4th order approximation of 2nd order  derivative 1)central differenicing let number of points=n;order of accuracy=a;order of derivative=o n=a+o-1 therefore n=5; now using taylor table method `(del^2u)/(delx^2)`=af(i-2)+bf(i-1)+cf(i)+d*f(i+1)+e*f(i+2) taylor table then coverting into matrix form `[[1,1,1,1,1],[-2,-1,0,1,2],[2,1/2,0,1/2,2],[-8/6,-1/6,0,1/6,8/6],[16/24,1/24,0,1/24,16/24]]`*`[[a],[b],[c],[d],[e]]`=`[[0],[0],[1],[0],[0]]`…

MacCormack method In Computatonal flud dynamics ,the MacCormack method is popularly used discretization method for hyperbolic partial differential equation MacCormack method provides 2nd order accurate solution without the involvement of the 2nd derivative Simulation of 1D supersonic nozzle flow:   we discuss the…

Theory: A backward-facing step is needed to be generated using OpenFoam which is sloved using icoFoam solver which is a transient solver for incompressible,laminar flow of Newtonian fluid. Here in this task cavity case from icoFoam solver which is part of incompressible tutorials is copied to run folder and blockMeshDict…

Finite Volume Method(FVM)The finite volume method is a discretization technique for partial differential equation, especially those arise from physical conservation laws. FVM uses a volume integral formulation of the problem with a finite partitioning set of volumes to discrete the equation.Differences between FDM & FVMIn…

Considering a cylindrical pipe with the working fluid water entering the pipe with laminar flow. The aim is to simulate the flow through a section of pipe and compare the flow with the Hagen Poiseuille’s equation. Hagen Poiseuuile’s equations In non ideal fluid dynamics, the Hagen-Poiseuille equation, also…

In the previous part we looked into the simulation results for a laminar ,incompressible flow through a pipe in OpenFoam .now in this section ,we attempt the same with symmetery boundary conditions   BlockMeshDict for 10deg /*--------------------------------*- C++ -*----------------------------------*\ ========= |…

Aim: To determine the heat transfer in T- pipe and study the mixing efficiency in the tee joint at the outlet by varying the momentum ratio at (velocity at cold inlet / velocity at hot inlet) and length of the pipe Step-up Step 1 Cad model is imported into space claim Inside Tee-volume is extracted Step 2 Meshing is done…

Objective Setup and run transient state simulation for flow over a throttle body. Post processes the results and show pressure and velocity contours. Show the plots for pressure, velocity, mass flow rate and total cell count. Calculations on how you calculate the end time for the simulation. Create an animation in which…

Objective: To perform Steady-state simulation of fluid flow over a throttle body To post convert the results and show pressure and velocity contours for the both the cases To show the plots for pressure, velocity, mass flow rate and total-cell-count Throttle body: A throttle is the mechanism by which fluid flow is managed…

Aim: Simulate the supersonic flow through the duct having the sharp corner Observe the effect of SGS parameter on the shock loaction and cell used by it Shock waves: Shock wave (also spelled shockwave), or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an…

Aim: To simulate conjugate heat transfer through a pipe Case step: Materials:   Simulation time parameters Boundary Conditions   Re=(rho*V*D)/(dynamic_viscosity) 7000=(1.161*V*0.04)/(1.85*10^-5); V=2.58m/s Regions and Initialization Physical Model Output_files Grid_Dependence_test Base grid of 1mm,2mm and 3mm…

Aim: Setup a transient shock tube simulation Plot the pressure and temperature history in the entire domain Plot the cell count as a function of time          Shock tube: The shock tube is an instrument used to replicate and direct blast waves at a sensor or a model in order…

Objective:Apply reynold's decomposition to the NS equations Understanding of the terms Reylond's stress Difference between turbulent and molecular viscosity Reynold's Decomposition: Is a mathematical technique used to separate the expectation value of a quantity from its fluctuations i.e given Instantaneous Velocity@ any…

Objective: 1.To setup and simulate full hydrodynamic case using PFI engine(by using converge and paraview) 2.Calculate the compression ratio and its efficiency ,power and torque of the engine from the plots Case setup:  Simulation Parameters: Intial Conditions and events: Region and intialisation: Entire geometry…

Objectives Q1. Describe Ahmed's body and its importance. Q2. Explain the reason for the negative pressure in the wake region.  Q3. Explain the significance of the point of separation.  Expected Results: 1. Velocity and pressure contours.  2. The drag coefficient plot for a refined case. (For velocity of 25m/sec, the drag…

Aim: Simulate the flow over a cylinder and explain the phenomenon of Karman Vortex Street Objective: Calculate the coefficient of drag and lift over a cylinder by setting the Reynolds number to 10,100,1000,10000 & 100000 Simulate the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100…

Introduction Conjugate Heat Transfer (CHT) is applicable whenever there are two adjacent domains and we wish to analyse the heat transfer between these domains. These domains can either be solid or fluid domains For many simulations of real world engineering applications, the predictions of heat transfer properties…

Objective What are some practical CFD models that have been based on the mathematical analysis of Rayleigh Taylor waves? In your own words, explain how these mathematical models have been adapted for CFD calculations. Perform the Rayleigh Taylor instability simulation for 2 different mesh sizes with the base mesh being…