Global Maxima of Stalagmite Function

BlockMesh Drilldown Boundary condition specification Follow the specifications that are provided in the following figure. Mesh specification Number of cells along the x direction (longer dimension) = 200 Number of cells along the y direction = 20  (For ease) Grading factor near all walls. (0.2,0.5,0.8) BlockMesh BlockMeshDict…

Objectives-1 : (1) To Write a program in Matlab that can generate the computational mesh automatically for any wedge angle and grading schemes. (2) For a baseline mesh, show that the velocity profile matches with the Hagen poiseuille's equation. Show that the velocity profile is fully developed. (3) Post…

Aim : Simulate the flow over a cylinder and explain the phenomenon of Karman vortex street.  PART-I Simulate the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100.  PART-II Calculate the coefficient of drag and lift over a cylinder by setting the Reynolds number to 10,100,1000,10000 &…

Mixing Efficiency Two versions of the mixing tee is made using CAD software.One of them is longer than the other. Steady-state simulation was set up to compare the mixing effectiveness when hot inlet temperature is 360C & the Cold inlet is at 190C.  Theory : A Tee is formed by two pipe sections joined at a right…

Need of Interpolation schemes in Finite Control Volume Method The approximation of surface and volume integral may require values of the variable at locations other than the computational nodes of C.V. So, values at these locations are obtained using Interpolation.  There are different Interpolation schemes such as…

Objective :  To solve the 1D supersonic nozzle flow equations using the Macormack Method. Compare the normalized mass flow rate between the conservative forms and non-conservative forms to make suitable conclusions. Figure out the minimum number of cycles for which the simulation should be run in order for convergence.…

In mathematics, an Ordinary Differential Equation (ODE) is a differential equation containing one or more functions of one independent variable and the derivatives of those functions. ODE is used to describe the Transient Behaviour of system. Here, motion of Simple Pendulum is also governing by Second Order ODE as…

Project-1 : Parsing NASA Thermodynamic Data NASA  came up with polynomials that can be used to evaluate thermodynamic properties such as Specific Heat, Enthalpy and Entropy. In this polynomials, first seven co-efficients are High-Temperature co-efficients and second seven co-efficients are Low-Temperature…

Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit (Closest Proximity) to a series of data points, possibly subject to constraints. By curve fitting, we can mathematically construct the functional relationship between the observed data set and parameter…

%Forward Kinematics of Robotic Arm %Octave Program l1=1; l2=0.5; theta1=linspace(0,90,10); theta2=linspace(0,90,10); ct=1; for i=1:length(theta1) THETA1=theta1(i); for j=1:length(theta2) THETA2=theta2(j); x0=0; y0=0; x1= l1*cosd(THETA1); y1= l1*sind(THETA1); x2= x1 +(l2*cosd(THETA2)); y2= y1 +(l2*sind(THETA2)); plot([x0…

In mathematics, Ordinary Differential Equation (ODE) is a differential equation containing one or more functions of one independent variable and the derivatives of those functions. In Engineering, ODE is used to describe the Transient Behaviour of system. Here, motion of Simple Pendulum is also governing by Second Order…

Aim :- To create a Data Visualizer Tool that does the following things. Data Visualizer  Your script should take column numbers as the input and plot the respective columns as separate images. Each file should be saved by the name of the column. The plot labels should be extracted from the file. If, I request…

Aim :- Write a code in MATLAB to optimise the Stalagmite function and find the global maxima of the Stalagmite function by using Genetic Algorithm. Genetic Algorithm :- A Genetic Algorithm is a search heuristic that is inspired by Charles Darwin\'s theory of natural evolution. This algorithm reflects the process of natural…

Curve Fitting is the process of constructing a curve, or mathematical function that has the best fit (closest proximity) to a series of data points. By Curve Fitting, we can mathematically construct a functional relationship between the observed data sets and parameter values.It is highly effective in mathematical…

#To plot a Velocity vs Drag Force Here, first assumption is that, cyclist is following Aero bars position. Aero bars position allow an individual to maintain an Aerodynamic Position. As per the data, Coefficient of Drag is 0.7 for Aero bars Position. Below is the wind tunnel data of rider in Aero bars position.…

Aim : To simulate flow over a cylinder at different reynolds number. Run a baseline simulation and then calculate the Reynolds number. Then increase the Reynolds number by a factor of 20%, 40%, and 100% then run the transient flow simulation. Parameters :  Cylinder Diameter : 50 mm Cylinder Length : 80 mm Baseline…

%Octave code for Engine Kinematics function [V] = engine_kinematics(bore,stroke,con_rod,cr,Start_crank,End_crank) a=stroke/2; R=con_rod/a; V_swept= pi/4*bore^2*stroke; V_clearance= V_swept/(cr-1); theta= linspace(Start_crank,End_crank,180); term1 = 0.5*(cr-1); term2 = R+1-cosd(theta); term3 = (R^2 - sind(theta).^2).^0.5;…

Aim : (1) Model the flow over a NACA0021 Airfoil          (2)  For the angle of attacks 0,2,4,6,8,10 compare the lift and drag forces. In fluid dynamics, Angle of Attack is the angle between a reference line on a body and the vector representing the relative motion between the body and…

Aim : To create a 3D model of a flow bench and run flow analysis. Grid dependence test :- For three grids run your simulation at a particular valve lift and explain your results. Effect of valve lift on mass flow rate :- Once you have decided the best grid, run a parametric study to show the effect of valve lift on…

Aim : To Create the 3D model for a centrifugal pump and then run the simulation of water flow through the pump to find out the mass flow rate at outlet & Pressure Ratio. A Centrifugal Pump converts rotational energy, often from a motor, to energy in a moving fluid. A portion of the energy goes into kinetic energy…

Aero Bars position allow a cyclist to maintain an Aerodynamic position. Here, first assumption is that cyclist is following Aero Bars position. Co-efficient of Drag for Aero Bars position is 0.7 Below is the wind tunnel data of cyclist in Aero Bars position. As per the above data, value of CDA is 0.250 CDA is the product…

Aim :- To minimize a simple non-linear function by using Lagrange Multipliers. Given Function : Given Constraint : Lagrange Multipliers In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equality constraints. The great advantage…

Otto cycle is an Air Standard cycle that is used in spark-ignition internal combustion engines (modern petrol engines). An Otto cycle consists of four processes: Two isentropic (reversible adiabatic) processes. Two isochoric (constant volume) processes. Process 1-2 : Isentropic Compression Process Process 2-3 : Constant…

Aim :- To determine the minimum cushion pressure needed to break a given thickness of iceusing an air cushion vehicle. In Mathematical Modeling: Classroom Notes in Applied Mathematics, SIAM 1987 , Muller derived the equation,                          …

#Python Program to Simulate Forward Kinematics of 2R Robotic Arm :- #Forward Kinematics of Robotic Arm #By DIPESH SALUNKE import math import matplotlib.pyplot as plt #Length of First Link l1=1 #Length of Second Link l2=0.5 n_theta=10 theta_start = 0 theta_end = math.pi/2 theta1 = [] #Empty Array for Angular Displacement…

Project-2 : Rankine Cycle Simulator                                                       Rankine Cycle The Rankine cycle is an idealized thermodynamic cycle of a heat engine…

Aim : To solve the 2D Heat Conduction equation using a Steady state solver and Transient solver using Iterative techniques like, 1. Jacobi 2. Gauss-seidel 3. Successive over-relaxation Absolute error criteria is 1e-4 Assume that the domain is a unit square.  Assume nx = ny [Number of points along the x direction is…