mtech asp question bank final r13

MALLAREDDY COLLEGE OF

ENGINEERING AND TECHNOLOGY

DEPARTMENT OF AERONAUTICAL

ENGINEERING

M-TECH AEROSPACE ENGINEERING

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MTECH AEROSPACE 1 DEPARTMENT OF AERONAUTICAL

M.TECH AEROSPACE ENGINEERING

I YEAR I SEMESTER

QUESTION BANK

CONTENTS

S.No SUBJECT PAGE NO

1 ACADEMIC STRUCTURE 3

2 ACADEMIC REGULATIONS 5

3 MATHEMATICAL MODELLING 14

4 ENGINEERING ANALYSIS OF FLIGHT

VEHICLES

21

5 CONTINUUM MECHANICS 27

6 AIR TRANSPORTATION SYSTEMS 35

7 AERODYNAMICS OF FLIGHT VEHICLES 40

8 FUNDAMENTALS OF AEROSPACE

ENGINEERING

45

9 MODELLING AND SIMULATION OF

FLUID FLOWS

53

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M. TECH. (AEROSPACE ENGINEERING)

I Year I Semester

COURSE STRUCTURE AND SYLLABUS

Code Group Subject L P Credits

Mathematical Modeling 3 0 3

Engineering Analysis of Flight Vehicles 3 0 3

Continuum Mechanics 3 0 3

Air Transportation Systems 3 0 3

Elective –I Fundamentals of Aerospace Engineering * Aerodynamics of Flight Vehicles Flight Vehicle Structures Air-breathing Propulsion Aircraft Systems

3 0 3

Elective –II Modeling and Simulation of Fluid Flows Computational Structural Analysis Flight Navigation and Surveillance Systems Airlines Operations and Scheduling Rotorcraft Aerodynamics

3 0 3

Lab Digital Simulation Lab-I 0 3 2

Seminar - - 2

Total Credits 18 3 22

I Year II Semester Code Group Subject L P Credits

Aircraft Control and Simulation 3 0 3

Space Transportation Systems 3 0 3

Computational Approaches to Aerospace Vehicle Design

3 0 3

Aerospace Sensors and Measurement Systems 3 0 3

Elective –III Aero-thermodynamics of Hypersonic Flight Dynamics and Control of Structures Missile Guidance Advanced Topics in Air Traffic Management Systems Spacecraft Dynamics and Control

3 0 3

Elective –IV Rocket and Spacecraft Propulsion Mechanics of Composite Materials Tactical Missile Design High Angle of Attack Aerodynamics Optimal Control

3 0 3

Lab Digital Simulation Lab-II 0 3 2

Seminar - - 2

Total Credits 18 3 22

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II Year I Semester

Code Group Subject L P Credits

Comprehensive Viva - - 2

Project Seminar 0 3 2

Project work - - 18

Total Credits - 3 22

II Year II Semester Code Group Subject L P Credits

Project work and Seminar - - 22

Total Credits - - 22

*Fundamentals of Aerospace Engineering (Required to be taken by all students other than B.Tech Aeronautical/ Aerospace Engineering degree holders)

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ACADEMIC REGULATIONS R13 FOR M. TECH. (REGULAR) DEGREE

COURSE

Applicable for the students of M. Tech. (Regular) Course from the Academic Year 2013-14 and onwards

The M. Tech. Degree of Jawaharlal Nehru Technological University Hyderabad shall be conferred on candidates who are admitted to the program and who fulfil all the requirements for the award of the Degree.

1.0 ELIGIBILITY FOR ADMISSIONS

Admission to the above program shall be made subject to eligibility, qualification and specialization as prescribed by the University from time to time.

Admissions shall be made on the basis of merit/rank obtained by the candidates at the qualifying Entrance Test conducted by the University or on the basis of any other order of merit as approved by the University, subject to reservations as laid down by the Govt. from time to time.

2.0 AWARD OF M. TECH. DEGREE

A student shall be declared eligible for the award of the M. Tech. Degree, if he pursues a course of study in not less than two and not more than four academic years. However, he is permitted to write the examinations for two more years after four academic years of course work. A student, who fails to fulfill all the academic requirements for the award of the degree within four academic years from the year of his admission, shall forfeit his seat in M. Tech. course.

The student shall register for all 88 credits and secure all the 88 credits.The minimum instruction days in each semester are 90.

A. COURSES OF STUDY

The following specializations are offered at present for the M. Tech. course of study.

1. Advanced Manufacturing Systems 2. Aerospace Engineering 3. Automation 4. Bio-Technology 5. CAD/CAM 6. Chemical Engineering 7. Communication Systems 8. Computer Networks 9. Computer Networks and Information Security 10. Computer Science 11. Computer Science and Engineering 12. Computers and Communication Engineering 13. Control Engineering 14. Control Systems 15. Design for Manufacturing/Design and Manufacturing 16. Digital Electronics and Communication Engineering 17. Digital Electronics and Communication Systems 18. Digital Systems and Computer Electronics 19. Electrical Power Engineering 20. Electrical Power Systems 21. Electronics & Instrumentation 22. Electronics and Communication Engineering 23. Embedded Systems 24. Embedded Systems and VLSI Design 25. Engineering Design 26. Environmental Engineering

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27. Geoinformatics and Surveying Technology 28. Geotechnical Engineering 29. Heating Ventilation & Air Conditioning 30. Highway Engineering 31. Image Processing 32. Industrial Engineering and Management 33. Information Technology 34. Machine Design 35. Mechatronics 36. Microwave & Radar Engineering 37. Nano Technology 38. Neural Networks 39. Parallel Computing 40. Power and Industrial Drives 41. Power Electronics 42. Power Electronics and Electrical Drives 43. Power Engineering and Energy Systems 44. Power Plant Engineering & Energy Management 45. Power System Control and Automation 46. Power System with Emphasis H.V. Engineering/H.V. Engineering 47. Production Engineering 48. Real Time Systems 49. Software Engineering 50. Structural Engineering 51. Systems & Signal Processing 52. Thermal Engineering 53. VLSI 54. VLSI and Embedded Systems 55. VLSI Design 56. VLSI System Design 57. Web Technology 58. Wireless and Mobile Communication

and any other course as approved by the University from time to time.

3.0 B. Departments offering M. Tech. Programmes with specializations are noted below:

Civil Engg. Geotechnical Engineering Highway Engineering Structural Engineering Geoinformatics and Surveying Technology Environmental Engineering

EEE Control Engineering Control Systems Electrical Power Engineering Electrical Power Systems Power and Industrial Drives Power Electronics Power Electronics and Electrical Drives Power Engineering and Energy Systems Power System with Emphasis H.V. Engineering/H.V. Engineering Power System Control and Automation

ME Advanced Manufacturing Systems Automation CAD/CAM Design for Manufacturing/Design and Manufacturing Heating Ventilation & Air Conditioning Industrial Engineering and Management Machine Design Mechatronics Thermal Engineering Production Engineering Power Plant Engineering & Energy Management Engineering Design

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ECE Communication Systems Computers and Communication Engineering Digital Electronics and Communication Engineering Digital Electronics and Communication Systems Digital Systems and Computer Electronics Electronics and Communication Engineering Electronics & Instrumentation Embedded Systems Embedded Systems and VLSI Design Systems and Signal Processing VLSI VLSI and Embedded Systems VLSI Design VLSI System Design Wireless and Mobile Communication Microwave & Radar Engineering

CSE Computer Networks Computer Networks and Information Security Computer Science Computer Science and Engineering Image Processing Information Technology Neural Networks Parallel Computing Real Time Systems Software Engineering Web Technology

Aeronautical Engg. Aerospace Engineering

Bio-technology Bio-Technology

Chemical Engg. Chemical Engineering

Nano Technology Nano Technology

4.0 ATTENDANCE

The programs are offered on a unit basis with each subject being considered a unit.

A student shall be eligible to write University examinations if he acquires a minimum of 75% of attendance in aggregate of all the subjects.

Condonation of shortage of attendance in aggregate up to 10% (65% and above and below 75%) in each semester shall be granted by the College Academic Committee.

Shortage of Attendance below 65% in aggregate shall not be condoned.

Students whose shortage of attendance is not condoned in any semester are not eligible to write their end semester examination of that class and their registration shall stand cancelled.

A prescribed fee shall be payable towards condonation of shortage of attendance.

A student shall not be promoted to the next semester unless he satisfies the attendance requirement of the present semester, as applicable. They may seek readmission into that semester when offered next. If any candidate fulfills the attendance requirement in the present semester, he shall not be eligible for readmission into the same class.

A candidate shall put in a minimum required attendance at least in three (3) theory subjects in the present semester to get promoted to the next semester. In order to qualify for the award of the M. Tech. Degree, the candidate shall complete all the academic requirements of the subjects, as per the course structure.

A student shall not be promoted to the next semester unless he satisfies the attendance requirements of the previous semester including the days of attendance in sports, games, NCC and NSS activities.

5.0 EVALUATION

The performance of the candidate in each semester shall be evaluated subject-wise, with a maximum of 100 marks for theory and 100 marks for practicals, on the basis of Internal Evaluation and End Semester Examination.

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For the theory subjects 75 marks shall be awarded based on the performance in the End Semester Examination and 25 marks shall be awarded based on the Internal Evaluation. The internal evaluation shall be made based on the average of the marks secured in the two Mid Term-Examinations conducted-one in the middle of the Semester and the other immediately after the completion of instruction. Each mid term examination shall be conducted for a total duration of 120 minutes with Part A as one compulsory question for 10 marks and Part B with 3 questions to be answered out of 5 questions each question for 5 marks. If any candidate is absent from any subject of a mid-term examination, an on-line test will be conducted for him by the University. End semester examination is conducted for 75 marks with Part A as a compulsory question for 25 marks and Part B for 50 marks with 5 questions to be answered out of 7 questions.

