Week 6 - Multivariate Newton Rhapson Solver

Objective: To write the code which will take entire reactions of GRI mechanism 3.0 and take out the most sensitive top 10 reactions. The main parameters are as follows: Write code to list out the top 10 most sensitive reactions from a list of all reactions from the GRI mechanism. The sensitivity parameters should be with…

Objective: To study auto-ignition using Cantera. Following are the tasks to perform using Cantera: Plot the variation of Auto Ignition time of Methane with a constant temperature of 1250K and pressure varying from 1 to 5 atm. Plot the variation of Auto Ignition time…

Objective: To solve a given set of Ordinary Differential equations using the Multi-Variate Newton Raphson Method. Given: The set of ODE's are given below: `dy_1/dt= - 0.04*y_1+10^4*y2*y3` `dy_2/dt=0.04*y_1-10^4*y_2*y_3-3*10^7*y_2^2` `dy_3/dt=3*10^7*y_2^2` The jacobian should be estimated numerically and not analytically.…

Objective: To review the literature about ODE and to write the python program to substantiate our results. Theory:                                                            …

Objective: To derive the reaction rate ODEs of a simple reaction mechanism using compact notations and write down the desired matrices. Given: The simple reaction mechanism is as follows: `CO + O_2 -> CO_2 + O` `O + H_2O->OH+OH` `CO+ OH -> CO_2 +H` `H+ O_2->OH+O` Theory: Compact Notations- This helps us to…

Objective:  Use of 'mole' function on an object and explain. Use mole_fraction_dict() and mass_fraction_dict() of object. Explain line no. 17 & 18 Compute moles of A to get the right value of AFT   Results: Mole & Mass function: Here, using this function we can change the size of 'quantity' by setting…

Objective:  Part_1 - To know the effect of the range of inlet air preheating from 298K to 600K on the adiabatic flame temperature of Methane. Part_2 - To know the effect of pre-heat temperature on combustion efficiency.  Given:  Device-  Recuperator (Constant pressure Heat exchanger)Fuel- CH4Programs…

Objective:  PART_1- To find out the effect of equivalence ratio on AFT(Adiabatic Flame temperature) assuming METHANE(CH4) in a constant volume chamber. PART-2- To find out the effect of equivalence ratio on AFT by considering Constant pressure reactor with heat loss. Test it for -ane, -ene, and -yne variants of 2…

Objective: To build a discretized model from CAD STL file using the GEM3D application and to explore the single-cylinder DI model with different discretizing length. Following parameters, we have to compare from the model Parameters-Torque, BSFC, max cylinder pressure Simulation time Given: Tutorial 1CyliDI-final present…

Objective: To explore and understand the Turbocharger model use in automotive. List down different TC and locate it into GT power Explore Tutorial 6 and 7 Plot operating point on compressor and turbine maps Benefits of VGT (Variable Geometry Turbine) Explore Diesel VGT EGR and understand the modeling part. Theory:  …

Objectives: To explore FRM (Fast Running model) model tutorial and to build the FRM model using the FRM builder approach for the following specifications. Bore- 102mm, Stroke- 115mm, CR- 17 CI engine, Nos. of cylinders- 6 Twin scroll turbine GT Controller Given: FRM converter tutorial no 9 which includes 8 steps given.…

Objective: To simulate flow over a cylinder and explain the phenomenon of Karmen vortex street Part-1: Simulate flow over the cylinder with STEADY and TRANSIENT STATE and Calculate Strouhal Number for Re.No.=100. Part-2: Calculate the Coefficient of Drag and lift for Re. No= 50,100,150,200,250,300 using STEADY STATE…

Objective: To explore the tutorial of the Single Cylinder CI engine. Compare SI vs CI and list down important parameters Comment on parameters: BSFC, Exhaust Temperature, A/F Ratio Change MFB50 and observe the impact on performance Given: Use the given tutorial inside GT-SUITE. Take 1cylDI-final.gtm file from the tutorial.…

