Newtonian Analysis of Rarified Flows
|
|
- Pierce Andrews
- 6 years ago
- Views:
Transcription
1 Atmospheric Regimes on Entry Basic fluid parameters Definition of Mean Free Path Rarified gas Newtonian flow Continuum Newtonian flow (hypersonics) SphereConeAero so ware 2012 David L. Akin - All rights reserved 1
2 Atmospheric Regimes on Entry 2
3 Basic Fluids Parameters M Mach Number = v a a speed of sound = γrt R = m 1 ordered energy random energy = 2 mv2 1 2 m v2 g 3 = v2 3RT = γ 3 Re Reynold s number = Re = ṁv τa = ρav2 µ v L A = ρvl µ v 2 a 2 = γ 3 M 2 inertial force viscous force
4 Random vs. Ordered Energy 4
5 More Fluid Parameters K Knudsen number K = number of collisions with body number of collisions with other molecules K = λ L λ mean free path L vehicle characteristic length 5
6 Estimating Mean Free Path Assume: All molecules are perfect rigid spheres Each has diameter σ, mass m, and velocity Consider a cube with side length L containing N molecules N/6 molecules are traveling in each direction ±X ±Y ±Z v 6
7 Consider Collisions in +Z Direction number of potential +Z collisions v v 2 v n(+z) = 1 6 N πσ2 L L 3 = 1 6 N πσ2 L 2 frequency of +Z collisions Area = πσ 2 f(+z) = n(+z) t = f(+z) = πρσ2 v 3m π 6 N σ2 L 2 L 2 v 7
8 Consider Collisions in +X Direction v v 2 v frequency of +X collisions f(+x) = n(+x) 2πρσ2 v = t 6m f( X) =f(+y )=f( Y )=f(+x) f( Z) =0 Total frequency of collisions f = π 3 ( ) ρσ2 v m 8
9 Mean Free Path λ = v f = m/σ 2 π 3 ( )ρ 1 ρ at sea level: λ = m at 100 km: λ =0.3 m 1 ft 9
10 Newtonian Flow Mean free path of particles much larger than spacecra --> no appreciable interaction of air molecules Model vehicle/ atmosphere interactions as independent perfectly elastic collisions α α 10
11 Newtonian Analysis mass flux = (density)(swept area)(velocity) ρ A sin(α) A dm dt =(ρ)(a sin α)( ) α 11
12 Momentum Transfer Momentum perpendicular to wall is reversed at impact Bounce momentum is transferred to vehicle Momentum parallel to wall is unchanged sin(α) F F = dm dt = ρ A sin α(2 sin α) =2ρ 2 A sin 2 α 12
13 Lift and Drag L = F cos α =2ρ 2 A sin 2 α cos α D = F sin α =2ρ 2 A sin 3 α c L = c D = L 1 2 ρ 2 A = 4 sin2 α cos α D 1 2 ρ 2 A = 4 sin3 α L D = cos α α D F L sin α = cot α 13
14 Flat Plate Newtonian Aerodynamics Angle of Attack (deg) Lift coeff. Drag coeff. L/D 14
15 Example of Newtonian Flow Calculations Consider a cylinder of length l, entering atmosphere transverse to flow da = rdθdl dṁ = ρda cos θ = ρ cos θrdθdl df = dṁ =2ρ 2 cos 2 θrdθdl dd = df cos θ =2ρ 2 cos 3 θrdθdl dl = df sin θ =2ρ 2 cos 2 θ sin θrdθd df r θ dl dd 15
16 Integration to Find Drag Coefficient Integrate from θ = π 2 π 2 D = + π 2 π 2 l 0 =2ρ 2 r dd =2ρ 2 r + π 2 + π 2 π 2 l 0 cos 3 θdθdl cos 3 θdθ = 8 3 ρ 2 r π 2 By definition, D = 1 2 ρ 2 Ac D and, for a cylinder A =2rl ρ 2 rc D = 8 3 ρ 2 r = c D =
17 Continuum Newtonian Flow (Hypersonics) Air molecules predominately interact with shock waves Effect of shock wave passage is to decelerate flow and turn it parallel to vehicle surface α Shock wave 17
18 Continuum Newtonian Flow (Hypersonics) Treat hypersonic aerodynamics in manner similar to previous Newtonian flow analysis All momentum perpendicular to wall is absorbed by the wall α 18
19 Mass Flux (unchanged) mass flux = (density)(swept area)(velocity) ρ A sin(α) A dm dt =(ρ)(a sin α)( ) α 19
