velocity and temperature profiles at different locations. 5. Mesh Refinement & Result (20%) Obtain solutions on a refined grid size. Discuss the features of your grids, why you have designed them this way, and how the grid refinement affects the solution. Suggest whether you have reached grid convergence. It is recommended to use somewhere between 100,000 to 500,000 cells, for a reasonable accuracy but still able to solve in a reasonable time. 6. Discretization Schemes & Convergence (15%) Obtain solutions using two different discretization schemes. Explain the scheme and the relative advantages / disadvantages. Are the results as you expect? Which scheme do you recommend for this problem? What convergence level do you suggest for your problem? Why? 7. Conclusion & Reference (5%) Summarise your analysis. Include your references.

For the hypothesis class H defined by the following family of subsets of the real line: [r,r+ 1] U [r + 2, 0), with r e R Determine the VC-dimension of H. Justify your answer, by giving a proof (in maxi-mum 1 page).

Part I - Theoretical Calculations Theoretical calculations or back-of-the-envelope calculations are very important to do before running a finite element analysis. They give us a sense of what to expect out of the analysis and how to set it up, i.e., how to choose an appropriate model, how to apply loads & boundary conditions, and how to interpret the results of the simulation. (i) Consider a cross section at (a) the fixed support, and (b) at 100 mm from the fixed support. Draw the free body diagrams for these isolations and show the internal resultant loads on these sections (using the sign convention discussed in class). Calculate the bending stress and transverse shear stress distribution on these 2 cross sections. Also calculate the deflection of the free end of the beam using beam theory from your mechanics class (you do not need to derive anything; you may use the relevant equations from the appendix of the Mechanics of Materials textbook by Hibbeler)./nPart II - 3D Solid Model (iii) Model the structure in 3D - you can create the cross section on the YZ plane and extrude it in the positive X direction for the appropriate length. This will ensure that the coordinate system is oriented in the same way that we consider in examples solved in class. (iv) Fix the back face of the beam using a fixed support. Recognize that this leads to a stress singularity at the corners of the back face of the beam. Explain why this stress singularity is seen and how you can deal with it using Saint Venant's principle. (v) Apply the loading to the cantilever beam in ANSYS. Mesh the model with a mesh element size of 50 mm. Determine the maximum deflection of the beam and the maximum normal and shear stress magnitudes at the fixed support. Compare these with the results of Part I above. What do you observe? Then mesh the model with a mesh element size of 35 mm, 25 mm, 12.5 mm, and 6.25 mm (let's call these iterations 2, 3, 4, and 5). Plot the maximum normal and shear stress magnitudes vs. the iteration number for the different values of the mesh element size - this is called a convergence analysis. What do you observe? Explain why you see this behavior. (vi) Insert a surface at the cross section (along the YZ plane) at a distance of 100 mm from the fixed support. Show figures of the variation of the bending stress and shear stress along this surface. (vii) Repeat the analysis above looking at the stress magnitudes at the cross section 100 mm from the fixed support. What do you observe? Explain this behavior. (viii) Determine the effect of the depth-to-span ratio of the beam on the ratio of the maximum transverse shear to the maximum bending stresses. Do this by varying the length of the beam - choose lengths of 1 m, 0.75 m, 0.5 m, 0.375 m, 0.25 m, and 0.125 m. Use the smallest mesh size (6.25 mm) to ensure convergence of the solution. Repeat the analysis/nPart III - 2D Plane Stress Model (ix) Model the structure as a 2D plane stress model by sketching a rectangle of dimensions 1m x 100 mm on the X-Y plane. Use the "Surfaces from Sketches" tool to create a surface body and set its thickness to 50 mm. (x) Repeat the analysis of (v) to (vii) from Part II above using the 2D plane stress model. Note that to repeat part (vi), you will need to create a path/line instead of a surface at 100 mm from the support for the 2D model. Compare results and comment on which model is more accurate (calculate a percentage difference of numerical results), as well as which is more efficient (compare the size of the model - i.e., the number of nodes and elements in the model).

The bracket in blue is welded to a support. A force of 10 kN is applied through bearing force on the lower half of the circle (distributed load on the lower half of the circle with a resultant of 10kN). The thickness of the bracket is 50 mm. ANSYS Workbench requirements: 1. Solve the problem :as a 3-dimensional problem using 3D solid element. 2. Solve the problem as a 2-dimensional problem using plane stress element. 3. Compare the results. 4. Verify the model and results. 1. There is no need to draw the support when solving the problem). 2. You may ignore the fillet during the 2D modelling of the problem. 3. Submit a report along with discussions (together with photos of your work). 4. Create a cover page on your own.

write a programs to compute the output sequence Yk, where the initial content of the unit delays are: W(0) = 1₂ w(1) = 1, W(2)=0 with Ux= (2/3) ². {x I) Print uck), w(K) and Y(K). I) Plot 3 and # ок U.D 14 W(k+2) U.D 318. 3/2 W(KH) U.D 1/2 W(K) + + Y(K) 518 White & program to calculate y(tx) by memerical convolution, whe

H=\bigcup_{i=1}^{k} H_{i} Consider two alternative approaches: 1. Learn on the sample using the ERM rule. 2. Divide that sample into a training set of size (1 – a)m, and a validation set of size amfor some a e (0,1). Then apply the approach of model selection using validation, i.e.: • First, train each class H¡ on the (1 – a)m training examples using the ERM rulew.r.t. H; and let h1,..,h be all the resulting hypotheses. • Second, apply the ERM rule w.r.t. to the finite class {h1,..,hg} on the am vali-dation examples. Under which conditions is the second approach better? Justify your answerformally (using maximum 2 pages). Let H1, … · ,Hk be hypothesis classes such that H1 C H2 C … c Hk and |H1 = 2', for every i E {1,..,k}. Suppose you are given a sample of size m (with each element chosen i.id.), and you want to learn the union of all these classes, that is you would like to learn the hypothesis class

Individual Assignment Procedure and discussion points: 1. Create the computational geometry in DesignModeler/ Solidwroks/any CAD software with the mentioned dimensions. 2. Build an appropriate mesh for the model and perform a grid refinement study. 3. Run the simulation for different flow condition (At least two different inlet condition. More than 2 are encouraged). 4. Using the converged grid, check the iterative convergence. 5. Draw the Velocity contour at different selected planes of your model and discuss your results. 6. Draw the pressure contour at different selected planes of your model and discuss your results. 7. Plot the temperature profile along a selected line from inlet to outlet and discuss. 8. Draw the wall shear stress and discuss. 9. Draw the turbulence intensity contour for different flow rates and discuss (If applicable) 10. Plot the axial velocity profile at any selected position of your model and discuss. 11. Draw the Velocity vectors at different selected planes of your model and discuss your results. 12. Calculate the drag and lift coefficient and discuss (if applicable). 13. Calculate the deposition efficiency deposition fraction and discuss (if applicable). 14. Draw the particle trajectories for different flow rates and discuss (if applicable). 15. Calculate the heat transfer coefficients (if applicable). 16. Calculate the Nusselt number from the following correlation and discuss (if applicable); Nitp=0.023 Re Pr 17. Connect your results with the existing literature. Submission: A written report is to be submitted including a short introduction and conclusion (one page long for each). The report should contain a discussion of the points bolded above with evidence to support the discussion together with relevant figures such as figures illustrating the mesh or element distribution, plots of the velocity profiles, contour plots, etc.