Week 3.5 - Deriving 4th order approximation of a 2nd order derivative using Taylor Table method

OBJECTIVE:  Simulate flow across the given pitot-tube geometry for the following parameters: Velocity(m/s) Gauge Pressure (Pa) 240 -2817 100 33287 62 65780 and compute the value of velocity. Compare the velocity obtained with the boundary condition and calculate the error percentage. THEORY: Source: Glenn Research…

OBJECTIVE: Simulate flow across a Converging-Diverging Nozzle, Plot: The pressure, velocity and temperature variations across the domain The interpretation of Mach number across the field and at what distance from the inlet does the flow become supersonic. THEORY: A converging-diverging nozzle is an asymmetric hourglass-shaped…

OBJECTIVE: Compare the results with higher wedge angle: 10 25 45 Simulate for both wedge and symmetry boundary conditions for each of the above angles and validate the results with analytical result: Validate Hydro-dynamic length with the numerical result Validate the fully developed flow velocity profile with its analytical…

OBJECTIVE Simulate an axi-symmetric flow across a pipe, applying wedge boundary condition with following parameters: `R_e  = 2100` Wedge Angle < 5 degress Pipe Diameter can be assumed Validate the simulation using Hagen-Poiseuille's equations for fully developed flow.Use MATLAB script to calculate relevant parameters…

OBJECTIVE: Create a Rankine Cycle Simulator using OCTAVE/MATLAB. The code should calculate the state points of the Rankine Cycle (any type of your choice) based on user inputs.  Plot the corresponding T-s and h-s plots for the given set of inputs. Title and axes labels are a must, while legends could be used if necessary.…

OBJECTIVE: 1. Write a function that extracts the 14 coefficients and calculates the enthalpy, entropy and specific heats for all the species in the  NASA thermodynamic data file.    2. Calculate the molecular weight of each species and display it in the command window. 3. Plot the Cp, Enthalpy…

 OBJECTIVE: Write a code in MATLAB to optimise the stalagmite function and find the global maxima of the function. Clearly explain the concept of genetic algorithm in your own words and explain the syntax for ga in MATLAB in your report. Make sure that your code gives the same output, even if it…

OBJECTIVE: The following ODE represents the equation of motion of a simple pendulum with damping: where, g = gravity in m/s2,L = length of the pendulum in m,m = mass of the ball in kg,b=damping coefficient. Write a program in Matlab\Octave that will simulate the pendulum motion. use, L=1 metre,m=1 kg,b=0.05.g=9.81 m/s2.…

OBJECTIVE: Write a program in Matlab to simulate the forward kinematics of a 2R Robotic Arm. THEORY: In Forward Kinematics, we calculate the orientation of the effector with the help of joint angles. A simple 2R robotic arm is shown below: Thus, from `theta_1` and `theta_2`, we can calculate where the end of link two 'C'…

OBJECTIVE: This is a simulation of the flow around an FSAE car with the following objectives: A baseline simulation of coarse mesh and publishing its results Refine the case for the following problem statement: ABCD Racing company is looking to perform Aero Simulations for their FSAE vehicle, and they have hired you to…

OBJECTIVE: We are to simulate flow over Ahmed's body and compare it with experimental results GEOMETRY: We are using the standard Ahmed Body geometry given by Ahmed et al. [1]: +     Creating the geometry in the cad package: The wind-tunnel cross-section area is the same as used to obtain experimental data[2],…

OBJECTIVE: Simulate flow over a 4-digit airfoil, i.e. NACA 2412 Airfoil, and calculate the following parameters: Drag coefficient Vs Angle of Attack Lift coefficient vs Angle of Attack Compare the effect of turbulence models on the above two results. Make sure that the inlet Reynolds number is 200,000 Above calculations…