20 Momentum Transfer Momentum perpendicular to wall is absorbed at impact and transferred to vehicle Momentum parallel to wall is unchanged sin(α) cos(α) F = dm dt = ρ A sin α( sin α) =ρ 2 A sin 2 α F 20
21 Lift and Drag L = F cos α = ρ 2 A sin 2 α cos α D = F sin α = ρ 2 A sin 3 α c L = c D = L 1 2 ρ 2 A = 2 sin2 α cos α D 1 2 ρ 2 A = 2 sin3 α α L D = cos α sin α = cot α D F L 21
22 Modified Newtonian Flow Coefficient of pressure in classical Newtonian flow c p =2sin 2 (α) Coefficient of pressure in modified Newtonian flow c p = c pmax sin 2 (α) Cp(max) is the pressure coefficient behind a normal shock at flight conditions c pmax = P shock P 1 2 ρ v 2 22
23 Maximum Coefficient of Pressure c pmax = 2 γm 2 (γ + 1) 2 M 2 γ γ 1 1 γ +2γM 2 4γM 2 2(γ 1) γ +1 1 as M c pmax (γ + 1) 2 4γ γ γ 1 4 γ +1 c pmax for γ =1.4 c pmax 2 for γ =1 23
Entry Aerodynamics MARYLAND U N I V E R S I T Y O F. Entry Aerodynamics. ENAE Launch and Entry Vehicle Design
Atmospheric Regimes on Entry Basic fluid parameters Definition of Mean Free Path Rarified gas Newtonian flow Continuum Newtonian flow (hypersonics) 2014 David L. Akin - All rights reserved http://spacecraft.ssl.umd.edu
More informationThe Space Environment
Lecture #07 - September 18, 2018 Course schedule updates Planetary environments Gravitation Electromagnetic radiation Atmospheric particles Newtonian flow Solar wind particles Ionizing radiation Micrometeoroids/orbital
More information1. Introduction Some Basic Concepts
1. Introduction Some Basic Concepts 1.What is a fluid? A substance that will go on deforming in the presence of a deforming force, however small 2. What Properties Do Fluids Have? Density ( ) Pressure
More informationLecture1: Characteristics of Hypersonic Atmosphere
Module 1: Hypersonic Atmosphere Lecture1: Characteristics of Hypersonic Atmosphere 1.1 Introduction Hypersonic flight has special traits, some of which are seen in every hypersonic flight. Presence of
More informationReview of Fluid Mechanics
Chapter 3 Review of Fluid Mechanics 3.1 Units and Basic Definitions Newton s Second law forms the basis of all units of measurement. For a particle of mass m subjected to a resultant force F the law may
More informationIntroduction and Basic Concepts
Topic 1 Introduction and Basic Concepts 1 Flow Past a Circular Cylinder Re = 10,000 and Mach approximately zero Mach = 0.45 Mach = 0.64 Pictures are from An Album of Fluid Motion by Van Dyke Flow Past
More informationThe Space Environment
The Space Environment Planetary environments Gravitation Electromagnetic radiation Atmospheric particles Newtonian flow Solar wind particles Ionizing radiation Micrometeoroids/orbital debris Spacecraft
More informationSummary of Dimensionless Numbers of Fluid Mechanics and Heat Transfer
1. Nusselt number Summary of Dimensionless Numbers of Fluid Mechanics and Heat Transfer Average Nusselt number: convective heat transfer Nu L = conductive heat transfer = hl where L is the characteristic
More informationIntroduction to Aerospace Engineering
Introduction to Aerospace Engineering Lecture slides Challenge the future 3-0-0 Introduction to Aerospace Engineering Aerodynamics 5 & 6 Prof. H. Bijl ir. N. Timmer Delft University of Technology 5. Compressibility
More informationIntroduction to Aerodynamics. Dr. Guven Aerospace Engineer (P.hD)
