This ODE for equation of motion of a simple pendulum with damping is given as. `(d^2theta)/dt^2+b/m*(d theta)/dt+g/L*sintheta=0` In the above equation, g = gravity in m/s2, L = length of the pendulum in m, m = mass of the ball in kg, b=damping coefficient. taking these values as L=1 metre, m=1 kg, b=0.05. g=9.81 m/s2.…

OBJECTIVE- Simulate Prandtl Meyer Shock problem and look at the effect of SGS temperature value on cell count and the shock location. Case-1:  For SGS value- 0.02 k (supersonic flow) Case-2: For SGS value- 0.05 k (supersonic flow) Case-3: For SGS value- 0.1 k (supersonic flow) Case-4:…

OBJECTIVE-Simulate a full hydro condition of Port fuel injection engine. Geometry-A 3d geometry ofPort fuel injection engine was imported to converge for analysis. Setup-  Application Type- Crank angle-based IC engine Physical Parameters: Bore =0.086 m Stroke = 0.09 m Connecting rod length = 0.18 m RPM = 3000 Materials-…

Program that compares the first, second and fourth order approximations of the first derivative against the analytical or exact derivative for a range of dx. `f(x)=sinx/x^3` The function is computed at x=pi/3 1. First order approximation=`(sin(x+dx)/(x+dx)^3-sin(x)/x^3)/dx` 2. Second order approximation=`(sin(x+dx)/(x+dx)^3-sin(x-dx)/(x-dx)^3)/(2*dx)`…

 Calculation for 4th order approximations of the second order derivative. for, 1. Central difference 2. Skewed right sided difference 3. Skewed left sided difference 1. Central difference: The second order derivative can be written as: `(del^2u)/(delx^2)=a*f(i-2)+b*f(i-1)+c*f(i)+d.f(i+1)+e*f(i+2)` solving for this…

Objective-To apply reynold's decomposition to the NS equations to get the RANS equations. Why we need Turbulence Modeling: Most flows occurring in nature  and in engineering applications are turbulent in nature.It is very difficult to define turbulence.The time scale associated with turbulence is very small.…

OBJECTIVE-Perform the simulation for two clearances of the gears and also using a different fluid. Analyse the flow pattern of the fluid for two different clearances of the same geometry. Steps involved in the simulation Geometry Mesh Setup Solution  Results   Case-1:Normal clearance(Lubricant-oil) Case-2:Normal…

OBJECTIVE-To run simulations for two types of pistons for diesel engine CAT3410 and characterize the emissions (Soot, Nox and UHC). Geometry-A 3d geometry of Port fuel injection engine was imported to converge for analysis. Make Engine Sector Surface: Using the make surface utility in converge studio both the…

Objective- To use the icoFOAM solver and simulate the flow through a pipe by creating wedge. To write a program in Matlab that can generate the computational mesh automatically for any wedge angle and grading schemes Dimensions of Pipe: Diameter(D)=10mm To calculate length of pipe entry length formula is used `Le=0.06*Re*D`…

OBJECTIVE- -Using conjugate heat transfer simulate flow through a solid pipe and understand super-cycling. -Perform Grid dependence test -Analyze the effect of supercycle stage interval   Geometry- Calculation of inlet velocity: Inlet Reynolds number =7000 Diameter of pipe=0.03 m Dynamic viscocity of air=1.81*10^-5…

OBJECTIVE-Simulate Flow of fluid over a throttle body in converge studio and post process the results using transient state solver. Geometry-The .stl file for 3d geometry of elbow was imported to converge. Setup- Applications- -General flow Materials- -Air Simulation Parameters: -Transient solver -Start time-0, End…

Objective-Stability analysis in the unsteady problem(2D heat equation). 1. When we derive a numerical scheme it needs to consistent and stable. Due to numerical approximations error are incorporated in the solution and these error magnifies with time. 2. An unstable simulation cannot be trusted for real world application.…

Objective- Your job is to setup steady state simulations to compare the mixing effectiveness. Case 1 (60 points) Short mixing tee with hot inlet velocity of 3m/s Momentum ratio of 2 Case 2 (60 points) Long mixing tee with hot inlet velocity of 3m/s Momentum ratio of 2 Case 3 (60 points) Short mixing with hot inlet velocity…

