Steady Unsteady 2D Heat Conduction

Here an effort is made to clean the Automobile 1985 dataset and perform the descriptive analytics and make the predicitive model using the Random Forest classifier. lets import all the required libraries. import numpy as np import pandas as pd import matplotlib.pyplot as plt from sklearn.datasets import load_iris from…

Here an effort is made to clean the Automobile 1985 dataset and perform the descriptive analytics. lets import all the required libraries. import numpy as np import pandas as pd import matplotlib.pyplot as plt from sklearn.datasets import load_iris from sklearn.metrics import confusion_matrix from sklearn.metrics import…

What is a Neural Network? Neural networks reflect the behavior of the human brain, allowing computer programs to recognize patterns and solve common problems in the fields of AI, machine learning, and deep learning. Neural networks, also known as artificial neural networks (ANNs) or simulated neural networks (SNNs),…

K-means Clustering for Car Dataset: The aim of this project is to cluster the data into different classes depending upon the price. Let us import all the required libraries. import pandas as pd import numpy as np import matplotlib.pyplot as plt import seaborn as sns from sklearn.cluster import KMeans Import the data into…

First all the required libraries are imported and the dataset is loaded. import numpy as np import pandas as pd import matplotlib.pyplot as plt from sklearn.datasets import load_iris from sklearn.metrics import confusion_matrix from sklearn.metrics import classification_report from sklearn.model_selection import train_test_split…

NOTE: For this assignment Iris dataset is used. First all the required libraries are imported and the dataset is loaded. Moreover, "target" column is added to the dataframe. import numpy as np import pandas as pd import matplotlib.pyplot as plt from sklearn.datasets import load_iris from sklearn.metrics import confusion_matrix…

 Perform Gradient Descent in Python with any loss function The data set used is as follows: Here an effort is made to use regression analysis for curve fitting. And, the loss function used to fit the curve is Mean square error. `J=(1/n) sum(y(i)-(mx(i)+b))^2` x(i) is the input m and b are slope and intercept. y(i)…

Calculate all 4 business moments using pen and paper for the below data set? First Business Moment - Mean `mu = sum(X_i*P(X_i))` `mu = (0xx0.35)+ (1xx0.25)+ (2xx0.15)+ (3xx0.15)+ (4xx0.1)` `mu = 1.4` Second Business Moment - Variance `σ^2 = sum((X_i-mu_x)^2*P(X_i))` `=(0-1.4)^2xx0.35+(1-1.4)^2xx0.25+(2-1.4)^2xx0.15+(3-1.4)^2xx0.15+(4-1.4)^2xx0.1`…

Why there is a difference in the formula of variance for population and sample ? In Statistics the term sampling refers to selection of a part of aggregate statistical data for the purpose of obtaining relevant information about the whole. The aggregate or whole of statistical information on a particular charcter of all…

Here, an effort is made to determine the common baby names as Word Cloud among various ethnicities, years, and gender using Python in Jupyter Notebook. An arbitrary file available on the internet is downloaded and processed.  The same .csv file can be obtained from the following link: <https://drive.google.com/drive/folders/1SpQr865ckvhPsrulHRJ7mZ9TfH1yKJf3?usp=sharing>…

The Continuous Stirring Tank Reactor (CSTR) model is as shown below: The CSTR model parameters are as shown below: Variable description of CSTR model parameters is as shown below: The non-linear dynamics of the CSTR model is governed by the following equations. `(dC_a)/dt=F/V(C_(a0)-C_a)-k_0exp(-E/(RT))C_a` `(dT)/dt=F/V(T_0-T)+(…

PART 1 - PFI Engine - surface Preparation, Boundary Flagging & No-Hydro Case Setup Introduction: After post-processing, the No-Hydro setup, and verifying the case parameters run as specified, part 2 of this project involves full hydrodynamic simulation including the combustion and spray modeling. This study is…

In this challenge, two different piston bowl configurations of CAT3410 Engine are analyzed and their emissions are characterized. Objectives: To make the engine sector surface by providing the bowl profile. (sector is made to be computationally efficient, rather than simulating the entire domain). To set up the case for…

In this project, a single-cylinder Port-fuel-injection (PFI) engine is setup for no-hydro simulation. Prior to it, surface preparation and boundary flagging are performed to make the geometry free from errors and to allocate the boundaries and regions. No-hydro simulation is performed to check the mesh generation and correctness…

