computational aerodynamics laboratory manual …

COMPUTATIONAL AERODYNAMICS

LABORATORY MANUAL

B.TECH

(IV YEAR – I SEM)

(2016-17)

Prepared by:

Mr. J. Sandeep, Assistant Professor

Mrs. D. Smitha, Associate Professor

Department of Aeronautical Engineering

MALLA REDDY COLLEGE

OF ENGINEERING & TECHNOLOGY (Autonomous Institution – UGC, Govt. of India)

Recognized under 2(f) and 12 (B) of UGC ACT 1956

Affiliated to JNTUH, Hyderabad, Approved by AICTE - Accredited by NBA & NAAC – A Grade - ISO 9001:2015 Certified)

Maisammaguda, Dhulapally (Post Via. Hakimpet), Secunderabad – 500100, Telangana State, India.

CA LAB MANUAL Dept of ANE, MRCET

DEPARTMENT OF AERONAUTICAL ENGINEERING

VISION

Department of Aeronautical Engineering aims to be indispensable source in Aeronautical

Engineering which has a zeal to provide the value driven platform for the students to acquire

knowledge and empower themselves to shoulder higher responsibility in building a strong nation.

MISSION

a) The primary mission of the department is to promote engineering education and research.

(b) To strive consistently to provide quality education, keeping in pace with time and technology.

(c) Department passions to integrate the intellectual, spiritual, ethical and social development of the

students for shaping them into dynamic engineers.


PROGRAMME EDUCATIONAL OBJECTIVES (PEO’S)

PEO1: PROFESSIONALISM & CITIZENSHIP

To create and sustain a community of learning in which students acquire knowledge and learn to

apply it professionally with due consideration for ethical, ecological and economic issues.

PEO2: TECHNICAL ACCOMPLISHMENTS

To provide knowledge based services to satisfy the needs of society and the industry by

providing hands on experience in various technologies in core field.

PEO3: INVENTION, INNOVATION AND CREATIVITY

To make the students to design, experiment, analyze, interpret in the core field with the help of

other multi disciplinary concepts wherever applicable.

PEO4: PROFESSIONAL DEVELOPMENT

To educate the students to disseminate research findings with good soft skills and become a

successful entrepreneur.

PEO5: HUMAN RESOURCE DEVELOPMENT

To graduate the students in building national capabilities in technology, education and research.


PROGRAM SPECIFIC OBJECTIVES (PSO’s)

1. To mould students to become a professional with all necessary skills, personality and sound

knowledge in basic and advance technological areas.

2. To promote understanding of concepts and develop ability in design manufacture and

maintenance of aircraft, aerospace vehicles and associated equipment and develop application

capability of the concepts sciences to engineering design and processes.

3. Understanding the current scenario in the field of aeronautics and acquire ability to apply

knowledge of engineering, science and mathematics to design and conduct experiments in the

field of Aeronautical Engineering.

4. To develop leadership skills in our students necessary to shape the social, intellectual, business

and technical worlds.


PROGRAM OBJECTIVES (PO’S)

Engineering Graduates will be able to:

1. Engineering knowledge: Apply the knowledge of mathematics, science, engineering

fundamentals, and an engineering specialization to the solution of complex engineering

problems.

2. Problem analysis: Identify, formulate, review research literature, and analyze complex

engineering problems reaching substantiated conclusions using first principles of

mathematics, natural sciences, and engineering sciences.

3. Design / development of solutions: Design solutions for complex engineering problems

and design system components or processes that meet the specified needs with

appropriate consideration for the public health and safety, and the cultural, societal, and

environmental considerations.

4. Conduct investigations of complex problems: Use research-based knowledge and

research methods including design of experiments, analysis and interpretation of data,

and synthesis of the information to provide valid conclusions.

5. Modern tool usage: Create, select, and apply appropriate techniques, resources, and

modern engineering and IT tools including prediction and modeling to complex

engineering activities with an understanding of the limitations.

6. The engineer and society: Apply reasoning informed by the contextual knowledge to

assess societal, health, safety, legal and cultural issues and the consequent responsibilities

relevant to the professional engineering practice.

7. Environment and sustainability: Understand the impact of the professional engineering

solutions in societal and environmental contexts, and demonstrate the knowledge of, and

need for sustainable development.

8. Ethics: Apply ethical principles and commit to professional ethics and responsibilities

and norms of the engineering practice.

9. Individual and team work: Function effectively as an individual, and as a member or

leader in diverse teams, and in multidisciplinary settings.

10. Communication: Communicate effectively on complex engineering activities with the

engineering community and with society at large, such as, being able to comprehend and

write effective reports and design documentation, make effective presentations, and give

and receive clear instructions.

11. Project management and finance: Demonstrate knowledge and understanding of the

engineering and management principles and apply these to one’s own work, as a member

and leader in a team, to manage projects and in multi disciplinary environments.

12. Life- long learning: Recognize the need for, and have the preparation and ability to

engage in independent and life-long learning in the broadest context of technological

change.


JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

IV Year B. Tech. A. E – I Sem

L T/P/D C

- -/3/- 2

(A72186)COMPUTATIONAL AERODYNAMICS LAB

LIST OF EXPERIMENT:

1. Introduction to any one of the suitable software employed in modeling and simulation of

aerodynamic problems.

2,3. Solution for the following equations using finite difference method(code development).

i) One dimensional wave equations using explicit method of lax

ii) One dimensional heat conduction equation using explicit method

4,5. Generation of the following grids(code development).

i) Algebraic Grid

iii) Elliptic Grids.

6,7,8,9,10. Numerical simulation of the following flow problems using commercial software

packages:

i) Flow over an airfoil.

ii) Supersonic flow over a wedge.

iii) Flat plate boundary layer.

iv) Laminar flow through pipe.

v) Flow past a cylinder.

Suggested software:

1. ANSYS FLUENT and CFX

2. MATLAB


CONTENTS

S.No Experiment Name Pg.No

1 Introduction to Modeling and simulation software to aerodynamicproblems 1

2 Solution for the one dimensional wave equations using explicit method of lax

using finite difference method (code development)

13

3 Solution for the one dimensional heat conduction equation using explicit

method using finite difference method (code development)

16

4 Generation of the Algebraic Grid (code development) 19

5 Generation of the Elliptic Grids (code development) 22

6 Introduction to ANSYS Modeling and simulation software to aerodynamicproblems Numerical simulation of Flow over an airfoil using commercial software

Packages

28

7 Numerical simulation of Supersonic flow over a wedge using commercial

software packages

39

8 Numerical simulation of Flat plate boundary layer using commercial software packages

43

9 Numerical simulation of Laminar flow through pipe using commercial

software packages

46

10 Numerical simulation of Flow past cylinder using commercial software

packages

51

11 Viva Questions 55


CODE OF CONDUCT FOR THE LABORATORIES

All students must observe the Dress Code while in the laboratory.

Sandals or open-toed shoes are NOT allowed.

Foods, drinks and smoking are NOT allowed.

All bags must be left at the indicated place.

The lab timetable must be strictly followed.

Be PUNCTUAL for your laboratory session.

Program must be executed within the given time.

Noise must be kept to a minimum.

Workspace must be kept clean and tidy at all time.

Handle the systems and interfacing kits with care.

All students are liable for any damage to the accessories due to their own negligence.

All interfacing kits connecting cables must be RETURNED if you taken from the lab supervisor.

Students are strictly PROHIBITED from taking out any items from the laboratory.

Students are NOT allowed to work alone in the laboratory without the Lab Supervisor

USB Ports have been disabled if you want to use USB drive consult lab supervisor.

Report immediately to the Lab Supervisor if any malfunction of the accessories, is there.

Before leaving the lab

Place the chairs properly.

Turn off the system properly

Turn off the monitor.

Please check the laboratory notice board regularly for updates.

1. INTRODUCTION TO MODELING AND SIMULATION

SOFTWARE TO AERODYNAMICPROBLEMS

A model is a mathematical object that has the ability to predict the behavior of a real system

under a set of defined operating conditions and simplifying assumptions

The term modeling refers to the development of a mathematical representation of a physical

situation

WHAT IS MODELING?

• Modeling is the process of producing a model.

• A model is a representation of the construction and working of some system of

interest.

• A model is similar to but simpler than the system it represents.

• One purpose of a model is to enable the analyst to predict the effect of changes to the

system. Generally, a model intended for a simulation study is a mathematical model

developed with the help of simulation software.

• Mathematical model classifications include

• Deterministic (input and output variables are fixed values) or Stochastic (at least one of the

input or output variables is probabilistic);

• Static (time is not taken into account) or

• Dynamic (time-varying interactions among variables are taken into account).

• Typically, simulation models are stochastic and dynamic.

Simulation is the process of exercising a model for a particular instantiation of the system

and specific set of inputs in order to predict the system response.

simulation refers to the procedure of solving the equations that resulted from model

development

WHAT IS SIMULATION?

• A simulation of a system is the operation of a model of the system.

• The operation of the model can be studied, and hence, properties concerning the

behavior of the actual system or its subsystem can be inferred.

• In its broadest sense, simulation is a tool to evaluate the performance of a system,

existing or proposed, under different configurations of interest and over long periods

of real time.

• Simulation is used

• before an existing system is altered or a new system built,

• to reduce the chances of failure to meet specifications,

• to eliminate unforeseen bottlenecks,

• to prevent under or over-utilization of resources,

• to optimize system performance.

How to select the best simulation software for an application arises?

Metrics for evaluation include

Dept of ANE, MRCET CA Lab Manual

1

• Modeling flexibility

• Ease of use

• Modeling structure (hierarchical v/s flat; object-oriented v/s nested)

• Code reusability

• Graphic user interface

• Animation, dynamic business graphics, hardware and software requirements

• Statistical capabilities

• Output reports and graphical plots

• Customer support and documentation

• Mathematical modeling - Aerospace Applications

• Using basic equations from dynamics, mathematical equations are written that

describe how the vehicle will move in response to forces that are applied to the

vehicle. For example, it is pretty easy to describe how a rocket will accelerate when a

constant thrust is provided by the rocket's engine.

• Another type of modeling problem would be to understand and predict, in a

mathematical equation, how an aircraft will respond to hitting an updraft in the

atmosphere, or how the aircraft will respond to the deflection of various control

surfaces at different airspeeds.

• An aerodynamic subsystem model describes how the vehicle will respond to forces

caused by motion of the vehicle through the atmosphere, and predicts the effects of

each different control surface (such as the flaps, rudders, ailerons, etc.) upon the

motion of the vehicle.

• A propulsion subsystem model describes how any motors or engines will behave and

what forces will act on the vehicle to which they are attached.

• A landing gear subsystem model is required when the vehicle is in contact with the

ground in order to model how the ground reaction forces are created and how they

affect the motion of the vehicle.

• An inertial properties subsystem model provides details about how the mass and

inertia of the vehicle might change with time.

• any electrical, mechanical, or electronic system that assists the pilot in moving the

control surfaces has to be described mathematically

The steps involved in developing a simulation model, designing a simulation experiment, and

performing simulation analysis are:

Step 1. Identify the problem.

Step 2. Formulate the problem.

Step 3. Collect and process real system data.

Step 4. Formulate and develop a model.

Step 5. Validate the model.

Step 6. Document model for future use.

Step 7. Select appropriate experimental design.

Step 8. Establish experimental conditions for runs.

Step 9. Perform simulation runs.

Step 10. Interpret and present results.

Step 11. Recommend further course of action.


2

MATLAB (matrix laboratory) is a multi-paradigm numerical computing environment and fourth-

generation programming language. Developed by MathWorks, MATLAB Allows matrix manipulations,

plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing

with programs written in other languages, including C, C++, Java, Fortran and Python.

Although MATLAB is intended primarily for numerical computing, an optional toolbox uses

the MuPAD symbolic engine, allowing access to symbolic computing capabilities. An additional

package, Simulink, adds graphical multi-domain simulation and model-based design for

dynamic and embedded systems.

Syntax

The MATLAB application is built around the MATLAB scripting language. Common usage of the

MATLAB application involves using the Command Window as an interactive mathematical shell or

executing text files containing MATLAB code.

Variables

Vectors and matrices

A simple array is defined using the colon syntax: init : increment : terminator. For instance:

>> array = 1:2:9

3

>> x = 17

x =

17

>> x = 'hat'

x =

hat

>> y = x + 0

y =

104 97 116

>> x = [3*4, pi/2]

x =

12.0000 1.5708

>> y = 3*sin(x)

y =

-1.6097 3.0000

Variables are defined using the assignment operator, = . MATLAB is a weakly typed programming

language because types are implicitly converted. It is an inferred typed language because variables can be

assigned without declaring their type, except if they are to be treated as symbolic objects,[9] and that their

type can change. Values can come from constants, from computation involving values of other variables,

or from the output of a function. For example:


3

https://en.wikipedia.org/wiki/Multi-paradigm_programming_language

https://en.wikipedia.org/wiki/Numerical_analysis

https://en.wikipedia.org/wiki/Fourth-generation_programming_language

https://en.wikipedia.org/wiki/Fourth-generation_programming_language

https://en.wikipedia.org/wiki/MathWorks

https://en.wikipedia.org/wiki/Matrix_/(mathematics/)

https://en.wikipedia.org/wiki/Function_/(mathematics/)

https://en.wikipedia.org/wiki/Algorithm

https://en.wikipedia.org/wiki/User_interface

https://en.wikipedia.org/wiki/C_/(programming_language/)

https://en.wikipedia.org/wiki/C%2B%2B

https://en.wikipedia.org/wiki/Java_/(programming_language/)

https://en.wikipedia.org/wiki/Fortran

https://en.wikipedia.org/wiki/Python_/(programming_language/)

https://en.wikipedia.org/wiki/MuPAD

https://en.wikipedia.org/wiki/Computer_algebra_system

https://en.wikipedia.org/wiki/Symbolic_computing

https://en.wikipedia.org/wiki/Simulink

https://en.wikipedia.org/wiki/Model-based_design

https://en.wikipedia.org/wiki/Dynamical_system

https://en.wikipedia.org/wiki/Embedded_system

https://en.wikipedia.org/wiki/Command_line_interface

https://en.wikipedia.org/wiki/Strong_and_weak_typing

https://en.wikipedia.org/wiki/MATLAB#cite_note-9

https://en.wikipedia.org/wiki/Constant_/(computer_science/)

defines a variable named (or assigns a new value to an existing variable with the name array )

which is an array consisting of the values 1, 3, 5, 7, and 9. That is, the array starts at 1 (the init value),

increments with each step from the previous value by 2 (the increment value), and stops once it reaches

(or to avoid exceeding) 9 (the terminator value).

the increment value can actually be left out of this syntax (along with one of the colons), to use a default

value of 1.

assigns to the variable named

used as the incrementer.

an array with the values 1, 2, 3, 4, and 5, since the default value of 1 is

Indexing is one-based,[10] which is the usual convention for matrices in mathematics, although not for

some programming languages such as C, C++, and Java.

