UTS: ENGINEERING 1 49312: ADVANCED FLOW MODELLING ASSIGNMENT 1 PART A INTRODUCTION TO CFD DUE DATE 09-09-2016 11:59pm SHARP ASSESSMENT% 25% INSTRUCTIONS PART A1: EVENLY SPACED MESH. PART A2: GEOMETRICALLY SPACED MESH. PART A3: Verification & Validation: COMPARING WITH ANALYTICAL SOLUTIONS. PART A4: PARABOLIC FLOW INLETS. PART A5: WRITTEN SECTION ANSWERS TO QUESTIONS ON READING & VIDEOS AIMS • To recognise the different methods of building meshes for a flow domain; • To recognise that all CFD solutions should be mesh independent; • To highlight the importance of using finer grids in flow regions with high gradients. • To compare with analytical solutions • To learn how to apply a parametric inlet • To learn how to estimate how far downstream the outlet boundary should be.UTS: ENGINEERING 2 INTRODUCTION TO PART A1 & PART A2 (2 MARKS & 2 MARKS) THE LID DRIVEN SQUARE CAVITY FLOW "The laminar incompressible flow in a square cavity whose top wall moves with uniform velocity in its own plane has served over and over again as a model problem for testing and evaluating numerical techniques" (from Ghia et al, 1982). The problem is now very well documented for 2-dimensional models. The principal feature of the flow is a primary vortex Figure 1. In addition there are secondary vortices of much lesser strength that rotate in the reverse sense, and these form in the corners opposite to the moving lid, BR1 (Bottom Right 1) and BL1 (Bottom Left 1). At higher Reynolds number a third vortex forms at the backside of the moving lid TL1 (Top Left 1). As the Reynolds number increases tertiary vortices form (BR2, BL2, TL2) and at even higher Reynolds number, higher-order vortices form, and so on and so on. Figure 2 shows stream function results of Ghia et al for Reynolds number (Re) of 7500, vortex formation is clearly seen. Figure 1: Boundary conditions and locations of primary, secondary, and possible higher order vortices Figure 2: Streamlines for Re=7500; from Ghia et al. (1982).UTS: ENGINEERING 3 Geometry, Fluid Properties and Boundary Conditions. As well as the aims stated a further aim of this assignment is to introduce the notion of nondimensionality. The Navier-Sokes equations lend themselves easily to non-dimensionalisation. You should be familiar with the Buckingham-Pi theorem. A measure of the ratio of the fluid inertial forces to viscous forces is the Reynolds Number, Re ρUL µ = If an objective is to compare your CFD "experiment" to someone else's CFD (or real-world) experiment at the same Re then the dimensions and fluid properties of your experiment are trivial. Construct an internal square flow geometry: height=1; length=1. The (upper wall) lid velocity is: U=1, V=0 The three other walls: U=V=0 Density, ρ=1 Dynamic viscosity, μ=1/Re. The Re to be investigated is 5000. The flow is steady, laminar, incompressible and isothermal. Begin with 21 X 21 grid points on each wall. A movie has been supplied to help you: LID_DRIVEN_CAVITY.mp4 Available on UTSOnline Objectives 1. For both Part A1 and Part A2 the velocity plots we require are: U(y) at x=0.5; plot V(x) at y=0.5. 2. For Part A1 only: Demonstrate/prove that your last solution is mesh independent i.e. The "latest" plots in Objective 1 is the same as the "previous" plot. This means your CFD solution is no longer mesh dependent. 3. For Part A2: using the largest mesh from Part A1 compare the same results as Part A1 for 3 different numerical resolutions: upwind, central, 2nd-order.UTS: ENGINEERING 4 Part A1: Evenly Spaced Mesh For Part A1, an evenly spaced structured mesh is to be used. This method can be considered a "brute force" solution method. I. Begin with an evenly spaced 21 X 21 mesh – complete Objective 1. II. Repeat the calculation on a 41 X 41 mesh – compare to the 21 X 21 mesh. III. Repeat (II) using an 81 X 81 mesh – compare to the 41 X 41 mesh. IV. Repeat (III) as necessary, again doubling the mesh, until you can demonstrate that your solution is mesh independent. Part A2: Symmetric Geometrically Spaced Mesh For Part A2, a symmetric geometrically spaced structured mesh is to be used. This method is worth using in regions where flow gradients are high e.g. close to wall. A reminder of geometric sequences is: http://en.wikipedia.org/wiki/Geometric_series. For us the important equations are: ( 1) 2 g n − = and g is the number of grid points per side and n is the total number of mesh elements per half-a-side length (i.e. 0.5). 1 AR r = ∆ ∆ = n / 1 n− and AR is the ratio of the first mesh element's length to the nth mesh element's length and r is the transition factor. ln ( ) exp ( 1) 1 2 AR r g     =   −  −         Hence this is the formula needed to find r. I. Use a g=257 X 257 mesh with AR=5. You will need to calculate r. II. Run two different solutions with the g=257 X 257 mesh at Re=5000 a. Upwind b. 2nd order III. Compare Objective 1 for your two solutions and the published data from Ref. 2. The data files will be given to you. References. 1. E. Erturk, 2009, Discussions on Driven Cavity Flow, International Journal for Numerical Methods in Fluids Vol 60, pp 275-294. 2. Ghia U, Ghia KN, Shin CT.. 1982, High-Re solutions for incompressible flow using the Navier– Stokes equations and a multigrid method. Journal of Computational Physics; 48:387–411. 3. Any other handouts given to you.UTS: ENGINEERING 5 Figure 3 Part A1 results requirement from Spring 2013 – NB your Re is different to theirs!UTS: ENGINEERING 6 Figure 4 Example of Part A2 results requirements from s2013.UTS: ENGINEERING 7 INTRODUCTION TO PART A3 (2 MARKS) FURTHER VALIDATION AND VERIFICATION. COMPARISON WITH AN ANALYTICAL SOLUTION. TILTED PAD THRUST BEARING HYDRODYNAMIC FLOW "Tilted pad thrust bearings are used in a variety of rotating machineries that have to withstand high thrust loading. The thrust load is transferred from a sliding part to a stationary part through hydrodynamic oil films. The tilted pad thrust bearing consists of a series of flat surfaces sliding over stationary tilted pads. The motion of the sliding flat surface drags the lubricant in towards the diminishing gap between the tilted pad and the sliding surface. The pressure developed in the lubricant between the sliding surface and the tilted pad counteracts the external load applied to the sliding surface and thus prevents contact between the two surfaces. Reynolds equation is solved on the surface of the tilted pad to find the pressure distribution on the surface of the tilted pad. (COMSOL User Notes) A hydrodynamically lubricated bearing is a bearing that develops load-carrying capacity by virtue of the relative motion of two surfaces separated by a fluid film. The processes occurring in a bearing with fluid film lubrication can be better understood by considering qualitatively the development of oil pressure in such a bearing. Many loads carried by rotary machinery have components that act in the direction of the shaft's axis