OBJECTIVE- Simulate channel flow for three different mesh sizes. Case-1:  Grid size- dx=3e-3 m, dy=3e-3 m, dz=3e-3 m Case-2: Grid size- dx=2.5e-3 m, dy=2.5e-3 m, dz=2.5e-3 m Case-3: Grid size- dx=2e-3 m, dy=2e-3 m, dz=2e-3 m Geometry-A geometry was created for the channel. Setup- Applications- -General flow…

OBJECTIVE-Perform a steady state CHT analysis on a graphics card.To find the maximum temperature attained by the processor and find potential hotspots on the model.  Simulations for 2 variations of the mesh: Case-1: CHT analysis on a graphics card with(baseline mesh) Case-1: CHT analysis on a graphics…

Objective- To use the icoFOAM solver and simulate the flow through a backward facing step.To create multiple meshes and compare the results obtained from each mesh. Mesh specification Number of cells along the x direction (longer dimension) = 200 Number of cells along the y direction = 10 Boundary condition specification…

OBJECTIVE-Perform a CHT analysis on an exhaust manifold. Why Conjugate Heat Transfer is required? The Conjugate heat transfer (CHT)  analysis allows the simulation of the heat transfer between Solid and Fluid domains by exchanging thermal energy at the interfaces between them. Example of CHT-Analysis…

Questions based on PFI Engine: 1. What is the Compression ratio for the engine? Compression ratio is the ratio of maximum volume of cylinder when the piston is at bottom dead center to the minimum volume of cylinder when the piston ia tdc. From the below graph Vmax and Vmin value were found out, Compression ratio=`V_max/V_min`…

 Program that compares the first, second and fourth order approximations of the first derivative against the analytical or exact derivative. `f(x)=sinx/x^3` The function is computed at x=pi/3 1. First order approximation=`(sin(x+dx)/(x+dx)^3-sin(x)/x^3)/dx` 2. Second order approximation=`(sin(x+dx)/(x+dx)^3-sin(x-dx)/(x-dx)^3)/(2*dx)`…

OBJECTIVE-Setup a transient shock tube simulation and plot the pressure and temperature history in the entire domain.Also plot the cell count as a function of time.  Geometry-A 3d geometry of shock tube was imported to converge studio. Setup- Applications- -General flow Materials- -Air Simulation Parameters: -Transient…

Objective-To compare fastest steady state simulation vs fastest transient simulation  Steady State Matlab code: %main program % steady state 2D heat conduction close all clear all clc nx=20; ny=20; tol=1e-4; % iterative_solver=1 (steady state jacobi) % iterative_solver=2 (steady state gauss seidal) % iterative_solver=3…

OBJECTIVE- 1. To write a code to solve the 1D linear wave equation equation numerically. Write a function that accepts time step as an argument and solves the same problem. You will compare the effect of time step on the numerical solution. 1. Set n = 80 2. Time steps to use = 1e-4, 1e-3, 1e-2, and 1e-1 3. In a single…

OBJECTIVE- To determine Eigen values of iteration matrix. To determine Spectral radius of iteration matrix. To Solve the system using Jacobi, Gauss-seidel and SOR methods Compute the iteration Matrix for the above mentioned iterative methods. Increase the Spectral radius to 1.1 by changing the diagonal terms suitably.…

OBJECTIVE-Simulate Flow of fluid over a throttle body in converge studio and post process the results using steady state solver.  Geometry-The .stl file for 3d geometry of elbow was imported to converge. Setup- Applications- -General flow Materials- -Air Simulation Parameters: -Pressure based steady state solver…

OBJECTIVE-For Re = 100, simulate the flow over a cylinder using steady and transient mode.  Steps involved in the simulation Geometry Mesh Setup Solution  Results   Flow over cylinder-Steady state Geometry-A 2d geometry was created for cylinder and a domain for analysis. Mesh- Element size-0.25 No of elements…

OBJECTIVE-Simulate the flow over backward facing step Case-1:  Grid size- dx=2e-3, dy=2e-3, dz=2e-3 Case-2: Grid size- dx=1.5e-3, dy=1.5e-3, dz=1.5e-3 Case-3: Grid size- dx=1e-3, dy=1e-3, dz=1e-3 Geometry-A geometry backward facing step was created. Setup- Applications- -General flow Materials- -Air Simulation…