Objective: To perform a 1D simulation of the Single Cylinder SI engine using GT-SUITE. 1. List down following parameters (for= 1800 RPM) Airflow rate BMEP BSFC In-cylinder pressure 2. Increase power output by 30% @ RPM= 3600. Given: Copy 1CySI-Final.gtm from a tutorial (Engine performance) and paste it into…

Objective: To understand the GUI of GT-SUITE.1. List down the modules available in GT-SUITE in a brief description.2. Locate the following settings: Time control flag Time step and solution control Integrator and solver type 3. Explore intercooler tutorial and note down all settings of: Run setup. Advanced setup.…

Objective: To Perform a combustion simulation on the combustor model and find out the effect of the addition of water content on the formation of Nox and soot. PART_1- Plot the variation of the mass fraction for CO2, H2O, CH4, N2, O2, NOx emissions & Soot formation. PART_2- Observe the effect of water content…

Objective: To perform an analysis of the cyclone separator and calculate the separation efficiency and pressure drop. 1. Four empirical models used for cyclone separator efficiency.2. Calculate the separation efficiency and pressure drop for particle size ranging from 1 µm to 10 µm.3. Calculate separation efficiency…

Objective: To simulate the Full-hydro case setup of PFI.            1. What is the compression ratio of the engine?           2. Calculate the Combustion efficiency of the Engine?           3. Determine Power and torque of engine…

Objective: To analyzed the flow pattern of fluid inside gearbox using various configurations. Cases to be considered:1. 20% immersion, Fluid- Engine oil2. 30% immersion, Fluid- Engine oil3. 20% immersion, Fluid- n-heptane liquid2. 30% immersion, Fluid- n-heptane liquid   Given: CAD file to import into Spaceclaim.…

Objective: To perform a parametric study on the gate valve simulation by setting the opening from 10% to 80%.  Taking Disc lift values like 10mm, 20mm, 30mm, 40mm, 50mm, 60mm, 70mm, and 80mm. 1. Find out mass flow rates at the outlet for each design point.2. Evaluate the flow coefficient and flow factor for each opening…

Objective: To perform a steady-state CHT analysis on a graphics card with 2 different mesh sizes. 1. Maximum Temperature attained by the processor.2. Convergence Plots3. Heat Transfer coefficients at different areas4. Potential hotspots. Given: CAD file of graphics card where most of the components are provided which are…

Objective: To run the simulation for 3 different mesh sizes and explain about Atwood number and its significance. Given: Computational domain created using Spaceclaim is as below:Use water and Air fluid with default properties.                   Theory:       …

Objective: To perform a CHT analysis on an exhaust manifold. Show the velocity, temperature, and heat transfer coefficient plots  Given: CAD model of the exhaust port is shown below:   Theory:                                  …

Objective: To perform a grid independency test on the Ahmed body. Expected Results: 1. Velocity and pressure contours.2. The drag coefficient plot for a refined case.3. The vector plot clearly showing the wake region. 4. Perform the grid independence test and provide the values of drag and lift with each case. …

Objective: To perform steady-state simulations on the mixing tee geometry. In a table, compare the following values from the 3 cases.  Cell count Average outlet temperature Number of iterations for convergence Expected results: Velocity and temperature contour plots on the cut planes along and across the pipe. Velocity…

Objective: To compute the first, second and fourth-order approximations for a given value of x. For this program, you need to do the following.1. For a range of dx, plot the first order, second and fourth-order error.2. Make sure that you plot dx vs error in a way that makes sense.3. Explain the results in the space provided.…

Objective: To run simulations for two types of pistons and characterize the emissions (Soot, Nox, and UHC)                 1. Omega piston / Re-entrant piston                 2. W-type piston / Open W piston To do:1. Create cut-plan…

Objective:  To apply Reynold\'s decomposition to the NS equations to get the RANS equations.                 1. Understanding of the terms Reynold\'s stress                 2. What is turbulent viscosity? How is it different…

Objective: To Setup a transient shock tube simulation.                1. To Plot the pressure and temperature history in the entire domain               2. Plot the cell count as a function of time. Given: Geometry of the shock tube is provided…