Introduction to Aerodynamics Dr. Guven Aerospace Engineer (P.hD) Aerodynamic Forces All aerodynamic forces are generated wither through pressure distribution or a shear stress distribution on a body. The
More informationUnsteady Wave Motion Shock Tube Problem - Shock Reflection
Unsteady Wave Motion Shock Tube Problem - Shock Reflection Niklas Andersson Division of Fluid Dynamics Department of Applied Mechanics Chalmers University of Tecnology 8 februari 09 Shock Reflection When
More informationCHAPTER 9 DIMENSIONAL ANALYSIS AND SCALING
CHAPTER 9 DIMENSIONAL ANALYSIS AND SCALING The Philosopher s approach The Mathematicians s approach The Engineer s approach Example - an orifice plate Example - an aeroplane Example - the drag force on
More information58:160 Intermediate Fluid Mechanics Bluff Body Professor Fred Stern Fall 2014
Professor Fred Stern Fall 04 Chapter 7 Bluff Body Fluid flows are broadly categorized:. Internal flows such as ducts/pipes, turbomachinery, open channel/river, which are bounded by walls or fluid interfaces:
More informationConsider a control volume in the form of a straight section of a streamtube ABCD.
6 MOMENTUM EQUATION 6.1 Momentum and Fluid Flow In mechanics, the momentum of a particle or object is defined as the product of its mass m and its velocity v: Momentum = mv The particles of a fluid stream
More informationSteady waves in compressible flow
Chapter Steady waves in compressible flow. Oblique shock waves Figure. shows an oblique shock wave produced when a supersonic flow is deflected by an angle. Figure.: Flow geometry near a plane oblique
More informationHigh Speed Aerodynamics. Copyright 2009 Narayanan Komerath
Welcome to High Speed Aerodynamics 1 Lift, drag and pitching moment? Linearized Potential Flow Transformations Compressible Boundary Layer WHAT IS HIGH SPEED AERODYNAMICS? Airfoil section? Thin airfoil
More information1. Fluid Dynamics Around Airfoils
1. Fluid Dynamics Around Airfoils Two-dimensional flow around a streamlined shape Foces on an airfoil Distribution of pressue coefficient over an airfoil The variation of the lift coefficient with the
More informationAE 2020: Low Speed Aerodynamics. I. Introductory Remarks Read chapter 1 of Fundamentals of Aerodynamics by John D. Anderson
AE 2020: Low Speed Aerodynamics I. Introductory Remarks Read chapter 1 of Fundamentals of Aerodynamics by John D. Anderson Text Book Anderson, Fundamentals of Aerodynamics, 4th Edition, McGraw-Hill, Inc.
More informationFLUID MECHANICS. Chapter 9 Flow over Immersed Bodies
FLUID MECHANICS Chapter 9 Flow over Immersed Bodies CHAP 9. FLOW OVER IMMERSED BODIES CONTENTS 9.1 General External Flow Characteristics 9.3 Drag 9.4 Lift 9.1 General External Flow Characteristics 9.1.1
More informationScaling Parameters in Rarefied Flow and the Breakdown of the Navier-Stokes Equations Mechanical Engineering Research Report No: 2004/09
Scaling Parameters in Rarefied Flow and the Breakdown of the Navier-Stokes Equations Mechanical Engineering Research Report No: 2004/09 Michael Macrossan, Centre for Hypersonics, University of Queensland
More informationPerformance. 5. More Aerodynamic Considerations
Performance 5. More Aerodynamic Considerations There is an alternative way of looking at aerodynamic flow problems that is useful for understanding certain phenomena. Rather than tracking a particle of
More informationGiven the water behaves as shown above, which direction will the cylinder rotate?
