Week 5.1 - Mid term project - Solving the steady and unsteady 2D heat conduction problem

Objective To apply Reynolds decomposition to the Navier Stokes equation and to determine the expression for Reynolds stress.   Navier Stokes Equations The movement of fluid in the physical domain is driven by various properties. For the purpose of bringing the behaviour of fluid flow to light and developing a mathematical…

Objective To set up a transient simulation in a shock tube using Converge CFD, where one side is filled with high pressure nitrogen and the other side with low pressure oxygen separated by a diaphragm, and to view the flow results.   Theory A shock tube is a device used for studying shock waves. Initially, a diaphragm…

Objective  To simulate the conjugate heat transfer flow with various grid sizes and super cycle time values and illustrate the results.   Theory CHT Analysis Conjugate heat transfer (CHT) analysis can accurate predict heat transfer by simultaneously solving all the relevant solid and flow field heat transfer…

Objective To simulate the Prandtl Meyer shock flow and analyse the effects of various sub grid criteria sizes on the results of subsonic and supersonic inlet velocities.   Shock wave A shock wave is a type of propogating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave,…

Objective To perform the steady state simulation of flow over a throttle body and analyse the results.   Solution The elbow stl file is imported into converge, and the geometry is scaled in order to convert units from mm to m.   The geometry consists of a thickness, because of an outer and an inner surface. The…

Objective To perform the steady state simulation of flow over a throttle body and analyse the results.   Solution The elbow stl file is imported into converge, and the geometry is scaled in order to convert units from mm to m.   The geometry consists of a thickness, because of an outer and an inner surface. The…

Objective To simulate the flow over backward facing step with different mesh sizes and compare the results   Solution The BFS stl file is imported into Converge and setup for simulation.  The dimensions of the geomtry are shown in the figure below   A time based simulation is selected with the material as…

Objective To perform the channel flow simulation using three different mesh sizes, and to compare the post processed results from.   Solution Geometry creation - Converge The geometry is created using the measurements shown in the figure below   The direction of the normals are reversed, such that they point…

Objective To simulate the airflow around an FSAE car for two different scenarios and analyze the results.   Geometry clean up - Converge The stl file is imported into Converge, and scaled to transform units from inches to metres. The model is then checked for geometry errors. There are 48 errors arising from non-manifold…

Objective To simulate the flow around an Ahmed body using converge CFD and compare the simulation results with the experimental data.   Theory The ahmed body is a  generic car body, which can be used to predict first aerodynamic simulation results. The airflow around the Ahmed body captures the essential flow…

Objective To simulate the flow over an airfoil for various angle of attacks and compare the effects of different turbulence models on the results.   Theory An airfoil is the cross sectional shape of a wing, blade (of a propeller, rotor, or turbine). An airfoil shaped body moving through a fluid produces an aerodynamic…

Objective To apply Reynolds decomposition to the Navier Stokes equation and to determine the expression for Reynolds stress.   Navier Stokes Equations The movement of fluid in the physical domain is driven by various properties. For the purpose of bringing the behaviour of fluid flow to light and developing a mathematical…

Objective To set up a transient simulation in a shock tube using Converge CFD, where one side is filled with high pressure nitrogen and the other side with low pressure oxygen separated by a diaphragm, and to view the flow results.   Theory A shock tube is a device used for studying shock waves. Initially, a diaphragm…

Objective  To simulate the conjugate heat transfer flow with various grid sizes and super cycle time values and illustrate the results.   Theory CHT Analysis Conjugate heat transfer (CHT) analysis can accurate predict heat transfer by simultaneously solving all the relevant solid and flow field heat transfer…

Objective To simulate the Prandtl Meyer shock flow and analyse the effects of various sub grid criteria sizes on the results of subsonic and supersonic inlet velocities.   Shock wave A shock wave is a type of propogating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave,…

Objective To perform the steady state simulation of flow over a throttle body and analyse the results.   Solution The elbow stl file is imported into converge, and the geometry is scaled in order to convert units from mm to m.   The geometry consists of a thickness, because of an outer and an inner surface. The…

Objective To perform the steady state simulation of flow over a throttle body and analyse the results.   Solution The elbow stl file is imported into converge, and the geometry is scaled in order to convert units from mm to m.   The geometry consists of a thickness, because of an outer and an inner surface. The…

Objective To simulate the flow over backward facing step with different mesh sizes and compare the results   Solution The BFS stl file is imported into Converge and setup for simulation.  The dimensions of the geomtry are shown in the figure below   A time based simulation is selected with the material as…

Objective To perform the channel flow simulation using three different mesh sizes, and to compare the post processed results from.   Solution Geometry creation - Converge The geometry is created using the measurements shown in the figure below   The direction of the normals are reversed, such that they point…