For practical subjects, 75 marks shall be awarded based on the performance in the End Semester Examinations and 25 marks shall be awarded based on the day-to-day performance as Internal Marks.

There shall be two seminar presentations during I year I semester and II semester. For seminar, a student under the supervision of a faculty member, shall collect the literature on a topic and critically review the literature and submit it to the department in a report form and shall make an oral presentation before the Departmental Academic Committee consisting of Head of the Department, Supervisor and two other senior faculty members of the department. For each Seminar there will be only internal evaluation of 50 marks. A candidate has to secure a minimum of 50% of marks to be declared successful.

There shall be a Comprehensive Viva-Voce in II year I Semester. The Comprehensive Viva-Voce will be conducted by a Committee consisting of Head of the Department and two Senior Faculty members of the Department. The Comprehensive Viva-Voce is intended to assess the students’ understanding of various subjects he has studied during the M. Tech. course of study. The Comprehensive Viva-Voce is evaluated for 100 marks by the Committee. There are no internal marks for the Comprehensive Viva-Voce. A candidate shall be deemed to have secured the minimum academic requirement in a subject if he secures a minimum of 40% of marks in the End semester Examination and a minimum aggregate of 50% of the total marks in the End Semester Examination and Internal Evaluation taken together.

In case the candidate does not secure the minimum academic requirement in any subject (as specified in 5.5) he has to reappear for the End semester Examination in that subject. A candidate shall be given one chance to re-register for each subject provided the internal marks secured by a candidate are less than 50% and so has failed in the end examination. In such a case, the candidate must re-register for the subject(s) and secure the required minimum attendance. The candidate’s attendance in the re-registered subject(s) shall be calculated separately to decide upon his eligibility for writing the end examination in those subject(s). In the event of the student taking another chance, his internal marks and end examination marks obtained in the previous attempt stand cancelled.

In case the candidate secures less than the required attendance in any subject, he shall not be permitted to write the End Examination in that subject. He shall re-register the subject when next offered.

Laboratory examination for M. Tech. courses must be conducted with two Examiners, one of them being the Laboratory Class Teacher and the second examiner shall be another Laboratory Teacher.

6.0 EVALUATION OF PROJECT/DISSERTATION WORK

Every candidate shall be required to submit a thesis or dissertation on a topic approved by the Project Review Committee.

A Project Review Committee (PRC) shall be constituted with Principal as Chairperson, Heads of all the Departments offering the M. Tech. programs and two other senior faculty members. Registration of Project Work: A candidate is permitted to register for the project work after satisfying the attendance requirement of all the subjects, both theory and practical. After satisfying 6.2, a candidate has to submit, in consultation with his project supervisor, the title, objective and plan of action of his project work to the Departmental Academic Committee for approval. Only after obtaining the approval of the Departmental Academic Committee can the student initiate the Project work. If a candidate wishes to change his supervisor or topic of the project, he can do so with the approval of the Departmental Academic Committee. However, the Departmental Academic Committee shall examine whether or not the change of topic/supervisor leads to a major change of his initial plans of project proposal. If yes, his date of registration for the project work starts from the date of change of Supervisor or topic as the case may be.

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A candidate shall submit his status report in a bound-form in two stages at least with a gap of 3 months between them. The work on the project shall be initiated at the beginning of the II year and the duration of the project is two semesters. A candidate is permitted to submit Project Thesis only after successful completion of theory and practical course with the approval of PRC not earlier than 40 weeks from the date of registration of the project work. For the approval of PRC the candidate shall submit the draft copy of thesis to the Principal through Head of the Department and make an oral presentation before the PRC. Three copies of the Project Thesis certified by the supervisor shall be submitted to the College/School/Institute. The thesis shall be adjudicated by one examiner selected by the University. For this, the Principal of the College shall submit a panel of 5 examiners, eminent in that field, with the help of the guide concerned and head of the department. If the report of the examiner is not favourable, the candidate shall revise and resubmit the Thesis, in the time frame as decided by the PRC. If the report of the examiner is unfavourable again, the thesis shall be summarily rejected. If the report of the examiner is favourable, Viva-Voce examination shall be conducted by a board consisting of the Supervisor, Head of the Department and the examiner who adjudicated the Thesis. The Board shall jointly report the candidate’s work as one of the following:

A. Excellent B. Good C. Satisfactory D. Unsatisfactory

The Head of the Department shall coordinate and make arrangements for the conduct of Viva- Voce examination. If the report of the Viva-Voce is unsatisfactory, the candidate shall retake the Viva-Voce examination only after three months. If he fails to get a satisfactory report at the second Viva- Voce examination, he will not be eligible for the award of the degree.

7.0 AWARD OF DEGREE AND CLASS

After a student has satisfied the requirements prescribed for the completion of the program and is eligible for the award of M. Tech. Degree he shall be placed in one of the following four classes:

Class Awarded % of marks to be secured

First Class with Distinction 70% and above

First Class Below 70% but not less than 60%

Second Class Below 60% but not less than 50%

Pass Class Below 50% but not less than 40%

The marks in internal evaluation and end examination shall be shown separately in the memorandum of marks.

8.0 WITHHOLDING OF RESULTS

If the student has not paid the dues, if any, to the university or if any case of indiscipline is pending against him, the result of the student will be withheld and he will not be allowed into the next semester. His degree will be withheld in such cases.

8.0 TRANSITORY REGULATIONS

Discontinued, detained, or failed candidates are eligible for admission to two earlier or equivalent subjects at a time as and when offered.

The candidate who fails in any subject will be given two chances to pass the same subject; otherwise, he has to identify an equivalent subject as per R13 academic regulations.

10. GENERAL

Wherever the words “he”, “him”, “his”, occur in the regulations, they include “she”, “her”, “hers”. The academic regulation should be read as a whole for the purpose of any interpretation.

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In the case of any doubt or ambiguity in the interpretation of the above rules, the decision of the Vice-Chancellor is final.

The University may change or amend the academic regulations or syllabi at any time and the changes or amendments made shall be applicable to all the students with effect from the dates notified by the University.

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MALPRACTICES RULES

DISCIPLINARY ACTION FOR / IMPROPER CONDUCT IN EXAMINATIONS

Nature of Malpractices/Improper conduct

Punishment

If the candidate: 1. (a) Possesses or keeps accessible in

examination hall, any paper, note book, programmable calculators, Cell phones, pager, palm computers or any other form of material concerned with or related to the subject of the examination (theory or practical) in which he is appearing but has not made use of (material shall include any marks on the body of the candidate which can be used as an aid in the subject of the examination)

Expulsion from the examination hall and cancellation of the performance in that subject only.

(b) Gives assistance or guidance or receives it from any other candidate orally or by any other body language methods or communicates through cell phones with any candidate or persons in or outside the exam hall in respect of any matter.

Expulsion from the examination hall and cancellation of the performance in that subject only of all the candidates involved. In case of an outsider, he will be handed over to the police and a case is registered against him.

2. Has copied in the examination hall from any paper, book, programmable calculators, palm computers or any other form of material relevant to the subject of the examination (theory or practical) in which the candidate is appearing.

Expulsion from the examination hall and cancellation of the performance in that subject and all other subjects the candidate has already appeared including practical examinations and project work and shall not be permitted to appear for the remaining examinations of the subjects of that Semester/year.

The Hall Ticket of the candidate is to be cancelled and sent to the University.

3. Impersonates any other candidate in connection with the examination.

The candidate who has impersonated shall be expelled from examination hall. The candidate is also debarred and forfeits the seat. The performance of the original candidate who has been impersonated, shall be cancelled in all the subjects of the examination (including practicals and project work) already appeared and shall not be allowed to appear for examinations of the remaining subjects of that semester/year. The candidate is also debarred for two consecutive semesters from class work and all University examinations. The continuation of the course by the candidate is subject to the academic regulations in connection with forfeiture of seat. If the imposter is an outsider, he will be handed over to the police and a case is registered against him.

4. Smuggles in the Answer book or additional sheet or takes out or arranges to send out the question paper during the examination or answer book or additional sheet, during or after the examination.

Expulsion from the examination hall and cancellation of performance in that subject and all the other subjects the candidate has already appeared including practical examinations and project work and shall not be permitted for the remaining examinations of the subjects of that semester/year. The candidate is also debarred for two consecutive semesters from class work and all University examinations. The continuation of the course by the candidate is

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subject to the academic regulations in connection with forfeiture of seat.

5. Uses objectionable, abusive or offensive language in the answer paper or in letters to the examiners or writes to the examiner requesting him to award pass marks.

Cancellation of the performance in that subject.

6. Refuses to obey the orders of the Chief Superintendent/Assistant – Superintendent / any officer on duty or misbehaves or creates disturbance of any kind in and around the examination hall or organizes a walk out or instigates others to walk out, or threatens the officer-in charge or any person on duty in or outside the examination hall of any injury to his person or to any of his relations whether by words, either spoken or written or by signs or by visible representation, assaults the officer-in- charge, or any person on duty in or outside the examination hall or any of his relations, or indulges in any other act of misconduct or mischief which result in damage to or destruction of property in the examination hall or any part of the College campus or engages in any other act which in the opinion of the officer on duty amounts to use of unfair means or misconduct or has the tendency to disrupt the orderly conduct of the examination.