Objective: To simulate the flow through a solid pipe \"Conjugate Heat Transfer\" and understand super-cycling. 1. Run grid dependence test on 3 grids2. Show that the outlet temperature converges to a particular value3. Effect of supercycle stage interval4. How does the total simulation time compare against the baseline…

Objective:  To work on the literature review on shock flows and associated boundary conditions1. To do a literature review on Shock flow boundary conditions2. What is a shock wave?3. Effect of SGS parameter on shock location. In the Prandtl Meyer shock problem, look at the effect of SGS temperature value on cell count…

Objective: To Simulate (Transient state) flow of fluid over a throttle body in converge studio and post-process the results. 1. To Show the mesh (i.e surface with edges)2. To post-process the results and show pressure and velocity contour3. To Show the plots for pressure, velocity, mass flow rate and total cell count.4.…

Objective: To simulate (Steady state) Flow of fluid over a throttle body in converge studio and post-process the results. 1. Show pressure and velocity contours.2. Show the mesh (i.e surface with edges).3. Show the plots for pressure, velocity, mass flow rate and total cell count. Given: Geometry of Elbow structure with…

Objective: Simulate the flow over a backward-facing step.1. Compare Mesh (i.e. surface with edges) for all 3 base mesh sizes.2. Show velocity and pressure contours3. Show the plots of velocity, pressure, mass flow rate and total cell count for all the 3 base mesh sizes4. Explain where and why separation is taking place…

Objective: To setup up a channel flow tutorial that is provided by Convergent Science. To show for all 3 different meshes 1. Velocity and Pressure contour for all given mesh size.2. Surface with edges for all base mesh size.3. Plots for velocity, pressure, mass flow rate and total cell count for all 3 base mesh sizes.…

Objective: To make the simulation work with Symmetry Boundary Condition. Write a Matlab program that takes an angle as input and generates a blockMesh file for the given angle.Angles to test: 10,25,45. Theory: SymmetryPlane BC:The symmetry boundary condition defines a mirror face/surface. The symmetry condition should…

Objective: Simulation of flow through pipe.        You need to calculate the length of the pipe Calculate length of the pipe using the entry length formula for laminar flow through a pipe Show that entry length is sufficient to produce a fully developed flow. You will have to compare…

Objective: To describe the need for interpolation schemes and flux limiters in the Finite Volume Method. Finite Volume Method (FVM): The finite volume method (FVM) is a method for representing and evaluating PDE in the form of algebraic equations. Similar to the finite difference method or finite-element method, values…

Objective:  To use the icoFOAM solver to simulate the flow through a backward-facing step. To create multiple meshes and compare the results obtained. Desired output How does the velocity magnitude profile change as a function of the mesh grading factor? Use factors, 0.2, 0.5,0.8 Measure the velocity profile at 0.085…

Objective: To understand the linear system i.e. to determine the Eigen Value and Spectral Radius of the given system of equations. Also, solve them using iterative techniques available. Given: The system of linear equation is given as: We can write it in coefficient form as, where, Solution matrix can be written as …

In this challenge, we are going to derive the 4th order approximations of the second-order derivative by the following methods. The methods we are going to use are: 1. Central Difference 2. Skewed right-sided difference 3. Skewed left-sided difference First, we use here is 1. Central Difference: Numerical stencil we will…

Objective: To write a program that solves the ODE which represents the equation of motion of a simple pendulum with damping. Simulate the motion between 0-20 sec Theory: In Engineering, ODE is used to describe the transient behavior of a system.  A simple example is a pendulum. The way the pendulum moves…

Objective: To write code to solve the 1D supersonic nozzle flow equations using the Macormack Method. 1. Implement both conservative and non-conservative forms of the governing equations.2. Perform a grid dependence test.3. Write separate functions for conservative and non-conservative forms.4. Compare the normalized mass…

  Objective: To Solve the 2D heat conduction equation by using the point iterative techniques                  (Jacobi, Gauss-Seidel, SOR) Theory: A generalized form of the equation can be written as for 3D space: where, dT/dt- time derivative term       …