water stream fixed but free to rotate Given the water behaves as shown above, which direction will the cylinder rotate? ) Clockwise 2) Counter-clockwise 3) Not enough information F y U 0 U F x V=0 V=0
More informationAerodynamic Performance 1. Figure 1: Flowfield of a Wind Turbine and Actuator disc. Table 1: Properties of the actuator disk.
Aerodynamic Performance 1 1 Momentum Theory Figure 1: Flowfield of a Wind Turbine and Actuator disc. Table 1: Properties of the actuator disk. 1. The flow is perfect fluid, steady, and incompressible.
More informationPh.D. Qualifying Exam in Fluid Mechanics
Student ID Department of Mechanical Engineering Michigan State University East Lansing, Michigan Ph.D. Qualifying Exam in Fluid Mechanics Closed book and Notes, Some basic equations are provided on an
More informationABSTRACT. Nomenclature
ABSTRACT The behavior of two different models of gas-surface interactions is studied using the Direct Simulation Monte Carlo (DSMC) method. The DSMC calculations examine differences in predictions of aerodynamic
More informationDepartment of Mechanical Engineering
Department of Mechanical Engineering AMEE401 / AUTO400 Aerodynamics Instructor: Marios M. Fyrillas Email: eng.fm@fit.ac.cy HOMEWORK ASSIGNMENT #2 QUESTION 1 Clearly there are two mechanisms responsible
More informationConservation of Momentum
Conservation of Momentum Newton: Quantity of Motion Forces applied for a period of time change an object s quantity of motion. F = ma F = m Δ v t F t = mδv = mv f mv i p mv Ft = Δp F = dp dt Conservation?
More informationThe E80 Wind Tunnel Experiment the experience will blow you away. by Professor Duron Spring 2012
The E80 Wind Tunnel Experiment the experience will blow you away by Professor Duron Spring 2012 Objectives To familiarize the student with the basic operation and instrumentation of the HMC wind tunnel
More informationRarefaction Effects in Hypersonic Aerodynamics
Rarefaction Effects in Hypersonic Aerodynamics Vladimir V. Riabov Department of Mathematics and Computer Science, Rivier College, 4 S. Main St., Nashua, NH 6, USA Abstract. The Direct Simulation Monte-Carlo
More informationLecture-4. Flow Past Immersed Bodies
Lecture-4 Flow Past Immersed Bodies Learning objectives After completing this lecture, you should be able to: Identify and discuss the features of external flow Explain the fundamental characteristics
More informationDefinitions. Temperature: Property of the atmosphere (τ). Function of altitude. Pressure: Property of the atmosphere (p). Function of altitude.