In case of students of the college, they shall be expelled from examination halls and cancellation of their performance in that subject and all other subjects the candidate(s) has (have) already appeared and shall not be permitted to appear for the remaining examinations of the subjects of that semester/year. The candidates also are debarred and forfeit their seats. In case of outsiders, they will be handed over to the police and a police case is registered against them.

7. Leaves the exam hall taking away answer script or intentionally tears of the script or any part thereof inside or outside the examination hall.

Expulsion from the examination hall and cancellation of performance in that subject and all the other subjects the candidate has already appeared including practical examinations and project work and shall not be permitted for the remaining examinations of the subjects of that semester/year. The candidate is also debarred for two consecutive semesters from class work and all University examinations. The continuation of the course by the candidate is subject to the academic regulations in connection with forfeiture of seat.

8. Possess any lethal weapon or firearm in the examination hall.

Expulsion from the examination hall and cancellation of the performance in that subject and all other subjects the candidate has already appeared including practical examinations and project work and shall not be permitted for the remaining examinations of the subjects of that semester/year. The candidate is also debarred and forfeits the seat.

9. If student of the college, who is not a candidate for the particular examination or any person not connected with the college indulges in any malpractice or improper conduct mentioned in clause 6 to 8.

Student of the colleges expulsion from the examination hall and cancellation of the performance in that subject and all other subjects the candidate has already appeared including practical examinations and project work and shall not be permitted for the remaining examinations of the subjects of that semester/year. The candidate is also debarred and forfeits the seat.

Person(s) who do not belong to the College will be handed over to police and, a

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police case will be registered against them.

10. Comes in a drunken condition to the examination hall.

Expulsion from the examination hall and cancellation of the performance in that subject and all other subjects the candidate has already appeared including practical examinations and project work and shall not be permitted for the remaining examinations of the subjects of that semester/year.

11. Copying detected on the basis of internal evidence, such as, during valuation or during special scrutiny.

Cancellation of the performance in that subject and all other subjects the candidate has appeared including practical examinations and project work of that semester/year examinations.

12. If any malpractice is detected which is not covered in the above clauses 1 to 11 shall be reported to the University for further action to award suitable punishment.

Malpractices identified by squad or special invigilators

1. Punishments to the candidates as per the above guidelines. 2. Punishment for institutions : (if the squad reports that the college is also involved in

encouraging malpractices) (i) A show cause notice shall be issued to the college. (ii) Impose a suitable fine on the college. (iii) Shifting the examination centre from the college to another college for a specific

period of not less than one year.

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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY

HYDERABAD

I Year M.Tech. AE- I Semester L P C

3 0 3

Aim:

MATHEMATICAL MODELING

The student shall be introduced to advanced mathematic modeling concepts.

Outcome: The student will be able mathematically describe the complex phenomena & can attempt solve

using various numerical tools.

UNIT-I: INTRODUCTION TO MODELING AND SINGULAR PERTURBATION

METHODS Definition of a model, Procedure of modeling: problem identification, model formulation,

reduction, analysis, computation, model validation, Choosing the model, Singular Perturbations:

Elementary boundary layer theory, Matched asymptotic expansions, Inner layers, Nonlinear

oscillations

UNIT-II: VARIATIONAL PRINCIPLES AND RANDOM SYSTEMS Variational calculus: Euler’s equation, Integrals and missing variables, Constraints and Lagrange

multipliers, Variational problems: Optics-Fermat’s principle, Analytical mechanics: Hamilton’s

principle, Symmetry: Noether’s theorem, Rigid body motion, Random systems: Random

variables, Stochastic processes, Monte Carlo method

UNIT-III: FINITE DIFFERENCES: ORDINARY AND PARTIAL DIFFERENTIAL

EQUATIONS ODE: Numerical approximations, Runge-Kutta methods, Beyond Runge-Kutta, PDE:

Hyperbolic equations-waves, Parabolic equations-diffusion, Elliptic equations-boundary values

CELLULAR AUTOMATA AND LATTICE GASES

Lattice gases and fluids, Cellular automata and computing

UNIT- IV: FUNCTION FITTING AND TRANSFORMS Function fitting: Model estimation, Least squares, Linear least squares: Singular value

decomposition, Non-linear least squares: Levenberg-Marquardt method, Estimation, Fisher

information, and Cramer-Rao inequality, Transforms:Orthogonal transforms, Fourier transforms,

Wavelets, Principal components

FUNCTION FITTING ARCHITECTURES Polynomials: Pade approximants, Splines, Orthogonal functions, Radial basis functions, Over-

fitting, Neural networks: Back propagation, Regularization

UNIT-V: OPTIMIZATION AND SEARCH

Multidimensional search, Local minima, Simulated annealing, Genetic algorithms

FILTERING AND STATE ESTIMATION

Matched filters, Wiener filters, Kalman filters, Non-linearity and entrainment, Hidden Markov

models

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TEXT BOOK The Nature of Mathematical Modeling, Neil Gershenfeld, Cambridge University Press, 2006,

ISBN 0-521-57095-6

REFERENCE BOOKS 1. Mathematical Models in the Applied Sciences, A. C. Fowler, Cambridge University

Press, 1997, ISBN 0-521-46140-5

2. A First Course in Mathematical Modeling, F. R. Giordano, M.D. Weir and W.P. Fox,

2003, Thomson, Brooks/Cole Publishers

3. Applied Numerical Modeling for Engineers, Donald De Cogan, Anne De Cogan, Oxford

University Press, 1997

Course Coverage Summary for

Mathematical Modelling

TEXT BOOK

TITLE

Chapters

in Text

Book

Units /

Topics

Covered

AUTHOR

PUBLISHERS

EDITION

& YEAR

The Nature of

Mathematical

Modeling

2-9

1-5

Neil

Gershenfeld

Cambridge

University

Press

2006

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Code No: D109117601

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

M. Tech I Semester Supplementary Examinations September 2010


(Aerospace Engineering)

Time: 3hours Max. Marks: 60

Answer any five questions

All questions carry equal marks

- - -

1. What are the features to be observed for identifying a singular perturbation

problem? Discuss Prandtl’s technique for the solution of the boundary value

problem

ε y’’

+ y’

+ y =0,

y(0)=α and y(1)=β

using the method of asymptotic expansions.

2. What is a variational principle? Derive Euler’s equation for a variational

extremum and illustrate it with an example to find minimum distance between

two points in a plane

3. Explain the Lax method for the following first order hyperbolic Partial

Differential Equation and conduct the stability analysis.

∂u / ∂t = -υ (∂u / ∂x)

4. Describe the fourth-order Runge-Kutta method for a system of first order ordinary

differential equations, and explain how the step size is chosen based on the

approximation error.

5. Distinguish between parametric and non-parametric function fitting. Explain the

technique of linear least squares fitting of observation data. Explain when one has

to go for Singular Value Decomposition (SVD) technique and briefly describe the

principle of SVD.

6. Define Discrete Fourier Transformation (DFT) and its corresponding inverse

transform for N-dimensional data vector. Explain the logic involved in enhancing

the computing speed of DFT by Fast Fourier Transform (FFT).

7. How are Genetic algorithms different from simulated annealing? Explain the steps

involved in applying genetic algorithm in optimization and search problems.

8. Explain the differences between Kalman filtering and Weiner filters. Discuss the

steps involved in Extended Kalman filter for non-linear systems.

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Code No: C7601


M.Tech I - Semester Examinations, March 2011


(AEROSPACE ENGINEERING)




- - -

1. Discuss the following with examples: i) Order symbols: Big ‘O’ and Small ‘o’ ii) Asymptotic sequence and asymptotic expansion

iii) Regular perturbation

iv) Singular perturbation [ 3+3+3+3]

2. State variational principle. Derive Euler’s equation for a variational extremum and apply

it to find minimum distance between two points in a plane. [ 12 ]

3. Describe fourth-order Runge-Kutta approximation for a system of ordinary differential

equations and discuss how to choose step size for desired accuracy in solving a given

problem. [ 12 ]

4. Explain cellular automata model for a lattice gas and discuss through schematic diagrams

how FHP rule operates in two dimensions on a triangular lattice. [ 12 ]

5. Define Discrete Fourier Transformation (DFT) and its corresponding inverse transform

for N-dimensional data vector. Explain the logic involved in enhancing the computing

speed of DFT by Fast Fourier Transform (FFT) [ 12 ]

6. Discuss with the help of a schematic diagram the steps involved in applying genetic

algorithms for search and optimization problems. [ 12 ]

7. Describe a neural network with one hidden layer using a schematic diagram and discuss

the steps involved in building a mathematical model using it [ 12 ]

8. Explain how extended Kalman filter is used for state estimation of non-linear systems

given measurements of observable quantities. [ 12 ]

*****

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Code No: C7601


M. Tech I - Semester Examinations, April/May-2012






- - -

1. Discuss the difference between a regular perturbation method and a singular

perturbation method with an example. Discuss Prandtl’s technique for the solution of

the boundary value problem

ε y" + y' + y = 0,

y(0) = α and y(1) = β

using the method of asymptotic expansions.

2. Explain the differences between Newtonian Mechanics and Analytical Mechanics.

Derive Euler-Lagrange equations for a conservative system using Hamilton’s

principle and illustrate with an example.

3. Describe cellular automata model for a gas and discuss through diagrams how FHP

lattice gas operates in two dimensions with the help of triangular lattice.

4. Explain the fourth-order Runge-Kutta method for a system of first order ordinary

differential equations, and discuss how the step size is chosen.