Matrices can be defined by separating the elements of a row with blank space or comma and using a

semicolon to terminate each row. The list of elements should be surrounded by square brackets: [].

Parentheses: () are used to access elements and sub arrays (they are also used to denote a function

argument list).

Sets of indices can be specified by expressions such as "2:4", which evaluates to [2, 3, 4].

>> A = [16 3 2 13; 5 10 11 8; 9 6 7 12; 4 15 14 1]

A =

16 3 2 13

5 10 11 8

9 6 7 12

4 15 14 1

>> A(2,3)

ans =

11

>> ari = 1:5

ari =

1 2 3 4 5

>> array = 1:3:9

array =

1 4 7

array =

1 3 5 7 9

array

ari


4

https://en.wikipedia.org/wiki/One-based_indexing


https://en.wikipedia.org/wiki/Matrix_/(mathematics/)

CA LAB MANUAL DEPT OF ANE, MRCET

A square identity matrix of size n can be generated using the function eye, and matrices of any size with zeros or ones can be generated with the functions zeros and ones, respectively.

Most MATLAB functions can accept matrices and will apply themselves to each element. For

example, will multiply every element in "J" by 2, and then reduce each element modulo

"n". MATLAB does include standard "for" and "while" loops, but (as in other similar applications such

as R), using the vectorized notation often produces code that is faster to execute. This code, excerpted

from the function magic.m, creates a magic square M for odd values of n (MATLAB

function is used here to generate square matrices I and J containing 1:n).

Structures

MATLAB has structure data types.[11] Since all variables in MATLAB are arrays, a more adequate name

is "structure array", where each element of the array has the same field names. In addition, MATLAB

supports dynamic field names (field look-ups by name, field manipulations, etc.). Unfortunately,

MATLAB JIT does not support MATLAB structures, therefore just a simple bundling of various

variables into a structure will come at a cost.

Functions

When creating a MATLAB function, the name of the file should match the name of the first function in

the file. Valid function names begin with an alphabetic character, and can contain letters, numbers, or

underscores.

Function handles

MATLAB supports elements of lambda calculus by introducing function handles, or function references,

which are implemented either in .m files or anonymous/nested functions.

[J,I] = meshgrid(1:n);

A = mod(I + J - (n + 3) / 2, n);

B = mod(I + 2 * J - 2, n);

M = n * A + B + 1;

>> eye(3,3)

ans =

1 0 0

0 1 0

0 0 1

>> zeros(2,3)

ans =

0 0 0

0 0 0

>> ones(2,3)

ans =

1 1 1

1 1 1

mod(2*J,n)

meshgrid


5

https://en.wikipedia.org/wiki/Identity_matrix

https://en.wikipedia.org/wiki/R_/(programming_language/)

https://en.wikipedia.org/wiki/Array_programming

https://en.wikipedia.org/wiki/Magic_square


https://en.wikipedia.org/wiki/Lambda_calculus

CA LAB MANUAL DEPT OF ANE, MRCET

Classes and Object-Oriented Programming

MATLAB's support for object-oriented programming includes classes, inheritance, virtual dispatch,

packages, pass-by-value semantics, and pass-by-reference semantics. However, the syntax and calling

conventions are significantly different from other languages. MATLAB has value classes and reference

classes, depending on whether the class has handle as a super-class (for reference classes) or not (for

value classes).

Method call behavior is different between value and reference classes. For example, a call to a method

can alter any member of object only if object is an instance of a reference class.

An example of a simple class is provided below.

MATLAB supports developing applications with graphical user interface features. MATLAB includes

GUIDE (GUI development environment) for graphically designing GUIs. It also has tightly integrated

graph-plotting features. For example the function plot can be used to produce a graph from two

vectors x and y. The code:

produces the following figure of the sine function:

x = 0:pi/100:2*pi;

y = sin(x);

plot(x,y)

classdef hello

methods

function greet(this)

disp('Hello!')

end

end

end

>> x = hello;

>> x.greet();

Hello!

When put into a file named hello.m, this can be executed with the following commands:

Graphics and graphical user interface programming

object.method();


6

https://en.wikipedia.org/wiki/Object-oriented_programming

https://en.wikipedia.org/wiki/Graphical_user_interface

https://en.wikipedia.org/wiki/Sine_wave

7

DEPT OF ANE, MRCET CA LAB MANUAL

A MATLAB program can produce three-dimensional graphics using the functions surf, plot3 or mesh.

This code produces a surface 3D plot of the two-dimensional unnormalized sinc function:

[X,Y] = meshgrid(-10:0.25:10,-10:0.25:10);

f = sinc(sqrt((X/pi).^2+(Y/pi).^2));

mesh(X,Y,f);

axis([-10 10 -10 10 -0.3 1])

xlabel('{\bfx}')

ylabel('{\bfy}')

zlabel('{\bfsinc} ({\bfR})')

hidden off

[X,Y] = meshgrid(-10:0.25:10,-10:0.25:10);

f = sinc(sqrt((X/pi).^2+(Y/pi).^2));

surf(X,Y,f);

axis([-10 10 -10 10 -0.3 1])

xlabel('{\bfx}')

ylabel('{\bfy}')

zlabel('{\bfsinc} ({\bfR})')


7

https://en.wikipedia.org/wiki/Sinc_function

'if' statements, 'for' and 'while' Loops

‘if’ statements

Purpose: Tests an expression and only executes the code if the expression is true.

Format:

if expression

statement(s) to be executed (know as the body of the loop)

end

Rules:

The variables in the expression to be tested must have values assigned prior to entering the IF statement.

The block of code will only execute if the expression is true. If the expression is false, then the code is

ignored.

Values assigned to the variables used in the expression may be changed in the block of code inside the IF

statement.

Examples:

x = 100;

y = -10;

if x < 50 %test to see if x is less than 50

z = x – y^2;

A = x + 12.5*y + z^3;

end

% won’t run because x is not less than 50

DEMO: Run a program using an IF statement (enter the following in an m-file):

x = input(‘Enter x’) % prompt to enter a value for x

if x < 4

disp (‘x is less than 4’) end


8

Enter several values of x, both greater than and less than 4 to see what happens. What do you expect if

you entered 3? What about 10?

'for' loops

Purpose: To repeat a statement or a group of statements for a fixed number of times.

Format:

for variable = expression

statement(s) to be executed (know as the body of the loop)

end

Rules:

FOR loops must end with the END statement (lower case).

The values for the loop variable are controlled by the expression

The first time through the loop, the variable is assigned the first value in the expression. For the second

time through, MATLAB automatically assigns to the variable the second value in the expression. This

continues for each value in the expression. The loop terminates after the body of the loop has been

executed with the loop variable assigned to each value in the expression.

The body of the loop is executed many times, but the loop is only executed once for each value in the

expression.

The expression in a FOR loop is an array of values. The number of times a loop executes equals the

number of values in the expression array.

After the loop is finished executing, the loop variable still exists in memory and its value is the last value

used inside the loop.

Any name can be used for a loop variable.

o If the name of the loop variable was already used in the program prior to execution of the loop, old values

of the variable are erased and the values of the variable are controlled by the loop.

o i, j, and k are common loop variables; they should not be used if working with complex numbers.

Loops can be nested.

Examples: Sequential numbers

for i=1:3 %executes three times

x=i^2

end

x =

1

x =

4

x =

9

Non-sequential numbers

for i=5:10:35 %executes four times

i

end

i =

5

i =

15

i =

25

i =


9

35

Nested (FOR loop inside a FOR loop)

for i=1:3 %executes three times

i

for j = 10:10:30

j

end

end

i =

1

j =

10

j =

20

j =

30

i =

2

j =

10

j =

20

j =

30

i =

3

j =

10

j =

20

j =

30

DEMO: Write a program using a FOR loop:

Variables: X, Y and loop variable i

Initialize X = 5 outside the loop

Loop variable, i, start = 0, end = 150, increment = 10

In the loop:

o Calculate Y = X*i

o Display i, X and Y to the screen using the command:

sprintf(‘Inside the loop: i = %3.0f X = %3.0f Y = %8.2f \n’,i,X,Y)

After the loop, write i, X, Y to the screen with the command:

sprintf(‘After the loop: i = %3.0f X = %3.0f Y = %8.2f \n’,i,X,Y)

Lessons learned:

o The FOR loop stops after executing with i=150

o The last values of i, X, Y inside the loop are the same as the values after completion of the FOR loop

'while' loops Purpose:To execute a statement, or a group of statements, for an indefinite number of times until the


10

condition specified by while is no longer satisfied.

Format:

while expression is true

statement(s) to be executed (known as the body of the loop)

end

Rules:

Must have a variable defined BEFORE the ‘while’ loop, so you can use it to enter the loop. The variable in the while statement must change INSIDE the while loop, or you will never exit the loop.

After the loop is finished executing, the loop variable(s) still exist in memory and its value is the last value

the variable had in the while loop.

Examples: Basic Execution

x = 0;

while x <= 100

x = x+30

end

% The while loop is executed 4 times.

% The values are:

x = 30

x = 60

x = 90

x = 120

% When x = 120, the test (x<=100) failed, so the loop was exited.

As a counter

x = 10;

y = 20;

i = 1; %initialize the counter

while(i<= 50)

x=x+(y^2) %calculate x

i=i+1 %increment the counter

end

%This loop will execute exactly 50 times.

-OR-

x = 10;

y = 20;

i = 0; %initialize the counter; starting with %i=0

while(i < 50) %test for i<50

x=x+(y^2) %calculate x

i=i+1 %increment the counter

end

%This loop will execute exactly 50 times.

DEMO: Write a program using a WHILE loop:

• Variables: X, Y and loop variable j


11

• Initialize X = 5 outside the loop

• Loop variable, j, start = 0, exit loop when j = 10

• In the loop:

o Calculate X = X*j

o Display j, and X to the screen using the command:

sprintf(‘Inside the loop: j = %3.0f X = %3.0f Y = %8.2f \n’,j,X,Y)

• After the loop, write j and x to the screen with the command:

sprintf(‘After the loop: j = %3.0f X = %3.0f Y = %8.2f \n’,j,X,Y)

Lessons learned:

o The 'while' loop stops after j = 10

o The last values of j and X inside the loop are the same as the values after completion of the ‘while' loop


12

2. SOLUTION FOR THE ONE DIMENSIONAL WAVE EQUATION

USING EXPLICIT METHOD OF LAX (CODE DEVELOPMENT).

The one dimensional scalar wave equation is given as

This equation represents a linear advection process with wave speed c = constant, which is

the speed of the travelling wave or the speed of propagation. u(x,t) is the signal or wave

information. The wave propagates at constant speed to the right if c > 0 and to the left if c <

1. The spatial domain can vary from -∞ to ∞. Suppose the initial conditions are

where is any function. The exact solution to the wave equation then is

is called the wave shape of wave form. Travelling or propagation here means that the

shape of the signal function with respect to x stays constant, however the function is

translated left or right with time at the speed c.

Numerical Solution

Method of discretization – finite difference form

Replace the spatial partial derivative with a central difference expression

Where n is the temporal index and j is the spatial index.

Replace the time derivative with a forward difference formula

We then have

Now let us replace by an average value between grid points j+1 and j-1 as

Substituting this in equation (1) we get the explicit method of Lax for the 1D scalar wave

equations as,


13

Test Case for the numerical solution Solve the one dimensional wave equation in the spatial domain of [0, 2*pi] with an initial step function condition given by

U0(x,0) = 1 for x pi-1 = 0 otherwise

Choose 100 grid points with and find the wave form at t = 0.2 s.

Matlab code for the one dimensional wave equation

% Solves the one dimensional scalar wave equation du/dt + du/dx = 0 [0,2*pi] % Using LAX METHOD clc; clear; t0 = 0; tf = 1; M = 100; % number of points in x direction

N = 100; % number of points in y direction

% define the mesh in space

dx = 2*pi/M;

x = 0:dx:2*pi;

% define the mesh in time

dt = (tf-t0)/N;

t = t0:dt:tf;

% calculate value for lamda

c = 1; lambda = c*dt/dx display('lambda should be less than 1 for stability:')

% choose the wave number of the initial data and give its decay rate

u0 = x<=(pi-1);

u = zeros(M+1,N+1);

u(:,1) = u0;

% Implement the time marching Lax scheme:

for n=1:N

for i=2:M

u(i,n+1) = (u(i+1,n)+u(i-1,n))/2-(lambda/2)*(u(i+1,n)-u(i-1,n));

end

end % Introduce exact values at the endpoints.

u(1,n+1)=1;

u(M+1,n+1)=0;

% plot the result in 21 intervals

for j=0:20

plot(x,u(:,1+5*j),'LineWidth',2); axis([0,2*pi,-0.5,1.5]); title('1D wave equation using explicit Lax Method','FontSize',12) xlabel('x');

ylabel('u'); pause(1) end %plot(x,u(:,101));


14

Results:

1.5

1D wave equation using explicit Lax Method

1

0.5

0

-0.5

0 1 2 3 4 5 6

x

u


15

3. SOLUTION FOR THE ONE DIMENSIONAL TRANSIENT HEAT

CONDUCTION EQUATION USING EXPLICIT METHOD (CODE

DEVELOPMENT)

The one dimensional transient (unsteady) heat conduction equation is given as

Where is the thermal diffusivity

This equation represents the conduction of heat energy in time and space. Transient nature of

this equation is represented in the dependence of temperature with time as opposed to a

steady state condition.

Numerical Solution

Method of discretization – finite difference form

Replace the time derivative with a forward difference expression

Where n is the temporal index and j is the spatial index.

Replace the second order spatial derivative on the RHS with a central difference formula

We then have

i.e. (2)

where � = � ∆�∆�2 Equation (2) is the final explicit update equation for the one dimensional transient heat conduction equation.

Test Case for the numerical solution

A country rock has a temperature of 300oC and the dike a width of 5m, with a magma

temperature of 1200oC. Total length of the rock formation is 100m. Initial conditions are

temperatures of 300oC and 1200

oC for the rock and dike respectively. Boundary conditions at

x = -L/2 and x = L/2 are at 300oC (see figure). Find the temperature distribution after 100

days. Use 200 grid points in the x direction with a 1 day time interval.