In this challenge, flow over a throttle body is simulated under steady-state conditions using converge 3.0. Two cases are investigated, at the first throttle body is completely open and in the second case, the throttle body is partially open (rotated by 25 degrees).  Physical Setup: General Steady State Pressure Based…

In this challenge, flow over a throttle body is simulated under transient conditions using Converge 3.0. The throttle is completely open during the first 0.002 seconds and for the rest of the simulation, the throttle is at 25 degrees.  Physical Setup: General Transient State Pressure Based Model RNG k-`ε`…

In this project, the Prandtl Meyer Shock problem is studied by using Converge 3.0, and the effect of Sub-Grid Scale (SGS) Temperature on the cell count and shock location are studied. Introduction: Shock Wave: A shock wave or shock is a type of propagating disturbance that moves faster than the local speed…

In this challenge conjugate heat transfer simulation of the Pipe flow is studied using converge 3.0. Geometry: The geometry of the pipe is as shown below. The length of the pipe is 0.2m, the external diameter is 0.04m and the internal diameter is 0.03m. The fluid flowing is air and the pipe is made up of Aluminum. …

In this project, the 3D Shock tube is simulated using Converge 3.0.  Shock tubes are used to replicate and direct blast waves in order to simulate actual explosions and their effects on a smaller scale. Moreover, they are used to investigate compressible flow phenomena and gas-phase combustion reactions. A shock…

The objective of this project is to apply Reynold's decomposition to the Navier-Stokes equation and to determine the expression for Reynold's Stress.  Navier Stokes Equations: The movement of fluid in the physical domain is driven by various properties. For the purpose of bringing the behavior of fluid flow to light…

Objective: The aim of this project is to reduce the reaction mechanism size from that of the GRI 3.0 Mechanism for methane (`CH_4`) fuel with various state values to compute the maximum temperature and the ignition delay for the given tolerance criteria(1%) based on the temperature sensitivity. Procedure: The code is done…

The aim of this project is to determine the 10 most sensitive reactions w.r.t temperature among the list of reactions in the GRI mechanism for the combustion.  Objectives: Plot the variation of temperature and molar concentration of species (viz., O2, OH & CH4 )w.r.t to time. Plot the bar graph showing the 10…

The aim of this project is to determine the effect of initial temperature and pressure in the ignition delay of the methane combustion process. A constant volume reactor and corresponding network objects are created in Cantera and the combustion process is simulated.  Objectives: Auto Ignition Delay for Methane Combustion.…

The objective of this project is to solve the set of equations using Multi-Variate Newton Raphson Solver. The system of equations is as follows: `(dy_1)/dt = -0.04y_1+10^4y_2y_3` `dy_2/dt = 0.04y_1-10^4y_2y_3-3*10^7y_2^2` `dy_3/dt=3*10^7y_2^2` The given set of equations are coupled and non-linear.  The set of equations…

The aim of this project is to obtain the compact notation of the reaction mechanism. Assumption: The given four reactions are assumed to take place in both forward and reverse directions. `CO+O_2 <=>CO_2+O` `O+H_2O<=>OH+OH` `CO+OH<=>CO_2+H` `H+O_2<=>OH+O` Let `K_(fN)`and `K_(rN)`be the…

The aim of this challenge is to discuss the stability of an ODE/PDE  system. Introduction: Before we begin, it is essential to understand the different ways in which an ODE/PDE system can be solved numerically. Numerical solution schemes can be classified into two main types viz., implicit and explicit schemes. In…

The aim of this project is to perform the combustion simulation on the combustor model and to plot the variation of different species in the combustor.  The 3D geometry is imported to SpaceClaim and is split to obtain the axisymmetric and 2D geometry. Geometry: Mesh: Mesh is obtained using a 1 mm element size and…

In this challenge, a furnace is used to combust methane and air. A recuperator is connected to utilize the waste heat and preheat the incoming air to the furnace. This study includes the effect of preheating on Adiabatic Flame Temperature (AFT), combustion efficiency and fuel saving.  Recuperator is a counter-flow…

The objective of this challenge is to determine the Adiabatic Flame Temperature for the combustion of methane and air at the stoichiometric conditions and constant pressure by handling mixtures of methane and air as two separate quantities using the \"Quantity Class\" in Cantera.  Here, the code given in the challenge…

