Central differencing: For Central difference the stencil has 5 nodes, they are i-2,i-1,i,i+1,i+2. For Central difference, we r having the formula to calculate the nodes.                no. of nodes = p+q-1 = 2+4-1 = 5. Here p = order of derivative         …

Simple pendulum: A simple pendulum consists of a mass m hanging from a string of length l and fixed at a pivot point P. When displaced to an initial angle and released, the pendulum will swing back and forth with the periodic motion. And it depends upon Newton's second law of motion. Given equation  d2θ/dt2 +…

The 2Dheat conduction equation is of 2 types: (i) steady-state (ii) unsteady-state The steady-state equation can be solved with the implicit method while coming to the unsteady state equation there is a time term, so it can be solved either explicit or implicit method.   For steady-state eq `((del^2T)/(delx^2)+(del^2T)/(dely^2))…

The governing equations of a mathematical model describe how the values of the unknown variables (i.e. the dependent variables) change when one or more of the known (i.e. independent) variables change. It is divided into 2 types. They are i  Conservative form ii  Non-Conservative form In the Conservative…

The main objective of this challenge is to produce the blockmesh by using the OpenFOAM software.  The given diagram is in the 2D view. It is divided into 5 blocks, which is shown below.                                     …

Finite Volume Method (FVM): The finite volume method is a method for representing and evaluating partial differencing equations in the form of algebraic equations. In the finite volume method, volume integrals in a partial differential equation that contain a divergence term are converted to surface integrals,…

The length of the entrance is the distance that fluid travels after entering a pipe before the full development of the flow. Entrance length refers to the length of the entry region, effected the pipe's interior wall spread as an expanding boundary layer into the flow. When the boundary layer extends to fill the entire…

In this challenge, the procedure is completely the same as the previous challenge with some modifications. The wedge angle is different, they are 10, 25, and 45. The steps are of the simulations are completely the same as the previous one. Here in the code, there is a need to change the theta values from 10 to 25 and 25…

Given In this challenge, there are two versions of mixing tee geometry.  The first one is a short tee and the second one is a long tee mixing geometry.  Temperature: Hot inlet(in x direction) = 36c Cold inlet(in y direction) = 19c Velocity: Hot inlet = 3m/s. Hot inlet = 3m/s. Momentum ratio = cold inlet…

Theory: Karman vortex street: Karman vortex street or a Von Karman vortex street is a repeating pattern of swirling vortices, caused by a called vortex shedding(it is an oscillating flow that takes place when a fluid such as air or water flows past a bluff body at certain velocities, depending on the size and shape of…

Introduction: Ahmed body: The Ahmed body is a bluff model body with basic aerodynamic properties of a vehicle. It was created by S.R. Ahmed in 1984. The simple geometrical shape has a length of 1.044 m, a height of 0.288 m, and a width of 0.389 m. .It also has 4 cylindrical legs of 0.5 m which are attached to the bottom…

CHT Analysis: Conjugate Heat Transfer(CHT) analysis type allows the simulation of heat transfer between solid and fluid domains by exchanging thermal energy at the interfaces between them. Which is more stable and provides faster convergence as the energy equation is strongly coupled between the solid and fluid regions.…

Rayleigh Taylor instability: 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…

Conjugate heat transfer analysis(CHT analysis):  The CHT analysis is a type that allows for the simulation of heat transfer between solid and liquid domains by exchanging thermal energy at the interfaces between them. This analysis is also used to correctly predict the surface temperature and heat exchanging capabilities…

Aim: To perform analysis on cyclone separator and calculate the separation efficiency and pressure drop.   Introduction of Cyclone separators: Cyclone separators or simply cyclones are separation devices (dry scrubbers) that use the principle of inertia to remove particulate matter from the flue gases(The gas exiting to…

Gate valve: A gate valve is a linear motion valve used to start or stop the fluid flow; however, it does not regulate or throttle flow. The gate valve is used to control the fluid flow through lifting and descending the gate. A gate valve functions by lifting a rectangular or circular gate out…