of rotation. These thrust loads are frequently carried by self-acting or hydrodynamic bearings of the form shown in Figure 5. A thrust plate attached to, or forming part of, the rotating shaft is separated from the sector-shaped bearing pads by a lubricant Him. The loadcarrying capacity of the bearing arises entirely from the pressures generated by the geometry of the thrust plate over the bearing pads. Figure 5 Thrust Bearing Geometry Figure 6 Thrust Bearing components Figure 7 Fixed inclined bearing Figure 8 Dimensionless Pressure distributionUTS: ENGINEERING 8 Theory Figure 7 shows a fixed-incline slider bearing. A fixed-incline slider consists of two nonparallel plane surfaces separated by an oil film. One surface is stationary while the other moves with a uniform velocity. The direction of motion and the inclination of planes are such that a converging oil film is formed between the surfaces and the physical wedge pressure-generating mechanism is developed in the oil film; it is this pressure-generating mechanism that makes the bearing able to support a load.UTS: ENGINEERING 9 Geometry, Fluid Properties and Boundary Conditions. The Navier-Sokes equations lend themselves easily to non-dimensionalisation. You should be familiar with the Buckingham-Pi theorem. A measure of the ratio of the fluid inertial forces to viscous forces is the Reynolds Number, Re ρUL µ = If an objective is to compare your CFD "experiment" to someone else's CFD (or real-world) experiment at the same Re then the dimensions of your experiment are trivial. Build a tilted pad thrust bearing as shown in Figure 7 using the parameters given in the Table below. • The upper wall is stationary: U=0, V=0 • The inlet is Constant Pressure type: set P=0 • The outlet is Constant Pressure type: by default it is set P=0 • The lower wall has velocity: U=1, V=0 • Density, ρ=1 • Dynamic viscosity, μ=1/Re. The Re to be investigated is 100. • The flow is steady, laminar, incompressible and isothermal. • Begin with a 250 X 50 mesh (i.e. 50 grids at the inlet, outlet 250 grids for upper and lower walls). VARIABLE VALUE L 1 h0 0.02 sh 0.1 hi 0.12 Ub 1 µ (their η0) 0.01 ρ 1 A movie has been supplied to help you: THRUST_PAD.mp4 Available on UTSOnline Objectives 1. Compare the Static Pressure data from your CFD solution with Equation 8.24. You will need to calculate Equation 8.24 at the same X as your CFD data using the geometry values given above.UTS: ENGINEERING 10 Figure 9: PART A3 output requirement -- Bruce's attempt (could be wrong so don't copy!) The maximum error [error=(analytic-cfd)/analytic *100%] at the peak is 3.3%. Figure 10: Mesh example Figure 11: P* surface plotUTS: ENGINEERING 11 INTRODUCTION TO PART A4 (2 MARKS) "Fluid flows in channels with flow separation and reattachment of the boundary layers are encountered in many flow problems. Typical examples are the flows in heat exchangers and ducts. Among this type of flow problems, a backward-facing step can be regarded as having the simplest geometry while retaining rich flow physics manifested by flow separation, flow reattachment and multiple recirculating bubbles in the channel depending on the Reynolds number and the geometrical parameters such as the step height and the channel height. In the literature, it is possible to find many numerical studies on the 2-D steady incompressible flow over a backward-facing step. In these studies one can notice that there used to be a controversy on whether it is possible to obtain a steady solution for the flow over a backward-facing step at Re = 800 or not. (Ref 1., Introductory remarks ) The principal feature of the flow is separation after the sudden expansion (or "step", Figure 12, from Ref. 1 for his Re=100). At even higher Reynolds number, further separation occurs, first on the upper wall, then again on the lower wall, and so on and so on. Figure 13 shows stream function results from Ertruk (Ref. 1) for Re=3000, the highest Re simulated by him. The inlet profile is assumed to be a fully developed plane-Poiseuille flow (i.e. parabolic). The downstream outlet profile should resume as a plane-Poiseuille flow if the outlet is far enough away from any flow separation. Figure 12: Streamlines are useful for identifying flow separation behind a step (sudden expansion) for Re=100. (Ref. 1) Figure 13: Streamlines are useful for identifying flow separation behind a step (sudden expansion) for Re=3000. (Ref. 1). There is no reason to assume that these separations will not occur ad-infinitum. In a "real world" experimental test, turbulence will develop when the Re is high enough. The stable vortices shall become lost in a haze of smaller, faster, turbulent eddies.UTS: ENGINEERING 12 Geometry, Fluid Properties and Boundary Conditions. Non-dimensionalise your simulation. * * * * * * * * 1 1; 1; ; 1 Re Re = = = = = inlet average inlet average U h U h ρ ρ µ µ Here, Uinlet average * is the average velocity of the parabolic inlet profile * 2 inlet maximum U U inlet average = 3 and h* is the step height. The expansion height, H is H = 2 . Your assignment is to simulate Re=200. Prove that your solution is mesh-independent. All walls are "non-slip" i.e. U V = = 0 . Start with a coarse mesh and continue to increase it until you believe you simulation is mesh-independent. Do not use more than 250000 grids. It is VERY important to locate the origin (0,0) as shown at the edge of the step. This is because the following parabola is with respect to the model origin. The inlet is a parabola of the type U y y y ( ) 6 (1 ) = − and you need to use the following example of the python commands OR use the technique as shown in the figure below. A movie has been supplied to help you: BACKWARD FACING STEP.mp4 Available on UTSOnline YOU COULD ALSO READ THE CFD-ACE TUTORIAL FOR LAMINAR FLOW OVER A BACKWARD FACING STEP. GuiFILE.DefineExpression("U", "6*Y*(1-Y)") GuiBC.Set([43], "Flow/U_eval_method", "Parametric") GuiBC.Set([43], "Flow/U_Para", "U")UTS: ENGINEERING 13 Use the same solution method as suggested i.e. CENTRAL differencing instead of the usual UPWIND The following figures should help you create your geometry.UTS: ENGINEERING 14 Objectives 1. Obtain a converged and mesh-independent solution for a Reynolds number of 200.. 2. Plot the u-velocity profile with the plane-Poiseuille flow e.g. every 5 step heights. i.e. compare with the theoretical profile ( ) 2 3 ( ) 4 U y y y = − . Figure 14 PART A4 output requirement -- Bruce's attempt (could be wrong so don't copy!) References. 