Definitions Chapter 3 Standard atmosphere: A model of the atmosphere based on the aerostatic equation, the perfect gas law, an assumed temperature distribution, and standard sea level conditions. Temperature:
More informationMARYLAND U N I V E R S I T Y O F. The Space Environment. Principles of Space Systems Design
Gravitation Electromagnetic Radiation Atmospheric Particles Solar Wind Particles Ionizing Radiation Micrometeoroids/Orbital Debris Spacecraft Charging Planetary Environments 2003 David L. Akin - All rights
More informationBallistic Atmospheric Entry
Ballistic Atmospheric Entry Standard atmospheres Orbital decay due to atmospheric drag Straight-line (no gravity) ballistic entry based on atmospheric density 1 2010 David L. Akin - All rights reserved
More informationSIMULATION OF GAS FLOW OVER MICRO-SCALE AIRFOILS USING A HYBRID CONTINUUM-PARTICLE APPROACH
33rd AIAA Fluid Dynamics Conference and Exhibit 3-6 June 3, Orlando, Florida AIAA 3-44 33 rd AIAA Fluid Dynamics Conference and Exhibit / Orlando, Florida / 3-6 Jun 3 SIMULATION OF GAS FLOW OVER MICRO-SCALE
More informationInitial Trajectory and Atmospheric Effects
Initial Trajectory and Atmospheric Effects G. Flanagan Alna Space Program July 13, 2011 Introduction A major consideration for an earth-based accelerator is atmospheric drag. Drag loses mean that the gun
More informationSPC Aerodynamics Course Assignment Due Date Monday 28 May 2018 at 11:30
SPC 307 - Aerodynamics Course Assignment Due Date Monday 28 May 2018 at 11:30 1. The maximum velocity at which an aircraft can cruise occurs when the thrust available with the engines operating with the
More informationDrag Force Experienced by a Body Moving through a Rarefied Gas. Bertúlio de Lima Bernardo, Fernando Moraes, and Alexandre Rosas
CHINESE JOURNAL OF PHYSICS VOL. 51, NO. 2 April 2013 Drag Force Experienced by a Body Moving through a Rarefied Gas Bertúlio de Lima Bernardo, Fernando Moraes, and Alexandre Rosas Departamento de Física,
More informationIMPACT Today s Objectives: In-Class Activities:
Today s Objectives: Students will be able to: 1. Understand and analyze the mechanics of impact. 2. Analyze the motion of bodies undergoing a collision, in both central and oblique cases of impact. IMPACT
More informationContents. I Introduction 1. Preface. xiii
Contents Preface xiii I Introduction 1 1 Continuous matter 3 1.1 Molecules................................ 4 1.2 The continuum approximation.................... 6 1.3 Newtonian mechanics.........................
More informationApplied Gas Dynamics Flow With Friction and Heat Transfer
Applied Gas Dynamics Flow With Friction and Heat Transfer Ethirajan Rathakrishnan Applied Gas Dynamics, John Wiley & Sons (Asia) Pte Ltd c 2010 Ethirajan Rathakrishnan 1 / 121 Introduction So far, we have
More informationEXTERNAL-JET (FLUID) PROPULSION ANALOGY FOR PHOTONIC (LASER) PROPULSION By John R. Cipolla, Copyright February 21, 2017
EXTERNAL-JET (FLUID) PROPULSION ANALOGY FOR PHOTONIC (LASER) PROPULSION By John R. Cipolla, Copyright February 21, 2017 ABSTRACT External-jet propulsion uses a narrow jet of high velocity water or conceptually
More informationRocket Thermodynamics
Rocket Thermodynamics PROFESSOR CHRIS CHATWIN LECTURE FOR SATELLITE AND SPACE SYSTEMS MSC UNIVERSITY OF SUSSEX SCHOOL OF ENGINEERING & INFORMATICS 25 TH APRIL 2017 Thermodynamics of Chemical Rockets ΣForce
More informationAnalysis of Bridging Formulae in Transitional Regime
Analysis of Bridging Formulae in Transitional Regime Luigi Morsa *, Gennaro Zuppardi *, Antonio Schettino ** and Raffaele Votta ** * Department of Aerospace Engineering University of Naples Federico II,
More informationAtmospheric Entry. Technology, Mathematical Model and Simulation
Atmospheric Entry Technology, Mathematical Model and Simulation Julian Köllermeier RWTH Aachen, August 26th 2016 Outline 1. Introduction to Atmospheric Reentry 2. Rarefied Gases: From Science Fiction to