  Simple pendulum: A simple pendulum is one that can be considered to be a point mass suspended from a string or rod of negligible mass. It is a resonant system with a single resonant frequency. Pendulum, body suspended from a fixed point so that it can swing back and forth under the influence of gravity.…

Combustion: Combustion is a chemical process in which a substance reacts rapidly with oxygen and gives off heat. The original substance is called the fuel, and the source of oxygen is called the oxidizer. The fuel can be a solid, liquid, or gas, although for airplane propulsion the fuel is usually a liquid. During…

Introduction: Genetic Algorithm(GA): The genetic algorithm is known as a search heuristic that is inspired by Charles Darwin's theory of natural evolution. This algorithm reflects the process of natural selection where the fittest individuals are selected for reproduction in order to produce offspring…

File parsing: Parsing, syntax analysis, or syntactic analysis is the process of analyzing a string of symbols, either in natural language, computer languages, or data structures, conforming to the rules of a formal grammar. The term parsing comes from Latin pars, meaning part. File parsing in computer language means…

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

Simple pendulum: A simple pendulum is one that can be considered to be a point mass suspended from a string or rod of negligible mass. It is a resonant system with a single resonant frequency. Pendulum, body suspended from a fixed point so that it can swing back and forth under the influence of gravity. These are used to…

Curve fitting:- curve fitting is a process of constructing a curve that has the closest similarity for the series of data being considered. Curve fitting examines the relationship between one and more predictors and a response variable with the defining the best model. The curve fit is classified into 3 types: Linear regression…

Data analysis:- It is defined as a process of cleaning, transforming, and modeling data to discover useful information for business decision-making. The purpose of Data Analysis is to extract useful information from data and taking the decision based upon the data analysis. Data visualizer:-…

Given: `CO + O_2 harr CO_2 + O` `O + H_2O harr OH + OH` `CO + OH harr CO_2 + H` `H + O_2 harr OH + O` Here there are 4 reactions(i) and 7 species(j). Compact notation: This helps to solve the reaction mechanism which includes a large number of species. `[[j,Species],[1,CO],[2,O_2],[3,CO_2],[4,O],[5,H_2O],[6,OH],[7,H]]`…

 Here from the equation of Methane: `CH_4 + 2(O_2 + 3.76N_2) to CO_2 + 2H_2O + 2(3.76N_2)` we mentioned that `O_2` = 0.21 and `N_2`= 0.79 which equals to 1. A contains 2 moles, which is a mixture of `O_2` and `N_2`.  1) Mole fraction = (Number of moles of particular species) / (Total number…

Aim: The aim of this project is to simulate the combustion of methane for the calculation of AFT. Objectives: Effect of equivalence ratio on AFT. Constant pressure process with heat loss parameters. AFT variation with respect to an alkane, alkyne, and alkene. Testing the different fuels with 2 carbon atom bonds. Adiabatic…

Aim: Finding the effect of preheating from 298 to 600K on AFT. The methane is mixed air and burnt in the furnace and a recuperator is connected to the furnace to recover some energy. Recuperator: A recuperator is a special purpose counter-flow energy recovery heat exchanger positioned within the supply and exhaust…

Introduction: There are 2 systems in mathematics, stable and unstable systems. In a stable system, a certain small amount of disturbance is inserted into the system, then it tends to minimize it. If the disturbance amplifies as the system progresses in time and does not decrease in value, then it is called an unstable…

Aim:- To find the solution for non-linear ordinary differential equations using Newton Raphsom's method, incorporating or including an implicit(Euler's backward differencing) scheme. ODE system: `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 basic formula…

Aim:- Write a code that calculates 10 most sensitivity values of temperature, for a given GRI30 mechanism file. The sensitivity parameter should be with respect to the temperature. Sensitivity Analysis:- Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system can…