ROCK

300oC

DIKE

1200oC

ROCK

300oC

L


16

Matlab code for the one dimensional transient heat conduction equation

% Solves the 1D heat equation with an explicit finite difference scheme

clear all clc %Physical parameters L = 100; % Length of modeled domain [m]

Td = 1200; % Temperature of magma [C] Tr = 300; % Temperature of country rock [C] kappa = 1e-6; % Thermal diffusivity of rock [m2/s]

W = 5; % Width of dike [m]

day = 3600*24; % # seconds per day

dt = 1*day; % Timestep [s] % Numerical parameters nx = 200; % Number of gridpoints in x-direction

nt = 100; % Number of timesteps to compute

dx = L/(nx-1); % Spacing of grid

x = -L/2:dx:L/2;% Grid

% Setup initial temperature profile

T = ones(size(x))*Tr;

T(abs(x)<=W/2) = Td;

time = 0; for n=1:nt % Timestep loop % Compute new temperature

Tnew = zeros(1,nx); for i=2:nx-1 Tnew(i) = T(i) + (kappa*dt/(dx)^2)*(T(i+1)-(2*T(i))+T(i-1));

end

% Set boundary conditions

Tnew(1) = T(1); Tnew(nx) = T(nx); % Update temperature and time T =

Tnew;

time = time+dt;

end

% Plot solution plot(x,Tnew); xlabel('x [m]') ylabel('Temperature [ˆoC]') title(['Temperature evolution after ',num2str(time/day),' days'])

% draw the dike boundaries

x1 = -2.5;

x2 = 2.5; y = linspace(300,800); % Plot the dike boundaries

hold on

plot(x1,y, x2, y);


17

Results:

800

Temperature evolution after 100 days

750

700

650

600

550

500

450

400

350

300

-50 -40 -30 -20 -10 0 10 20 30 40 50

x [m]

Te

mpera

ture

[ˆoC]


18

4. GENERATION OF THE ALGEBRAIC GRIDS

Problem Generate an algebraic grid about the upper surface of the airfoil. Points are clustered in j

direction near the lower surface (using β=1.05 in algebraic grid). Make sure the number of

points in i and j are flexible.

Introduction, Theory, & Formulations

A key component of grid generation is the conversion from the physical domain to the

computational domain, in order to allow for equidistant grid lines in rectangular form. In

considering a simple two dimensional case, physical coordinates x and y must be converted

to computational coordinates ξ and η. These computational coordinates are furthermore

known via the rectangular grid relations. As a result, they must be converted back into

physical coordinates in order to be of use. For the particular case concerning an airfoil placed

on the x axis, the following relationships exist:

As can be seen, Eq. (1) simply states that the x coordinate is the ξ coordinate, as there exists

no irregularities to alter that axis. The precise relationship in Eq. (2) is due to a required

clustering near the bottom surface. Here, β represents the clustering parameter, which is

given, and H represents the total height along the y axis. However, this does not account for

the geometry of the airfoil, wherein its top surface coordinate is a function of the distance

along the x axis. The exact equation is:

Here, y represents the max height of the airfoil, which would thus be the correspond to y=0 in

Eq.(2). Height is determined by subtracting this value from maximum height. This allows a

total expression for the grid y coordinative can be obtained. Note that the x used in Eq. (3)

assumes 0 at the nose of the airfoil and 1 at the tail. The previous equations effectively define

all that is needed to generate an algebraic grid. However, this grid will simply be used as a

starting point for the generation of an elliptic grid. Thus, once x and y are obtained

algebraically, they will be set as initial conditions for the x and y values used in order to

perform iterations of the developed finite difference equations.


19

MATLAB code for Algebraic Grid Generation

%Algebraic Grid Generation

clear; clc; %Assign values for t and beta t=0.15;

beta=1.05; %Prompt user for number of grid points n=input('Enter the number of grid points in the i direction: '); m=input('Enter the

number of grid points in the j direction: ');

%Create zeroes matrix for surface plots

z=zeros(n,m);

%Assign lengths and values for eta and xi L=3;

eta=linspace(0,1,m);

xi=linspace(0,L,n);

%x is equal to xi X=xi;

%Find height ytop=2;

for i=1:n if

X(i) < 1

ybottom(i)=0;

elseif X(i) > 2

ybottom(i)=0;

else x2(i)=X(i)-1;

ybottom(i)=(t/.2)*(0.2969*x2(i)^.5-0.126*x2(i)-

0.3516*x2(i)^2+0.2843*x2(i)^3-0.1015*x2(i)^4); end

H(i)=ytop-ybottom(i);

end

%Loop to calculate coordinates zeta=beta+1;

gamma=beta-1;

alpha=zeta/gamma; for

i=1:n

for j=1:m chi=1-

eta(j);

y(i,j)=H(i)*(zeta-gamma*alpha^chi)/(alpha^chi+1)+ybottom(i); x(i,j)=X(i);

end

end

surface(x,y,z); xlabel ('x'); ylabel ('y'); title ('Algerbraic Grid');


20

Discussion of Results

Enter the number of grid points in the i direction: 50

Enter the number of grid points in the j direction: 50

Algerbraic Grid

2

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0 0 0.5 1 1.5 2 2.5 3

x

Figure shows the algebraic grid generation with the growth rate β=1.05 the grids are very fine

at y=0 and it gets coarser as the y increases.

The value of growth rate β can be varied and you can see the difference in the growth rate of

the grid.

y


21

5. GENERATION OF THE ELLIPTIC GRIDS

Problem Starting with an algebraic grid, generate an elliptic grid about the upper surface of the airfoil.

Points are clustered in j direction near the lower surface (using β=1.05 in algebraic grid).

Make sure the number of points in i and j are flexible.

Using a predetermined algebraic grid, an elliptic grid can be generated in order to fine tune

the results for airfoil flow. Coding an algebraic grid necessitates an accounting for the

geometry of the airfoil, as well as clustering via appropriate equations. Once these issues are

addressed, partial differential equations can be utilized in order to generate an elliptic grid.

Introduction, Theory, & Formulations A key component of grid generation is the conversion from the physical domain to the

computational domain, in order to allow for equidistant grid lines in rectangular form. In

considering a simple two dimensional case, physical coordinates x and y must be converted

to computational coordinates ξ and η. These computational coordinates are furthermore

known via the rectangular grid relations. As a result, they must be converted back into

physical coordinates in order to be of use. For the particular case concerning an airfoil placed

on the x axis, the following relationships exist:

As can be seen, Eq. (1) simply states that the x coordinate is the ξ coordinate, as there exists

no irregularities to alter that axis. The precise relationship in Eq. (2) is due to a required

clustering near the bottom surface. Here, β represents the clustering parameter, which is

given, and H represents the total height along the y axis. However, this does not account for

the geometry of the airfoil, wherein its top surface coordinate is a function of the distance

along the x axis. The exact equation is:

Here, y represents the max height of the airfoil, which would thus be the correspond to y=0 in

Eq.(2). Height is determined by subtracting this value from maximum height. This allows a

total expression for the grid y coordinative can be obtained. Note that the x used in Eq. (3)

assumes 0 at the nose of the airfoil and 1 at the tail. The previous equations effectively define

all that is needed to generate an algebraic grid. However, this grid will simply be used as a

starting point for the generation of an elliptic grid. Thus, once x and y are obtained

algebraically, they will be set as initial conditions for the x and y values used in order to

perform iterations of the developed finite difference equations.

Two elliptic partial differential equations must be solved in order to fully define the desired

grid. In doing this, boundary conditions are required. For this case, x and y values along the


22

edges of the defined physical domain will be left in place. These being predefined allows all

interior coordinates to be developed. The following system of elliptic partial differential

equations can be used to define the domain:

Here, the subscripts denote second order derivative of that variable. Notice that these

equations do not express x and y as dependent variables. Rather, they are treated as the

independent variables, requiring a transformation. When such a mathematical transformation

is preformed Eqs. (4) And (5) become, respectively:

Where,

The previously stated equations must all be expressed in terms of finite differences. Once this

is done, x and y at each grid point can be found through iterations. Expanding Equation (8)

through (10) explicitly in central space yields:


23

Here, the superscript, n, indexes the iteration, where n is the current iteration and n+1 is the

following iteration. These equations are written this way due to the fact that points above and

to the right of the point being evaluated are unknown, and, thus, old values must be used. The

same procedure of finite differencing can be applied to Eqs. (6) and (7). However, results

from these will be of the same form; that is, only the terms x and y will be different.

Considering the expansion of Eq. (6) yields:

This equation can then be explicitly solved for the value which is the coordinate of

interest.

Doing so yields:

Similarly,

Considering the expansion of Eq.(7) and solving it for value of :

This formula can then be implemented through coding in order to find all values of x. The

formulation is exactly the same for the y value. Through code, multiple iterations will occur

until convergence is reached; that is, the desired x values will be found once the difference

between and is below tolerance and the desired y values will be found once

the difference between and falls below said tolerance. These values, when

plotted, should produce an elliptic grid that can be utilized to determine flow within the

domain containing the airfoil.

Considering,


24

MATLAB code for Elliptic Grid Generation

%Elliptic Grid Generation clear; clc; %Assign values for t and beta t=0.15;

beta=1.05; %Prompt user for number of grid points n=input('Enter the number of grid points in the i direction: '); m=input('Enter the

number of grid points in the j direction: ');

%Create zeroes matrix for surface plots

z=zeros(n,m);

%Assign lengths and values for eta and xi L=3;

eta=linspace(0,1,m);

xi=linspace(0,L,n);

%x is equal to xi X=xi;

%Find height ytop=2;

for i=1:n if

X(i) < 1

ybottom(i)=0;

elseif X(i) > 2

ybottom(i)=0;

else x2(i)=X(i)-1;

ybottom(i)=(t/.2)*(0.2969*x2(i)^.5-0.126*x2(i)-

0.3516*x2(i)^2+0.2843*x2(i)^3-0.1015*x2(i)^4); end

H(i)=ytop-ybottom(i);

end

%Loop to calculate coordinates zeta=beta+1;

gamma=beta-1;

alpha=zeta/gamma; for

i=1:n

for j=1:m chi=1-

eta(j);

y(i,j)=H(i)*(zeta-gamma*alpha^chi)/(alpha^chi+1)+ybottom(i); x(i,j)=X(i);

end

end

%Elliptic initial conditions xold=x; yold=y; %Calculate computational step sizes

delta_eta=1/(m-1); delta_xi=L/(n-1); dx=1; %Conditions to start loop dy=1;

%Conditions to start loop

%Assign tolerance value

tol=.0001;


25

%Nested loop to determine elliptic grid xdiff=0;

ydiff=0;

count=0;

while dy > tol || dx > tol for

i=2:n-1

for j=2:m-1 a1=(xold(i,j+1)-x(i,j-1))/(2*delta_eta); a2=(yold(i,j+1)-y(i,j-1))/(2*delta_eta);

a=a1^2+a2^2; c1=(xold(i+1,j)-x(i-1,j))/(2*delta_xi); c2=(yold(i+1,j)-y(i-1,j))/(2*delta_xi);

c=c1^2+c2^2;

b=a1*c1+a2*c2;

alpha=a/delta_xi^2;

beta=-2*b/(4*delta_xi*delta_eta);

gamma=c/delta_eta^2;

theta=1/(2*alpha+2*gamma);

phi_1=beta*(xold(i+1,j+1)-xold(i+1,j-1)-xold(i-1,j+1)+x(i-1,j-1));

x(i,j)=theta*(alpha*(xold(i+1,j)+x(i-1,j))+gamma*(xold(i,j+1)+x(i,j-

1))+phi_1); xdiff=x(i,j)-xold(i,j)+xdiff; phi_2=beta*(yold(i+1,j+1)-yold(i+1,j-1)-yold(i-1,j+1)+y(i-1,j-1));

y(i,j)=theta*(alpha*(yold(i+1,j)+y(i-1,j))+gamma*(yold(i,j+1)+y(i,j- 1))+phi_2);

ydiff=y(i,j)-yold(i,j)+ydiff; end end dx=xdiff;

dy=ydiff;

xdiff=0; ydiff=0;

xold=x; yold=y;

count=count+1; end fprintf('The solution took %i iterations to converge. \n \n', count); surface(x,y,z); xlabel ('x'); ylabel ('y'); title ('Elliptic grid over an Airfoil');


26

Result and Discussion

In the plot of an Elliptical, the Grid lines have been smoothed out due to the elliptic

equations, eliminating extreme jaggedness resulting from the algebraic grid. This would

ensure a more accurate flow model.

Enter the number of grid points in the i direction: 50

Enter the number of grid points in the j direction: 50

The solution took 2434 iterations to converge.

2

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

Elliptic grid over an Airfoil

Overall, an elliptic grid was shown to provide desired results for discretization. It succeeded

in smoothing out otherwise rough edges created through algebraic grid generation. At the

same time, the algebraic grid provided a suitable starting point for the generation of the

elliptic grid.

0 0.5 1 1.5

x

2 2.5 3

y


27

INTRODUCTION TO ANSYS ANSYS ICEM CFD meshing software starts with advanced CAD/geometry readers and repair tools to

allow the user to quickly progress to a variety of geometry-tolerant meshers and produce high-quality

volume or surface meshes with minimal effort. Advanced mesh diagnostics, interactive and automated

mesh editing, output to a wide variety of computational fluid dynamics (CFD) and finite element analysis

(FEA) solvers and multiphysics post-processing tools make ANSYS ICEM CFD a complete meshing

solution. ANSYS endeavors to provide a variety of flexible tools that can take the model from any

geometry to any solver in one modern and fully scriptable environment.

Mesh from dirty CAD and/or faceted geometry such as STL

Efficiently mesh large, complex models

Hexa mesh (structured or unstructured) with advanced control

Extended mesh diagnostics and advanced interactive mesh editing

Output to a wide variety of CFD and FEA solvers as well as neutral formats

ANSYS ICEM CFD is a popular proprietary software package used for CAD and mesh generation. Some

open source software includes OpenFOAM, FeatFlow, Open FVM etc. Present discussion is applicable

to ANSYS ICEM CFD software.

It can create structured, unstructured, multi-block, and hybrid grids with different cell geometries.

GEOMETRY MODELLING

ANSYS ICEM CFD is meant to mesh a geometry already created using other dedicated CAD packages.

Therefore, the geometry modelling features are primarily meant to 'clean-up' an imported CAD model.

Nevertheless, there are some very powerful geometry creation, editing and repair (manual and

automated) tools available in ANSYS ICEM CFD which assist in arriving at the meshing stage quickly.