OBJECTIVE: This project deals with the Prandtl-Meyer Expansion Fan Problem. There are two objects of interest from a conceptual perspective: Shock Waves Boundary Conditions in Supersonic flow Practically, we will be simulating the problem and determining how Sub-Grid Scaling(SGS) will affect the case. THEORY: Shock Waves: …

OBJECTIVE: Apply Reynold's decomposition to the NS equations and develop the expression for Reynold's stress. Explain your understanding of the terms Reynold's stress What is turbulent viscosity? How is it different from molecular viscosity? THEORY: RANS: The Reynolds-averaged Navier-Stokes (RANS) equations are the time-averaged…

OBJECTIVE: We will be simulating a transient shock tube problem and observing the result GEOMETRY: The following geometry has been provided: It consists of two cuboids joined together, we will delete the joining face highlighted by the purple outline and our geometry is ready to be used. BOUNDARY FLAGGING: BOUNDARY CONDITIONS:…

OBJECTIVE: In this challenge, we familiarise ourselves with the tools and the know-how of setting up a CHT problem in Converge. We will set up a simple thick pipe flow that is heated through an external flux as fluid moves through it. Once the case is set, we will perform a grid dependence test to establish whether grid…

OBJECTIVE: We will be performing a transient analysis on the same geometry as the previous study and document our observations as the throttle moves along with contours, plots and animations. GEOMETRY: We will be using the same elbow geometry: CASE SETUP: We will be using the same case inputs, except this time we will…

OBJECTIVE: We will be performing a stead-state simulation over a throttle body in an elbow and document our observations with velocity and pressure contours. GEOMETRY: The following geometry is used for simulation: The geometry has some thickness to it so we will be removing the outer shell and the edges which creates…

OBJECTIVE: We are to simulate flow over a backwards-facing step for the following three mesh sizes: dx = dy = dz =2e-3 m dx = dy = dz =1.5e-3 m dx = dy = dz =1.0e-3 m INTRODUCTION: Backward-facing step is one of the standard problems in CFD. It is a representative model for flow separation study and is crucially important…

OBJECTIVE: We are to run a simple channel flow simulation to test our setup and familiarise ourselves with CONVERGE basics. We will be simulating 3 cases:  dx = 2e-4m,              dy = 2e-4m,       dz = 2e-4m  dx = 1.5e-4m,         …

OBJECTIVE: For the given model, check and solve all geometrical errors and Assign appropriate PIDs. Perform meshing with the suitable Target length and element Quality criteria. PROCEDURE: We have the following model of a Tesla Cybertruck: First, we will apply TOPO to see if there are any surfaces missing and actual…

OBJECTIVE: For the given models, check for the geometrical errors and delete surfaces which are unwanted for Surface wrap as shown in the videos. After clearing geometry, Merge all 3 models and perform surface wrap. Target length for Wrap = 3 mm PROCEDURE: We have three models to work with in this challenge, the first…

OBJECTIVE: For the given model, check and solve all geometrical errors on half portion and Assign appropriate PIDs. Perform meshing with the given Target length and element Quality criteria. After meshing the half model, Do symmetry to the other side. Target lengths for the different parts of a model are as follow: Body…

OBJECTIVE: For the given model, check for the geometrical errors to make appropriate volumes. Create and assign PIDs. Perform surface mesh with the given target lengths as per PIDs: Blade stage-1 = 1 mm Blade stage-2 = 1 mm Impeller = 2 mm Shaft rotor = 1 mm Turbo casing = 5 mm Compressor casing = 5 mm Inlet casing cover…

OBJECTIVE: For the given model, check for the geometrical errors and perform Topology cleanup accordingly. Set three different target lengths as three different cases and mesh the model.  Target length = 1mm, 3 mm and 5 mm (i.e. 3 cases) Element type = Tria TOPOLOGICAL CLEANUP: We have the following geometry:  …

OBJECTIVE: We are to simulate Methane Combustion on a combustor model and derive the following two results: The variation of the mass fraction of the different species in the simulation using line probes at other locations of the combustor  Add the water content in the fuel from 5% to 30% by mole and observe its effect…

