Derivation of 4th order approximation of 2nd order derivative  required number of nodes = order of approximation +order of derivative-1 required number of nodes= 4+2-1=5 1. Central Difference Scheme: (five nodes are i-2, i-1, i, i+1, i+2) `(del^2f)/(delx^2)=af(i-2)+bf(i-1)+cf(i)+df(i+1)+ef(i+2)`----------(1) now using…

Generalised 2-D heat conduction equation `(del^2T)/(delx^2)+(del^2T)/(dely^2)=1/alpha(delT)/(delt)` Discretised form `(T_(i+1,j)-2 T_(i,j)+ T_(i-1,j))/(Deltax^2) +(T_(i,j+1) -2 T_(i,j) +T_(i,j-1))/(Deltay^2)=1/alpha(T_(i,j)^(n+1)-T_(i,j)^n)/(Deltat)` Given boundary conditions are:  Top boundary, `T_T =600K` Bottom…

Main Code clc; close all; clear all %% Domain information (Reference:John D.Anderson) L=3; nx=31; x=linspace(0,L,nx)'; dx=x(2)-x(1); C=0.5; % Courant number nt=1400; gamma=1.4; A=1+2.2*(x-1.5).^2; [rho1,V1,T1,p1,M1,m1,rho_t1,V_t1,T_t1,p_t1,M_t1,m1_t1,residual1]=non_conservative(x,dx,A,C,nt,gamma); [rho2,V2,T2,p2,M2,m2,rho_t2,V_t2,p_t2,T_t2,M_t2,m_t2,residual2]=conservative(x,dx,A,C,nt,gamma);…

Finite Volume Method: it is a method of representing and evaluating the partial differential equation in the form of algebraic equations. by using the gauss divergence theorem, the volume integrals in a partial differential equation that contains the divergence of a vector field converts into a surface integral of a vector…

Aim:  set up steady-state simulations to compare the mixing effectiveness when hot inlet temperature is 360C & Cold inlet is at 190C.  Introduction:  Use the `k-epsi` and `k-omega`  SST model for the first case and based on your judgment use the more suitable model for further cases.…

Aim:  Simulate the flow over a cylinder and explain the phenomenon of Karman vortex street. Introduction:   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…

1. Background:  the movement of air over the roof of the car is separated at the end of the roof; a phenomenon is known as the wake. The wake is a low-pressure zone and its location is behind the car. The shape of the rear of the car is more important than the shape of the front because of the wake. Figure 1.1: Flow…

Introduction: Exhaust port:           The exhaust manifold is a key component of 4 stroke I.C. engine. the exhaust manifold is mounted on the cylinder head of the engine.  the exhaust manifold collects the exhaust gases from multiple cylinders into one pipe. at the exhaust stroke, the exhaust…

Rayleigh Taylor Instability: RT instability (after Lord Rayleigh and G. I. Taylor) is the instability of the interface between two immiscible fluids of different densities which occurs when lighter fluid is pushing the heavier fluid.  if `rho_1>rho_2` then it is a stable configuration if `rho_2>rho_1` then it is an unstable…

Aim: Plot the variation of mass fraction of species `CO_2, H_2O, CH_4, N_2, O_2, NOx` emissions and soot formation. Observe the effect of the addition of water content in fuel from 5% to 30% by mole. Introduction: What is Natural Gas :  it is also called fossil gas or sometimes just gas. it is a naturally occurring…

Aim: Perform steady-state conjugate heat transfer analysis on a model of a graphics card. Objectives: Run the simulation for velocity v=1 m/s, 3 m/s and 5 m/s Find maximum temperature and convective heat transfer coefficient attained by the processor achieve convergence identify potential hotspots on the model Introduction:…

Aim: Parametric study on Gate Valve. Objectives:  Obtain the mass flow rates at the outlet for each design point. Calculate the flow coefficient and flow factor for each opening and plot the graph Discuss the results of the mass flow rate and flow coefficient Introduction: it is also known as a sluice valve.…

Aim:-  To perform analysis on cyclone separator and calculate the separation efficiency and pressure drop.   Objective:- To write a few words about any four empirical models used to calculate the cyclone separator efficiency.  To perform an analysis on a given cyclone separator model by varying the…

`l_1`=length of link 1 `l_2`=length of link 2 `theta_1`=Angle made by link 1 with horizontal `theta_2`=Angle made by link 2 with horizontal `x_1=l_1costheta_1`,`y_1=l_1sintheta_1` `x_2=x_1+l_2costheta_2, y_2=y_1+l_2sintheta_2` MATLAB Code %% Programming of 2R Robotic Arm clear all close all clc %% Inputs % length of first…