5. Define Discrete Fourier Transformation (DFT) and its corresponding inverse

transform for n-dimensional data vector. Discuss the logic involved in enhancing the

computing speed of DFT by Fast Fourier Transform (FFT).

6. Explain simulated annealing technique used in optimization and search problems.

How is it different from Genetic algorithms?

7. Discuss with help of a diagram the procedure involved in building a mathematical

model using artificial neural networks.

8. How is a Kalman filter different from a Weiner filter? Discuss the steps involved in

Kalman filter for linear systems with the help of a schematic diagram.

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Aim:


M. Tech – I Year – I Sem. Aerospace Engg.

ENGINEERING ANALYSIS OF FLIGTHT VEHICLES

The student shall be introduced to the advanced engineering analysis aspects of flight vehicles.

Outcome: The student will be in a position to take up some specific tasks in flight vehicle engineering

analysis.

UNIT-I: THE MORPHOLOGY OF FLIGHT VEHICLES

Introduction, Key factors affecting vehicles configuration, Some representative flight vehicles.

UNIT-II: EQUATIONS OF MOTION FOR RIGID FLIGHT VEHICLES Definitions, Vector and Scalar realizations of Newton’s second law, The tensor of inertia, Choice

of vehicle axes, Operation of the vehicle relative to the ground; flight determination,

Gravitational terms in the equations of motion, The state vector.

INTRODUCTION TO VEHICLE AERODYNAMICS Aerodynamics contributions to X, Y and M, dimensionless coefficients defined, equations of

perturbed longitudinal motion.

UNIT-III: AIRCRAFT DYNAMICS Equations of Motion of Aircraft including forces and moments of control surfaces, Dynamics of

control surfaces

STATIC STABILITY, TRIM STATIC PERFORMANCE AND RELATED SUBJECTS

Impact of stability requirements on design and longitudinal control, Static performance

UNIT-IV: DYNAMIC PERFORMANCE OF SPACECRAFT WITH RESPECT TO NON-

ROTATING PLANETS Introduction, Numerical integration of ordinary differential equations, Simplified treatment of

boost from a non-rotating planet, An elementary look at staging, Equations of boost from a

rotating planet.

UNIT-V: DYNAMIC PERFORMANCE OF SPACECRAFT Equations of Motion of Launch Vehicles with respect to a rotating planet, Motion of Spacecraft

with respect to a rotating planet.

DYNAMIC PERFORMANCE-ATMOSPHERIC ENTRY

Equation of motion, Approximate analysis of gliding entry into a planetary atmosphere.

MRCET


Course Coverage Summary

ENGINEERING ANALYSIS OF FLIGHT VEHICLES

TEXT

BOOK

TITLE

Chapters

in Text

Book

Units /

Topics

Covered

AUTHOR

PUBLISHERS

EDITION

& YEAR

Engineering

Analysis of

Flight

Vehicles,

1,2,3,6,

7,8,9,11

1-5

Holt

Ashley

Dover

Publications

1992

MRCET


Code No: C7602


M.Tech I - Semester Examinations, March/April 2011

ENGINEERING ANALYSIS OF FLIGHT VEHICLES (AEROSPACE ENGINEERING)




- - -

1. Explain the major factors affecting the configuration of a reusable space transport

vehicle. [12]

2. Starting from the six degrees of freedom equations of motion of a rigid body

under the effect of moments about X, Y and Z axes, in terms of, derive the

equations in terms of the Inertia tensor. [12]

3. Derive the equation for flow turning angle in Prandtl -Meyer expansion of a

supersonic flow. [12]

4. Starting from the equations of motion of a rigid body acted upon by forces along

the three body axes, derive the perturbation equations of motion. [12]

5. Explain Elevator Hinge Moment and Stick Force to trim. [12]

6. Derive the equation for acceleration of a rocket in ‘field-free space’ including the

effect of drag. [12]

7. A two stage rocket is launched vertically from a place on the equator under the

following conditions. Specific impulse, propellant fractions are 200 seconds and

0.9 respectively for both the stages. Mass of each motor at launch is 1000 kg and

the payload mass is 100 kg. Compute the velocity of the rocket, considering the

earth rotational velocity. [12]

8. Derive the equation for the flight path angle of a lifting re-entry vehicle. [12]

* * * * * *

R09

MRCET


Code No: C7602


M.TECH I SEMESTER EXAMINATIONS, APRIL/MAY 2012

ENGINEERING ANALYSIS OF FLIGHT VEHICLES


Time: 3hours Max.Marks:60



- - -

1. Compare and contrast the external configurations of a subsonic and a supersonic

aircraft with the help of neat sketches.

2. Derive the equations of motion of an aircraft symmetrical about the plane passing

through the longitudinal and yaw axes. The sketches should be neat and the

symbols used should be explained very clearly.

3.(a) Describe the aerodynamic forces acting on an aircraft and the vehicle parameters

that influence the magnitudes of these forces.

(b) Explain the variations of the aerodynamic forces and moments occurring on an

airfoil as the relevant parameters vary.

4. State the equations of motion of an aircraft, and from them, derive the small

perturbation equations of motion in longitudinal plane.

5.(a) Explain the forces and moments acting on an aircraft in the pitch plane.

(b) Derive an expression for the elevator deflection angle required to ensure a

trimmed flight in longitudinal plane.

6. Explain, in the case of a vehicle boosting from a non-rotating planet,

(a) Thrust and characteristic velocity,

(b) Change in speed,

(c) Effect of gravity,

(d) Loss due to drag.

7. Derive the equations of motion of a rocket lifting from the earth, considering the

effect of angular velocity of the earth.

8. Define non-dimensional altitude used to define the density of earth’s atmosphere.

With the help of this, derive the equations of motion of a reentry body.

****

R09

MRCET


MRCET


Aim:



CONTINUUM MECHANICS

The student shall be given the in depth understanding of continuum mechanics as applicable to

aerospace structures.

Outcome: The student will be solve complex problems in fluid structure interactions in continuum frame

work.

UNIT I: INTRODUCTION, VECTORS AND TENSORS

Background and Overview, Vector Algebra - Definition of a Vector, Scalar and Vector Products,

Plane Area as a Vector, Components of a Vector, Summation Convention, Transformation Law

for Different Bases; Theory of Matrices - Definition, Matrix Addition and Multiplication of a

Matrix by a Scalar, Matrix Transpose and Symmetric Matrix, Matrix Multiplication, Inverse and

Determinant of a Matrix; Vector Calculus - Derivative of a Scalar Function of a Vector, The del

Operator, Divergence and Curl of a Vector, Cylindrical and Spherical Coordinate Systems,

Gradient, Divergence and Curl Theorems; Tensors- Dyads and Polyads, Nonion Form of a

Dyadic, Transformation of Components of a Dyadic, Tensor Calculus, Eigenvalues and

Eigenvectors of Tensors

UNIT II: KINEMATICS OF CONTINUA Introduction, Description of Motion- Configurations of a Continuous Medium, Material

Description, Spatial Description, Displacement Field; Analysis of Deformation- Deformation

gradient tensors, Isochoric, Homogeneous and Inhomogeneous Deformations, Change of volume

and surface; Strain Measures- Cauchy-Green deformation tensors, Green Strain tensor, Physical

Interpretation of the Strain Components, Cauchy and Euler Strain Tensors, Principal Strains;

Infinitesimal Strain Tensor and Rotation Tensor- Infinitesimal Strain Tensor, Physical

Interpretation of Infinitesimal Strain Tensor Components, Infinitesimal Rotation Tensor,

Infinitesimal Strains in Cylindrical and Spherical Coordinate Systems; Rate of Deformation and

Vorticity Tensors- Definitions, Relationship between D and E, .Polar Decomposition Theorem,

Compatibility Equations, Change of Observer- Material Frame Indifference.

UNIT III: STRESS MEASURES Introduction, Cauchy Stress Tensor and Cauchy’s Formula, Transformation of Stress

Components and Principal Stresses- Transformation of Stress Components, Principal Stresses

and Principal Planes, Maximum Shear Stress. Other Stress Measures - Preliminary Comments,

First Piola- Kirchhoff Stress Tensor, Second Piola- Kirchhoff Stress Tensor, Equations of

Equilibrium.

CONSERVATION OF MASS, MOMENTA AND ENERGY Introduction, Conservation of Mass - Preliminary Discussion, Material Time Derivative,

Continuity Equation in Spatial Description, Continuity Equation in Material Description

,Reynolds Transport Theorem. Conservation of Momenta - Principle of Conservation of Linear

Momentum, Equation of Motion in Cylindrical and Spherical Coordinates, Principle of

Conservation of Angular Momentum, Thermodynamic Principles - Introduction, The First Law

of Thermodynamics: Energy Equation, Special Cases of Energy Equation, Energy Equation for

One-Dimensional Flows , The Second Law of Thermodynamics.

MRCET


UNIT IV: CONSTITUTIVE EQUATIONS Introduction, Elastic Solids - Generalized Hooke’s Law, Material Symmetry, Monoclinic

Materials, Orthotropic Materials, Isotropic Materials, Transformation of Stress and Strain

Components, Nonlinear Elastic Constitutive Relations, Constitutive Equations for Fluids - Ideal

Fluids, Viscous Incompressible Fluids, Non-Newtonian Fluids, Heat Transfer - General

Introduction, Fourier’s Heat Conduction Law, Newton’s Law of Cooling, Stefan-Boltzmann

Law, Electromagnetics - Maxwell’s Equation, Constitutive Relations.