Unlike the concept of volume in tools like GAMBIT, ICEM CFD rather treats a collection of surfaces

which encompass a closed region as BODY. Therefore, the typical topological issues encountered in

GAMBIT (e.g. face cannot be deleted since it is referenced by higher topology) don't show up here. The

emphasis in ICEM CFD to create a mesh is to have a 'water-tight' geometry. It means if there is a source

of water inside a region, the water should be contained and not leak out of the BODY.


28

Apart from the regular points, curves, surface creation and editing tools, ANSYS ICEM CFD especially

has the capability to do BUILD TOPOLOGY which removes unwanted surfaces and then you can view

if there are any 'holes' in the region of interest for meshing. Existence of holes would mean that the

algorithm which generates the mesh would cause the mesh to 'leak out' of the domain. Holes are typically

identified through the colour of the curves. The following is the colour coding in ANSYS ICEM CFD,

after the BUILD TOPOLOGY option has been implemented:

YELLOW: curve attached to a single surface - possibly a hole exists. In some cases this might be

desirable for e.g., thin internal walls require at least one curve with single surface attached to it.

RED: curve shared by two surface - the usual case.

BLUE: curve shared by more than two surface.

Green: Unattached Curves - not attached to any surface

MESHING APPROACH AND MESH

There are often some misunderstandings regarding structured/unstructured mesh, meshing algorithm and

solver. A mesh may look like a structured mesh but may/may not have been created using a structured

algorithm based tool. For e.g., GAMBIT is an unstructured meshing tool. Therefore, even if it creates a

mesh that looks like a structured (single or multi-block) mesh through pain-staking efforts in geometry

decomposition, the algorithm employed was still an unstructured one. On top of it, most of the popular

CFD tools like, ANSYS FLUENT, ANSYS CFX, Star CCM+, OpenFOAM, etc. are unstructured solvers

which can only work on an unstructured mesh even if we provide it with a structured looking mesh

created using structured/unstructured algorithm based meshing tools. ANSYS ICEM CFD can generate

both structured and unstructured meshes using structured or unstructured algorithms which can be given

as inputs to structured as well as unstructured solvers, respectively.

Structured meshing strategy

While simple ducts can be modelled using a single block, majority of the geometries encountered in real

life have to be modelled using multi-block strategies if at all it is possible.

The following are the different multi-block strategies available which can be implemented using ANSYS

ICEM CFD.

O-grid

C-grid

Quarter O-grid

H-grid

Unstructured meshing strategy

Unlike the structured approach for meshing, the unstructured meshing algorithm is more or less an

optimization problem, wherein, it is required to fill-in a given space (with curvilinear boundaries) with

standard shapes (e.g., triangle, quadrilaterals - 2D; tetrahedrals, hexahedrals, polyhedrals, prisms,

pyramids - 3D) which have constraints on their size. The basic algorithms employed for doing

unstructured meshing are:

Octree (easiest from the user's perspective; robust but least control over the final cell count which is

usually the highest)


29

Advancing front (performs very smooth transition of the element sizes and may result in quite accurate

but high cell count)

Best practices

If using Octree -

Perform volume meshing

Improve the quality of the volume mesh using Edit Mesh options

Create prism layers for boundary layer near the walls

Improve the total mesh quality using Edit Mesh options

If using Delaunay or Advancing Front -

Perform surface meshing

Improve the quality of the surface mesh using Edit Mesh options

Perform volume meshing

Improve the quality of the volume mesh using Edit Mesh options

Create prism layers for boundary layer near the walls

Improve the total mesh quality using Edit Mesh options

basic viewport interaction

use the left mouse button and drag to rotate the view

use the middle mouse button to pan the view

importing data

CREATING A STRUCTURED GRID

The first thing to do when creating a structured grid is to create the geometry or a .tin file in ICEM. You

can do this by manually creating it in ICEM or importing data into ICEM, for example 3-dimensional

point data from a .txt file.

The tools available are specified under the geometry tab. There are quite a number of tools and they can

be quite useful. However, it is suggested that some planning is done before beginning to make a

geometry. There are tools specifically for curves.

curves can be split or joined to other curves.

Points can be created at cross-sections of curves.

Surfaces can be created from curves.

All of this gives extra flexibility in the methods of designing a grid.

Tip

A tip that is quite useful is the use of

the F9 key to "pause" the tool being

used so the grid can be moved or

zoomed in to.

Also, different parts of the grid can be saved under a part

name which can be switched off or on if you want certain things

to be invisible like points or curves or certain surfaces. You can

also copy an entire set of geometry by selecting the parts you

want and translating it to a specified point using the

Delaunay (better control over the final cell count but may have sudden jumps in the size of the elements) Dept of ANE, MRCET CA Lab Manual

30

'translation' tool. This is useful, especially when creating a symmetrical object such as a wing, where

the aerofoil can be copied to another location and then joined up to the original aerofoil with curves.

Once the geometry is created, the next step is to create the actual grid. Note that the tolerances of the

geometry plays an important role in the accuracy of the grid. So make sure that depending on what you

want, the tolerances are high enough. Using the blocking tab, a block can be created around the entire

geometry and then split up into sections. The mesh is created by specifying the distribution of points

along the edges of the blocks. Therefore the more blocks you have, the more flexibility you have in

changing the distribution of points along the edges. The edges and vertices of the blocks must be

assosciated with the geomery curves and points.

Once the blocks have been created and all the required points and curves assosciated, the number of

points and the distribution can be set along each edge. In somecases, you want the density of cells to be

high, for example at the boundary layer of an object, whereas to save time, you may want the cells

further away to be large. There are various types of distribution such as linear, geometrical and

exponential variation that can be used. The premesh tool can then be used to view the meshing. There is

also a quality check tool, where one can specify how you want to check the quality of the blocking. For

example, one can check the variation in volume size to see if it varies smoothly, or if there are any

negative volumes, which would suggest that the grid crosses into solid surfaces.

The blocking is saved as a .blk file. When all is done, the mesh can be made readable by a solver by

specifying what type of solver is to be used in the "output tab".

CREATING AN UNSTRUCTURED GRID

Once the curves and surfaces have been created, click the mesh tab -> surface mesh and define the mesh

density on the surfaces.


31

The surface menu is shown on the right, and to select surfaces, click the button next to it and start

selecting surfaces, using middle-click when done. Then select a mesh density (0.05 in this case, but will

vary with each case) and checkremesh selected surfaces if needed, and click ok.

Then, click volume mesh, and select the method (tetra for tetragonal unstructured meshes) to generate the

unstructured grid, press 'ok' and wait for the grid to be generated and review the result.

ANSYS computational fluid dynamics (CFD) simulation software allows you to predict, with

confidence, the impact of fluid flows on products — throughout design and manufacturing as

well as during end use. The software's unparalleled fluid flow analysis capabilities can be used

to design and optimize new equipment and to troubleshoot already existing installations.

Whatever phenomena you are studying — single- or multi-phase, isothermal or reacting,

compressible or not — ANSYS fluid dynamics solutions give you valuable insight into your

product's. ANSYS CFD analysis tools include the widely used and well-validated ANSYS

Fluent and ANSYS CFX, available separately or together in the ANSYS CFD bundle. Because

of solver robustness and speed, development team knowledge and experience, and advanced

modeling capabilities, ANSYS fluid dynamics solutions provide results you can trust. The

technology is highly scalable, providing efficient parallel calculations from a few to thousands

of processing cores. Combining Fluent or CFX with the full-featured ANSYS CFD-Post post-

processing tool allows you to perform advanced quantitative analysis or create high-quality

Visualizations and animations.

As a result of these tight connections, ANSYS CFX delivers benefits that include the ability TO:

Quickly prepare product/process geometry for flow analysis without tedious rework.

Avoid duplication through a common data model that is persistently shared across physics —

beyond basic fluid flow.

Easily define a series of parametric variations in geometry, mesh, physics and post-processing,

enabling automatic new CFD results for that series with a single mouse click

Improve product/process quality by increasing the understanding of variability and design

sensitivity.

Easily set up and perform multiphysics simulations


32

http://www.ansys.com/Products/Simulation%2BTechnology/Fluid%2BDynamics/Fluid%2BDynamics%2BProducts/ANSYS%2BFluent

http://www.ansys.com/Products/Simulation%2BTechnology/Fluid%2BDynamics/Fluid%2BDynamics%2BProducts/ANSYS%2BFluent

http://www.ansys.com/Products/Simulation%2BTechnology/Fluid%2BDynamics/Fluid%2BDynamics%2BProducts/ANSYS%2BCFX

http://www.ansys.com/Products/Simulation%2BTechnology/Fluid%2BDynamics/Results%2BAnalysis%2BProducts/ANSYS%2BCFD-Post

Numerical simulation of the following flow problems using commercial

software packages:

6. FLOW OVER AN AEROFOIL

AIM: To simulate flow over NACA 0012 airfoil

Problem description:

Consider air flowing over NACA 0012 airfoil. The free stream Mach number is 1.2.

Assume standard sea-level values for the free stream properties:

Pressure = 101,325 Pa

Density = 1.2250 kg/m3

Temperature = 288.16 K

Kinematic viscosity v = 1.4607e-5 m2/s

Steps Involved In ICEM

CFD: Creation of Geometry in ICEM CFD:

Importing the Aerofoil coordinates

File→Import Geometry→Formatted point data→Select the file of aerofoil

coordinates which is in DAT format→ok. Now the coordinates will be

displayed.

Geometry→Create/modify curve→From points→Select above points and

leave last 2 points→middle click

Similarly on bottom side

Join the end points of the curves


33

1) Creation of parts:

Parts in the tree→Right click→Create part→

Select Upper curve: Suction

Select Lower curve: Pressure

3rd

Line: TE

2) Creation of Domain:

Create points (-1,1),(-1,-1),(2,1),(2,-1)

Join these points

Create parts as Inlet, Outlet, Top & Bottom

Geometry→Create/Modify surface→Simple surface→Select all the lines of

domain→ok

Create the new part as: Surface

3) Saving the Geometry:

File→Change working directory→Choose the folder

File→Geometry→Save Geometry as→Give the name.

4) Creation of Blocking and Association:

Blocking→Create block→Initialize blocks→Type as:2D Planar→ok

Associate→Associate vertex to point→Select a vertex and a point→Apply→

Similarly associate remaining 3 vertices to points

Associate→Associate edge to curve→Select a edge and a curve →Apply→

Similarly associate remaining 3 edges to curves

Split block→Select the edges→Create the blocks as shown in figure

Split block→O grid →Select edges→Select last 2 edges in the middle

row→ok→Select blocks→Select last 2 blocks in the middle row→ok


34

Thus the O grid has been generated as shown in below fig.

AssociateAssociate vertex to pointSelect the vertex of the O grid and the

2nd

point on the upper curve(suction)ok

Similarly associate remaining 3 vertices of the O grid to the points on the

aerofoil as shown in the below fig.


35

Associate→Associate edge to curve→Select the 3 edges of block which is

inside of the aerofoil and select the suction & pressure curves→ok

Similarly associate the TE edge to TE curve.

Delete block→Select the block inside the aerofoil→ok

5) Generation of Mesh:

Pre-mesh parameters→Edge parameters→Switch ON the Copy Parameters→

Select the edges and give desired no. of nodes→ok

Switch ON Pre-mesh in the tree→click yes to compute the meshing

Pre-mesh→Right click→Convert to unstructured mesh

Now the required mesh has been generated as shown in below fig.

6) Saving the Project:

File→Save Project as→Give the name.

7) Writing output file:

Output→Select solver→Output solver as: Fluent_V6→Common Structural

solver as: ANSYS→ok

Write input→Click NO→Open the file→Click 2D→ok


36

Steps Involved in Fluent:

8) Importing the mesh file:

File→Read→mesh→Choose the output file written in ICEM CFD

Now the mesh has imported into the fluent solver.

9) Problem setup:

General→Type as: Pressure based

Models→Energy ON→Viscous-laminar

Materials→Air

Cell zone conditions→Type as: fluid→ok

Boundary conditions→Select inlet→Edit→Give velocity magnitude as:

400m/s.

Boundary conditions→Select outlet→Edit→Give gauge pressure as: 0 Pa

10) Solution:

Select the required monitors

Solution initialization→Compute from: inlet→Initialize

Run calculations→Enter the no. of iterations as: 1000→Calculate

11) Results:

Graphics and animations→select the required flow parameters in the

contours and vectors.

The results are shown below as:


37


38

7. SUPERSONIC FLOW OVER A WEDGE

Problem description:

Consider air flowing over wedge. The free stream Mach number is 3 and the angle of

attack is 5°. Assume standard sea-level values for the free stream properties:

Pressure =101,325Pa

Density =1.2250kg/m3

Temperature =288.16K

Kinematic viscosity v = 1.4607e-5 m2/s

Steps Involved In ICEM CFD:

12) Creation of Geometry in ICEM CFD:

Geometry→Create point→Explicit coordinates→Enter the coordinates as

given in table shown:

Geometry→Create/modify curve→From points→Select any 2

points→ok→Similarly create the curves to all points

Geometry→Create/Modify surface→Simple surface→Select all the lines of

domain→ok

X

0 0 0.5 1.5 1.5 0.5

Y

0 1.259 1.259 1.259 0268 0

Z

0 0 0 0 0 0


39

13) Creation of parts:

Parts in the tree→Right click→Create part→

Select Left curve: Inlet

Select Right curve: Outlet

Select Top curve: Top

Select inclined curve: Wedge

Select bottom curve: Front_wedge

14) Saving the Geometry:

File→Change working directory→Choose the folder

File→Geometry→Save Geometry as→Give the name.

15) Creation of Blocking and Association:

Blocking→Create block→Initialize blocks→Type as:2D Planar→ok

Associate→Associate vertex to point→Select a vertex and a point→Apply→

Similarly associate remaining 3 vertices to points

Associate→Associate edge to curve→Select a edge and a curve →Apply→

Similarly associate remaining 3 edges to 5 curves

16) Generation of Mesh:


Select the Horizontal edge and give no. of nodes as: 100→ok


Select the Vertical edge and give no. of nodes as: 100→Spacing as:

0.001→Ratio as: 1.1→ok


40

Switch ON Pre-mesh in the tree→click yes to compute the meshing

Pre-mesh→Right click→Convert to unstructured mesh

Now the required mesh has been generated as shown in below fig:

17) Saving the Project:

File→Save Project as→Give the name.