  Let `theta`=angular displacement of the pendulum in a counterclockwise direction.  then after restoring torques will act on the pendulum to come back to its original position.   `Iddottheta`=Inertia torque in a clockwise direction where I=moment of inertia of mass m about a fixed point through which…

Rankine cycle: The ideal cycle for the vapour power cycle Many of the impracticalities associated with the Carnot cycle can be eliminated by superheating the steam in the boiler and condensing it completely in the condenser, as shown schematically on a T-s diagram. The cycle that results is the Rankine cycle, which is…

1. Geometry Figure: 2-D geometry of the convergent-divergent nozzle    2. Meshing Figure: Meshing    Figure: Named Selection   3. Setup   Figure: Solver   Figure: Turn on the Energy equation   Figure: Viscous model   Figure: Pressure Inlet boundary condition   Figure: Temperature…

1(a). Pitot and Pitot-Static Probes: Pitot probes (also called pitot tubes) and pitot-static probes, named after the French engineer Henri de Pitot (1695-1771), are widely used for flow speed measurement.  A pitot tube is just a tube with a pressure tap at the stagnation point that measures stagnation pressure, while…

literature review on Flow analysis around a golf ball Question: Why the surface of a golf ball is not smooth but rather there are a lot of dents? Answer: The reason is that those dents called dimples reduce air drag on a golf ball. Such a minuscule difference in the surface helps reduce air drag, and as a result, helps…

Introduction:  Stationary (or inertial) Reference Frame: Ansys Fluent solves the equation of the heat transfer and fluid flow, by default, in a stationary reference frame. However, there are many problems where it is advantageous to solve equations in a moving(non-inertial) reference frame. such problem typically…

Aim:  Simulate the motion of blades in a generic turbomachinery component using an unsteady approach Step1: Reading multiple mesh files:  There may be some cases in which we will need to read multiple mesh files (subdomains) to form our computational domain. Three ways of reading multiple mesh files in Ansys…

Aim: Describe Ahmed's body and its importance. Setup the domain and set up assuming the body is travelling at 110 kmph Run the setup till convergence and plot for static pressure and coefficient of drag and lift to check for convergence Turn on Broadband- modelling and detail the acoustic field study over Ahmed's body.…

Introduction: Before understanding the SCRAMJET engine, first, need to understand the TURBOJET engine and RAMJET engine.   TURBOJET Engine: The turbojet is an airbreathing jet engine typically used in aircraft. It consists of a gas turbine and a propelling nozzle. The gas turbine has an air inlet…

Aim:  setup the domain for analysis of flow over an airfoil at the subsonic and supersonic regimes.  airfoil will be analysed at `5^o, 10^o and 15^o` angles of attack and compare the lift and drag coefficient in all cases.  Introduction:   The wings of birds were the original inspiration for…

  What is a Pressure Safety Valve (PSV): The primary purpose of PSV is the protection of life, property and the surrounding(environment). It will start working during overpressure events in pressurised vessels or equipment.  Reason for excess pressure in the system: Outlet is blocked Control valve failure/abnormal…

Aim:  For the given model, check for the geometrical errors to make appropriate volumes. Create and assign PIDs Perform surface mesh with the given target lengths as per PIDs Blade stage-1 = 1 mm Blade stage-2 = 1 mm Impeller = 2 mm Shaft rotor = 1 mm Turbo casing = 5 mm Compressor casing = 5 mm Inlet casing cover…

Aim:  For the given model, check and solve all geometrical errors on half portion and Assign appropriate PIDs. Perform meshing with the given Target length and element Quality criteria. After meshing the half model, Do symmetry to the other side. Target lengths for the different parts of a model are as follow: Body…

Aim: For the given models, check for the geometrical errors and delete surfaces which are unwanted for the Surface wrap After clearing geometry, Merge all 3 models and perform surface wrap. Introduction: Surface wrapping: surface wrapping is a meshing technique that should be used when the input data are either too…

Aim:  CFD Meshing for Tesla Cyber Truck Objectives:  check and solve all geometrical errors Assign appropriate PIDs Perform meshing with the suitable Target length and element Quality criteria Introduction of ANSA 1. What is ANSA? ANSA is a preprocessing Computer Aided Engineering (CAE) tool used in Finite Element Analysis…