LINEARIZED ELASTICITY Governing Equations, The Navier Equations, The Beltrami-Michell Equations, Types of

Boundary Value Problems and Superposition Principle. Clapeyron’s theorem and Reciprocity

Relations - Clapeyron’s theorem, Betti’s Reciprocity Relations, Maxwell’s Reciprocity Relation,

Solution Methods, Types of Solution Methods, Example: Rotating Thick Walled Cylinder; Two-

Dimensional Problems, Airy Stress Function, End Effects: Saint-Venant’s Principle, Torsion of

Noncircular Cylinders. Principle of Minimum Total Potential Energy - Total Potential Energy

Principle, Derivation of Navier’s Equations, Castiglian’s Theorem I . Hamilton’s Principle-

Hamilton’s Principle for a Rigid Body, Hamilton’s Principle for a Continuum

UNIT V: FLUID MECHANICS AND HEAT TRANSFER Governing Equations- Preliminary Comments, Summary of Equations, Viscous Incompressible

Fluids, Heat Transfer; Fluid Mechanics Problems - Inviscid Fluid Statics, Parallel Flow (Navier-

Stokes Equations), Problems with Negligible Convective Terms; Heat Transfer Problems- Heat

Conduction in a Cooling Fin, Axisymmetric Heat Conduction in a Circular Cylinder, Two-

Dimensional Heat Transfer, Coupled Fluid Flow and Heat Transfer

LINEAR VISCOELASTICITY Preliminary Comments- Initial Value Problem, the Unit Impulse, and the Unit Step Function,

The Laplace Transform Method, Spring and Dashpot Models - Creep Compliance and

Relaxation Modulus, Maxwell Element , Kelvin-Voigt Element, Three-Element Models , Four-

Element Models , Integral Constitutive Equations, Hereditary Integrals, Hereditary Integrals for

Deviatoric Components, The Correspondence Principle, Elastic and Viscoelastic Analogies

TEXT BOOK

1. An Introduction to Continuum Mechanics, J.N. Reddy, Cambridge University Press, 2007

REFERENCE BOOKS

1. Continuum Mechanics, George. E. Mase, Schaum’s Outline Series, McGraw-Hill Book

Company, 1969 2. Continuum Mechanics, Ellis H. Dill, CRC Press, 2006

3. Continuum Mechanics for Engineers, Second Edition, George E. Mase, G.Thomas Mase

CRC Press,1999

4. Computational Continuum Mechanics, Ahmed A. Shabana, Cambridge University Press,

2008

5. Introduction to Computational Mechanics, Fourth Edition, W. Michael Lai, David Rabin

and Erhard krempl, .Elsevier Inc, 2010

6. Introduction to the Mechanics of a Continuous Medium, Lawrence E. Malvern, Prentice-

Hall, 1969

7. A First Course in Continuum Mechanics, Y. C. Fung, Prentice Hall, 1994

MRCET


Course Coverage Summary for

CONTINUUM MECHANICS

TEXT

BOOK

TITLE

Chapters

in Text

Book

Units /

Topics

Covered

AUTHOR

PUBLISHERS

EDITION

& YEAR

An

Introduction

to Continuum

Mechanics

1-9

1-5

J.N. Reddy

Cambridge

University Press

2007

MRCET


Code No: C7603


M.Tech I Semester Examinations March/April-2011

CONTINUUM MECHANICS





- - -

1. Derive the equations of Equilibrium for 3D element subjected to normal and

shear stresses causing deformation? Express the conditions of Equilibrium for

plane stress. [12]

2. A cantilever beam of length L and depth ‘2h’ is in a state of plane stress subjected

to uniformly distributed load, ω having unit thickness. Show that the stress

function Ax2 Bx

2 y cy

3 D 5x2 y

3 y5 is valid for the beam and evaluate

the constants A, B, C and D. [12]

3.a) Define Continuum Mechanics and explain its various engineering applications.

b) Explain the strain displacement relations with the help of 3D element under

deformation. [12]

4. Derive the equation for stresses on a ‘2D’ inclined plan in a 2D stress system.

Also derive the conditions for principal stresses, and Maximum shear stress. [12]

5. Given the following stress field in a body in Equilibrium and referred to spherical

coordinate system

Where A, B, C constants, determine if the stress field satisfies the equilibrium

equations when the body forces are zero and all other stresses are zero. [12]

6.a) Explain Reynold’s transport theorem.

b) Explain the principle of conservation of linear momentum and angular momentum

with illustrations. [12]

7.a) Explain various modes of heat transfer.

b) Explain Fourier’s heat conduction law with the help of composite walls. [12]

8.a) Derive the Navier-Stokers Equations for laminar viscous flow.

b) Using Navier-stokes Equation, establish the equation for maximum velocity

through a pipe. Also find the head loss due to friction. [12]

--oOo--

R09

MRCET


Code No: C7603


M.TECH I SEMESTER EXAMINATIONS APRIL/MAY-2012

CONTINUUM MECHANICS





- - -

1.a) Establish the following identity using the index notation:

div (A x B) = x A . B - x B . A

b) For an arbitrary second order tensor S, determine the expression for x S.

2. Derive the expressions for the components of Green – Lagrange strain tensor in

cylindrical coordinate system.

3. The components of a stress dyadic at a point, referred to the Cartesian system, are

Find the principal stress and the principal plane associated with the maximum stress.

4. Derive the energy equation for one-dimensional flow.

5. Derive the Newtonian constitutive equation for stress tensor in a fluid motion.

6. Derive Michell’s equations for an elastic system.

7. Derive the Navier – Stokes equations in Cartesian coordinate system.

8. Write short notes on

a) Maxwell element

b) Creep response

c) Kelvin – Voigt element.

* * * * * *

R09

MRCET


MRCET




AIR TRANSPORTATION SYSTEMS

Aim & Objectives:

The subject will introduce the air transportation systems in advanced level.

Outcome:

The student with acquire the operational knowledge of air transport.

UNIT – I: THE AVIATION INDUSTRY Introduction, history of aviation - evolution, development, growth, challenges. The aerospace

industry, airline industry – structure and economic characteristics

UNIT – II: AIR TRANSPORTATION SYSTEMS – OBJECTIVES, CONSTRAINTS Air transportation systems – objectives, environment, operational constraints - statutory

compliance with safety, security and environmental regulations, financial viability – demand,

costs, efficiency and effectiveness, compatibility with operational infrastructure – aircraft,

airports, facilities, equipment, crew and personnel, the atmosphere, air space..

STRATEGIES TO MEET OBJECTIVES Analysis, understanding, forecasting, planning, marketing, management of resources. Adoption

of improved technologies, optimal operational procedures, synthesis, implementation

UNIT –III: THE SYSTEM ELEMENTS – AIRCRAFT The system elements – the aircraft, airlines, airports, airspace. Aircraft - costs, compatibility with

objectives, and operational infrastructure, direct and indirect operating costs, safety, security,

efficiency and effectiveness.

AIRLINES – OBJECTIVES, PLANNING, OPERATIONS – PROCEDURES Route selection and development, fleet planning and acquisition, airline schedule development,

fleet assignment, aircraft routing, gate assignment, flight operations - irregular operations,

schedule recovery and robustness. Maintenance of aircraft and equipment. Airline operating

costs and measure of productivity.

UNIT –IV: AIRPORTS Airports - demand, siting, runway characteristics, capacity, pavement strength, maneuvering

area, aprons, passenger terminals, safety, security. Airport operations –. Airport demand,

capacity and delays

UNIT – V: AIRSPACE Airspace management – Communication, navigation, surveillance systems - categories of

airspace, sectors, separation minima, capacity, demand, delay. The ATC systems - evolution,

equipment and operations. ICAO future air navigation systems

CHALLENGES OF THE FUTURE Coping with future changes. Critical issues and prospects

for airline industry

MRCET


TEXT BOOKS 1. The Air Transport System, Hirst, M.,Woodhead Publishing Ltd, (also AIAA), 2008,

ISBN-13: 978 1845693251.

2. Airline Operations and Scheduling, Bazargan, M.,Ashgate, 2004, ISBN – 075463616X.

3. Air Transportation – A Management Perspective, Wensveen,J.G., Ashgate, 2007, ISBN

978-0-7546-7171-8.

4. Global Airline Industry, Belobaba, P. et al., AIAA,2009.


AIR TRANSPORT SYSTEM

TEXT

BOOK

TITLE

Chapters

in Text

Book

Units /

Topics

Covered

AUTHOR

PUBLISHERS

EDITION

& YEAR

The Air

Transport

System

1-8

1-5

Hirst, M

Woodhead

Publishing Ltd

2008

MRCET


Code No: C7604








- - -

1. Discuss through a diagram the series of traffic management phases that an aircraft

is subjected to and how they help in making an assessment of Air Traffic

Management System (ATM). [12]

2. Describe with a test case the types of disruptions that affect the air carriers. [12]

3. Explain the ATM Interaction Architecture stating assumptions involved. [12]

4. Describe the modeling aspects of departure and arrival processes at airports using

queuing theory. [12]

5. Discuss with the help of diagrams the safety feedback based ATM design and

ATM safety iceberg used in accident risk assessment for advance air traffic

management. [12]

6. Explain why humans are necessary in Air Traffic Management. [12]

7. What are the tools used for the assessment of the wake vortex induced accident

and incident risks? Discuss flight path evolution model. [12]

8. Describe the geometric approaches used for conflict prediction of aircraft

trajectories in Air Traffic Management and discuss their limitations. [12]

*****

R09 MRCET


Code No: C7604








- - -

1. Comment on the oligopolistic nature of the airline industry and give points to

support your comments.