OBJECTIVE: For this challenge, We will perform a parametric study on the gate valve simulation by setting the opening from 10 % to 80% considering the following points: Obtain the mass flow rates at the outlet for each design point. Calculate the flow coefficient and flow factor for each opening and plot the graph. Discuss…

OBJECTIVE: We will be performing an analysis on a cyclone separator and calculating its separating efficiency and pressure drop. This analysis is focused on two parameters: Particle Diameter and Particle Velocity. Two types of cases will be simulated: Varying particle size from 1 micron to 5 microns at constant velocity…

OBJECTIVE: We are to run Conjugate Heat Transfer(CHT) analysis on a graphics card and do the following: Run the simulation by varying the velocity from 1m/sec to 5m/sec for at least 3 velocities and discuss the results. Find out the maximum temperature and heat transfer coefficient attained by the processor. Prove that…

AIM: The aim of this study is to simulate the Rayleigh-Taylor Instability(RTI) with 2 different meshes and 2 different sets of Fluids. Draw inferences from the simulation and give a brief overview of RTI, its significance and practical applications. INTRODUCTION: Rayleigh-Taylor Instability(RTI) also called RT…

AIM: We are to simulate a Conjugate Heat Transfer (CHT) on an exhaust port model with 4 outlets and 1 inlet and find answers to the following series of questions: Why and where a CHT analysis is used? Maintain the y+ value according to the turbulence model and justify the results.  Calculate the wall/surface heat…

OBJECTIVE: We are to run a simulation on Ahmed Body to find answers to the following questions: Describe Ahmed's body and its importance. Explain the reason for the negative pressure in the wake region.  Explain the significance of the point of separation.  INTRODUCTION: AHMED BODY: Ahmed body is a standard wind…

AIM: The aim of this simulation is to study the flow over a cylinder and study the phenomenon of Vortex Shedding, and display the formation of Karman Vortex Street. Two cases will be studied: Simulation of Steady and Unsteady Case and Calculation of Strouhal Number at Re = 100 Calculation of Drag and Lift Coefficient over…

AIM: For this challenge, we have created two versions of the mixing tee. One of them is longer than the other. We will set up steady-state simulations to compare the mixing effectiveness when the hot inlet temperature is 360C & the Cold inlet is 190C.  We Use the k-epsilon and k-omega SST model for the first case…

We are to simulate a 1D Supersonic nozzle flow using Macormack Method. Let us first understand the MacCormack Method. MACCORMACK METHOD: MacCormack method is a discretizing scheme used in Computational Fluid Dynamics to sole hyperbolic partial differential equations numerically. Consider a First order hyperbolic partial…

FINITE VOLUME METHOD: Finite Volume method is one of the discretization method used in numerical calculus, the others being, finite element method and finite difference method. In this method, the conservation statement or physical law represented by PDE is applied in a form applicable to a space or finite volume. This…

We will be simulating an incompressible laminar-viscous flow over a backward step geometry. According to OpenFOAM documentation: hence, we will be using the icofoam solver and as a result use the cavity tutorial from the incompressible tutorials to set up our case.First, we will copy the tutorial to our working directory…

We will be using iterative point techniques to solve the 2D Heat-Conduction Equation for this exercise. We have  the following Boundary Conditions: Top Boundary(`T_T`) = 600 K Bottom Boundary(`T_B`) = 900 K Left Boundary(`T_L`) = 400 K Right Boundary(`T_R`) = 800 K and we will assume the initial temperature to…

We are to calculate fourth-order approximation for f'' using central, left-skewed and right-skewed differencing methods. We know that: `f_i^q = (af_alpha + bf_beta ...+nf_lambda)/(Deltax^q) + O(Deltax^p) - - - - - - (i)` here, `p` = order of accuracy and `q` = order of differentiation CENTRAL-DIFFERENCE SCHEME: We are…