More informationFundamentals of Aerodynamics
Fundamentals of Aerodynamics Fourth Edition John D. Anderson, Jr. Curator of Aerodynamics National Air and Space Museum Smithsonian Institution and Professor Emeritus University of Maryland Me Graw Hill
More informationFluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay
Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay Lecture No. # 35 Boundary Layer Theory and Applications Welcome back to the video course on fluid
More informationChapter 12. Answers to examination-style questions. Answers Marks Examiner s tips
(a) v esc = gr = (.6 740 0 3 ) ½ = 400 m s (370 m s to 3 sig figs) (b) (i) Mean kinetic energy = 3_ kt =.5.38 0 3 400 = 8.3 0 J (ii) Mass of an oxygen molecule m= molar mass/n A 0.03 = kg 6.0 0 3 Rearranging
More informationTutorial 10. Boundary layer theory
Tutorial 10 Boundary layer theory 1. If the velocity distribution law in a laminar boundary layer over a flat plate is assumes to be of the form, determine the velocity distribution law. At y = 0, u= 0
More informationA Balance for Measurement of Yaw, Lift and Drag on a Model in a Hypersonic Shock Tunnel
, July 6-8, 2011, London, U.K. A Balance for Measurement of Yaw, Lift and Drag on a Model in a Hypersonic Shock Tunnel S. Trivedi, and V. Menezes Abstract This paper describes the design of an accelerometer
More informationEffective Boundary Conditions for Continuum Method of Investigation of Rarefied Gas Flow over Blunt Body
Effective Boundary Conditions for Continuum Method of Investigation of Rarefied Gas Flow over Blunt Body I.G. Brykina a, B.V. Rogov b, I.L. Semenov c, and G.A. Tirskiy a a Institute of Mechanics, Moscow
More informationLecture 7 Boundary Layer
SPC 307 Introduction to Aerodynamics Lecture 7 Boundary Layer April 9, 2017 Sep. 18, 2016 1 Character of the steady, viscous flow past a flat plate parallel to the upstream velocity Inertia force = ma
More informationNotes 4: Differential Form of the Conservation Equations
Low Speed Aerodynamics Notes 4: Differential Form of the Conservation Equations Deriving Conservation Equations From the Laws of Physics Physical Laws Fluids, being matter, must obey the laws of Physics.
More informationFOUNDATION STUDIES EXAMINATIONS June PHYSICS Semester One February Main
FOUNDATION STUDIES EXAMINATIONS June 203 PHYSICS Semester One February Main Time allowed 2 hours for writing 0 minutes for reading This paper consists of 4 questions printed on 0 pages. PLEASE CHECK BEFORE
More informationHypersonic Flight Effects on Optical Sensors
A Tutorial Of: Hypersonic Flight Effects on Optical Sensors Matt Salem The University of Arizona: OPTI 521 12/4/2016 Background: In recent years hypersonic vehicles have received a lot of attention from
More informationLinear Cascade Analyses
An Internet Book on Fluid Dynamics Linear Cascade Analyses The fluid mechanics of a linear cascade will now be examined in more detail, so that the role played by the geometry of the blades and information
More information4 Compressible Fluid Dynamics
4 Compressible Fluid Dynamics 4. Compressible flow definitions Compressible flow describes the behaviour of fluids that experience significant variations in density under the application of external pressures.
More informationGet Discount Coupons for your Coaching institute and FREE Study Material at Force System
Get Discount Coupons for your Coaching institute and FEE Study Material at www.pickmycoaching.com Mechanics Force System When a member of forces simultaneously acting on the body, it is known as force
More informationHypersonic flow and flight
University of Stuttgart, Aerospace Engineering and Geodesy Dept. - Lecture - Hypersonic flow and flight Master Level, Specialization 4 lecture hours per week in WS, 3-6 LPs/ECTS Lecturer: Dr. Markus J.
More informationModule 9: Packed beds Lecture 29: Drag, particles settling. Flow through a packed bed of solids. Drag. Criteria of settling.