2. Explain the challenges faced by the air transportation industry in meeting the

requirements of the market and focus on the strategies followed to overcome these

challenges.

3. Explain the operational aspects of an Airline and Airport. What are the major

hurdles in their development? Discuss.

4. What are the characteristics of good operable runway? Discuss.

5.a) Define communication, navigation and surveillance systems.

b) Write a short note on ICAO future air navigation system.

6. Discuss how the maintenance of an aircraft is carried out. Briefly explain the

importance of ‘D’ check.

7. Focus on the critical issues which constrain the growth of aerospace industry and

how they are handled.

8. Discuss the factors to be considered during airline scheduling.

* * * * * *

R09

MRCET


MRCET


Aim:


I Year M.Tech., AE- I Semester

AERODYNAMICS OF FLIGHT VEHICLES

(ELECTIVE-I)

The student shall be taught advanced concepts in aero dynamics of flight vehicles.

Outcome:

The student will able tackle complex aero dynamics problems.

UNIT-I: AERODYNAMIC CHARACTERISTICS OF AIRFOILS: Vortex sheet, Vortex

sheet in thin-airfoil theory, Planar wing, Properties of symmetrical airfoil, Properties of

cambered airfoil, Flapped airfoil, Numerical Solution of thin airfoil problem, Airfoil of arbitrary

thickness and camber

UNIT-II: THE FINITE WING: Flow fields around finite wings, Downwash and induced drag,

Fundamental equations of finite-wing theory, Elliptical lift distribution, Arbitrary circulation

distribution, Twisted wing: Basic and Additional lift, Approximate calculation of additional lift,

Winglets, Stability and trim of wings, Higher approximations, The complete airplane,

Interference effects,

AIRFOILS IN COMPRESSIBLE FLOWS: Boundary conditions, Airfoils in subsonic flow:

Prandtl-Glauert transformation, Critical Mach number, Airfoils in transonic flow, Airfoils in

supersonic flow

UNIT-III: WINGS AND WING-BODY COMBINATIONS IN COMPRESSIBLE FLOW: Wings and bodies in compressible flows: Prandtl-Glauert-Goethert transformation, Influence of

sweepback, Design rules for wing-fuselage combinations

LAMINAR BOUNDARY LAYER IN COMPRESSIBLE FLOW: Conservation of energy in

the boundary layer, Rotation and entropy gradient in the boundary layer, Similarity

considerations for compressible boundary layers, Solution of energy equation for Prandtl number

unity, Temperature recovery factor, Heat transfer versus skin friction, Velocity and temperature

profiles and skin friction, Effects of pressure gradient

UNIT-IV: FLOW INSTABILITIES AND TRANSITION FROM LAMINAR TO TURBULENT FLOW: Gross effects, Reynolds experiment, Tollmien-Schlichting instability

and transition, Natural laminar flow and laminar flow control, Stability of vortex sheets,

Transition phenomenon, Methods for experimentally detecting transition, Flow around spheres

and circular cylinders

UNIT-V: TURBULENT FLOWS: Description of turbulent field, Statistical properties, Conservation

equations, Laminar sub-layer, Fully developed flows in tubes and channels, Constant-pressure

turbulent boundary layer, Turbulent drag reduction, Effects of pressur gradient, Stratford

criterion for turbulent separation, Effects of compressibility on skin friction, Reynolds analogy:

Heat transfer and temperature recovery factor, Free turbulent shear flows

MRCET


AIRFOIL DESIGN, MULTIPLE SURFACES, VORTEX LIFT, SECONDARY FLOWS, VISCOUS EFFECTS: Airfoil design for high C l max , Multiple lifting surfaces, Circulation

control, Streamwise vorticity, Secondary flows, Vortex lift strakes, Flow about three-

dimensional bodies, Unsteady lift



Elective-I

TEXT BOOK

TITLE

Chapters

in Text

Book

Units /

Topics

Covered

AUTHOR

PUBLISHERS

EDITION

& YEAR

Foundations of

Aerodynamics:

Bases of

Aerodynamic

Desig

4-19

1-5

Arnold M.

Kuethe and

Chuen-

Yen Chow

John Wiley &

Sons, Inc.

Fifth

Edition,

1997

MRCET


Code No: C7606








- - -

1. Discuss the properties of symmetric and cambered airfoils. Compare the

circulation distribution and aerodynamic characteristics of symmetric and

cambered airfoils. [12]

2. Prove that elliptic distribution of lift over a finite wing yields minimum induced

[12]

aerodynamic

[12]

[12]

and

b) Discuss the solution of energy equation for Prandtl number unity. [12]

6. Briefly discuss:

a) Compressibility, turbulence and noise and Centrifugal instability.

b) Flow around spheres and circular cylinders. [12]

7. Discuss fully developed flows in tubes and channels. [12]

8. Discuss airfoil design for maximum lift coefficient. [12]

* * * * *

R09

drag.

3. Compare the subsonic and supersonic airfoils

characteristics.

and their

4. Discuss Prandtl – Glauert – Goethert transformation.

5. a) Derive Crocco’s relation

MRCET


Code No: C7606


M. TECH. I SEMESTER EXAMINATIONS, APRIL/MAY-2012



Time: 3 hours Max. Marks: 60



- - -

1. Prove that the velocity induced in the region surrounding a doubly infinite vortex

sheet of constant strength satisfies equation of continuity everywhere in that

region.

2.a) Derive the fundamental equation of finite wing theory.

b) State and explain Biot - Savart law and Helmholtz’s theorem.

3.a) Derive velocity potential equation for a subsonic flow over an airfoil.

b) Explain, briefly, the concept of critical Mach number for an airfoil. Derive the

expression for the coefficient of pressure over an airfoil,

Explain all the terms used, clearly .

4. Write Notes on:

a) Prandtl - Glauert transformation,

b) Area rule for transonic flow,

c) Effect of sweep back angle.

5.a) Explain the flow in the boundary layer including entropy gradient.

b) Compare the incompressible and compressible boundary layers.

6.a) Explain transition in the context of boundary layers. What are the different

methods available for experimentally detecting transition?

b) Describe Tollmien – Schlichting instability.

7. What is a turbulent flow? What are its properties?

8.a) Define and explain ‘vorticity’ and ‘streamwise vorticity’. b) Derive an expression for the velocity over a sphere.

*****

R09

MRCET


MRCET




FUNDAMENTALS OF AEROSPACE ENGINEERING

(ELECTIVE-I) Aim: To impart fundamental and advanced aspects of aerospace engineering to non B. Tech

aeronautical engineering students.

Outcome: The non B. Tech aeronautical engineering students will gain insights to various

aspects of aircraft structures flight systems and flight mechanics.

UNIT-I: INTRODUCTION TO AERONAUTICS AND ASTRONAUTICS: Historical

Perspective of Aeronautics and Astronautics, Anatomy of the Airplane, Anatomy of a Space

Vehicle, Aerodynamic forces, Parameters affecting aerodynamic forces: Dimensional analysis;

Theory and experiment: wind tunnels, Atmosphere: Properties of U.S. standard atmosphere,

Definitions of altitude,

UNIT-II: ONE DIMENSIONAL FLOWS IN INCOMPRESSIBLE AND COMPRESSIBLE FLUIDS: Continuity equation, Bernoulli’s equation, Application of

Bernoulli’s equation: Airspeed indicators and wind tunnels, One-dimensional compressible flow

concepts, Speed of sound, Compressible flow equations in a variable-area stream tube,

Application to airspeed measurement, Applications to channels and wind tunnels

TWO-DIMENSIONAL FLOW AND FINITE WING: Limitations of one-dimensional flow

equations, Theory of lift: circulation, Airfoil pressure distribution, Helmholtz vortex theorems,

Simulating the wing with a vortex line, Downwash, Elliptic lift distribution, Lift and drag:

momentum and energy, Slope of finite wing lift curve, Verification of Prandtl wing theory,

Additional effects of wing vortices, Search for reduced induced drag

UNIT-III:

VISCOUS EFFECTS, TOTAL DRAG DETERMINATION AND HYPERSONIC FLOWS: Boundary layer, Boundary layer on bluff bodies, Creation of circulation, Laminar and turbulent

boundary layers: skin friction, Nature of Reynolds number, Effect of turbulent boundary layer on

separation; Parasite drag, Drag due to lift, Importance of aspect ratio; Prediction of drag

divergence Mach number, Sweptback wings, Total drag, Supersonic flow: shock waves and

Mach waves, Supersonic wing lift and drag, Area rule, Supersonic aircraft, Hypersonic flows:

Temperature effects, Newtonian theory

AIRFOILS, WINGS AND HIGHLIFT SYSTEMS: Early airfoil development, Modern

airfoils, Supersonic airfoils, Airfoil pitching moments, Effects of sweepback on lift, airfoil

characteristics, Airfoil selection and wing design; Airfoil maximum lift coefficient, Leading and

trailing edge devices, Effect of sweepback, Deep stall, Effect of Reynolds number, Propulsive

lift

UNIT-IV: AIRPLANE PERFORMANCE, STABILITY AND CONTROL: Level flight performance,

Climb performance, Range, Endurance, Energy-state approach to airplane performance, Takeoff

performance, Landing performance; Static longitudinal stability, Dynamic longitudinal stability,

Dynamic lateral stability, Control and Maneuverability: turning performance, Control systems,

Active controls

MRCET


UNIT-V: AEROSPACE PROPULSION AND AIRCRAFT STRUCTURES: Aerospace

Propulsion: Piston engines, Gas turbines, Speed limitations of gas turbines: ramjets, Propellers,

Overall propulsion efficiency, Rocket engines, Rocket motor performance, Propulsion-airframe

integration; Aircraft structures: Importance of structural weight and integrity, Development of

aircraft structures, Importance of fatigue, Materials, Loads, Weight estimation

ROCKET TRAJECTORIES, ORBITS AND REENTRY: Rocket trajectories, Multistage

rockets, Escape velocity, Circular orbital or satellite velocity, Elliptical orbits, Orbital

maneuvers, Atmospheric entry: ballistic entry and lifting entry, Entry heating.



