Introduction This project is to derive an equation to calculate the 2nd order numerical derivative for central difference,skewed right sided and skewed left sided schemes of 4th order accuracy. Also to find the 2nd order derivatives of exp(x)*cos(x) function and to compute the erro between its analytical and numerical…

Introduction In this challenge we are required to solve the 2D heat conduction equation for both steady state and transient state.We have to find the temperature gradient on the domain of size 1x1 unit for the given boundary conditions. Theory Transient state equation  The 2D transient heat conduction equation is: `(delT)/(delt)+alpha((del^2x)/(delt^2)+(del^2y)/(delt^2))=0` `…

Introduction We are required to simulate an isentropic flow through a convergent divergent nozzle. Both the conservative and non conservative form of the governing equation is solved using the MacCormack's technique.  Theory The flow through a nozzle that has a gradual decrease and increase in area is reversible,…

Introduction We are required to simulate an incompressible-laminar-viscous flow over a backward facing step geometry for two seperate cases one with no grading factor and another with a grading factor of 0.2 using OpenFoam.    Explanation of the simulation and the steps followed   PRE-PROCESSING 1.Determination…

Introduction Finite volume method (FVM) is a discredizing scheme to solve partial differential equations.    Difference between FVM and FDM 1.In finite difference method complex geometries cannot be modeled easily as in finite differnece method the mesh lines generated must be parallel to the x and y coordinate…

INTRODUCTION In this challenge we have to simulate a flow through a pipe using OpenFoam.The flow is taken to be a laminar flow of 2100 reynolds number.The results obtained after the simulation is validated using the Hagen-Poiseuille equation.Also we are required to 1.Calculate the hydrdynamic length and validate the velocity…

INTRODUCTION In this challenge we are required to simulate the flow through a pipe as a continutation of the previous challenge but here we are required to create the wedge with 3 different angles and also show use the symmetry boundary condition and compare the effects of symmetry vs wedge BC. Here we are going to compare…

Aim: In this project we will be setting channel flow using converge software with air as the medium.The simulation is run for 3 different mesh sizes. The mass flow, velocity,pressure and total cell count count w.r.t number of cycles is obtained from converge plot for all 3 mesh sizes.Velocity and pressure distribution…

Aim: Simulate flow through a backward facing step (BFS) and post process the results for 3 base mesh sizes 1e-3m,1.5e-3m & 2e-3m.   Theory: Backward Facing Step Flow through a BFS is an example of seperation flow as the flow gets seperated at the step of the BFS.The sepreated flow occurs mainly due to the sudden…

  Aim: In this project we run a steady state simulation of air over a throttle body using converge cfd and post process the results.    Theory: A throttle is used to control the amount of fluid flowing.The throttle in open position allows the full passage of fluid whereas a throttle in closed position is…

Aim: In this project we run a transient simulation of air over a throttle body using converge cfd and post process the results. The throttle body is at `0^o`the beginning of the simualtion and is rotated to about `25^o` till the end of simulation.   Theory: A throttle is used to control the amount of fluid flowing.The…

Introduction This project involves the simulation of Prandtl-Meyer shock problem in a convex corner .The simulation is performed and results are post processed.    Theory Shock Waves Shock waves are pressure disturbances that move at a speed greater than the speed of sound i.e. M>1. There is a discontinuity…

Introduction In this project we are required to setup a conjugate heat transfer flow through a pipe.The fluid flowing thorugh the pipe is air with a reynold's number of 7000 and the outer walls are being heated with a flux of -1000 W/m2.   Theory Conjugate Heat Transfer Conjugate Heat Transfer Analysis is used when…