1. E. Erturk, 2008, Numerical solutions of 2-D steady incompressible flow over a backward-facing step, Part I: High Reynolds number solutions, Computers & Fluids Vol 37, pp 633-655.UTS: ENGINEERING 15 INTRODUCTION TO PART A5 (5*1 MARKS) WRITTEN ANSWERS TO COMPULSORY READINGS AND VIEWINGS This part of the assignment is to ensure you have a quick review of some concepts of Fluid Mechanics. It consists of watching a number of videos on Youtube and – if you wish – you can follow each film with scripts (where available) as well as prescribed reading with question and answer requirements: Low-Reynolds-Number Flows film: https://www.youtube.com/watch?v=51-6QCJTAjU&list=PL0EC6527BE871ABA3&index=7&feature=plpp_video Script: http://web.mit.edu/hml/ncfmf/07LRNF.pdf QUESTION A5-1: Explain the significance of a flow's Reynolds Number, Re. Refer to an example from the film. Fundamentals of Boundary Layers film: https://www.youtube.com/watch?v=wMxK2GtFFq0&list=PL0EC6527BE871ABA3&index=11&feature=plpp_video Script: http://web.mit.edu/hml/ncfmf/10FBL.pdf QUESTION A5-2: Explain the difference between Laminar and Turbulent boundary layers. Turbulence film: https://www.youtube.com/watch?v=1_oyqLOqwnI&list=PL0EC6527BE871ABA3&index=12&feature=plpp_video Script: http://web.mit.edu/hml/ncfmf/11TUR.pdf QUESTION A5-3: Describe the fluid flow phenomenon of Turbulence. Pretend you are talking to a stranger Read "Chapter 1 Introduction" of the textbook Computational Fluid Dynamics: A Practical Approach by Jiyuan Tu, Guan Heng Yeoh, and Chaoqun Liu. Read "Lecture 1" slides by Dr Andre Bakker Answer the following questions: QUESTION A5-4: Outline the steps required to successfully carry out a CFD investigation. QUESTION A5-5: List advantages and disadvantages of CFD compared to experimental investigations of fluid flows. Each answer shall be 1/2 page maximum (11pt text, 1.5 line spacing, and no figures).UTS: ENGINEERING 16 APPENDIX A: CFD-GEOM INSTRUCTIONS STEP FIGURE NOTES G-1 • Start CFD-GEOM • Give your model a name e.g. CAVITY • DO NOT ACCEPT THE DEFAULT DIRECTORY – YOU WILL LOSE THE DATA. Make sure you browse to your H:\ drive or your USB drive. • Activate Journaling • Accept the default units of Meters • OK G-2 • Begin Geometry creation • Create 4 points using Coordinate/Screen-Pick • 0, 0, 0 • 1, 0, 0 • 1, 1, 0 • 0, 1, 0UTS: ENGINEERING 17 G-3 • Your screen should look like this • Quit G-4 • Create four lines to represent the four walls with the Create Line(s) command • Pick two points then middle-mouse-button (MMB) to create a lineUTS: ENGINEERING 18 G-5 • Your screen should look like this • Quit G-6 • Click on the Mesh tab • The next step is to Create/Edit Edge – this is the process of adding grid points which will then be used to create the meshUTS: ENGINEERING 19 G-7 • In the example shown graded grids are being constructed • To create an evenly spaced grid use: o Num. grid points = 21 o Type = Geometric o Transition Factor = 1 and o Symmetric • If you are building a geometry for Part A2 o Num. grid points = 257 o Transition Factor = 1.0127534 G-8 • Your screen should look like this • QuitUTS: ENGINEERING 20 G-9 • Create a structured face from the four edges of grids with the Face From Edges command • Choose one edge and MMB to accept • Complete the other 3 edges similarly G-10 • This figure shows three edges completed so far, one more to goUTS: ENGINEERING 21 G-11 • Your screen should look like this • Quit G-12 • The last step is to Create 2-D Block • This converts the structured face into a mesh – in this case a mesh that forms the fluid.UTS: ENGINEERING 22 G-13 • Select the grey 2-d structured face • It should become green. G-14 • MMB to acceptUTS: ENGINEERING 23 G-15 • The last part of geometry construction is to set Boundary Conditions (BC) and Volume Conditions (VC) • Select the BC/VC tab • Select the button • Select 2-D for Dimension • Select CFD-ACE as the Solver • Apply then Quit G-16 • The next step is to select the four lines/edges and to Name them and set their Type (all are walls) • Select the inlet/outlet button • Select the upper line, Name it LID and set its Type to WALL. • Select Apply • Select the left line, Name it LWALL and set its Type to WALL. • Select Apply • Select the bottom line, Name it BWALL and set its Type to WALL. • Select Apply • Select the right line, Name it RWALL and set its Type to WALL. • Select ApplyUTS: ENGINEERING 24 G-17 • The next step is to group all the walls apart from the LID • Select LWALL, BWALL, RWALL – use your CTRL key to add each wall to the selection • Select Add To Group and name the group WALLS_0 G-18 • The last step is to set the main area as a fluid • Select the volume button (third button from the top) • Select the fluid • Name the fluid WET_STUFF and ensure the Type is Fluid • Select Apply • Quit • SAVE your file as a GGD file • Also save your file as a DTF file which is the file CFDACE will read. Use the SAVE AS commandUTS: ENGINEERING 25 CFD-ACE INSTRUCTIONS STEP FIGURE NOTES A-1 Begin with the DTF file you saved from CFD-GEOM (my example will be for the 21X21 geometry) A-2 Choose the FLOW module A-3 Give it a Title if you wish e.g. LCD_21X21UTS: ENGINEERING 26 A-4 Choose the VC tab, go to the bottom of the window and make sure you have selected "wet_stuff" [not shown] Choose "Fluid Subtype" as "liquid" On the "Phys" tab set Rho=1 On the "Fluid" tab set Mu=2e-4 A-5 Choose the BC tab, go to the bottom window and make sure you have selected "Lid" Set U=1 V=0 Choose "Apply" We can ignore the other walls; they are U=0, V=0 by default. A-6 Now go to the Solver Control tab (SC). Set "Max. Iterations" to 10000 And "Convergence Crit" to 0.00001UTS: ENGINEERING 27 A-7 Go to the "Run" tab Slect "Submit to Solver" When it asks for you to check the filename give is a new filename (so you do not loose you set-up) e.g. 21X21_out.dtf A-8 Then choose the "View Residuals" tab Watch it go down to ~ 1e-5. A-9 Now choose the "eye" icon to view your resultsUTS: ENGINEERING 28 CFD-VIEW INSTRUCTIONS STEP FIGURE NOTES G-1 When CFD-VIEW starts make sure you choose the "wet_stuff" To check click on the "Color" tab – you should see all the fluid properties; Rho, U, V, W, etc If you don't something has gone screwed and you have no fluid data. If all good choose the "line probe" icon on the right hand side – it is on the 2nd row and is 5th across G-2 By default you get the line required for your 1st probe V as a function of x across the middle of the cavity Choose V as a function of chordlength. You will need to choose the "plot" icon. 3rd row; 3rd column. Change the variable from "rho" to "V" The window will disappear, just click on it from all your open windows icons.UTS: ENGINEERING 29 G-3 It might be back-to-front!! Save the plot as a ".csv" file. You can plot all your files in Excel, etc, later for your report. Next choose the existing "2D Line Probe" In the right hand column. Change the co-ordinates to "Tail 0.5 0.0" And Head to "0.5 1.0" This gives you U(y) i.e. the U velocity up the x=0.5 line. G-4 Make the X-axis U And the Y-axis "chordlength" Save the plot as a ".csv" fileUTS: ENGINEERING 30 49312: ADVANCED FLOW MODELLING ASSIGNMENT 1 PART B • TIME–MARCHING SOLUTIONS • • TIME–DEPENDENT FLOW SOLUTIONS • • AXISYMMETRIC FLOW SIMULATIONS • • THE CONSERVATION EQUATIONS OF A FLUID • • Introduce the "time–marching" solution technique; • Recognise that a symmetric geometry does not guarantee a symmetric flow; • Introduce the "time–dependent" solution technique; • Estimate the average drag force acting on a cylinder and compare to published data; • Introduce more dimensionless groups; • Simplify a 3D axisymmetric flow to 2D; • Review basic vector notation and operations; • Derive and explain the Conservation of Mass equation for a fluid; • Derive and explain the Conservation of Momentum equation for a fluid; and • Derive and understand the Conservation of Energy equation for a fluid. PART B1: THE TIME-MARCHING SOLUTION METHOD This part of the assignment introduces "time–marching" as a solution method for difficult to solve "steady–state" flows. Difficult "steady– state" flows include flows of moderate to high Reynolds number (Re) with regions of flow separation and recirculation.UTS: ENGINEERING 31 The lid–driven cavity (LDC) and backward–facing step (BFS) from Assignment 1 are examples of low Re flows with separation and recirculation and, as you observed, were not difficult to solve using the "brute force" steady–state method. PART B1: TIME–DEPENDENT FLOWS. VORTEX SHEDDING OFF A TWO–DIMENSIONAL CYLINDER Fluid flows are inherently unstable. As you observed in Assignment 1, fluid flows can separate from boundaries and even reverse in flow direction. A measure of the inherent stability is the Reynolds number (Re), with is the ratio of inertial forces to viscous forces. A high Re indicates a dominance of the inertial forces over the viscous forces and the flow will be prone to instability influences such as surface roughness and adverse pressure gradients. An important consequence of fluid flow instability and the effect of Re leads the following: "A symmetric geometry does not necessarily ensure a symmetric flow." Unsteady flow–or "transient"–simulations require time, t, to be part of the solution domain as well as the three spatial dimensions x, y and z. A well-documented example of a transient flow is vortex shedding from a cylinder. A vortex is a coherent structure of fluid flow that is predominantly rotational. A familiar example is the tornado storm. Although these structures are 3-dimensional in nature, we will simplify the simulation to two dimensions. PART B3: AXISYMMETRIC FLOWS (SIMULATING A 3–D FLOW IN 2–D) VORTEX BREAKDOWN IN A CYLINDER WITH A ROTATING BASE Part B3 of the assignment introduces axi-symmetric flows and their solution using CFD. You will compare your results of a welldocumented experiment with a published CFD result. A flow is considered axi–symmetric if: • It is steady–state; and • Its geometry is symmetric about an axis. If the above two conditions are true there is no need to do a full 3– dimensional calculation. The flow geometry can be simplified to a 2–UTS: ENGINEERING 32 dimensional plane that must include the axis of symmetry. Unlike the LDC, BFS and 2–d vortex shedding simulations an axi-symmetric simulation is still fully 3–d, that is to say, all three-velocity components, U, V and W, are solved. PART B4: WRITTEN ANSWERS TO QUESTIONS ON COMPULSORY READING AND YOUTUBE VIEWING For this part of the assignment you are required to read and view sources of information of the following topics: • Review basic vector notation and operations; • Derive and explain the Conservation of Mass equation for a fluid; • Derive and explain the Conservation of Momentum equation for a fluid; and • Derive and understand the Conservation of Energy equation for a fluid. SUBMISSION INSTRUCTIONS Checklist 1. Part B1: I would like two figures similar to Figure 0.2 and Figure 0.3. 2. Part B2: I would like two figures similar to Figure 0.1 shown on pg13. 3. Part B3: I would like two figures similar to Figure 0.7 and Figure 0.8. 4. Part B4-1: your written answer must be ½ pg of text maximum (11pt text, 1.5 line spacing, and no figures). 5. Part B4-2: your written answer must be ½ pg of text maximum (11pt text, 1.5 line spacing, and no figures). 6. Part B4-3: your written answer must be ½ pg of text maximum (11pt text, 1.5 line spacing, and no figures).UTS: ENGINEERING 33 PART B1: THE TIME–MARCHING SOLUTION METHOD. HIGH Re FLOW OVER THE BACKWARD FACING STEP. (3 MARKS) INTRODUCTION #There is no movie for this part yet, only screen grabs and python scripts should you need to use them# Use your geometry and/or input python files for the BFS from Assignment 1 BUT solve for Re=400. You will to change the dynamic viscosity µ = − 2.5 03 e . In addition, you will need to lengthen your model and you should double the downstream outlet to 70 step heights. This is my suggestion–you can choose to ignore it. There is a python file in the Appendix if you are stuck, or lost for ideas. Using this file will cost you 0.5 marks. For the same mesh geometry that you construct, compare the flow field for a "steady–state" solution with a converged "timemarching" solution. I recommend that you stop the "steady–state" calculation after 1000 iterations. See Figure 0.1 The figures shown are examples of what is expected in your assignment submission. Do not submit Figure 0.1–it is an example of how my "steady–state" solution failed to converge. I made Figure 0.2 and Figure 0.3 by adding switching on "contours" coloured by the "stream function." I chose the maximum number of contours of 256 and left the minimum and maximum values as they are. The colour sample is zebra shading. I also changed the aspect ratio of the screen to 5 for "y" to make it easier to distinguish the recirculating regions of flow.UTS: ENGINEERING 34 Figure 0.1 A plot of the error residuals for the BFS at Re=400 (not required to hand-in) Figure 0.2: 256 stream function contours for the BFS at Re=400 after 1000 iterations (required to hand-in) Figure 0.3 Twenty Stream - function contours for the BFS at Re=400 after 400s total calculation time (required to hand-in)UTS: ENGINEERING 35 CFD-ACE SET-UP FOR TIME-MARCHING The screen grabs below show the new set-up steps you need to carry out to establish a time-marching solutionUTS: ENGINEERING 36 APPENDIX PYTHON FILE FOR BFS GEOMETRY SET-UP # This file was journaled by CFD-GEOM import GUtils import GGeometry import GMesh import GFileIO import GBCVC # Note that if you plan to run this script outside CFD-GEOM, # (such as in Simulation Manager or a standalone Python interpreter), # please ensure that the CFD-GEOM portion of the script is wrapped # by calls to GUtils.StartGeom() and GUtils.StopGeom(). GUtils.SetUnits( 0 ) geom_point1 = GGeometry.CreatePoint(0.0, 0.0, 0.0) geom_point2 = GGeometry.CreatePoint(-10, 0.0, 0.0) geom_point3 = GGeometry.CreatePoint(-10, 1, 0.0) geom_point4 = GGeometry.CreatePoint(0, 1, 0.0) geom_point5 = GGeometry.CreatePoint(0, -1, 0.0) geom_point6 = GGeometry.CreatePoint(5, -1, 0.0) geom_point7 = GGeometry.CreatePoint(5, 0, 0.0) geom_point8 = GGeometry.CreatePoint(5, 1, 0.0) geom_point9 = GGeometry.CreatePoint(75, 1, 0.0) geom_point10 = GGeometry.CreatePoint(75, 0, 0.0) geom_point11 = GGeometry.CreatePoint(75, -1, 0.0) geom_line1 = GGeometry.CreateLine( geom_point2, geom_point3 ) geom_line2 = GGeometry.CreateLine( geom_point5, geom_point1 ) geom_line3 = GGeometry.CreateLine( geom_point6, geom_point7 ) geom_line4 = GGeometry.CreateLine( geom_point1, geom_point4 ) geom_line5 = GGeometry.CreateLine( geom_point7, geom_point8 ) geom_line6 = GGeometry.CreateLine( geom_point11, geom_point10 ) geom_line7 = GGeometry.CreateLine( geom_point10, geom_point9 ) geom_line8 = GGeometry.CreateLine( geom_point2, geom_point1 ) geom_line9 = GGeometry.CreateLine( geom_point5, geom_point6 ) geom_line10 = GGeometry.CreateLine( geom_point3, geom_point4 ) geom_line11 = GGeometry.CreateLine( geom_point4, geom_point8 ) geom_line12 = GGeometry.CreateLine( geom_point1, geom_point7 ) geom_line13 = GGeometry.CreateLine( geom_point6, geom_point11 ) geom_line14 = GGeometry.CreateLine( geom_point7, geom_point10 ) geom_line15 = GGeometry.CreateLine( geom_point8, geom_point9 ) geom_edge1 = GMesh.CreatePowerLawEdge(geom_line1, 20, 1, 1) geom_edge2 = GMesh.CreatePowerLawEdge(geom_line2, 20, 1, 1) geom_edge3 = GMesh.CreatePowerLawEdge(geom_line4, 20, 1, 1) geom_edge4 = GMesh.CreatePowerLawEdge(geom_line3, 20, 1, 1) geom_edge5 = GMesh.CreatePowerLawEdge(geom_line5, 20, 1, 1) geom_edge6 = GMesh.CreatePowerLawEdge(geom_line6, 20, 1, 1) geom_edge7 = GMesh.CreatePowerLawEdge(geom_line7, 20, 1, 1) geom_edge8 = GMesh.CreatePowerLawEdge(geom_line8, 200, 1, 1)UTS: ENGINEERING 37 geom_edge9 = GMesh.CreatePowerLawEdge(geom_line10, 200, 1, 1) geom_edge10 = GMesh.CreatePowerLawEdge(geom_line9, 100, 1, 1) geom_edge11 = GMesh.CreatePowerLawEdge(geom_line12, 100, 1, 1) geom_edge12 = GMesh.CreatePowerLawEdge(geom_line11, 100, 1, 1) geom_edge13 = GMesh.CreatePowerLawEdge(geom_line13, 1200, 1, 1) geom_edge14 = GMesh.CreatePowerLawEdge(geom_line14, 1200, 1, 1) geom_edge15 = GMesh.CreatePowerLawEdge(geom_line15, 1200, 1, 1) geom_face1 = GMesh.CreateFace( geom_edge8, geom_edge3, geom_edge9, geom_edge1 ) geom_face2 = GMesh.CreateFace( geom_edge2, geom_edge10, geom_edge4, geom_edge11 ) geom_face3 = GMesh.CreateFace( geom_edge11, geom_edge5, geom_edge12, geom_edge3 ) geom_face4 = GMesh.CreateFace( geom_edge4, geom_edge13, geom_edge6, geom_edge14 ) geom_face5 = GMesh.CreateFace( geom_edge5, geom_edge14, geom_edge7, geom_edge15 ) geom_2d_sdomain1 = GMesh.Create2DBlock( geom_face1 ) geom_2d_sdomain2 = GMesh.Create2DBlock( [geom_face3, geom_face2, geom_face4, geom_face5] ) GBCVC.SetBC( geom_edge1, 'INLET', 'Inlet' ) GBCVC.SetBC( geom_edge6, 'OUTLET1', 'Outlet' ) GBCVC.SetBC( geom_edge7, 'OUTLET2', 'Outlet' ) GBCVC.AddEntitiesToBCGroup( [geom_edge6, geom_edge7], 'OUT' ) GBCVC.SetVC( [geom_face1, geom_face5, geom_face4, geom_face2, geom_face3], 'WET_STUFF', 'Fluid' ) GBCVC.AddEntitiesToVCGroup( [geom_face1, geom_face5, geom_face4, geom_face2, geom_face3], 'WETSTUFF' ) #GBCVC.SetVC( [geom_face1, geom_face5, geom_face4, geom_face2, geom_face3], 'WET_STUFF', 'Fluid' ) GFileIO.ExportDTF('C:/CFD/BFS/BFS_MESH_75.DTF', 2, 1, 0) PYTHON FILE FOR BFS STEADY–STATE SIMULATION SET-UP import GuiVersion import GuiDBM import GuiFILE import GuiML import GuiPT import GuiMO import GuiVC import GuiBC import GuiIC import GuiPC import GuiFan import GuiMacP import GuiMR import GuiMRF import GuiSC import GuiOut import GuiRun #The following line is for backwards-compatibility, DO NOT DELETE IT. GuiVersion.RecordVersion("2013.0.10.10140") GuiFILE.SetMode("ACEU") GuiFILE.Open("C:/CFD/BFS/BFS_MESH_75.DTF") GuiPT.Set("Flow", 1) GuiMO.Set("Shared/Title", "BACKWARD FACING STEP RE=400") GuiMO.Set("Flow/RefPressure", 0) GuiVC.Set([42, 44, 43, 45, 46], "Shared/FluidSubtype", "Liquid")UTS: ENGINEERING 38 GuiVC.Set([42, 44, 43, 45, 46], "Shared/MaterialName", "WET") GuiVC.Set([42, 44, 43, 45, 46], "Shared/Density", 1) GuiVC.Set([42, 44, 43, 45, 46], "Shared/Mu", 0.0025) #Expression definition GuiFILE.DefineExpression("U_IN", "6*Y*(1-Y)") GuiBC.Set([27], "Flow/U_eval_method", "Parametric") GuiBC.Set([27], "Flow/U_Para", "U_IN") GuiIC.Set([42, 44, 43, 45, 46], "Flow/U", 0.67) GuiSC.Set("Iter/Max_Iteration", 1000) GuiSC.Set("Spatial/Velocity_diff_method", "2ndOrder") GuiOut.Set("Graphic/LaminarViscosity", 0) GuiOut.Set("Graphic/Vorticity", 1) GuiOut.Set("Print/MassFlow_Sum", 1) GuiFILE.SaveAs("C:/CFD/BFS/BFS_RUN75_400_SS.DTF") GuiFILE.SaveAs("C:/CFD/BFS/BFS_RUN75_400_SS.DTF") GuiRun.Submit() GuiFILE.CloseCurrentSim() PYTHON FILE FOR BFS TIME–MARCHING SIMULATION SET-UP import GuiVersion import GuiDBM import GuiFILE import GuiML import GuiPT import GuiMO import GuiVC import GuiBC import GuiIC import GuiPC import GuiFan import GuiMacP import GuiMR import GuiMRF import GuiSC import GuiOut import GuiRun #The following line is for backwards-compatibility, DO NOT DELETE IT. GuiVersion.RecordVersion("2014.0.0.11217") GuiFILE.SetMode("ACEU") GuiFILE.Open("C:/CFD/BFS/BFS_MESH_75.DTF") GuiPT.Set("Flow", 1) GuiMO.Set("Shared/Title", "BFS_RE400_DT") GuiMO.Set("Shared/Transient_eval_method", "Transient") GuiMO.Set("Shared/NSteps", 40000) #GuiMO.Set("Shared/NSteps", 10000) GuiMO.Set("Shared/DT", 20E-3) GuiMO.Set("Shared/TimeAccuracy", "Euler") GuiMO.Set("Flow/RefPressure", 0)UTS: ENGINEERING 39 GuiVC.Set([42, 44, 43, 45, 46], "Shared/MaterialName", "WET_STUFF") GuiVC.Set([42, 44, 43, 45, 46], "Shared/FluidSubtype", "Liquid") GuiVC.Set([42, 44, 43, 45, 46], "Shared/MaterialName", "WET_STUFF") GuiVC.Set([42, 44, 43, 45, 46], "Shared/Density", 1) GuiVC.Set([42, 44, 43, 45, 46], "Shared/Mu", 2.5E-3) #Expression definition GuiFILE.DefineExpression("U_IN", "6*Y*(1-Y)") GuiBC.Set([27], "Flow/U_eval_method", "Profile Y") GuiBC.Set([27], "Flow/U_eval_method", "Parametric") GuiBC.Set([27], "Flow/U_Para", "U_IN") GuiIC.Set([42, 44, 43, 45, 46], "Flow/U", 0.67) GuiSC.Set("Iter/Max_Iteration", 100000) GuiSC.Set("Spatial/Velocity_diff_method", "2ndOrder") GuiOut.Set("Output/Output_Interval", 100) GuiOut.Set("Monitor/Monitor_Points", 1) GuiOut.SetArraySize("Monitor/TotalMonitorPoints", 1) GuiOut.SetArray("Monitor/MP_X", 1, 35) GuiOut.SetArray("Monitor/MP_Y", 1, 0) GuiOut.Set("Monitor/U", 1) GuiOut.Set("Monitor/V", 1) GuiFILE.SaveAs("C:/CFD/BFS/BFS_400_DT_RUN75.DTF") GuiFILE.SaveAs("C:/CFD/BFS/BFS_400_DT_RUN75.DTF") GuiRun.Submit()UTS: ENGINEERING 40 PART B2: TIME–DEPENDENT FLOWS. VORTEX SHEDDING FROM A TWO–DIMENSIONAL CYLINDER. (3 MARKS) INTRODUCTION ".. the flow past a blunt object such as a circular cylinder also varies with Reynolds number." In general, the larger the Reynolds number, the smaller the region of the flow field in which viscous effects are important. For objects that are not sufficiently streamlined an additional characteristic of the flow is observed. This is termed "flow separation" and is illustrated in Figure 0.2. Low Reynolds number flow (Re UD = < ρ µ 1) past a circular cylinder is characterized by the fact that the