Flow through a packed bed of solids Drag Criteria of settling Hindred settling file:///d /Web%20Course/Dr.%20Nishith%20Verma/local%20server/fluid_mechanics/lecture29/29_1.htm[5/9/2012 3:38:37 PM] Flow
More informationConvection. forced convection when the flow is caused by external means, such as by a fan, a pump, or atmospheric winds.
Convection The convection heat transfer mode is comprised of two mechanisms. In addition to energy transfer due to random molecular motion (diffusion), energy is also transferred by the bulk, or macroscopic,
More informationFOUNDATION STUDIES EXAMINATIONS June PHYSICS Semester One February Main
1 FOUNDATION STUDIES EXAMINATIONS June 2013 PHYSICS Semester One February Main Time allowed 2 hours for writing 10 minutes for reading This paper consists of 4 questions printed on 10 pages. PLEASE CHECK
More informationFundamentals of Fluid Dynamics: Ideal Flow Theory & Basic Aerodynamics
Fundamentals of Fluid Dynamics: Ideal Flow Theory & Basic Aerodynamics Introductory Course on Multiphysics Modelling TOMASZ G. ZIELIŃSKI (after: D.J. ACHESON s Elementary Fluid Dynamics ) bluebox.ippt.pan.pl/
More informationFlight Vehicle Terminology
Flight Vehicle Terminology 1.0 Axes Systems There are 3 axes systems which can be used in Aeronautics, Aerodynamics & Flight Mechanics: Ground Axes G(x 0, y 0, z 0 ) Body Axes G(x, y, z) Aerodynamic Axes
More informationHypersonic flow: introduction
Hyersonic flow: introduction Van Dyke: Hyersonic flow is flow ast a body at high ach number, where nonlinearity is an essential feature of the flow. Also understood, for thin bodies, that if is the thickness-to-chord
More informationKinetic Effects in Spherical Expanding Flows of Binary-Gas Mixtures
Kinetic Effects in Spherical Expanding Flows of Binary-Gas Mixtures Vladimir V. Riabov Rivier College, Nashua, New Hampshire, USA Abstract. Diffusion effects in the spherical expanding flows of argon-helium
More informationMDTS 5705 : Aerodynamics & Propulsion Lecture 2 : Missile lift and drag. G. Leng, MDTS, NUS
MDTS 5705 : Aerodynamics & Propulsion Lecture 2 : Missile lift and drag 2.1. The design of supersonic airfoils For efficient lift generation at subsonic speeds, airfoils look like : So why can t a similar
More informationGiven a stream function for a cylinder in a uniform flow with circulation: a) Sketch the flow pattern in terms of streamlines.
Question Given a stream function for a cylinder in a uniform flow with circulation: R Γ r ψ = U r sinθ + ln r π R a) Sketch the flow pattern in terms of streamlines. b) Derive an expression for the angular
More informationRocket Science 102 : Energy Analysis, Available vs Required
Rocket Science 102 : Energy Analysis, Available vs Required ΔV Not in Taylor 1 Available Ignoring Aerodynamic Drag. The available Delta V for a Given rocket burn/propellant load is ( ) V = g I ln 1+ P
More informationCompressible Flow. Professor Ugur GUVEN Aerospace Engineer Spacecraft Propulsion Specialist
Compressible Flow Professor Ugur GUVEN Aerospace Engineer Spacecraft Propulsion Specialist What is Compressible Flow? Compressible Flow is a type of flow in which the density can not be treated as constant.