18) Writing output file:

Output→Select solver→Output solver as: Fluent_V6→Common Structural

solver as: ANSYS→ok

Write input→Click NO→Open the file→Click 2D→ok

Steps Involved in Fluent:

19) Importing the mesh file:

File→Read→mesh→Choose the output file written in ICEM CFD

Now the mesh has imported into the fluent solver.

20) Problem setup:

General→Type as: Density based

Models→Energy ON→ Select Viscous-laminar→Edit→Set model as: k-

omega(2 equ)

Materials→Air→Create/Edit→Set density as: Ideal-gas→Set viscosity as:

Sutherland→Change

Cell zone conditions→ Type as: fluid→Set operating conditions→Set

operating pressure as: 0Pa


41

Boundary conditions→Select inlet→Give type as: pressure-far-

field→Edit→Give Gauge pressure as: 101325Pa→Set Mach as: 3→ok

Boundary conditions→Select outlet→Edit→Give gauge pressure as: 0Pa

21) Solution:

Select Solution Controls→Set Courant number as: 1

Select the required monitors

Solution initialization→Compute from: inlet→Initialize

Run calculations→Enter the no. of iterations as: 1000→Calculate

22) Results:

Graphics and animations→Select the required flow parameters in the contours

and vectors.

The results are shown below as:


42

8. FLOW OVER A FLAT PLATE

Aim: To study the characteristics of flow over a flat plate

Description: Consider a plate of 1m and the flow of air is 0.00133 m/s. The plate is an

stationary solid wall having no slip as its boundary condition.

Procedure:

Geometry→ create point→ explicit coordinates→ 1(0,0,0), 2(1,0,0), 3(1,1,0) and

4(0,1,0) → ok

Create/modify curve→ select 2 points→ middle click

Select all points to make a rectangle

Create/modify surface→ select the entire lines→ surface is created

Create part→ name inlet→ select the left edge→ middle click

similarly create outlet, top and bottom

Switch off points and curves→ create part→ name surf→ click on surface→ ok

Blocking→ create block→ select entities→ click spectacles→ middle click→ switch

on points and curves

Go to association→ associate vertex→ select the point→ double click on the point

Associate→ edge to curve→ select the edge→ ok→ again select the edge→ ok

Similarly for the remaining edges

Premesh parameters→ edge parameters→ select any edge→ click on copy

parameters→ nodes-60, spacing-0.01, ratio-1.1→ ok

Blocking tree→ premesh→ right click→ convert structured to unstructured mesh


43

Change the working directory

output→ output solver→ fluent V6→ common-ansys→ ok

FLUENT:

Folder→ general→ mesh→ fluent mesh→ ok

Click on check→ done

Models→ viscous laminar→ materials→ air

Cell zone conditions→ solid→ ok

Boundary conditions→ bottom→ edit→ stationary wall→ ok, inlet→ velocity-

0.00133→ ok, outlet→ guage pressure-0→ ok, top→ edit→ moving wall→ ok

Dynamic mesh→ solution→ solution method-simple, solution controls-

0.3,1,0.3→ ok

Monitor initializer→ compute from inlet→ x=0.00133→ initialize

Calculation activities→ no of iterations-200→ run calculations→ click on

calculate→ ok


44

Results→ graphics and animations→ contour→ set up→ display options→

filled→ display

Contour→ velocity→ display

vector→ velocity→ display

For residue→ contour→ residue→ display


45

9. LAMINAR FLOW THROUGH PIPE

AIM: To study characteristics of laminar flow through a pipe.

DESCRIPTION: Consider a pipe of radius 0.05 and 1 m length. The freestream velocity

considered is 40m/s.

STEPS INVOLVED:

1) Create A Geometry: a) Create a point: Geometry →create point →explicit coordinates→(X, Y, Z) =

(0, 0, 0) →apply→(X, Y, Z) = (1, 0, 0) →ok.

b) Create a pipe: Geometry→Create/modify surfaces→Standard shapes→

cylinder→radius1=radius2 = 0.05→select the 2 points →ok

2) Generation of parts:

Part →create part→inlet→select inlet→ok.

Part →create part →outlet →select outlet →ok.

Part →create part →pipe →select pipe without inlet and outlet →ok.

3) Generation of blocking:

Blocking →create block →solid →select pipe element with inlet and outlet→

apply→ok.

Blocking →associate →edge to curve →select the 4 edges of the blocking at

inlet →apply →select the inlet curve→ok.


46

Blocking→associate →edge to curve→select the 4 edges of the blocking at

outlet →apply→select the outlet curve→ok.

Associate→faces to surface→select inlet face → apply →select as

inlet→accept →ok.

Associate → faces to surface →select outlet face →apply →select as outlet

→accept →ok.

Associate →face to surface →select pipe faces →apply →select as pipe →

accept →ok.

Blocking →split block →O grid block →select the 2 faces (inlet & outlet)

→apply →ok.

4) Generation of Meshing:

Blocking →pre-mesh parameters →edge parameters → switch on the copy

parameters →select 1 edge →give no. of nodes =20→ok.

Repeat the above steps to the remaining edges also and then apply.

Blocking →pre-mesh →compute.

Blocking →pre-mesh →convert to unstructured mesh.

5) Generation of Solver file :

Output→select solver→ansys.cfx→ANSYS→ok.

Output →write input →done →check the file is saved folder →ok.


47

6) Solution in CFX Solver:

Start →programs →ANSYS →fluid dynamics →CFX →ok.

Change the working directory (where ICEM CFD mesh file was

saved)→Click on CFX-PRE.

7) CFX-PRE:

File→new case→general→ok.

File→import→mesh→select the meshed filed→ok.

Boundary→Boundary1→Boundary type as: inlet→location as:

inlet→boundary conditions as: velocity=40m/s→ok.

Boundary→Boundary2→boundary type as: outlet→location as:

outlet→boundary conditions as: static pressure=0→ok.

Boundary→Boundary3→boundary type as: wall→location as:

pipe→boundary conditions as: no slip condition, smooth wall→ok.

Domain→basic settings→location as: solid→domain type as: fluid

domain→material as: air→ok.

Solver control→basic settings→ max.itterationsas:1000→residual target as:

0.000000001→ok.

Write solver input file→give the name of the file→ok.


48

8) CFX-Solver Manager:

File→Define run→Solver input file→Select the file→Start run.

Incoming flow through inlet

9) CFX-POST:

FileLoad resultsOk.

LocationPlaneOkEnter the CoordinatesApply.

ContoursOkSet domain as: fluidSet location as: planeSet range as:

localSet boundary data as: conservativeApply. The results are shown below as:


49

pressure contour

velocity vector


50

10.FLOW PAST OVER A CYLINDER

AIM : To study the characteristics of flow over a cylinder.

DESCRIPTION: Consider a cyclinder of 3m radius and 6m height. The free stream velocity

considered 20m/s. the properties of air is ρ=1.18kg/m3.

PROCEDURE:

CREATION OF GEOMETRY:

Geometry → create point → explicit coordinates → (0,0,0)

Geometry → create surface → standard shapes → box → (36 18 18) → apply →

solid simple display

Geometry → create point → based on 2 locations → select 2 diagonal points of face

Geometry → transform geometry → copy → select point → Z-offset =6 → apply →

z-offset=12→ ok.

Geometry → surfaces → standard shapes → cylinder r1=3.r2=3 → select 2 points of

cylinder → apply

CREATION OF PARTS AND MESH GENERATION:

parts→ create parts → ( part name) → select entities → middle click (create

parts according to the problem i.e. inlet, outlet, cylinder & free slip wall)

geometry → solid → part(mp) → select two points lying outside the cylinder

→ apply.

Mesh → mesh parameters → cylinder -1.5, inlet-2.5, outlet-2.5, slipfree-0.7

Mesh → global mesh setup → global mesh size → max element size (3) →

apply.

Mesh → compute mesh → compute.


51

Output → outpur solver- ANSYS CFX → common solver → ANSYS →

APPLY

WRITE INPUT → OK

PROBLEM DEFINITION IN CFX-PRE: CFX → change the working directory → cfx-pre File

→ new case → general → apply.

Mesh → import mesh → ICEM CFD → OK

domain → fluid domain → air at 25c

Boundary → inlet → domain: inlet → velocity=40m/s.

Boundary → outlet → domain outlet → static pressure=0 Pa → apply

Boundary → freeslip → domain free slip → free slip → ok.

Solver settings → 1000 iterations → apply. Define

solver → solver input file → ok


52

Solve:

CFD solver → open cfx file → define run → ok

Post processing:

CFD post → load result → select .res file

Location → plane → Z=9 apply

Contours → domain: plane1 → velocity → local → conservative →

apply.

Contours → domain: plane1 → pressure→ local → conservative → apply.


53

Vectors → domain: plane 1 → local → conservative →

apply

Stream lines → domain : plane 1 → local → conservative → apply.


54

VIVA QUESTIONS:

1. Define CFD?

2. What are the three major steps of CFD?

3. What are the governing equations of CFD?

4. What is meant by Discretization?

5. Which type of Discretization is used in CFD?

6. Difference between forward and backward differencing scheme?

7. What is Explicit method and Implicit method?

8. What is LAX method?

9. What is a stability criterion?

10. What is thermal diffusivity?

11. Define Grid?

12. Difference between Structured and Unstructured grid?

13. What is meant by Grid Independence study?

14. What is linspace command in MATLAB?

15. How to give titles to X and Y axis of a graph?

16. How to create Hybrid mesh in ICEM?

17. How to create structured grid in ICEM?

18. What is the importance of Body point in ICEM?

19. How to define material properties in CFX or FLUENT?

20. What is meant by convergence criteria?

21. How to define supersonic inlet conditions in CFX?

22. What is Grid adaption technique?

23. What is meant by parallel and serial processing?

24. In how many ways CFD results can be presented?

25. How to define formulas in CFD Post?

26. What are the causes for reverse flow or diverged flow during CFD iterations?

27. What are the relaxations factors in FLUENT?

28. What is courant number and how does it affects the solution?

29. What are the different types of turbulence models in CFD?

30. Difference between free slip and no-slip conditions?


55

COMPUTATIONAL STRUCTURES

LABORATORY MANUAL

B.TECH

(IV YEAR – I SEM)

(2016-17)

Prepared by:

Ms. A.UDAYA DEEPIKA, Assistant Professor

Mrs. L.SUSHMA, Assistant Professor

Department of Aeronautical Engineering

MALLA REDDY COLLEGE

OF ENGINEERING & TECHNOLOGY (Autonomous Institution – UGC, Govt. of India)

Recognized under 2(f) and 12 (B) of UGC ACT 1956

Affiliated to JNTUH, Hyderabad, Approved by AICTE - Accredited by NBA & NAAC – A Grade - ISO 9001:2015 Certified)

Maisammaguda, Dhulapally (Post Via. Hakimpet), Secunderabad – 500100, Telangana State, India.

COMPUTATIONAL STRUCTURES LAB Pg. No: 2

DEPARTMENT OF AERONAUTICAL ENGINEERING

VISION

Department of Aeronautical Engineering aims to be indispensable source in Aeronautical

Engineering which has a zeal to provide the value driven platform for the students to acquire

knowledge and empower themselves to shoulder higher responsibility in building a strong

nation.

MISSION

a) The primary mission of the department is to promote engineering education and research.

(b) To strive consistently to provide quality education, keeping in pace with time and

technology.

(c) Department passions to integrate the intellectual, spiritual, ethical and social development

of the students for shaping them into dynamic engineers.


PROGRAMME EDUCATIONAL OBJECTIVES (PEO’S)

PEO1: PROFESSIONALISM & CITIZENSHIP

To create and sustain a community of learning in which students acquire knowledge and learn

to apply it professionally with due consideration for ethical, ecological and economic issues.

PEO2: TECHNICAL ACCOMPLISHMENTS

To provide knowledge based services to satisfy the needs of society and the industry by

providing hands on experience in various technologies in core field.

PEO3: INVENTION, INNOVATION AND CREATIVITY

To make the students to design, experiment, analyze, interpret in the core field with the help

of other multi disciplinary concepts wherever applicable.

PEO4: PROFESSIONAL DEVELOPMENT

To educate the students to disseminate research findings with good soft skills and become a

successful entrepreneur.

PEO5: HUMAN RESOURCE DEVELOPMENT

To graduate the students in building national capabilities in technology, education and

research.


PROGRAM SPECIFIC OBJECTIVES (PSO’s)

1. To mould students to become a professional with all necessary skills, personality and

sound knowledge in basic and advance technological areas.

2. To promote understanding of concepts and develop ability in design manufacture and

maintenance of aircraft, aerospace vehicles and associated equipment and develop

application capability of the concepts sciences to engineering design and processes.

3. Understanding the current scenario in the field of aeronautics and acquire ability to apply

knowledge of engineering, science and mathematics to design and conduct experiments in

the field of Aeronautical Engineering.

4. To develop leadership skills in our students necessary to shape the social, intellectual,

business and technical worlds.


PROGRAM OBJECTIVES (PO’S)

Engineering Graduates will be able to: 1. Engineering knowledge: Apply the knowledge of mathematics, science,

engineering fundamentals, and an engineering specialization to the solution of

complex engineering problems.

2. Problem analysis: Identify, formulate, review research literature, and analyze

complex engineering problems reaching substantiated conclusions using first

principles of mathematics, natural sciences, and engineering sciences.

3. Design / development of solutions: Design solutions for complex engineering

problems and design system components or processes that meet the specified needs

with appropriate consideration for the public health and safety, and the cultural,

societal, and environmental considerations.

4. Conduct investigations of complex problems: Use research-based knowledge and

research methods including design of experiments, analysis and interpretation of

data, and synthesis of the information to provide valid conclusions.

5. Modern tool usage: Create, select, and apply appropriate techniques, resources,

and modern engineering and IT tools including prediction and modeling to

complex engineering activities with an understanding of the limitations.

6. The engineer and society: Apply reasoning informed by the contextual knowledge

to assess societal, health, safety, legal and cultural issues and the consequent

responsibilities relevant to the professional engineering practice.

7. Environment and sustainability: Understand the impact of the professional

engineering solutions in societal and environmental contexts, and demonstrate the

knowledge of, and need for sustainable development.

8. Ethics: Apply ethical principles and commit to professional ethics and

responsibilities and norms of the engineering practice.

9. Individual and team work: Function effectively as an individual, and as a

member or leader in diverse teams, and in multidisciplinary settings.

10. Communication: Communicate effectively on complex engineering activities with

the engineering community and with society at large, such as, being able to

comprehend and write effective reports and design documentation, make effective

presentations, and give and receive clear instructions.

11. Project management and finance: Demonstrate knowledge and understanding of

the engineering and management principles and apply these to one’s own work, as

a member and leader in a team, to manage projects and in multi disciplinary

environments.