presence of the cylinder and the accompanying viscous effects are felt throughout a relatively large portion of the flow field. As is indicated in Figure 0.1, for (Re UD = = ρ µ 0.1) the viscous effects are important several diameters in any direction from the cylinder. A rare characteristic of this flow is that the streamlines are essentially symmetric about the centre of the cylinder—the streamline pattern is the same in front of the cylinder as it is behind the cylinder. Figure 0.1: Character of the viscous flow past a circular cylinder: low Reynolds number flow As the Reynolds number is increased, the region ahead of the cylinder in which viscous effects are important becomes smaller, with the viscous region extending only a short distance ahead of the cylinder. The viscous effects are convected downstream and the flow loses its symmetry. Another characteristic of external flows becomes important—the flow separates from the body at the separation location as indicated in Figure 0.2. With the increase in Reynolds number, the fluid inertia becomes more important and at some location on the body, denoted the separation location, the fluid's inertia is such that it cannot follow the curved path around to the rear of the body. The result is a separation bubble behind the cylinder in which some of the fluid is actually flowing upstream, against the direction of the upstream flow. Figure 0.2 Character of the viscous flow past a circular cylinder: moderate Re flow,UTS: ENGINEERING 41 At still larger Reynolds numbers, the area affected by the viscous forces is forced farther downstream until it involves only a thin layer, δ, known as the boundary layer, (δ  D) on the front portion of the cylinder and an irregular, unsteady (perhaps turbulent) wake region that extends far downstream of the cylinder. The fluid in the region outside of the boundary layer and wake region flows as if it were "inviscid", that is, apparently unaffected by viscosity. However, we know the fluid viscosity is the same throughout the entire flow field. Whether viscous effects are important or not depends on which region of the flow field we are considering and its "local" Reynolds number. As an example, the velocity gradients within the boundary layer and wake regions behind the cylinder are much larger than those in the remainder of the flow field. The shear stress (i.e., viscous effect) is the product of the fluid viscosity and the fluid's velocity gradient. It follows that viscous effects are confined to the boundary layer and wake regions… " Figure 0.3: Character of the viscous flow past a circular cylinder: high Reynolds number flow THREE NEW DIMENSIONLESS PARAMETERS New dimensionless parameters are needed for a full understanding of your assignment requirements. The Lift Coefficient The Lift Coefficient, CL, is the non-dimensionlised lift force 1 2 2 L x C L = ρU A . L is the force normal to the flow and Ax is the swept area parallel to the flow. For a 2-D cylinder Ax is the diameter per unit length i.e. Ax = 1, and U=1, and ρ = 1 . The Drag Coefficient The Drag Coefficient, CD, is the non-dimensionlised drag force 1 2 2 D x C D = ρU A . Here, D is the force parallel to the flow. Note that the total drag force consists of two components: pressure drag force and shear stress drag force. Both CL and CD are functions of time, t. Examples from last year's class are shown below (do not pay attention to the values; your Re is different to last year's). Note that CL oscillates around a mean value of zero and CD oscillates about a non-zero mean value. The figures show the unsteady, non – constant "start–up" values of CL and CD. These values begin at zero for t=0 and increase to reach their "periodic/repeatable" values. It is only this "periodic/repeatable" range that we are interested in.UTS: ENGINEERING 42 Figure 0.1: The drag coefficient for both a smooth cylinder and a sphere as a function of Re. The Strouhal Number The Strouhal number, St, is the non-dimensionlised vortex frequency 0.21 0.22 inlet fD St U = ≈ − f is the vortex shedding frequency, D is the cylinder diameter and U is the inlet flow velocity. It is well known from the literature that for our Re a value of 0.21-0.22 is expected. By knowing St for our flow, we calculate the frequency of vortex-shedding, f, and from this, we calculate the period 1 τ = f of a single vortex-shedding occurrence. We then make an assumption of how many time-steps are required for a fully resolved vortexshedding occurrence and this gives dt for the simulation. Use dt = τ 50 to ensure very well resolved vortex-shedding. The last step is total simulation time Figure 0.2: This is an example of CL(t) and CD(t) from last year's class. They did Re=1000. You are required to hand in this figure and estimate CL and to 95% confidence – use the "Descriptive Statistics" function in Excel (DATA -> DATA ANALYSIS -> Descriptive StatisticsUTS: ENGINEERING 43 REQUIREMENTS Geometry, Fluid Properties and Boundary Conditions. The aims of this study is to setup and solve for the unsteady flow past a circular cylinder and to study the vortex shedding process. Flow past a circular cylinder is one of the classical problems of fluid mechanics. The geometry suggests a steady and symmetric flow pattern. For lower value of Reynolds number, the flow is steady and symmetric. Any disturbance introduced at the inlet or by roughness on the cylinder surface is damped by the viscous forces. As the Reynolds number is increased, the disturbed upstream flow cannot be damped. This leads to a very important periodic phenomenon downstream of the cylinder, known as "vortex shedding" and in honour of Theodore von Karman; it is often called the "von Karman vortex street". This objectives of this assignment include the following: • Set-up a quality grid with the given dimensions; • Solve a time dependent simulation; • Understand new dimensionless groups–the lift and drag coefficients, and the Strouhal number. • Set time monitors for lift and drag coefficient and observe vortex shedding; Set up an animation to demonstrate the vortex shedding. Non-dimensionalise your simulation: 1 1; 1; ; 1; Re 500 Re = = = = = = inlet inlet U D ρ µ U D ρ µ Here, Uinlet is the inlet velocity and is a constant function and D is the cylinder diameter. The Reynolds number to solve for is Re=500. The cylinder walls are "non-slip" i.e. U V = = 0 .UTS: ENGINEERING 44 The upper and lower edges of the flow domain (which are "wall" GEOM entities) are considered to be "far-field". You set them in CFD-ACE as "symmetry walls" withU V = = 1; 0 . To help you choose your dimensionless time step * ∆t assume a Strouhal number * * * 0.22 . inlet f D St U = = Here f * is the predominant vortex shedding frequency. The period of vortex shedding is therefore τ * * = ≈ 1 4.55 f and I suggest you try a time step of ∆t* * = ≈ τ 50 0.1 to be sure to capture the shape of the velocity shedding