The aim of this project is to determine the Adiabatic Flame Temperature (AFT) at various conditions of the combustor and fuels using Python and Cantera. The objectives are as follows: To determine the effect of equivalence ratio on AFT for methane in a constant volume reactor. To determine the effect of heat loss on Flame…

The objective of this project is to perform gear sloshing simulation using Ansys Fluent for two different gearboxes with different clearance and two lubricants. Sloshing is the phenomenon that happens within the closed container or when any object rotates or translates in the container that contains fluid. Gearbox sloshing…

The aim of this project is to simulate the flow in the pipe for various opening conditions of the gate valve. The geometry of the valve is imported to SpaceClaim and the fluid domain is extracted accordingly. The inlet and outlet of the pipe are extended on either side by 800 mm.  Geometry: Fluid Domain: Mesh: Sectional…

Cyclone separator is a device that employs centrifugal force generated by a spinning gas stream to separate particles from the carrier gas. Their simple design, low maintenance costs, and adaptability to a wide range of operating conditions such as sizes and flow rates makes cyclone separator one of the most widely used…

CHT Analysis of Graphic Card Assembly: In the following project CHT analysis on a processor assembly is carried out to find out velocity variation of air over the assembly, temperature distribution and heat transfer coefficient are determined. Two simulations with the baseline mesh and refined mesh are carried out and…

The Rayleigh–Taylor instability, or RT instability (after Lord Rayleigh and G. I. Taylor), is the instability of an interface between two fluids of different densities which occurs when the lighter fluid is pushing the heavier fluid. Examples include the behavior of water suspended above oil in the gravity of Earth,…

Why and Where CHT Analysis is used? The term conjugate heat transfer (CHT) is used to describe processes that involve variations of temperatures within solids and fluids, due to thermal interaction between the solids and fluids. The exchange of thermal energy between the two physical bodies is called the study of Heat…

The objective of this project is to perform the simulation of flow through the pipe using icoFoam solver in OpenFOAM. Here, a section of pipe (wedge-shaped geometry) is selected to simulate the flow through the pipe. The fluid chosen is water and the flow is laminar and incompressible. Hence, the icoFoam solver is used…

The objective of this project is to perform the simulation of the backward facing step by creating multiple meshes using icoFoam solver in OpenFOAM for the geometry provided below.  Geometry XY Plane YZ Plane BlockMeshDict file from the system folder is edited to obtain the above geometry with five blocks and…

1. Ahmed Body and its Importance: Ahmed's body is one of the benchmark problems for validating the simulating tools and to check the veracity of simulating tools.  Ahmed's body is a simplified car body and was created by SR Ahmed (SAE-840300, 1984). It is a kind of baseline geometry for automobile bodies and maintains…

Objective - The aim of this project is to learn the MacCormack\'s technique. We will be solving 1D supersonic nozzle flow for which the analytical solutions are available. Thus we can evaluate our findings with the analytical results to verify the degree of accuracy obtained.  MacCormack\'s Technique: The…

Abstract: In this project, the Stone’s strongly implicit pre-conditioner (SIP) is utilized to solve the Poisson equation for determining temperature distribution in a rectangular bar. Stone’s SIP is found to be more efficient than the other iterative methods, it requires less computational time, converges faster…

In this challenge, 2 3D geometries of mixing Tee are simulated for varying momentum ratios. Geometry: Two variants of mixing Tee were modeled using SolidWorks provided in the model files. One of them is of length 650 mm while the other is longer with a length of 1150 mm. Mesh Generation: The tetrahedral mesh was generated…

Steady State Solver: The steady state heat equation is as follows: `(∂^2 T)/(∂x^2 )+(∂^2 T)/(∂y^2 )=0` The above problem is of Elliptic type. Hence, we use relaxation technique to solve the problem. Discretizing the above equation using the central difference scheme with second-order approximation. …

Given below is the ODE describing the transient behavior of the Pendulum system. `(d^2theta)/dt^2+b/m(dθ)/dt+g/Lsintheta=0` Second order ODE can be solved using 'ode45' predefined MATLAB function by resolving the second order ODE into two first-order ODE's. let us rewrite the equation as  `(d^2theta)/dt^2 =…