Elective-I

TEXT

BOOK

TITLE

Chapters

in Text

Book

Units /

Topics

Covered

AUTHOR

PUBLISHERS

EDITION

& YEAR

Introduction

to Flight

1-6 & 9

1, 4 & 5

John D.

Anderson,

Jr

Tata McGraw-

Hill Publishing

Company

Fifth

Edition,2007

Fundamentals

of

Aerodynamics

4,5&11

2 & 3

John D.

Anderson,

Jr

Tata McGraw-

Hill Publishing

Company

Fifth

Edition,2007

MRCET


R09

Code No: D109117605


M.Tech I Semester Regular Examinations March/April 2010






- - -

1. What are various parts of an aero plane and give the functioning

of control surfaces? How are aero dynamic forces developed on an

aero plane? Describe the parameters affecting these aero dynamic

forces through dimensional analysis.

2. Derive the compressible flow equations in a variable area stream tube.

A DC-10 is crusing at its assigned mach number of 0.85. The outside

air temperature is 232K. At a given point on the upper surface of

the wing the pressure measured is 20,100N/m2. The temperature at

this point is 221K. What is the lift force, pressure, density and true

speed of airplane?

3. State Helmholtz vortex theorems. Applying these theorems on to

flow over a wing calculate induced drag coefficient for an elliptical

lift distribution?

4. Discuss in detail about

a. Boundary layer formation on bluff bodies

b. Importance of aspect ratio & its effect on aerodynamic forces.

5. Write a short note on

a) Development of airfoils

b) Airfoil selection & wing design

c) Leading & trailing edge devices

d) Propulsive lift.

6. How do you calculate range and endurance of an airplane?

7. Explain about various types of propulsion systems used in aircraft

and compare the working of piston engine and turbojet engine?

8. Discuss in detail about orbital maneuvers and atmospheric entry. A

satellite is to be boosted to an orbital altitude of 500Km. What is

orbital velocity & orbital period?

**********

MRCET


Code No: C7605








- - -

1. Explain the variation of temperature with altitude. Define various altitudes and

give the relationships between them. Calculate the pressure, pressure ratio,

temperature, density & density ratio at an altitude of 14 km. [12]

2. Starting from continuity equation derive Bernoulli’s equation and explain its

application in air speed indicators and wind tunnels. A wind tunnel located at a

pressure altitude of 500 meters (ρ = 1.1674 kg/m3, p = 95472 N/m

2), has a

circular test section with 3 meter diameter. The air speed is 80 m/sec in the test

section, which is vented to the ambient atmosphere. The air speed in the larger

diameter section just upstream of the contraction is 16 m/sec. Calculate upstream

diameter, dynamic pressure in the test section, upstream pressure and height of

mercury column. [12]

3. Explain in detail about vortex flow and generation of lift through circulation.

[12]

4. Describe about supersonic flow and temperature effect of hypersonic flow?

[12]

5. Discuss in detail about:

a) Leading & trailing edge devices.

b) Deep stall.

c) Effect of sweep back on maximum lift.

d) Airfoil selection & wing design. [12]

6. Describe about stability and control of an airplane and give the conditions for

static longitudinal stability. Also explain about static margin and neutral point.

[12]

7. What are the structural elements and materials used in the construction of an

aircraft? [12]

8. Explain in detail about elliptical orbits & Kepler’s laws of planetary motion.

[12]

R09

MRCET


Code No: C7605

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD M.Tech I Semester Examinations October/November-2011






- - -

1. a) Define the ‘Standard Atmosphere’ and ‘Altitude’. Obtain a relation between

Geopotential and Geometric altitudes. (6)

b) Write a detailed note on anatomy of the airplane, with a clear description of various

lift devices incorporated in its design. (6)

2. a) Explain the basic principles of measurement of air speed employing a pitot-static

tube. (6)

b) Obtain compressible flow equations in a stream line tube with variable area. (6)

3. a) State Helmholtz vortex theorems and apply it to discuss the characteristics of flow

over the wing with a vortex line. (6)

b) Calculate induced drag coefficient for an elliptical lift distribution over the wing.

(6)

4. a) Discuss the effects of friction in case of a stream line flow over a cylindrical body.

Extend the discussion to the viscous flow over an airfoil surface. (8)

b) Write short notes on swept back wings. (4)

5. a) Write a detailed note on development of airfoils basing on early design concepts that

led to recent supersonic airfoil design. . (8)

b) What does ‘Propulsive lift’ mean? (4)

6.

Write short notes on the following:

a) Takeoff performance

(4)

b) Dynamic lateral stability (4)

c) Turning performance. (4)

7. a) With the help of a neat sketch explain the working of gas turbine. Enumerate speed

limitations that arise in case of its operation. (6)

b) Structural design of an airplane is an intricate arrangement of various structural

elements, such as wing spars, fuselage longerons, stringers, and stiffeners. Elaborate

with the help of neat sketches. (6)

8. a) Write a note on ‘circular orbital velocity’ and ‘satellite velocity’. (6)

b) Write short notes on

i) Space vehicle reentry heating, and

ii) Escape velocity. (6)

R09

MRCET


Code No: C7605








- - -

1.a) Explain the working principle of a low-speed subsonic wind tunnel.

b) Write a detailed note on the anatomy of a space vehicle. Differentiate between

expendable and recoverable launch vehicles.

2.a) Discuss Bernoulli’s equation in detail and apply it to the operation of an air speed

indicator.

b) Define ‘Mach number’ and obtain an expression for it. Distinguish between

subsonic, and supersonic regions in terms of Mach number.

3.a) Write detailed notes on laminar and turbulent boundary layers.

b) Discuss the characteristics of supersonic flow with special emphasis on

shock waves and Mach waves.

4.a) Introduce the term ‘Reynolds number’ and discuss its nature.

b) Discuss how the drag coefficient (Cd) varies with Mach number (M) and how

prediction of the drag divergence Mach number is carried out.

5.a) Explain in detail the effect of wing sweep back on lift produced.

b) Write a brief note on ‘leading edge’ and ‘trailing edge’ devices designed for

producing high lift.

6. Taking all the basic forces acting on an airplane under steady, unaccelerated

conditions, describe a method to estimate its rate of climb as a function of excess

power.

7.a) Differentiate between the working principles of ‘gas turbine’ and ‘ramjet’ propulsive

systems. Use neat sketches to support the explanation.

b) Bring out the importance of fatigue with reference to aircraft structural design.

8.a) Illustrate the need for developing multistage rockets and explain various

configurations currently in use.

b) Discuss in detail orbital maneuvers with the help of neat sketches.

* * * * * *

R09

MRCET


MRCET


Aim:

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY

HYDERABAD


MODELLING AND SIMULATION OF FLUID FLOWS

(Elective-II)

The student is exposed to advanced topics in fluid flow to tackle engineering problems in aircraft

fluid systems.

Outcome:

The student can resolve fluid flow issues in aircraft systems in mathematically.

UNIT-I: BASIC EQUATIONS OF FLUID DYNAMICS AND DYNAMICAL LEVELS OF APPROXIMATION: General form of a conservation law, Mass conservation equation,

Momentum conservation law or equation of motion, Energy conservation equation; Navier–

Stokes equations, Approximations of turbulent flows, Thin shear layer approximation, Parabolized

Navier–Stokes equations, Boundary layer approximation, Distributed loss model, Inviscid flow

model: Euler equations, Potential flow model.

UNIT II: MATHEMATICAL NATURE OF THE FLOW EQUATIONS AND THEIR BOUNDARY CONDITIONS: Simplified models of a convection–diffusion equation, Definition

of the mathematical properties of a system of PDEs, Hyperbolic and parabolic equations:

characteristic surfaces and domain of dependence, Time-dependent and conservation form of the

PDEs, Initial and boundary conditions

UNIT III: DISCRETIZATION TECHNIQUES Finite Difference Method for Structured Grids: Basics of finite difference methods,

Multidimensional finite difference formulas, Finite difference formulas on non-uniform grids,

General method for finite difference formulae, Implicit finite difference formulae; Finite Volume

Method: Conservative discretization, Basis of finite volume method, Practical implementation of

finite volume method; Introduction to Finite Element Method: Finite element definition of

interpolation functions, Finite element definition of the equation discretization: integral

formulation, Method of weighted residuals or weak formulation, Galerkin method, Finite

element Galerkin method for a conservation law; Structured and Unstructured Grid Properties:

Structured grids, Unstructured grids, Surface and volume estimations, Grid quality and best

practice guidelines

UNIT IV: ANALYSIS OF NUMERICAL SCHEMES Consistency, stability and error analysis of numerical schemes: Basic concepts and definitions,

Von Neumann method for stability analysis, New Leapfrog, Lax-Fredrichs and Lax-Wendroff

schemes for the linear convection equation, Spectral analysis of numerical errors; General

Properties and High Resolution Numerical Schemes: General formulation of numerical schemes,

Generation of new schemes with prescribed order of accuracy, Monotonicity of numerical

schemes, Finite volume formulation of schemes and limiters

TIME INTEGRATION METHODS FOR SPACE DISCRETIZED EQUATIONS Analysis of spacediscretized systems, Analysis of time integration schemes, Selection of time integration

methods, Implicit schemes for multidimensional problems: Approximate factorization methods

MRCET


UNIT –V: ITERATIVE METHODS FOR RESOLUTION OF ALGEBRAIC SYSTEMS Basic iterative methods, Overrelaxation methods, Preconditioning techniques, Nonlinear

problems, Multigrid method.

