Week 6 - Multivariate Newton Rhapson Solver

Understand the concept of Rankine cycle by referring to standard thermal engineering text book. Create a Rankine Cycle Simulator using OCTAVE/MATLAB. Your code should calculate the state points of the Rankine Cycle (any type of your choice) based on user inputs.  Then, plot the corresponding T-s and h-s plots for…

Take a look at the data analysis video before you attempt this challenge. Your task is to write a script that does the following. Data visualizer (100 points) 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…

Curve fitting:       Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a…

Equation: n 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. Write a program in Python that will simulate the pendulum motion, just like the one shown in the start of this challenge. use, L=1 metre, m=1 kg, b=0.05. g=9.81 m/s2. Simulate the motion…

Otto cycle:       An Otto cycle is an idealized thermodynamic cycle that describes the functioning of a typical spark ignition piston engine. It is the thermodynamic cycle most commonly found in automobile engines. The Otto cycle is a description of what happens to a mass of gas as it is subjected to changes…

Write a function that extracts the 14 co-efficients and calculates the enthalpy, entropy and specific heats for all the species in the data file. You will be reading this file NASA thermodynamic data(Tip: use fopen and fgetl). The formulae are shown below.  Here R is the universal gas constant, T is…

Genetic algorithm:      In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are commonly used to generate high-quality solutions to optimization…

Equation: 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. Write a program in Matlab\Octave that will simulate the pendulum motion, just like the one shown in the start of this challenge. use, L=1 metre, m=1 kg, b=0.05. g=9.81 m/s2. Simulate…

Questions based on PFI Engine: Q1. What is the Compression ratio for the engine?        The compression ratio is the ratio between the volume of the cylinder and combustion chamber in an internal combustion engine at their maximum and minimum values.  A fundamental specification for such engines,…

Aim: To run the IC engine simulation for two pistons and compare the emission characteristics Case setup preparation: Engine sector data: The iput data like bore, stroke and connecting rod is provided then the bowl profile is imported. Thus completing the preparation of design make surface option is selected to create…

Geometry: Preparation: Application type: Gas simulation: Parcel simulation: Reaction mechanism: Species: Run Parameter: Simulation time parameter: Boundary Conditions: Regions: Events: Spray model: Combustion model(SAGE): Turbulance model: Source/sink model: Base grid: Adaptiv Mesh Refinement: Fixed Embedding:   Results:…

Input geometery: Error faced: With the errors faced everthing must be cleared with one be one so that the simulation can be run.  Thus to solve the geometrical errors one by  one the geometry is flagged and seperated every part. Boundary Flagging: Normal error:      The Normal error  is simple…

RANS derivation and analysis:        The Reynolds-averaged Navier–Stokes equations (or RANS equations) are time-averaged[a] equations of motion for fluid flow. The idea behind the equations is Reynolds decomposition, whereby an instantaneous quantity is decomposed into its time-averaged and fluctuating…

Geometry: High pressure geometry: Low pressure geometry: run parameter: Simulation time parameter: Turbulance model: High pressure region: Low pressure region: Event: Adaptive Mesh refinement: results: Mesh animation: Velocity graph: Velocity animation: Mass fraction of N2 animation: Pressure graph: Pressure animation:…

Baseline configuration Setup a flow simulation through a pipe Inlet Reynolds number should be 7,000 HINT : Use the below formula to calculate velocity for corresponding value of REYNOLD NUMBER and give DIRICHLET BC for velocity at inlet and specify the value for velocity calculated at INLET BC using below formula…

Boundary Condition:       In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to the differential equation which…

Geometry: Throttle geometry: throttle through inlet: run parameters: Stimulation time parameters: End time calculation: The characteristics length would be approximately 0.2 m. The average velocity from steady state calculation is 200ms^-1. So for a single pass, its takes 0.2/200 = 0.001 seconds. The throttle movement…

Geometry:       The geometry of the elbow is cleaned and patched so that the geometry is used to run the steady state stimulation is run through the elbow with throttle. Throttle geometry top: throttle geometry through inlet:       Once the geometry is cleaned and patched, the case setup is…

Backward facing step:      The backward facing step is an interesting case for studying the performance and solution strategy of a turbulence model. In this case, the flow is subjected to a sudden increase of cross-sectional area, resulting in a separation of flow starting at the point of expansion. Spatial…

Aim:      To run a channel flow stimulation for three different mesh size and interpret the results. Mesh cases dx(m) dy(m) dz(m) case1 2e-4 2e-4 2e-4 case2 1.5e-4 1.5e-4 1.5e-4 case3 1e-4 1e-4 1e-4   Preparation:        A channel geometry is created and the Case setup is done using…

When does a ODE become unstable? In order to find the unstable condition for a ODE lets assume a equation for ODE and run the program for various dt. Equation:  f(y) = dy/dt = - 1000y-e^-t        For this equation we find the analytical results along with explicit and implicit methods for…

 Sensitivity analysis:        Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be divided and allocated to different sources of uncertainty in its inputs. A related practice is uncertainty analysis, which has a greater focus on uncertainty…

  Auto-Ignition Temperature:      The autoignition temperature or kindling point of a substance is the lowest temperature in which it spontaneously ignites in a normal atmosphere without an external source of ignition, such as a flame or spark. This temperature is required to supply the activation energy…

The equation to solve: Boundary Condition: Y1 = 1 Y2 = 0 y3 = 0 Alpha = 1 Time to run = 10 mins Procedure:      The process of solving the set of equation with respect to time.  The equation has to be solved every timestep. So the newton-rahpson method is used to solve in timestep and the results if…

Combustion stimulation: Geometry:    The sectioned view of combustor model is shown here. In this geometry in order to use a refined mesh the geometry is cut to quatre its size and and plane is taken out for the CFD stimulation. In this plane the parts are combined together. 2D geometry: Mesh:     The…

CHT analysis:       The contemporary conjugate convective heat transfer model was developed after computers came into wide use in order to substitute the empirical relation of proportionality of heat flux to temperature difference with heat transfer coefficient which was the only tool in theoretical…

Q1. Describe Ahmed's 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 and characterized in the experimental work of Ahmed.  Ahmed body…

Given data: cold inlet temprature X=190C.  hot inlet temperature Y= 360C There are two cases short and long pipes cases respectively.  momentum ratio = 2,4.  hot inlet velocity of 3m/s.  Thus with two Momentum ratio the two sub cases of cold inlet  velocity is 6m/s and 12m/s. …

    Using the values from  previous challege, leght of pipe is 5mm and average velocity is 0.1602m/s. This matlab program will provide the geometry file for any wedge angle. thus it needs the angle as input. Matlab Program for different wedge angle: clear all close all clc wedge_angle = input('enter the…

Simulation of Flow through a pipe:       Assume that water at temperature 303K, flowing through a pipe of 10mm diameter with a laminar flow of Re=2000. we need to find the entrance lenght(le), lenght of pipe(l), average velocity(Vavg) and pressure drop using Hagen poiseuille's equation.  …

Mesh specification Number of cells along the x direction (longer dimension) = 200 Number of cells along the y direction = 10 Use a graded mesh. Grading factor near all walls should be 0.     First the geometry has to be created.  So the apprapriate solver is choosed and geotmetry is created in the blockMeshDict…

 To simulate the isentropic flow through a quasi 1D subsonic-supersonic nozzle: subsonic-supersonic nozzle to be solved using two form.  They are conservation and non-conservation forms. Conservation form equation: ∂(ρ’A’)/ ∂t’ + ∂(ρ’A’v’)/ ∂x’…