which will be approximately sinusoidal as shown in the figures for CL and CD. A total run time of 300s should be more than sufficient. Suggested Flow Domain. The cylinder diameter is equal to 1 i.e. D* = 1 and located at x* = 0 . Refine the structured grid around the cylinder surface and the region of the wake. The upstream inlet is located at x* = −30 , the downstream outlet is located at x* = 100 and the upper and lower domain limits are located at y* = 25 and y* = −25 respectively. Some examples of possible structured and unstructured1 meshes are shown below. Read the document "grid suggestions.pdf" available on UTSonline Don't do it like this – too much waste 1 We have yet to study unstructured meshing. This will be done in Assignment 2.UTS: ENGINEERING 45 This is a better way to model the flow domainUTS: ENGINEERING 46 Wastage! A good idea Another type of mesh that clusters the grid points in the region of interest.UTS: ENGINEERING 47 Suggested Solution Method: Solver Settings •Read the document "CFD-ACE Setup.pdf" available here: https://www.dropbox.com/s/n86r294tb61o2fl/CFD-ACE%20SETUP.pdf?dl=0 Objectives Obtain a converged and mesh-independent solution for the Reynolds number = 500 Requirements Include a ½ page plot of the drag coefficient versus time. Estimate the averaged value and compare to Figure 0.4 for Re=500. Include a ½ page plot of the lift coefficient versus time. See my instructions on how to get the required data here: https://www.dropbox.com/s/n9xv9z86xsj99nb/LIFT%20DRAG%20INSTRUCTIONS.pdf?dl=0 Note that the drag and lift coefficients oscillate in time and we are not interested in the initial "start–up" time region. References. 4. B. R. Munson, T. H. Okiishi, W. W. Huebsch, and A. P. Rothmayer, 2002, Fundamentals of Fluid Mechanics, 7th Ed., Wiley & Sons, New York. Any other handouts given to you Appendix A: Unsteady and Separated Flows If your background in Fluid Mechanics is weak or non–existent you would do well to read the following: • Wikipedia's page on Flow Separation; • Uni of Sydney's Aero Dept. page on Flow Separation; • eFluids page on "Bicycle AeroDynamics" • University of Texas pages on Boundary Layer Separation The above four documents are available on UTSOnlineUTS: ENGINEERING 48 PART B3: AXISYMMETRIC FLOWS (SIMULATING A 3–D FLOW IN 2–D) VORTEX BREAKDOWN IN A CYLINDER WITH A ROTATING BASE. (3 MARKS) INTRODUCTION #There is no movie for this part yet, only screen grabs and python scripts should you need to use them# Vortex breakdown in swirling flows has been the subject of much attention since first recognized in the tip vortices of aircraft wings. It is also a serious problem at high angle of attack for highly manoeuvrable military aircraft. The term "vortex breakdown" is associated with an abrupt change in the character of a columnar vortex at some axial station. It is observed as a sudden widening of the vortex core together with a deceleration of the axial flow and is often followed by a region or regions of recirculation. (J. M. Lopez, J. Fluid Mech. (1990). vol. 221, p. 533-552). In the laboratory, it is desirable to establish a well-controlled and repeatable experiment to study vortex breakdown. To do this, a cylinder is filled with a liquid. The cylinder has a rotating end wall with the opposite end wall stationary along with the sidewalls. A confined swirling flow is created by the rotating end wall, pumping fluid up the sidewalls, where it meets and travels to the centre of the stationary end-wall and then makes its way down along the axis of symmetry to spread out along the rotating end-wall and continues the cycle. A columnar vortex is established along the centre axis of the experiment. The use of a laser activated fluorescent dye makes flow visualisation possible. The figures shown are from the paper of Escudier. Escudier carried out one of the more thorough investigations of vortex breakdown in a cylindrical flow with a rotating base. His main findings are that the nature of vortex breakdown is a strong function of Reynolds number (defined as: ρ R2 µ Ω ) and cylinder aspect ratio(H R) . H is the cylinder height, R is the cylinder radius and Ω is the cylinder's angular velocity. M. P. Escudier, Experiments in Fluids 2, 189-196 (1984) A flow is considered axi–symmetric if: • It is steady–state; and • Its geometry is symmetric about an axis. If the above two conditions are true there is no need to do a full 3–dimensional calculation. The flow geometry can be simplified to a 2–dimensional plane that must include the axis of symmetry. Unlike the LDC, BFS and 2–d vortex shedding simulations an axi-symmetric simulation is still fully 3–d, that is to say, all three-velocity components, U, V and W, are solved for.UTS: ENGINEERING 49 Figure 0.1 Schematic diagram of experimental arrangement Figure 0.2 Stability boundaries for single, double and triple breakdowns, Figure 0.3 Visualisation of changes in entire flow structure with increasing QR^2/v for H/R = 2UTS: ENGINEERING 50 Figure 0.4 Visualisation ofchangesin vortex structure with increasing QR^2/v for H/R= 1.5UTS: ENGINEERING 51 Figure 0.5 Visualisation ofchangesin vortex structure with increasing QR^2/v for H/R =2.5 Figure 0.6 Visualisation ofchangesin vortexstructure withincreasing QR^2/v for H/R=3.25UTS: ENGINEERING 52 You are required to simulate two "steady–state" flows: • AR = 1.5, Re = 1492 • AR = 2.5, Re = 2126 The first simulation should result in one vortex breakdown. The second should result in two vortex breakdowns. An example of the geometry is shown below. It is a simple 2–d rectangle with, importantly, the axis of symmetry lying on the x-axis. Our simulation is tilted over compared to the experiment. The radius, R = 1, the height H = AR. Note that the base is rotating out of the page Python scripts are available in the Appendix. Their use will cost you 0.5 marks. This is an example only. I have used CFD-VIEW to superimpose vectors (10% scale I think) with a number of stream–function contours. I only chose those contours that highlight regions of vortex breakdown. I have used the free graphic manipulation program "Gimp" to rotate and mirror a screen dump from CFD-VIEW.UTS: ENGINEERING 53UTS: ENGINEERING 54UTS: ENGINEERING 55 Figure 0.7 This figure required, hand-in Figure 0.8 This figure required, hand-in This is a meaty topic and is appropriate for an Individual Project For example, you could try to simulate an unsteady flow–which would require a full 3-D and time–dependent solution. I would only attempt this is you have a very good PC–or you might be able to apply for CPU time of the University's super-duper computer. See here: https://clusterportal.feit.uts.edu.au/pages/home PYTHON FILE FOR AXI-SYMMETRIC STEADY–STATE SIMULATION SET-UP # This file was journaled by CFD-GEOM import GUtils import GGeometry import GMesh import GFileIO import GBCVCUTS: ENGINEERING 56 # Note that if you plan to run this script