12. Life- long learning: Recognize the need for, and have the preparation and ability

to engage in independent and life-long learning in the broadest context of

technological change.


COMPUTATIONAL STRUCTURES LAB

1.2. Introduction to the features and application of any one of the professional

software employed in modeling and analysis of aircraft structures.

MODLING, ANALYSIS (MAXIMUM STRESSES, DEFLECTIONS) AND

CODE DEVELPOMENT, OF STRUCTURAL ELEMENTS UNDER

ARBITRARY STATIC LOADING-VALIDATION OF SOLUTIONS

WITH PROFESSIONAL SOFTWARE

3. Bending of uniform cantilever beams.

4. Compressive strength of rectangular stiffened plane panels of uniform cross-

section.

5. Shear and torsion of stiffened thin walled open and closed sections.

6. Statically indeterminate trusses.

7. Free vibration of uniform cantilever beams-determination of natural

frequencies and mode shapes.

MODELING AND ANALYSIS OF SIMPLE AIRCRAFT COMPONENTS

USING PROFESSIONAL SOFTWARE

8. 3 dimensional landing gear trusses.

9. Tapered wing box beams.

10. Fuselage bulkheads.

Suggested soft wares

ANSYS

NASTRAN

PATRAN


LIST OF EXPERIMENTS

SL NO EXPERIMENT NO NAME OF THE EXPERIMENT

PAGE

NO

1 INTRODUCTION INTRODUCTION TO ANSYS 8

2 EXPERIMENT -1

TWO DIMENSIONAL STATIC

LINEAR ANALYSIS OF A

CANTILEVER BEAM

14

2 EXPERIMENT: 2 COMPRESSIVE STRENGTH OF

RECTANGULAR STIFFENED

PLANE PANEL OF UNIFORM

CROSS-SECTION

20

3 EXPERIMENT -3(A)

SHEAR OF STIFFENED THIN

WALLED OPEN SECTION BEAM

27

4 EXPERIMENT -3(B)

TORSIONAL STRENGTH OF A

THIN WALLED OPEN SECTION

BEAM

34

5 EXPERIMENT: 3(C)

SHEAR FORCE OF STIFFENED

THIN WALLED CLOSED

SECTION BEAM

42

6 EXPERIMENT: 3(D)

TORSIONAL STRENGTH OF A

THIN WALLED CLOSED

SECTION BEAM

50

7 EXPERIMENT: 4

2-D STATIC LINEAR ANALYSIS

OF A TRUSS STRUCTURE

58

8 EXPERIMENT -5

MODAL ANALYSIS OF

UNIFORM CANTILEVER BEAM

64

9 EXPERIMENT: 6

ANALYSIS OF A LANDING

GEAR

68

10 EXPERIMENT: 7

STATIC ANALYSIS OF

TAPERED WING BOX

75

11 EXPERIMENT: 8

ANALYSIS OF A FUSELAGE

79


INTRODUCTION ANSYS is a general purpose finite element modelling package for numerically

solving a wide variety of mechanical problems. These problems include: static/dynamic

structural analysis (both linear and non-linear), heat transfer and fluid problems, as well as

acoustic and electro-magnetic problems.

In general, a finite element solution may be broken into the following three stages. This is a

general guideline that can be used for setting up any finite element analysis.

1. Pre-processing: defining the problem; the major steps in pre-processing are given

below:

Define keypoints/lines/areas/volumes

Define element type and material/geometric properties

Mesh lines/areas/volumes as required.

The amount of detail required will depend on the dimensionality of the analysis (i.e.

1D, 2D, axi-symmetric, 3D).

2. Solution: assigning loads, constraints and solving; here we specify the loads (point

or pressure), constraints (translational and rotational) and finally solve the resulting

set of equations.

3. Postprocessing: further processing and viewing of the results; in this stage one

may wish to see:

o Lists of nodal displacements

o Element forces and displacements

o Deflection plots

o Stress contour diagrams


1. ANSYS 13.0 Environment

The ANSYS Environment for ANSYS 13.0 contains 2 windows: the Main Window and an

Output Window. Note that this is somewhat different from the previous version of ANSYS

which made use of 6 different windows.

1. Main Window

a. Utility Menu The Utility Menu contains functions that are available throughout the ANSYS

session, such as file controls, selections, graphic controls and parameters.

b. Input Window The Input Line shows program prompt messages and allows you to type in

commands directly.

c. Toolbar The Toolbar contains push buttons that execute commonly used ANSYS

commands. More push buttons can be added if desired.

d. Main Menu The Main Menu contains the primary ANSYS functions, organized by

preprocessor, solution, general postprocessor, design optimizer. It is from this

menu that the vast majority of modelling commands are issued. This is where

you will note the greatest change between previous versions of ANSYS and

version 7.0. However, while the versions appear different, the menu structure

has not changed.


e. Graphics Window The Graphic Window is where graphics are shown and graphical picking can

be made. It is here where you will graphically view the model in its various

stages of construction and the ensuing results from the analysis.

2. Output Window

The Output Window shows text output from the program, such as listing of data etc. It

is usually positioned behind the main window and can de put to the front if necessary.

2. ANSYS Files

Introduction

A large number of files are created when you run ANSYS. If you started ANSYS without

specifying a jobname, the name of all the files created will be FILE.* where the * represents

various extensions described below. If you specified a jobname, say Frame, then the created

files will all have the file prefix, Frame again with various extensions:

frame.db Database file (binary). This file stores the geometry, boundary conditions and any

solutions.

frame.dbb Backup of the database file (binary).

frame.err Error file (text). Listing of all error and warning messages.

frame.out Output of all ANSYS operations (text). This is what normally scrolls in the output

window during an ANSYS session.

frame.log Logfile or listing of ANSYS commands (text). Listing of all equivalent ANSYS

command line commands used during the current session.

etc... Depending on the operations carried out, other files may have been written. These files may

contain results, etc.


3. Plotting ANSYS Results to a File

Plotting of Figures

There are two major routes to get hardcopies from ANSYS. The first is a quick a raster-based

screen dump, while the second is a scalable vector plot.

1.0 Quick Image Save

When you want to quickly save an image of the entire screen or the current 'Graphics

window', select:

'Utility menu bar'/'PlotCtrls'/'Hard Copy ...'.

In the window that appears, you will normally want to select 'Graphics window',

'Monochrome', 'Reverse Video', 'Landscape' and 'Save to:'.

Then enter the file name of your choice.

Press 'OK'

This raster image file may now be printed on a PostScript printer or included in a document.

Display and Conversion

The plot file that has been saved is stored in a proprietary file format that must be

converted into a more common graphic file format like PostScript, or HPGL for example.

This is performed by running a separate program called display. To do this, you have a

couple of options:

1. Select display from the ANSYS launcher menu (if you started ANSYS that way)

2. Shut down ANSYS or open up a new terminal window and then type display at the

Unix prompt.

Either way, a large graphics window will appear. Decrease the size of this window, because it

most likely covers the window in which you will enter the display plotting commands. Load

your plot file with the following command:

file,frame,pic

if your plot file is 'plots.pic'. Note that although the file is 'plots.pic' (with a period), Display

wants 'plots,pic'(with a comma). You can display your plots to the graphics window by

issuing the command like

plot,n

where n is plot number. If you plotted 5 images to this file in ANSYS, then n could be any

number from 1 to 5.

Now that the plots have been read in, they may be saved to printer files of various formats:

1. Colour PostScript: To save the images to a colour postscript file, enter the following

commands in display:

2. pscr,color,2

3. /show,pscr

4. plot,n

Where n is the plot number, as above. You can plot as many images as you want to

postscript files in this manner. For subsequent plots, you only require the plot,n

command as the other options have now been set. Each image is plotted to a postscript

file such as pscrxx.grph, where xx is a number, starting at 00


.

Note: when you import a postscript file into a word processor, the postscript image

will appear as blank box. The printer information is still present, but it can only be

viewed when it's printed out to a postscript printer.

Printing it out: Now that you've got your color postscript file, what are you going to

do with it? Take a look here for instructions on colour postscript printing at a couple

of sites on campus where you can have your beautiful stress plot plotted to paper,

overheads or even posters!

5. Black & White PostScript: The above mentioned colour postscript files can get very

large in size and may not even print out on the postscript printer in the lab because it

takes so long to transfer the files to the printer and process them. A way around this is

to print them out in a black and white postscript format instead of colour; besides the

colour specifications don't do any good for the black and white lab printer anyways.

To do this, you set the postscript color option to '3', i.e. and then issue the other

commands as before

6. pscr,color,3

7. /show,pscr

8. plot,n

4. Mechanical APDL Documentation Descriptions

The manuals listed below form the ANSYS product documentation set. They include

descriptions of the procedures, commands, elements, and theoretical details needed to use

ANSYS. A brief description of each manual follows.

Advanced Analysis Techniques Guide: Discusses techniques commonly used for complex

analyses or by experienced ANSYS users, including design optimization, manual rezoning,

cyclic symmetry, rotating structures, submodeling, substructuring, component mode

synthesis, and cross sections.

ANSYS Connection User's Guide: Gives instructions for using the ANSYS Connection

products, which help you import parts and models into ANSYS.

ANSYS Parametric Design Language Guide: Describes features of the ANSYS Parametric

Design Language (APDL), including parameters, array parameters, macros, and ways to

interface with the ANSYS GUI. Explains how to automate common tasks or to build your

model in terms of parameters. Includes a command reference for all APDL-related

commands.

Basic Analysis Guide: Describes general tasks that apply to any type of analysis, including

applying loads to a model, obtaining a solution, and using the ANSYS program's graphics

capabilities to review results.

Command Reference: Describes all ANSYS commands, in alphabetical order. It is the

definitive reference for correct command usage, providing associated menu paths, product

applicability, and usage notes.

http://www.mece.ualberta.ca/tutorials/unix/unixmain.html#color


Contact Technology Guide: Describes how to perform contact analyses (surface-to-surface,

node-to-surface, node-to-node) and describes other contact-related features such as multipoint

constraints and spot welds.

Coupled-Field Analysis Guide: Explains how to perform analyses that involve an interaction

between two or more fields of engineering.

Distributed ANSYS Guide: Explains how to configure a distributed processing environment

and proceed with a distributed analysis.

Element Reference: Describes all ANSYS element, in numerical order. It is the primary

reference for correct element type input and output, providing comprehensive descriptions for

every option of every element. Includes a pictorial catalog of the characteristics of each

ANSYS element.

Modeling and Meshing Guide: Explains how to build a finite element model and mesh it.

Multibody Analysis Guide: Describes how to perform a multibody simulation to analyze the

dynamic behavior of a system of interconnected bodies comprised of flexible and/or rigid

components.

Operations Guide: Describes basic ANSYS operations such as starting, stopping, interactive

or batch operation, using help, and use of the graphical user interface (GUI).

Performance Guide: Describes factors that impact the performance of ANSYS on current

hardware systems and provides information on how to optimize performance for different

ANSYS analysis types and equation solvers.

Rotordynamic Analysis Guide: Describes how to perform analysis of vibrational behavior in

axially symmetric rotating structures, such as gas turbine engines, motors, and disk drives.

Structural Analysis Guide: Describes how to perform the following structural analyses: static,

modal, harmonic, transient, spectrum, buckling, nonlinear, material curve fitting, gasket joint

simulation, fracture, composite, fatigue, p-method, beam, and shell.

Theory Reference for the Mechanical APDL and Mechanical Applications: Provides the

theoretical basis for calculations in the ANSYS program, such as elements, solvers and

results formulations, material models, and analysis methods. By understanding the underlying

theory, you can make better use of ANSYS capabilities while being aware of assumptions

and limitations.

Thermal Analysis Guide: Describes how to do steady-state or transient thermal analyses.


EXPERIMENT: 1

TWO DIMENSIONAL STATIC LINEAR ANALYSIS OF A

CANTILEVER BEAM

Experiment as given in the JNTUH curriculum.

BENDING OF UNIFORM CANTILEVER BEAM

AIM: To determine the stresses acting on a cantilever beam with a point load of -10000 N

acting at one of its ends and perpendicular to the axis of the beam.

Young’s modulus = 2e5

Poisson’s ratio = 0.3

Length of the beam = 2m = 2000mm

Breadth of the beam = 10 cm = 100mm

Height of the beam = 50mm

PROCEDURE:

PRE PROCESSING

STEP 1: From the Main menu select preferences

Select structural and press OK

STEP 2: From the main menu select Pre-processor

Element type Add / edit/Delete Add BEAM – 2D Elastic 3 Apply

Close

Material properties material models Structural Linear Elastic Isotropic

EX = 2e5; PRXY = 0.3


Sections Beam Common Sections Select subtype as Rectangular section

Enter B = 100, H = 50 Apply Preview

Real constants Add Add Ok Geometric Properties Area = 5000, Izz =

4170000, Height = 50 Ok Close

STEP 4: From the main menu select Pre-processor Modelling

Create the key points in the Workspace

Create Key points in active CS

X 0 2000

Y 0 0

Click APPLY to all the points and for the last point click OK

Create LINES using the Key points

Create Lines Lines Straight Line Click on Key points to generate lines

Select Plot controls from menu bar Capture image file save as and save your file


Figure: Model

STEP 4: Meshing the Geometry

From the main menu select Meshing

Meshing Size controls Manual size Lines All lines – Number of element

divisions = 20 Click OK

Meshing Mesh Lines – pick all

Figure: Meshed Model

SOLUTION PHASE: ASSIGNING LOADS AND SOLVING

STEP 5: From the ANSYS main menu open Solution

Solution Analysis type new analysis – Static

STEP 6: Defining loads at the Key points

Solution Define Loads Apply Structural Displacement On key points

Left end – ALL DOF arrested

Solution Define loads Apply Structural Force/moment On key Points

Right end – Apply a load of FY = -1000N



Figure: Model with boundary conditions

STEP 7: Solving the system

Solution Solve Current LS

POSTPROCESSING: VIEWING THE RESULTS

1. Deformation

From the main menu select General post processing

General post processing Plot Results Deformed Shape

Select 'Def + undef edge' and click 'OK' to view both the deformed and the

undeformed object

Figure: Deformed and undeformed Model

Nodal solution

From the Utility menu select PLOT

PLOT Results Contour plot Nodal solution – DOF solution – Y component of

displacement – OK


Figure: Y-Component displacement of the Model

RESULT:

Case: 1:- To determine the stresses acting on a cantilever beam with a point load of -

10000 N acting at one of its ends and perpendicular to the axis of the beam.

1. DMX = 31.974

SMN = -31.974

PROBLEM DEFINITIONS DIFFERENT FROM JNTU TOPICS



1. DMX = 28.777

SMN = -28.777



1. DMX = 25.58

SMN = -25.58




1. DMX = 22.382

SMN = -22.382



1. DMX = 19.185

SMN = -19.185




1. DMX = 15.988

SMN = -15.988

VIVA QUESTIONS 1. If a cantilever beam has a uniformly distributed load, will the bending moment diagram

be quadratic or cubic?