Auto Ignition:- The ignition is the process of starting the combustion of fuel in the cylinders of an internal combustion engine. Auto-ignition is the self-ignition of the fuel/air mixture before the spark has fired. This can be caused by hot combustion residuals or hot parts of the cylinder wall. Auto-ignition leads…

Aim:- To simulate the flow of air through a channel using converge CFD. Theory:- The flow-through channels are basically of 2 types: 1. Open channel flow: In this type, the flow is only for liquids. Here the flow with a free surface opens to the atmosphere.  2. Closed channel flow: Example pipe…

Aim: To simulate the airflow over a backward-facing step using converge studio. To study the turbulent flow characteristics downstream to backward-facing step. To compare the flow over backward-facing step for different mesh grading of 2e-3, 1.5e-3, and 1.0e-3.  Theory:  Flow separation: Flow separation or boundary…

Aim: Setup and run the simulation.  Plot pressure, velocity, mass flow rate, and total cell count and show the velocity and pressure counters. Study the results and analyze the flow happening over and around the body.   Theory: Throttle body:-   A throttle is a mechanism by which fluid flow is managed by constriction or…

Aim: Setup and run the simulation.  Plot pressure, velocity, mass flow rate, and total cell count and show the velocity and pressure counters. Study the results and analyze the flow happening over and around the body.   Theory: Throttle body:-   A throttle is a mechanism by which…

Aim:  Simulate the supersonic and subsonic flow through a duct having a sharp edge.  Study the formation of shock waves and observe the effect of SGS parameter on shock location and cell count. What is a Shock wave? A shock wave or shock is a type of propagating disturbance that moves faster…

Aim: Setup a transient simulation through the shock tube. plot the cell count, pressure, and temperature plots wrt time.  Theory: The shock tube is an instrument used to replicate and direct blast waves at a sensor or a model in order to simulate actual explosions and their effects, usually on a smaller…

Aim: Derive the Reynolds Averaged Navier Stokes equation(RANS equation) and find an expression for Reynolds stress. Determine the terms Reynolds stress, turbulent viscosity, and molecular viscosity.  Introduction: The Reynolds-averaged Navier–Stokes equations (or RANS equations) are time-averaged…

Aim: To perform the boundary flagging and surface preparation for a 4-stroke IC engine and run with a no-hydro simulation. Theory: The most widely produced internal combustion engines were of the Port Fuel Injected (PFI) design, where the fuel is sprayed into the intake ports to mix with incoming air. A four-stroke (also four-cycle) engine is…

Aim: To simulate the port fuel injection engine in converge CFD by using hydro simulation and calculate the important parameters like Compression ratio, Power, Combustion efficiency, and Torque. Theory: Fuel injection is the introduction of fuel in an IC engine, most commonly automotive engines, through an injector.…

Aim: To simulate fuel spray and combustion in two different piston profiles in the cylinder head and study the effect of piston profiles on the key performance parameters and emissions. Theory: A diesel engine population has created pressures on controlling diesel PM(Particulate matter) and NOx emissions. The initial…

Port fuel injection(PFI): 1. Compression ratio(`r_c`): Compression ratio is the ratio of the total cylinder volume when the piston is at the bottom dead centre(`V_t`) to the clearance volume. It is denoted by the letter `r_c`. `r_c` = `V_t/V_c = (V_c+V_s)/V_c` `V_c` = clearance volume and `V_s` = Swept or…

Aim: Simulate conjugate heat transfer for airflow through aluminum pipe.  Run grid independence test on 3 grid sizes and analyze the effect of supercycle stage interval at 0.01, 0.02, and 0.03.   Theory: Conjugate heat transfer(CHT): The term 'conjugate heat transfer' refers to a heat transfer process…

Gearbox: The gearbox is a mechanical method of transferring energy from one device to another and is used to increase torque while reducing speed. The main purpose of the gearbox is to increase or reduce speed. As a result, the torque output will be the inverse of the speed function. If the enclosed…