outside CFD-GEOM, # (such as in Simulation Manager or a standalone Python interpreter), # please ensure that the CFD-GEOM portion of the script is wrapped # by calls to GUtils.StartGeom() and GUtils.StopGeom(). GUtils.SetUnits( 0 ) geom_point1 = GGeometry.CreatePoint(0.0, 0.0, 0.0) geom_point2 = GGeometry.CreatePoint(2.5, 0.0, 0.0) geom_point3 = GGeometry.CreatePoint(2.5, 1, 0.0) geom_point4 = GGeometry.CreatePoint(0, 1, 0.0) geom_line1 = GGeometry.CreateLine( geom_point1, geom_point2 ) geom_line2 = GGeometry.CreateLine( geom_point4, geom_point3 ) geom_line3 = GGeometry.CreateLine( geom_point2, geom_point3 ) geom_line4 = GGeometry.CreateLine( geom_point1, geom_point4 ) geom_edge1 = GMesh.CreatePowerLawEdge(geom_line1, 321, 1.3, 3) geom_edge2 = GMesh.CreatePowerLawEdge(geom_line2, 321, 1.3, 3) geom_edge3 = GMesh.CreatePowerLawEdge(geom_line3, 161, 1.3, 3) geom_edge4 = GMesh.CreatePowerLawEdge(geom_line4, 161, 1.3, 3) geom_face1 = GMesh.CreateFace( geom_edge1, geom_edge3, geom_edge2, geom_edge4 ) geom_2d_sdomain1 = GMesh.Create2DBlock( geom_face1 ) GBCVC.SetBC( geom_edge2, 'WALL_SIDE', 'Wall' ) GBCVC.SetBC( geom_edge1, 'AXIS_OF_SYMMETRY', 'Symmetry' ) GBCVC.SetBC( geom_edge3, 'LID', 'Wall' ) GBCVC.SetBC( geom_edge4, 'ROTATING_BASE', 'R_wall' ) GFileIO.ExportDTF('C:/CFD/ROTATE/ROTATING_BASE.DTF', 2, 1, 0, 0) GFileIO.ExportDTF('C:/CFD/ROTATE/ROTATING_BASE.DTF', 2, 1, 0, 0)UTS: ENGINEERING 57 PYTHON FILE FOR AXI-SYMMETRIC SIMULATION SET-UP import GuiVersion import GuiDBM import GuiFILE import GuiML import GuiPT import GuiMO import GuiVC import GuiBC import GuiIC import GuiPC import GuiFan import GuiMacP import GuiMR import GuiMRF import GuiSC import GuiOut import GuiRun #The following line is for backwards-compatibility, DO NOT DELETE IT. GuiVersion.RecordVersion("2014.0.0.11217") GuiFILE.SetMode("ACEU") GuiFILE.Open("C:/CFD/ROTATE/ROTATING_BASE.DTF") GuiPT.Set("Flow", 1) GuiMO.Set("Shared/Title", "ROTATING_BASE_RE2000_AR2") GuiMO.Set("Shared/Polar", "Axisymmetric") GuiMO.Set("Flow/RefPressure", 0) GuiMO.Set("Flow/Swirl", 1) GuiVC.Set([13], "Shared/Density", 1) GuiVC.Set([13], "Shared/MaterialName", "WET_STUFF") GuiVC.Set([13], "Shared/Mu", 5E-4) GuiBC.Set([12], "Flow/Wx", 1) GuiIC.Set([13], "Flow/Omega", 1) GuiSC.Set("Iter/Max_Iteration", 10000) GuiSC.Set("Spatial/Velocity_diff_method", "2ndOrder") GuiOut.Set("Graphic/Vorticity", 1) GuiOut.Set("Graphic/StrainRate", 1) GuiOut.Set("Graphic/WallShearStress", 1) GuiFILE.SaveAs("C:/CFD/ROTATE/ROTATING_BASE_OUT1.DTF") GuiFILE.SaveAs("C:/CFD/ROTATE/ROTATING_BASE_OUT1.DTF") GuiRun.Submit()UTS: ENGINEERING 58 PART B4: THE EQUATIONS OF FLUID MECHANICS. (1, 1, 1 = 3 MARKS) Question B4-1: DIV, CURL and GRAD and the Continuity Equation (Conservation of Mass) First, you MUST* watch the YouTube lecture on the DEL operator here: https://www.youtube.com/watch?v=sWZ8r5REvXA * MUST: Not really, only if you don't know the material or don't have your own source of information If you wish, you may like to also read the Wikipedia page: https://en.wikipedia.org/wiki/Vector_calculus_identities then, you MUST* watch the YouTube lecture on the Derivation of the Continuity Equation here: https://www.youtube.com/watch?v=Ls5HS2MLXpg * MUST: Not really, only if you don't know the material or don't have your own source of information You MUST* read Section 3.2 from the text, Computational Fluid Dynamics: A Practical Approach, by Tu, Heng Yeoh, and Liu. (In the set of books I gave you).UTS: ENGINEERING 59 * MUST: Not really, only if you don't know the material or don't have your own source of information Equations D.1a and D.1b are forms of Mass Conservation. Differential Form of the Continuity Equation Vector Form of the Continuity Equation ( ) ( ) ( ) 0 A B u v w t x y z ∂ρ ∂ ∂ ∂ ρ ρ ρ + + + = ∂ ∂ ∂ ∂ (D.1a) 0 B A V ρ t ρ ∂ +∇• = ∂  (D.1b) Q-B4-1: Explain the meaning of terms A and B shown above. What is the ∆ symbol and how is it being used in Equation D.1b? What is an incompressible flow and how would D.1a and D.1b be written for an incompressible flow? (Total answer ½ page maximum) Question B4-2: The Linear Momentum Equation (Conservation of Linear Momentum)* * We ignore Angular Momentum for now First, you MUST* watch the YouTube lecture series on Conservation of Momentum: https://www.youtube.com/watch?v=dpFOdRvmrCk&index=1&list=PLBAcrca02tZcjbtpp_RBqGp4yTtyUnqVE https://www.youtube.com/watch?v=IXkmXBYpB8U&index=2&list=PLBAcrca02tZcjbtpp_RBqGp4yTtyUnqVE https://www.youtube.com/watch?v=uCPivZ5V130&index=3&list=PLBAcrca02tZcjbtpp_RBqGp4yTtyUnqVE https://www.youtube.com/watch?v=tIuCbp2DydA&index=4&list=PLBAcrca02tZcjbtpp_RBqGp4yTtyUnqVE https://www.youtube.com/watch?v=1S3VOWNrEi4&index=5&list=PLBAcrca02tZcjbtpp_RBqGp4yTtyUnqVE * MUST: Not really, only if you don't know the material or don't have your own source of informationUTS: ENGINEERING 60 If you wish, you may like to also read the Wikipedia page: https://en.wikipedia.org/wiki/Momentum#Conservation (just the section on Deformable bodies and fluids) You MUST* read Section 3.3 as well as Appendix A pg. 410-412 (up to Eq. A.14) from the text, Computational Fluid Dynamics: A Practical Approach, by Tu, Heng Yeoh, and Liu. (In the set of books I gave you). * MUST: Not really, only if you don't know the material or don't have your own source of information Equations D.2a and D.2b are forms of Linear Momentum Conservation. Differential Form of the Linear Momentum Equation 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 x D A B C y D A B C A B u u u u p u u u u v w B t x y z x x y z v v v v p v v v u v w B t x y z y x y z w w w w p w w w u v w t x y z z x y z ρ µ ρ ρ µ ρ ρ µ   ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂     + + + = − + + + +     ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂     ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂     + + + = − + + + +     ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂     ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂   + + + = − + + +   ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ 2 C ρBz D     +   (D.2a) Vector Form of the Linear Momentum Equation V 2 V V p V B t ρ µ ρ   ∂   + ∇ = −∇ + ∇ +   ∂       (D.2b) Q-B4-2: In Equation (D.2a) explain the terms (A), (B), (C) and (D). In Equation (D.2b) discuss the termsV V   ∇ , and ∇p and ∇2V  . Are these terms linear or non-linear? (Total answer ½-page maximum).UTS: ENGINEERING 61 Question B4-3: The Energy Equation (Conservation of Energy)* * Again, only Linear for now You MUST* read Section 3.4 as well as Appendix A pg. 412-413 (starting after Eq. A.14) from the text, Computational Fluid Dynamics: A Practical Approach, by Tu, Heng Yeoh, and Liu. (In the set of books I gave you). * MUST: Not really, only if you don't know the material or don't have your own source of information Q-B4-3: Name and describe the sources of energy that contribute to the (linear) energy equation (Total answer ½-page maximum).