NUMERICAL SIMULATION OF INVISCID FLOWS Euler equations, Potential flow

model, Numerical solutions for the potential equation, Finite volume discretization of the Euler

equations, Numerical solutions for the Euler equations

NUMERICAL SOLUTIONS OF VISCOUS LAMINAR FLOWS Navier-Stokes Equations

for laminar flows, Density based methods for viscous flows, Numerical solutions with the

density-based method, Pressure correction method, Numerical solutions with pressure correction

method.

TEXT BOOK Numerical Computation of Internal and External Flows, Second Edition, Charles Hirsch,

Elsevier Publication, 2007

REFERENCES

1. Computational Fluid Dynamics: The Basics with Applications, John David Anderson,

McGraw Hill, 1995

2. Computational Fluid Mechanics and Heat Transfer, 2nd Edition, John C. Tannehill, Dale A. Anderson, Richard H. Pletcher, Taylor & Francis, 1997.


MODELLING AND SIMULATION OF FLUID FLOWS

(Elective-II)

TEXT BOOK

TITLE

Chapters

in Text

Book

Units /

Topics

Covered

AUTHOR

PUBLISHERS

EDITION

& YEAR

Numerical

Computation of

Internal and

External Flows

1-12

1-5

Charles

Hirsch

Elsevier

Publication

Second

Edition &

2007

MRCET


Code No: A7610


M.Tech I Semester Regular Examinations March/April 2010

MODELING AND SIMULATION OF FLUID FLOWS





- - -

1. Discuss the physical interpretation of substantial derivative. Derive differential form of

general convection-diffusion conservation equation.

2. Discuss about thin shear layer approximation and boundary layer approximation for

Navier-Stokes equation and explain when these models are used.

3. Derive finite difference schemes for the following partial differential equations and

indicate their order of accuracy: (i) (∂u / ∂t )+ a (∂u / ∂x ) = 0.

(ii) (∂u / ∂t ) = a (∂2u / ∂x2

).

(iii) (∂2u / ∂x2

) + (∂2u / ∂y2

) = 0.

4. What are structured and unstructured grids? Discuss about body-fitted and multi-block

structured grids with the help of diagrams.

5. Define consistency, stability and convergence and describe Von Neumann method for

stability analysis of a numerical scheme.

6. Explain the concept of monotonicity and its importance in a numerical scheme. Derive

monotonicity condition for one-dimensional diffusion equation with explicit first order

difference in time and central discretization in space.

7. Write short notes on the following time integration methods for space-discretized

equations occurring in numerical simulation of fluid flows:

(i) Multistep methods.

(ii) Predictor-Corrector Methods.

(iii) Runge-Kutta Methods.

8. Describe briefly the potential flow model and explain the various steps involved in the

numerical solution of incompressible potential flow around a circular cylinder.

---o0o---

NR

MRCET


R09

Code No: C7610

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD M.Tech I- Semester Supplementary Examinations September, 2010






- - -

1. State the conservation law for a quantity U. Derive scalar conservation law in the

integral conservation form and comment on its properties

2. Discuss the salient features of the following approximations of Navier-Stokes

equations

i) Thin shear layer approximation

ii) Parabolized Navier-Stokes approximation.

3. Describe the cell-centered and cell-vertex approaches of finite volume method.

Compare finite element and finite volume methods and bring out their similarities

and differences.

4. Define structured and unstructured grids. What are the options that can be

considered for the treatment of curved solid boundaries using Cartesian type

grids? Describe different configurations of body-fitted structured grids (H-mesh,

C-mesh, O-mesh, I-mesh) with the help of diagrams.

5. a) State the Equivalence theorem of Lax and explain through a diagram its

implication on the relationship between the three properties of consistency,

stability and convergence of a numerical scheme.

b) Explain the physical significance of Courant-Freidrichs-Lewy (CFL) condition

through figures giving geometrical, characteristic interpretation for an example of

hyperbolic equations.

6. State Godunov’s theorem. Discuss the concept and methodology of limiters

introduced in high resolution schemes with the help of an example and relevant

diagrams. Describe the essential points to remember for the practical

implementation of selected limiters.

7. Write short notes on the basic ideas involved in the following overrelaxation

methods for the solution of algebraic systems widely used in CFD

i) Jacobi overrelaxation

ii) Successive Overrelaxation.

iii) Symmetric successive overrelaxation.

iv) Successive line overrelaxation.

8. Explain the basic approach of Pressure Correction Methods.

*****

MRCET


Code No: C7610


M.Tech I - Semester Examinations, March/April-2011






- - -

1.a) Briefly discuss about mass conservation equation, momentum conservation

equation and the energy conservation equation.

b) Derive the Navier-Stokes equations of a motion for a fluid flow. [12]

2.a) Describe about boundary layer approximations including separation of boundary

layer.

b) Write a short note on various flow models. [12]

3.a) Discuss about parabolic and hyperbolic equations in detail.

b) Differentiate between finite difference formulae and implicit finite difference

formulae. [12]

4.a) What is meant by finite element method and finite volume method? Explain it.

b) Discuss about finite element Galerkin method for a conservation law. [12]

5.a) Explain in detail about Von Neuman method for stability analysis.

b) What is the spectral analysis of numerical errors? [12]

6.a) Discuss in detail about an advanced addition to the accuracy barrier.

b) What is meant by monotonicity of numerical schemes? Explain about it. [12]

7.a) Briefly discuss about an analysis of the space-discretized systems.

b) Mention the various iterative methods for the resolution of algebraic systems.

Discuss it. [12]

8.a) Write a short note on potential flow model.

b) Briefly explain about finite volume discretization of the Euler equations. [12]

* * * * * *

R09 MRCET


Code No: C7610


M.Tech I Semester Examinations October / November 2011






- - -

1. Derive the general conservation form of momentum equation. Make necessary

assumptions. [12]

2. Give the classification of Partial differential equations? Explain the characteristic of each

type of Partial differential equations along with illustrations. [12]

3. Explain the term Consistency in numerical schemes and in detail explain the behavior of

errors and analyze them. [12]

4. What are different methods to evaluate Matrix inverse for the solution of simultaneous

algebraic equations? Compare them. [12]

5. A rod of length 0.4 m is maintained at temperatures of 1000C and 400

0C at its two ends.

Along the lateral surface, the rod is insulated. The cross sectional area of the rod is 10 X

10-3

m2

and its thermal conductivity is 1000 W/m-K. Express the resultant simultaneous equations in the matrix form and explain the type of coefficient matrix. [12]

6. What are the four basic rules of finite volume formulation? Hence obtain the discretized

form of one dimensional elliptic equation. Make the necessary assumptions. [12]

7. What are the difficulties arise due to discretization of pressure and velocity terms in

convection diffusion problem? How these difficulties are resolved and hence derive the

pressure correction equation. [12]

8. Write short notes on any two of the following:

a. Initial and boundary conditions

b. Weighted residual method

c. Potential flow model of Euler equation. [6+6]

********

R09

MRCET


Code No: C7610


M.TECH I - SEMESTER EXAMINATIONS, APRIL/MAY-2012 MODELING

AND SIMULATION OF FLUID FLOWS





- - -

1.a) List the basic equations of motion for a two dimensional, constant property and steady

flow field.

b) What are boundary layer approximations? Using the order of magnitude approach,

explain how the pressure at a location along the flat plate is evaluated for laminar

boundary layer flow over a flat plate.

2. Give the classification of Partial Differential Equations, explaining the characteristics

of each type of PDE.

3. a) Using the Taylor’s series approximation, derive the finite difference expressions for

first order and second order differential terms of variable, Φ.

b) Explain the Method of Weighted Residuals to solve PDEs using FEM.

4. Using the Von Neumann Stability Analysis, derive the criterion for stability Analysis

of Parabolic PDE. Make necessary assumptions, but state them clearly.

5. What are the different methods of obtaining the matrix inverse? Briefly explain each

one, mentioning their relative advantages and disadvantages.

6. An Aluminum rod, 2.5 cm in diameter and 15 cm long protrudes from a wall

maintained at 3000C. The environment temperature is 38

0C. The surface heat transfer

coefficient is 17 W/m2K. Taking the mesh size as 5 cm, obtain the nodal equations,

considering the fin as short. What is the type of coefficient matrix? What is the suitable

matrix inversion technique? Using that technique, obtain the nodal temperatures

using FDM.

7.a) Illustrate the Lax-Wendroff Technique for unsteady, two dimensional inviscid flow.

b) Explain ADI Technique for solving 2D, unsteady diffusion problem.

8. Write short notes on the following.

a) SIMPLE Algorithm for Pressure Linked Equations.

b) Numerical methods for solving potential equations.

c) Basic rules of Finite Volume Method.

******

R09 MRCET


MRCET


mtech asp question bank final r13

Documents

aerospace sensors

total credits

aerospace vehicle design

semester code group

academic year

air transportation systems

p credits aircraft control

p credits project work