OBJECTIVE- To write a code to solve the 1D linear wave equation equation numerically. 1. Assume that the domain length is L = 1m 2. The initial velocity profile is a step function. It is equal to 2m/s between x= 0.1 and 0.3 and 1m/s everywhere else 3. Use first order forward differencing for the time derivative…

Objective- To use the icoFOAM solver and simulate the flow through a pipe by creating a wedge and providing symmetry boundary condition. To write a program in Matlab that can generate the computational mesh automatically for any wedge angle and grading schemes. Compare the results for symmetry,wedge and HP equation.…

Objective-  To write code to solve the 1D supersonic nozzle flow equations using the Macormack Method by implementing both the conservative and non-conservative forms of the governing equations. Perform grid dependence test. To figure out the minimum number of cycles for which the simulation should be run in…

OBJECTIVE-Perform the Rayleigh Taylor instability simulation for 3 different mesh sizes with the base mesh being 0.5 mm. Case-1:Rayleigh Taylor instability simulation with mesh size 0.5 mm Case-2:Rayleigh Taylor instability simulation with mesh size 0.35 mm Case-3:Rayleigh Taylor instability simulation with mesh size 0.25…

Objective-To solve the 2D conduction equation using a Transient solver and a Steady state solver using Iterative techniques (Jacobi,Gauss Seidal,SOR). 1. Assume that the domain is a unit square.  2. Assume nx = ny [Number of points along the x direction is equal to the number of points along the…

OBJECTIVE-Simulate the flow over a ahmed body. Perform a grid dependency test and compare the results.  Ahmed body and its importance: The Ahmed body is a generic car body (a simplified vehicle model). The airflow around the Ahmed body captures the essential flow features around an automobile and was first defined…

Obejective-To Calculate the Adiabatic Flame Temperature. Case-1:Determine the effect of equivalence ratio on AFT in a constant volume chamber for methane. Write a program in Python to plot the effect of equivalence ratio on the final adiabatic flame temperature. Compare the results with Cantera. Case-2:(i)To calculate…

OBJECTIVE:Derive the reaction rate ODEs of a simple reaction mechanism.To use the compact notation and find out the desired matrices. Reaction Mechanism: CO + O2 `harr_(k_(r1))^(k_(f1))` CO2 + O O + H2o `harr_(k_(r2))^(k_(f2))` OH + OH CO + OH `harr_(k_(r3))^(k_(f3))` CO2 + H H + O2 `harr_(k_(r4))^(k_(f4))` OH + O…

Objective-To solve the set of ODE equations using Multivariate Newton Rhapson Technique. The given set of ODE's are: `(dy1)/dt=-0.04*y1+10^4*y2*y3` `(dy2)/dt=0.04*y1-10^4*y2*y3-3*10^7*y2^2` `(dy3)/dt=3*10^7*y2^2`  The problem is discretized using Implicit Euler Method/Backward Differencing. `(y1^n-y1^(n-1))/(Deltat)=-0.04*y1+10^4*y2*y3`…

Objective-Simulate the Auto Ignition Time for Methane under the following conditions, (simulation time = 10 secs) Part-1 Plot the variation of Auto Ignition time of Methane with a constant temperature of 1250K and pressure varying from 1 to 5 atm. Plot the variation of…

Objective-Write a code that takes all the reactions from the GRI mechanism and calculates 10 most sensitive reactions.The sensitivity parameter should be with respect to the Temperature (It should find the sensitivity with respect to the temperature.)  Sensitivity Analysis: In chemistry sensitivity analysis is peformed…

Objective-Write a code to perform a 1D Flame Speed Analysis for Methane and Hydrogen using a separate Hydrogen mechanism to perform Flame Speed Analysis for Hydrogen. Coding Approach: 1. A instance gas object is created by passing the the 'gri30.xml' mechnism file and 'gri30_mix' transport properties file.For…

Objective-To write a Reaction Reduction Mechanism code for the GRI3.0 mechanism. The code structure will do the following, First, it should run a reference Ignition delay and Max temperature Analysis for the unreduced mechanism for a set of state values (Temperature, Pressure and Equivalence ratio) for a time duration…

Objective- 1. Perform surface repair for a Glider plane model in Star ccm+. 2. Scale the geometry of Ahmed body by 3 times and rotate so that the angle of attack will be 35 degrees.   Types of errors:  1. Pierced face -A Pierced face is a face that is intersected by one or more edges of another surface.This…