DERIVATION OF FOURTH ORDER APPROXIMATION OF SECOND ORDER DERIVATIVE: To derive the fourth order approximation of the second order derivative, the following schemes can be used: 1.CENTRAL DIFFERENCING SCHEME: This scheme makes use of points from both sides of the present point in the stencil. The number of points to be…

2D HEAT CONDUCTION EQUATION: `(partialT)/(partialt) = alpha((partial^2T)/(partialx^2)+(partial^2T)/(partialy^2))` Given domain: 1. Assume that the domain is a unit square.      L=1m, A=1x1 `m^2` 2. Assume nx = ny [Number of points along the x direction is equal to the number of points…

SIMULATION OF QUASI-ONE-DIMENSIONAL SUPERSONIC NOZZLE FLOW USING MACCORMACK'S TECHNIQUE: Let us consider the steady, isentropic flow through a convergent-divergent nozzle as show in the following figure: INLET: Subsonic flow (M<1). Stagnation properties (P0, T0, `rho0`) Area is considered to be infinitely large…

Aim: To find the change in velocity magnitude profile with respect to simple grading factors for the given geometry. Mesh Specifications: Number of cells along the x-direction (longer dimension) = 200 Number of cells along the y-direction = 10 Use a graded mesh. The grading factor near all walls should be 0.2, 0.5, 0.8…

FINITE VOLUME METHOD - LITERATURE REVIEW The conservation laws of fluid motion are described either in differential form or in integral form. When the integral form of governing equations are solved, the domain is divided into small volumes. In these elementary volumes, the conservation laws can be applied. This is called…

SIMULATION OF FLOW THROUGH A PIPE IN OPENFOAM Objectives: To write a program in Matlab/Octave that can generate the computational mesh automatically for any wedge angle and grading schemes. To validate the numerical solution with the Hagen-Poiseuille's equation. Hagen-Poiseuille flow: Hagen-Poiseuille flow (or simply Poiseuille…

SYMMETRY VS WEDGE VS HP EQUATION: Aim: To simulate the flow through a pipe using wedge and symmetry boundary conditions and compare the results with the analytical solution for angles `theta` = 10, 25, and 45. Wedge: This type of boundary condition is used for two-dimensional axisymmetric cases e.g. a cylinder. The…

MIXING TEE SIMULATION OBJECTIVES: To simulate the turbulent mixing of hot and cold airstreams in a mixing tee using Ansys. To study the effects of length and momentum ratio (MR) on mixing effectiveness. INTRODUCTION: A mixing tee is used to mix cold air with hot air to obtain the desired temperature at the outlet. The…

SIMULATION OF FLOW OVER A CYLINDER AIM: To simulate the flow with the steady-state and unsteady-state flow and calculate the Strouhal number for Re = 100. (PART I) To calculate the coefficient of drag `C_d` and coefficient of lift `C_l` by setting Re = 10, 100, 1000, 10000, and 100000 (with steady-state solver)…

EXTERNAL FLOW SIMULATION OVER AN AHMED BODY AIM:  To simulate the flow over an Ahmed body by using a steady-state solver and also to perform a grid independency test. IMPORTANCE OF AHMED BODY: The flow around road vehicles under normal operating conditions is principally turbulent which is characterized by large-scale…

CHT ANALYSIS ON EXHAUST PORT Introduction: Conjugate heat transfer corresponds with the combination of heat transfer in solids and heat transfer in fluids. Conjugate heat transfer is observed in many situations. For example, heat sinks are optimized to combine heat transfer by conduction in the heat sink with the convection…

RAYLEIGH-TAYLOR INSTABILITY Introduction: The Rayleigh-Taylor instability is the instability of an interface between two fluids of different densities which occurs when the lighter fluid is pushing the heavier fluid. As the RT instability develops, the initial perturbations progress from a linear growth phase into a non-linear…

CHT ANALYSIS ON A GRAPHICS CARD Aim: To perform a steady-state analysis on the graphics card model by choosing the appropriate material. Introduction: Conjugate means coupled, connected, or related. Heat is defined as the energy transferred by temperature difference. The term conjugate heat transfer analysis allows for…