Objective: To simulate the flow through a pipe for three different wedge angles using the Symmetry boundary condition and compare the results.   Solution The fluid properties are the same as in the previous part of the challenge (Challenge 11). Diameter = 0.004m Rho = 1000 kgm^-3 Re = 2100 Entrance length Le = 0.05*Re*D…

Objective To calculate the flow variables anaytically and compare them with the numerical results and to study the velocity profile at various sections over the length of the pipe.   Solution The flow of the fluid over the length of the pipe is assumed as laminar. The Reynolds number given is 2100. The working fluid…

Objective To describe the differences between finite difference method (FDM) and finite volume method (FVM) and to describe the need for interpolation schemes and flux limiters in FVM   Finite Difference Method It is a numerical method used in CFD to solve the Navier Stokes equation. It makes use of discrete points…

Aim To perform the simulation of backward facing step using OpenFOAM and compare the results of two different mesh growth factors - 1 and 0.2.   Theory Geometry of backward facing step The above geometry has to be discretized into a number of blocks and combined together. The domain is divided into 5 blocks, as shown…

Objective: To simulate the isentropic flow through a 1D subsonic - supersonic nozzle using both conservative and non conservative forms of the governing equations and solving them using the Maccormack technique, and analyse the results.   Solution Theory We conside the isentropic flow through a convergent - divergent…

Aim 1. To simulate the steady state 2D heat equation using iterative solvers 2. To simulate the transient 2D heat equation using implicit and explicit schemes   Solution Heat equation - Theory The general 3D heat equation can be written as `(delu)/(delt) + alpha((∂^2 T )/(∂ x^2) + (∂^2 T)/(∂ y^2)…

Aim: To derive the fourth order approximations of the second order derivative using the central difference, skewed right hand, and skewed left hand schemes and compare them with the results of the analytical derivative.   Function : `f(x) = e^x cos(x)` Analytical first derivative: `f'(x) = e^x (cos(x) -sin(x))` Analytical…

Objective: To simulate the impact of a bird strike on the blades of an aeroplane turbine, using the given Aero and bird FE models.   Model setup The main file contains the four main parts of the model namely the casing, hub, blade and the bird. They have to be segregated and saved as separate .k files, so that they…

Objective: To illustrate the mechanism of spherical, cylindrical, translational and revolute joints between rigid bodies and deformable bodies. The various types of joints can be created in LS-Dyna using the CONSTRAINED_JOINT keyword.   1. Joints between rigid bodies The various types of joints between rigid bodies…

Objective: To calculate the Mooney Rivlin and Ogden material constants from the material data and validate them using stress-strain data from the tensile test of a dogbone specimen.   MAT 77 - Hyperelastic Step 1: Material test data - Engineering stress vs Engineering strain The given stress - strain data in imported…

Objective: To extract the stress-strain data points from the image and input them into LS-Dyna, and compare the results of the simulation with that obtained from the raw data.   Step 1: Extraction of data The data digitizer tool is used to extract the data from curve 2 of the image given.   These data points,…

Objective To study the effects of mass scaling on the run-time and the accuracy of the model, while keeping the percentage of mass addition less than 8%.   Step 1: Explicit Analysis The given model is opened in LS-Dyna and simulated first with default parameters. The unit system is kg-m-sec. The parameters of the…

Objective: To simulate the head impact using a simple head model and a headform against a simple rigid wall and a hood, and analyse the results.   Case 1: Impact of the Simple head model against the rigid wall   Step 1: Model setup with Section and Materials The simple head solid model is imported into LS Dyna…

Objective: To simulate the tensile behaviour of a solid block with different element formulations and compare the stretch ratios from each case.   Step 1: Solid block creation and section definition The given keyword file, which contains the Ogden Material definition is opened in LS Dyna. The default values of the…

Objective: To model spotwelds between the given surfaces using Beam and Solid elements and compare the results.   Spotwelds using beam elements Step 1: Creating spotwelds in the model The model containing the upper and lower surfaces can be visualized in LS - Prepost as shown below.   The spotwelds using beam…

Objective: To simulate the impact of the crash box against a rigid wall with two different thickness - 1.2mm and 1.5 mm.   1) Thickness 1.2 mm Step 1: Setting up the Simulation The .K file containing the crash box is imported into LS dyna as shown below. A planar rigid wall is created using the RIGIDWALL keyword and…

Objective: To set-up the simulation of a phone falling on a rigid plate.   Step - 1:Importing the model in LS-Dyna The .K file is imported into LS Dyna and the components can be viewed as shown below.   The model has three components 1. Phone - solid elements 2. Rigid plate - shell elements 3. Rigid plate - solid…

Objective: To simulate a side crash of the given BIW with a cylindrical pole and analyse the results for the various important result points of the side part of the car.   Step 1: Setting up the Simulation - Hypermesh The given file is imported into Hypermesh and the various components of the model can be viewed as…

Objective: To simulate a frontal crash of the given BIW and analyse the results for the various important result points of the front part of the car.   Step 1: Setting up the Simulation - Hypermesh The given file is imported into Hypermesh and the various components of the model can be viewed as shown below. The unit…