2. Name the element type used for beams?

3. Define Analysis and its Purpose?

4. What are the modules in Ansys Programming?

5. What are the Real Constants & Material Properties in Ansys? Explain?


EXPERIMENT: 2 COMPRESSIVE STRENGTH OF RECTANGULAR STIFFENED

PLANE PANEL OF UNIFORM CROSS-SECTION


Compressive strength of rectangular stiffened plane panel.

AIM: To analyze the compressive strength of rectangular stiffened plane panel of uniform

cross-section which is subjected to a pressure of 12000 Pa.

APPARATUS: Ansys 13.0

GIVEN DATA:

Young’s modulus = 2e11

Thickness I=1.2, J=1.2


Density = 7850kg/m3

PROCEDURE:

PRE PROCESSING


Select structural→ h-method and press OK


Element type Add / edit/Delete Add select shellelastic 4 node 63ok

Real constants Add Addselect type1 shellok

ThicknessI=1.2, J=1.2ok


EX = 2e11; PRXY = 0.27; Density = 7850

STEP 3: From the main menu select Pre-processor Modeling


Create Key points In active CS

X Y Z

0 0 0

6 0 0

6 4 0

0 4 0



Create Lines Straight Line select 1-2, 2-3, 3-4, 4-1 Key points to generate

lines

STEP 4: Modeling create Areas arbitrary by lines select all four lines ok




Meshing mesh attributes all areas select the area shell ok

Meshing Size controls Manual size by areas all areas Number of

element edge length = 1 Click ok

Meshing Mesh areas mapped 3 or 4 sided select area ok



Solution Analysis type new analysis Static

STEP 6: Defining loads

Loads define loads Apply Structural Displacement On lines select

line 1-2 & 1-4 ok

Select ALL DOF arrested

Define loads Apply Structural Pressure select on lines 2-3 & 3-4 ok

Enter pressure = 12000 ok





2. Deformation




undeformed object


Nodal solution


PLOT Results Contour plot Nodal solution

Result DOF solution Y component of displacement OK

Result stress Von mises stress

RESULT:

Case: 1:- To determine the stresses acting on a rectangular plane with a pressure load of

12000 N acting on the lines 2 & 3.

DMX = 0.187e-07

SMX = 939.279



11000 N acting on the lines 2 & 3

DMX = .224e-07

SMX = 1127




DMX = 0.224e-06

SMX = 4747



DMX = 0.224e-06

SMX = 1127




DMX = 0.224e-06

SMX = 1127




DMX = 0.224e-06

SMX = 1127

VIVA QUESTIONS

1. What do you mean by degrees of freedom?

2. Define key points, lines, nodes, elements?

3. Can meshing is done after elements are created?

4. Types of co-ordinate systems?

5. What is symmetry and types of symmetry?


EXPERIMENT: 3 a) SHEAR OF STIFFENED THIN WALLED OPEN SECTION BEAM


Shear of stiffened thin walled open section

AIM: To analyze shear of stiffened thin walled open section beam which is subjected to a

pressure of 50 MPa.


GIVEN DATA:

Young’s modulus = 0.7e11

Thickness I = 1.3, J = 1.3


Density = 2700 kg/m3

PROCEDURE:

PRE PROCESSING




Element type Add / edit/Delete Add select shellelastic 4 node

63applysolidquad 4 node 182ok

Real constants Add Addselect type1 shellok enter

ThicknessI =1.3, J=1.3 ok close


EX = 0.7e11; PRXY = 0.3 & Density = 2700 ok close




X Y Z

0 0 0

2 0 0

2 0.2 0

0.2 0.2 0

0.2 1.8 0

0.5 1.8 0

0.5 2 0

0 2 0



Create Lines Straight Line Select 1-2, 2-3, 3-4, 4-5, 5-6, 6-7, 7-8, 8-1 Key

points to generate lines



Modeling operate extrude areas along normal select the area ok

enter the extrude length as 0.5


Figure: Open section beam model



Meshing mesh attributes all areas select the element type no shell ok

Select All volumes select the element type number plane ok


element edge length = 0.025 Click ok

Meshing Mesh areas free select box type instead of single select the

total volume ok


Figure: Open section beam meshed model




Loads define loads Apply Structural Displacement On areas select

the bottom edge ok all DOF ok


Define loads Apply Structural Pressure on areas select box

type (instead of single) select the top flange ok

Enter pressure = 12000 ok

Figure: Boundary and operating conditions model




1. Deformation




undeformed object

Figure: Deformed and undeformed model


Nodal solution



2. Select DOF solution X component of displacement OK

Figure: X-Component of displacement model

3. Select stress XY shear stress

Figure: XY shear stress model

4. Select stress Von mises stress


Figure: Von mises stress model

RESULT:

Case: 1:- To analyze shear of stiffened thin walled open section beam which is subjected

to a pressure of 50 MPa.

1. DMX = 0.917E-03

2. DMX = 0.917E-03

SMN = 0.598E-06

SMX = 0.902E-03

3. DMX = 0.917E-03

SMN = 0.468E+07

SMX = 0.120E+08

4. DMX = 0.917E-03

SMX = 0.563E+08




1. DMX = 0.935E-03

SMX = 0.574E+08




1. DMX = 0.954E-03

SMX = 0.586E+08



1. DMX = 0.972E-03

SMX = 0.597E+08



1. DMX = 0.990E-03

SMX = 0.608E+08




1. DMX = 1.08E-03

SMX = 0.620E+08


EXPERIMENT: 3 B TORSIONAL STRENGTH OF A THIN WALLED OPEN SECTION

BEAM


TORSION OF STIFFENED THIN WALLED OPEN SECTION

AIM: To analyze Torsion of stiffened thin walled open section beam which is subjected to a

pressure of 20 MPa.


GIVEN DATA:





PROCEDURE:

PRE PROCESSING













X Y Z

0 0 0

2 0 0

2 0.2 0

0.2 0.2 0

0.2 1.8 0

0.5 1.8 0

0.5 2 0

0 2 0










Figure: Open section beam model




Select all volumes select the element type number plane ok




total volume ok

Figure: Open section beam meshed model




the front C/S area and select the bottom flange free end area ok all DOF ok


Define loads Apply Structural Pressure on areas select the frontal area

of web and free end area of top flange (20Mpa) ok


Define loads Apply Structural Pressure on areas select the back end

area of web (-20 MPa) ok





1. Deformation




undeformed object


Nodal solution



2.Select DOF solution Y component of rotation OK


Figure: Y- component of rotation model

3.Select DOF solution X component of displacement OK

Figure: X- component of displacement model

4. Select stress YZ shear stress

Figure: YZ shear stress model




RESULT:

Case: 1:- To analyze Torsion of stiffened thin walled open section beam which is

subjected to a pressure of 20 MPa.

1. DMX = 0.108E-04

2. DMX = 0.108E-04

SMN = -0.261E-04

SMX = 0.242E-05

3. DMX = 0.108E-04

SMX = 0.100E-04

4. DMX = 0.108E-04

SMN = 0.187E+07

SMX = 0.199E+07

5. DMX = 0.108E-04

SMX = 0.258E+08




1. DMX = 0.113E-04

SMX = 0.270E+08




1. DMX = 0.119E-04

SMX = 0.283E+08



1. DMX = 0.124E-04

SMX = 0.295E+08




1. DMX = 0.130E-04

SMX = 0.308E+08



1. DMX = 0.135E-04

SMX = 0.321E+08


VIVA QUESTIONS

1. Define shear flow.

2. Define Torsion.

3. Write down the torsion equation.

4. Define von mises stress.

5. Define elastic constants.


EXPERIMENT: 3 C SHEAR FORCE OF STIFFENED THIN WALLED CLOSED SECTION

BEAM


Shear force of stiffened thin walled closed section

AIM: To analyze shear of stiffened thin walled closed section beam which is subjected to a

pressure of 50 MPa.


GIVEN DATA:





PROCEDURE:

PRE PROCESSING













X Y Z

0 0 0

1 0 0

0.2 0.2 0

0.8 0.2 0

0.2 1.8 0

0.8 1.8 0

0 2 0

1 2 0





STEP 4: Modeling create Areas arbitrary by lines select all lines ok





Figure: Closed section beam model








total volume ok


Figure: Closed section beam meshed model





the bottom edge ok all DOF ok


Define loads Apply Structural Pressure on areas select surface

of web ok

Enter pressure = 50 MPa ok





1. Deformation




undeformed object



Nodal solution



2. Select DOF solution Y component of displacement OK

Figure: Y-Component of displacement model

3. Select stress XZ shear stress

Figure: XZ shear stress model




RESULT:

Case: 1:- To analyze shear of stiffened thin walled closed section beam which is


1. DMX = 0.001421

2. DMX = 0.001421

SMN = -0.108E-06

SMX = 0.517E-03

3. DMX = 0.001421

SMN = -0.820E+07

SMX = 0.820E+07

4. DMX = 0.001421

SMX = 0.135E+09




DMX = 0.001383

SMX = 0.138E+09




DMX = 0.00141

SMX = 0.140E+09



DMX = 0.001437

SMX = 0.143E+09




DMX = 0.001464

SMX = 0.145E+09



DMX = 0.001491

SMX = 0.147E+09


EXPERIMENT: 3 D TORSIONAL STRENGTH OF A THIN WALLED CLOSED SECTION

BEAM


Shear of stiffened thin walled closed section

AIM: To analyze shear of stiffened thin walled closed section beam which is subjected to a

pressure of 20 MPa.


GIVEN DATA:





PROCEDURE:

PRE PROCESSING













X Y Z

0 0 0

1 0 0

0.2 0.2 0

0.8 0.2 0

0.2 1.8 0

0.8 1.8 0

0 2 0

1 2 0





STEP 4: Modeling create Areas arbitrary by lines select all lines ok





Figure: Closed section beam model








total volume ok

Figure: Closed section beam meshed model




the bottom edge and end C/S area of beam ok all DOF ok


Define loads Apply Structural Pressure on areas select the extreme

right of web (20Mpa) ok


Define loads Apply Structural Pressure on areas select the extreme

left of web (-20 MPa) ok

Figure: Boundary and operating condition model




1. Deformation




undeformed object


Nodal solution




2. Select DOF solution Y component of rotation OK

Figure: Y- component of rotation model

3. Select DOF solution X component of displacement OK

Figure: X- component of displacement model

4. Select stress YZ shear stress


Figure: YZ shear stress model



RESULT:

Case: 1:- To analyze Torsion of stiffened thin walled closed section beam which is


1. DMX = 0.255E-04

2. DMX = 0.255E-04

SMN = -0.261E-04

SMX = 0.242E-05

3. DMX = 0.255E-04

SMX = 0.238E-04

4. DMX = 0.255E-04

SMN = -0.344E+07

SMX = 0.309E+07

5. DMX = 0.255E-04

SMX = 0.285E+08





DMX = 0.268E-04

SMX = 0.299E+08



DMX = 0.280E-04

SMX = 0.313E+08



DMX = 0.293E-04

SMX = 0.327E+08




DMX = 0.305E-04

SMX = 0.341E+08



DMX = 0.318E-04

SMX = 0.355E+08


VIVA QUESTIONS

1. Define stiffness.

2. What are Boolean operations?

3. Define truss?

4. Name all the types of elements used in Ansys with example?

5. What is Poisson’s ratio and give the steps for obtaining Poisson’s ratio value.


EXPERIMENT: 4 2-D STATIC LINEAR ANALYSIS OF A TRUSS STRUCTURE


Statically indeterminate truss.

AIM: To determine the nodal deflections, reaction forces, and stress of the indeterminate

truss system when it is subjected to a load of 8000 N. (E = 200GPa, A = 3250mm2)

PROCEDURE:

PREPROCESSING



STEP 2: From the main menu select Preprocessor

Element type Add / edit/Delete Add Link – 2D spar 8 ok close

Real constants Add Geometric Properties Area = 3250


EX = 2e5; PRXY = 0.3



Pre-processor Modeling Create Nodes In active CS

X Y Z

0 0 0

5 0 0

10 0 0

15 0 0

2.5 2.5 0

7.5 2.5 0

12.5 2.5 0


Create LINES using the Elements

Pre-processor Modeling Create Elements Auto numbered through

nodes select node 1&2 apply 2&3 apply3&4 apply1&5

apply5&2 apply 2&6 apply6&3 apply 3&7 apply 7&4

apply 5&6 apply 6&7 ok close


Figure: Model



Solution Analysis type new analysis – Static

STEP 6: Defining loads at the Key points

Solution Define Loads Apply Structural Displacement On nodes

select node 1&4 ok select All DOF ok

Left end – ALL DOF arrested

Solution Define loads Apply Structural Force/moment On nodes

Select node 2&3 ok FY direction Give force value as -8000N ok close

Figure: Model with boundary conditions




1. Deformation



Select 'Def + undef edge' and click 'OK' to view both the deformed and the undeformed

object.


Figure: Deformed and undeformed Model

Nodal solution


PLOT Results Contour plot Nodal solution DOF solution Y component

of displacement OK

RESULT:

Case: 1:- To Determine the nodal deflections, reaction forces, and stress for the truss

system shown below (E = 200GPa, A = 3250mm2). At load -8000N

1. DMX = .461E-03

SMN = -.461E-03

Figure: Y-Component displacement of the Model





2. DMX = .404E-03

SMN = -.404E-03



3. DMX = .346E-03

SMN = -.346E-03



4. DMX = .288E-03

SMN = -.288E-03




5. DMX = .519E-03

SMN = -.519E-03



6. DMX = .577E-03

SMN = -.577E-03


VIVA QUESTIONS

1. Ansys needs the final element model(FEM) for its final solution.(T/F)

2. Element attributes must be set before meshing the solid model. (T/F)

3. In a plane strain, the strain in the direction of thickness is assumed to be zero.(T/F)

4. The ______ elements are used for in-plane bending problems.

5. Which one of the following elements is required to define the thickness as a real

constant?

a. Beam

b. Shell

c. Solid

d. None


EXPERIMENT: 5 MODAL ANALYSIS OF UNIFORM CANTILEVER BEAM


Free vibration of uniform cantilever beam.

Aim: Analyze the given uniform cantilever beam using Ansys and find out the variation in

the frequencies for 5 mode shapes.

Apparatus: ANSYS Software 13.0

Given Data: Young’s Modulus: 2e5

Poisson’s Ratio: 0.27

Length of the beam: 1000

Steps of Modeling:

Preferences ► Structural ► H- method ► OK

Preprocessor ► Element Type ► Add ► Add ► Beam ► 2D elastic 3 ► Apply► OK

Real constants ► add ► beam 3 ► Area = 1025

► Izz = 450

► thickness = 6 & width 25 mm

Material Properties ► Material Models ► Structural ► Linear ► Elastic ► Isotropic ►

EXX: 2e5

PRXY: .27

Density: 2870

Modeling ► Create ► Key points ► In Active CS X Y Z

1. 0 0 0

2. 1000 0 0

Pre-processor Modelling Create Lines Straight Line Click on Key points to

generate lines

Meshing the Geometry


Meshing Size controls Manual size Lines All lines – Number of element

divisions = 1 Click OK

Meshing Mesh Lines – pick all

Defining loads

Loads ► Define Loads ► Apply ► Structural ► Displacement ► On nodes ► Select node 1 ► Select All DOF ► OK

Solution Loads ► Analysis Type ► New Analysis ► Select Modal ► OK

Loads ► Analysis Option ► No.of Mode Shapes = 5 ► OK

Enter the Start Freq = 0

End Frequency = 0 ► OK

Solution ► Solve ► Current LS ► Warnings can be ignored ► Solution is Done


RESULTS:

General Post Processor ► Read Results ► by Pick

RESULT:

Case: 1:- To determine the 1st mode frequency acting on cantilever beam.

DMX: 0.369e-04

Frequency: 0.310e-05


Case: 2:- To determine the 2nd

mode frequency acting on cantilever beam.

DMX: 0.369e-04



Case: 3:- To determine the 3rd


DMX: 0.369e-04




DMX: 0.369e-04





DMX: 0.369e-04


VIVA QUESTIONS

1. Name the types of meshing.

2. Explain the Main Steps involved in Ansys Programming.

3. What is Modal Analysis? Write the Steps involved in Modal Analysis.

4. How do you see the Animations of the Deformed Shapes in Ansys?

5. Write the Procedure for finding the SFD & BMD of a Link.


EXPERIMENT: 6 ANALYSIS OF A LANDING GEAR


3 dimensional landing gear trusses.

Aim: Analyze the given landing gear structure with applied load of 10000N.

Apparatus: Ansys Software 13.0 Version

Given Data:

Angle (Strut):30 degrees

Poisson’s Ratio=0.3

Steps of Modeling:

Preferences ► Structural ► H-Method ► OK

Preprocessor ► Element Type ► Add ► Add ► Select Link ► Spar 8 ► Apply

Preprocessor ► Element Type ► Add ► Add ► Select Beam ► 2 Node 188 ► OK ►

Close

Real Constants ► Add ► Add ► Select Type Link 8 ► Click OK

Enter the cross sectional area =1 ► OK ► Close

Material Properties ► Material Models ► Structural ► Linear ► Elastic ► Isotropic

Enter the Young’s Modulus (EXY) = 2e5

Poisson’s Ratio (PRXY) = 0.3

Sections ►Beam ►Common Sections ►Subtype ► Select Solid Circle

R=1

N=24

T=0, Click Ok

Preprocessor ► Modeling ► Create ► Key points ► In Active CS ► Create the keypoints according to the table

KP no X Y Z

1. 0 0 0

2. 8 0 0

3. 0 26 0

4. 0 50 0

5. -6 50 0

6. 14 50 0

7. 16 50 0

8. 14 48 0

9. 3 26 0

10. 0 26 -3

11. 0 50 -24

Modeling ► Create ► Lines ► Lines ► Straight Lines ►


Join the keypoints according to table

Line no Join

1. 1 & 2

2. 1 & 3

3. 3 & 4

4. 4 & 5

5. 4 & 6

6. 6 & 7

7. 6 & 8

8. 3 & 9

9. 3 & 10

10. 8 & 9

11. 10 & 11

Main menu ► Plot Cntrls ► Numbering ►

Click in the box against Line Numbers, Apply then Ok

Plots ► Lines

Preprocessor ► Meshing ► Mesh Attributes ► All lines ►

Select element type Beam 188, Ok

Meshing ► Mesh Attributes ► Picked Lines ►

Pick lines 11 & 10, Ok

Select element type link 8, Ok

Meshing ► Size Cntrls ► Manual Size ► Lines ► All Lines ►

Edge length = 1

No of divisions should be left blank (not zero or anything else)

Meshing ► Size Cntrls ► Manual size ► lines ► Picked lines ►

Pick lines 11 & 10, Ok

Edge length should be left blank (not zero or anything else)

No of divisions = 1

Meshing ► Mesh ► Lines

Pick all Lines, Ok

Main menu► plot Cntrls ► Style ► Size and Shape

Click in the box against Display Element Type,

Change the Real Constants Multiplier to 1, Apply then Ok

Plot Cntrls ►Numbering ►


Click in the box against Keypoint Numbers

Click n the box against Line Numbers (off), Apply then Ok

Plots ► Key points ► Key points

Solution ► Define Loads ► Apply ► Structural ► Displacement ► On key Points ►

Select keypoints 5 & 7, Ok

Select UY & UZ, Apply

Select keypoint 11, Ok

Select UX, UY & UZ, Ok

Solution ► Define Loads ► Apply ► Structural ► Force/Moment ► On keypoints


Select FY and Give the value below as 14672, Apply


Select FZ and give the value below as 3119, Ok

Main menu ► Plots ► Multiplots Solution ► Solve ► current LS ► Ok

Close the Status Command window after solving is complete.

General postproc ► Plot Results ► Contour Plots ► Element Solu ► Stress ► Von Mises Stress, Click Ok

Element Table ► Define Table ►Click Add, From the list to the lefts select By Sequence Number,

From the list to the right select SMISC, type 1 beside SMISC, Apply

From the list to the lefts select By Sequence Number,

From the list to the right select LS, type 1 beside LS, Ok then Close

(NOTE: LS1-Axial stress, SMISC1-Axial force)

Element Table ► List Elem Table ►

Select LS1 from the list, Apply

Select SMISC1 from the list and unselect LS1, Ok


Result:

Von Misses Stress

Y Component Displacement

RESULT:

Case: 1 (Load FY direction 14672 N and FZ direction 3119 N)

Y Component Displacement Von Misses Stress

2. DMX = 3.156 DMX = 3.156

SMN = -0.170816 SMX = 186772

SMX = 2.123


Case: 2 (Load direction 14000 N and FZ direction 3000 N)


1. DMX = 3.02 DMX = 3.02

SMN = -0.110897 SMX = 178631

SMX = 1.1304




1. DMX = 2.777 DMX = 2.777

SMN = -0.10781 SMX = 165449

SMX = 1.249



1. DMX = 2.647 DMX = 2.647

SMN = -0.107276 SMX = 158014

SMX = 1.221




1. DMX = 2.552 DMX = 2.552

SMN = -0.106165 SMX = 152311

SMX = 1.194



1. DMX = 2.428 DMX = 2.428

SMN = -0.102159 SMX = 144856

SMX = 1.143


VIVA QUESTIONS

1. If a cantilever beam has a uniformly distributed load, will the bending moment diagram

be quadratic or cubic?

2. Name the element type used for beams?

3. Define Analysis and its Purpose?

4. What are the modules in Ansys Programming?

5. What are the Real Constants & Material Properties in Ansys? Explain?


EXPERIMENT: 7

STATIC ANALYSIS OF TAPERED WING BOX


Tapered wing box beam.

Aim: Analyze the given wing structure using Ansys and find out the variation in the

Structure of the Wing.

Apparatus: ANSYS Software 13.0

Given Data: Young’s Modulus: 7e10

Poisson’s Ratio: 0.3

Length of the Wing: 30

Steps of Modeling:

Preferences ► Structural ► H- method ► OK

Preprocessor ► Element Type ► Add ► Add ► Solid ► Brick 8 Node 45 ► Apply

Beam ► 2 node 188 ► Apply ► Shell ► elastic 4 node 63 ► Click OK

Real constants ► Add ► shell 63 ► I = 1.2, j = 1.7, k = 2.2

Material Properties ► Material Models ► Structural ► Linear ► Elastic ► Isotropic ►

EXX: 7e10

PRXY: 0.3

Density: 2700

Modeling ► Create ► Key points ► In Active CS X Y Z

1. 0 0 0

2. 8 4 0

3. 8 -4 0

4. -6 3 0

5. -6 -3 0

6. 6 3 30

7. 6 -3 30

8. -4 -2 30

9. -4 2 30

Modeling ► Create ► Lines ► straight lines ► 2, 3 - 2, 4 - 4, 5 - 5, 3 ► Apply

Lines ►6, 8 - 6, 7 - 7, 9 - 8, 9 ► Apply

Lines ► 8, 4 & 9, 5

Lines ► 2, 6 & 7, 3 ► OK

Modeling ► Create ► Areas ► Arbitrary ► by lines ► Select Upper Lines of Both sides ► Left Line, Right Lines ► Click Apply ► Select Lower Lines of both the sides ► Left Line and Right Line Click Apply ► Click OK


Modeling ► Create ► Volumes ► Arbitrary ► by Areas ► Box Selection ► Select all the Areas ► Click OK ► Hence a Solid Volume is created

Meshing ► Mesh Attributes ► all lines ► Select beam 188 ► OK

Meshing ► Mesh Attributes ► All Areas ► Select shell 63 ► OK

Meshing ► Mesh Attributes ► All Volumes ► Select solid 45 ► OK

Meshing ► Size control ► manual size ► pick all lines ► Enter the Element Edge Length as 1 ► OK

Meshing ►size control ► areas ► Box Selection ► Enter the Element Edge Length as 1 ► OK

Meshing ► Mesh ► Volumes ► free ► Select the box ► select full body ► OK

Loads ► Define Loads ► Apply ► Structural ► Displacement ► On Areas ► Select the Large Airfoil Area ► Click Apply ► Select All DOF ► OK

Loads ► Define Loads ► Apply ► Structural ► Pressure ► On Areas ► Select the upper and lower surface ► Click Apply ► Enter the Load Value =10000N & -10000N

Loads ► Analysis Type ► New Analysis ► Select Static ► OK

Solution ► Solve ► Current LS ► Warnings can be ignored ► Solution is done

RESULTS:

General Post Processor ► Plot Results ► Deformed Shape ► Deformed + Undeformed ► OK

General Post Processor ► Plot Results ► Contour Plot ► Nodal Solution ► DOF Solution Case: 1:- To determine the stresses acting on a tapered wing with a pressure load of

10000 & -10000 N acting on the lines upper and lower surfaces.

Y Component of Displacement = 0.527e-04

Von Mises Stress = 338872


Case: 2:- To determine the stresses acting on a tapered wing with a pressure load of









Case:4:- To determine the stresses acting on a tapered wing with a pressure load of













VIVA QUESTIONS

1. The _____ analysis is used to calculate the vibration characteristics of a structure.

2. The SI unit of frequency is _________.

3. Ansys report is saved with the _______ file extension.

4. The images captured using the Ansys report generator are saved with a_______ file

extension.

5. The maximum stress value should be less than the applied stress bound value. (T/F)


EXPERIMENT: 8

ANALYSIS OF A FUSELAGE


Fuselage bulkhead.

AIM: - To Calculate the deformation of the aluminum fuselage section under the application

of internal load of 100000 Pa.

PREPROCESSING




Element type Add / edit/Delete Add Solid – 10 node 92 Apply

Add Beam 2 Node 188 Apply Add Shell Elastic 4 node 63

Real Constants Add Select shell give thickness (I) = 1 ok close.


EX = 0.7e11; PRXY = 0.3; Density = 2700


Pre-processor modelling Create Areas Circle Annulus

WP x = 0 ; WP y = 0; Rad – 1 = 2.5; Rad -2 = 2.3 OK

Pre-processor Modelling Create Circle Solid –

WP x = 0; X = 2.25; Y = 0 Radius = 0.15 Apply

WP x = 0; X = -2.25; Y = 0 Radius = 0.15 Apply

WP x = 0; X =0; Y = 2.25; Radius = 0.15 Apply

WP x = 0; X = 0; Y = -2.25 Radius = 0.15 OK

Pre-processor Modelling Operate Booleans Add Areas – Pick all OK

Pre-processor Modelling Operate Extrude Areas By XYZ offset

X= 0; Y=0; Z = 5



Pre-processor Meshing Size controls Manual Size All Areas give

element edge length as 0.15 ok

Meshing Size controls Manual Size All lines give element edge length as

0.15 ok

Meshing Mesh areas free select box type instead of single select the total

volume ok

SOLUTION PHASE:


STEP 6: Loads define loads Apply Structural Displacement On areas

select box type select box (4 points at centre) all DOF ok Select ALL

DOF arrested

Define loads Apply Structural Pressure on areas select the internal

surface of the fuselage and give value (100000) ok




RESULT:

Case: 1:- To Calculate the deformation of the aluminum fuselage section under the

application of internal load at 1e5.

Y COMPONENT OF DISPLACEMENT

DMX = .194E-04

SMN = -.194E-04

SMX = .194E-04


VON MISSES STRESS

DMX = .194E-04

SMX = .124E+07



application of internal load at 1.1e5.


DMX = .819E-05

SMN = -.819E-05

SMX = .819E-05

VON MISSES STRESS

DMX = .819E-05

SMX = 559474





DMX = .893E-05

SMN = -.893E-05

SMX = .893E-05

VON MISSES STRESS

DMX = .893E-05

SMX = 610335


application of internal load 0.9e5.


DMX = .670E-05

SMN = -.670E-05

SMX = .670E-05

VON MISSES STRESS

DMX = .670E-05

SMX = 457751





DMX = .595E-05

SMN = -.595E-05

SMX = .595E-05

VON MISSES STRESS

DMX = .595E-05

SMX = 406890




DMX = .521E-05

SMN = -.521E-05

SMX = .521E-05

VON MISSES STRESS

DMX = .521E-05

SMX = 356029


VIVA QUESTIONS 1. Difference between interactive mode and batch mode.

2. What are different types of structural analysis used in ansys?

3. What are the different types of thin walled beams?

4. Define Harmonic analysis.

5. Define Spectrum Analysis.

computational aerodynamics laboratory manual …

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