Objectives 1. To mesh the bumper model with a model size of 6 mm. 2. To study the effect of notches and various interface formulations on the simulation of a crush tube.   1. Bumper model The bumper model is opened in Hypermesh and the edge connectivity can be checked as shown below. There are free edges in the connections…

Objective To compare and study the simulation results of the 7 different cases and identify the differences in the key result parameters.   Case 1: M2 - JOHNSON COOK - EPS P MAX FAILURE MODE The given model FAILURE_JOHNSON_0000.rad is imported into RADIOSS and the two components - the circular plate and the rigid…

ObjectiveThe goal of this assignment is to compare the results of the simulation of a beam against a rigid wall with two different 2D element formulations. Base SimulationStep 1: Loading the model The base file is loaded into Hypermesh and the model can be observed as shown below.   Step 2: Modification…

Objectives: 1. To calculate the speed of sound through steel and the critical timestep for the given length. 2. To edit the radioss engine file with the critical timestep and the frequency at which output plots are generated, for 20 steps. 3. To 3D mesh the housing assembly in Hypermesh using a tetramesh with a target…

Objective:                  The given geometries must be cleaned of any free edges, and the midsurface has to be extracted by neglecting small pinholes and fillets. Subsequently, the 2D mesh has to be created in accordance with the given quality…

Introduction: Explicit and Implicit methods are numerical methods to solve a time-dependent differential equation.   Explicit method: The value of the calculated variable at the previous time-step is used to calculate the required value at the current time-step. Explicit methods are conditionally stable, which means…

The solution has been described in the report attached below    

The solution has been described in the report attached below.   The links for the associated Matlab M-file and the excel sheet are https://drive.google.com/drive/folders/1RThFbT5d9o_EUmuYyBguDIWemdJLD8ph?usp=sharing    

The solution has been described in the report attached below.   The associated assembly and subsystem files of the front and rear suspension can be found under the link https://drive.google.com/drive/folders/199kTo8HT8NUZCcxBkHuwoRH2ptvaKzZH?usp=sharing    

The solution has been described in the report attached below.   The associated assembly and subsystem files of the rear multi-link suspension system can be found under the link https://drive.google.com/drive/folders/14a1hVZno3FoMJhxQm-RHI9o6NHnIxF99?usp=sharing    

The solution has been described in the report attached below.   The associated assembly and subsystem files of the SLA suspension model can be found under the link https://drive.google.com/drive/folders/16eLYJNyCozgixem6PwkuqAeOlS9D78t-?usp=sharing    

The solution has been described in the report attached below.   The following files can be found in the drive under the link below 1. Suspension subsystem 2. Steering subsystem 3. Suspension + Steering assembly 4. Plot config (.plt) file 5. Numerical data (.dat) file 6. Video of opposite wheel travel (.avi) file https://drive.google.com/drive/folders/1ddu3ZF0fIRZY0oq5SwEiU_L-GwDzTIKp?usp=sharing…

The solution has been described in the report attached below.

The solution can be found in the report attached below.   The google drive link to the Matlab M-files are https://drive.google.com/drive/folders/1Ca6WEoan5mzqNCTZxxAkshWWjPf0-oiF?usp=sharing   1) Flat ride.m - contains the first part of the calculations 2) Flat ride plot.m - contains the bump oscillation profiles.

1.The wheel center rate (Kw) is the rate of wheel displacement and the spring rate is the spring stiffness. They are related to each other by the installation ratio or the motion ratio. Kw = Ks * (mr)^2. Normally the wheel rate is always lesser than the spring rate in a double wishbone setup, because a 1:1 motion ratio…

The solution has been described in the PDF under the link https://drive.google.com/drive/folders/18mP44WYxwj_XVCO5wHMdTfDg2h0R8aSz?usp=sharing    

The solution can be found in the pdf attached in the google drive   The link https://drive.google.com/drive/folders/18mP44WYxwj_XVCO5wHMdTfDg2h0R8aSz?usp=sharing    

The solution has been described in the report attached below.   The link for the associated MATLAB M-file and the excel sheet is https://drive.google.com/drive/folders/1VaegHUYKxCpp6WATExYFnSUQlA0Wh2pD?usp=sharing    

The solution has been described in the PDF attached below.   The associated Matlab M-files can be found using the link below https://drive.google.com/drive/folders/1Bp4LT_vq_HVdXcKVYermKK-quIk2mCKi?usp=sharing    

The solution has been described in the pdf which can be found in the link below.   https://drive.google.com/drive/folders/13QjKNWUh2laovq25foLsv1KWV6WqKMDj?usp=sharing    

The solution is described in the report attached below.   The link to the excel sheet is https://drive.google.com/drive/folders/1nGmWbSzGcutiuTPV9UUJADJmQLI__J4S?usp=sharing