More informationFriction Factors and Drag Coefficients
Levicky 1 Friction Factors and Drag Coefficients Several equations that we have seen have included terms to represent dissipation of energy due to the viscous nature of fluid flow. For example, in the
More informationThe Navier-Stokes Equations
s University of New Hampshire February 22, 202 and equations describe the non-relativistic time evolution of mass and momentum in fluid substances. mass density field: ρ = ρ(t, x, y, z) velocity field:
More informationSIMULATION TECHNIQUES IN HYPERSONIC AEROTHERMODYNAMICS
ICAS CONGRESS SIMULATION TECHNIQUES IN HYPERSONIC AEROTHERMODYNAMICS Vladimir V. Riabov Rivier College, Nashua, New Hampshire 36, USA Keywords: hypersonic non-equilibrium rarefied-gas flows, aero- & thermodynamic
More informationINTERNATIONAL JOURNAL OF ADVANCED RESEARCH IN ENGINEERING AND TECHNOLOGY (IJARET) HYPERSONIC SIMILITUDE FOR PLANAR WEDGES. Asha Crasta 1, S. A.
INTERNATIONAL JOURNAL OF ADVANCED RESEARCH IN ENGINEERING AND TECHNOLOGY (IJARET) International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 ISSN 0976-6480 (Print) ISSN
More informationDRAG REDUCTION FOR HYPERSONIC RE- ENTRY VEHICLES
International Journal of Mechanical Engineering and Technology (IJMET) Volume 8, Issue 10, October 2017, pp. 878 885, Article ID: IJMET_08_10_095 Available online at http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=8&itype=10
More information2 Internal Fluid Flow
Internal Fluid Flow.1 Definitions Fluid Dynamics The study of fluids in motion. Static Pressure The pressure at a given point exerted by the static head of the fluid present directly above that point.
More informationAerodynamics. Basic Aerodynamics. Continuity equation (mass conserved) Some thermodynamics. Energy equation (energy conserved)
Flow with no friction (inviscid) Aerodynamics Basic Aerodynamics Continuity equation (mass conserved) Flow with friction (viscous) Momentum equation (F = ma) 1. Euler s equation 2. Bernoulli s equation
More informationOn the Coefficients in Meteor Physics Equations
On the Coefficients in Meteor Physics Equations aria Yu. Khanukaeva epartment of Applied Mathematics, Moscow Institute of Physics and Technology (State University), Institutsky 9, 141700 olgoprudny, Moscow
More informationMissile Interceptor EXTROVERT ADVANCED CONCEPT EXPLORATION ADL P Ryan Donnan, Herman Ryals
EXTROVERT ADVANCED CONCEPT EXPLORATION ADL P- 2011121203 Ryan Donnan, Herman Ryals Georgia Institute of Technology School of Aerospace Engineering Missile Interceptor December 12, 2011 EXTROVERT ADVANCED
More informationMasters in Mechanical Engineering. Problems of incompressible viscous flow. 2µ dx y(y h)+ U h y 0 < y < h,
Masters in Mechanical Engineering Problems of incompressible viscous flow 1. Consider the laminar Couette flow between two infinite flat plates (lower plate (y = 0) with no velocity and top plate (y =
More informationNumerical Simulation of Flow Field around an Inflatable Vehicle during a Reentry Demonstration Flight considering Membrane Deformation
Numerical Simulation of Flow Field around an Inflatable Vehicle during a Reentry Demonstration Flight considering Membrane Deformation Dongheun HA 1,Yusuke TAKAHASHI 1 Kazuhiko YAMADA 2 1) Hokkaido Univ.
More informationPRACTICE QUESTION PAPER WITH SOLUTION CLASS XI PHYSICS
PRACTICE QUESTION PAPER WITH SOLUTION CLASS XI PHYSICS. A given quantity has both magnitude and direction. Is it necessarily a vector? Justify your answer.. What is the rotational analogue of the force?.
More informationV. MODELING, SIMILARITY, AND DIMENSIONAL ANALYSIS To this point, we have concentrated on analytical methods of solution for fluids problems.
V. MODELING, SIMILARITY, AND DIMENSIONAL ANALYSIS To this point, we have concentrated on analytical methods of solution for fluids problems. However, analytical methods are not always satisfactory due
More information8th European Symposium on ATD for Space Vehicle, Lisbon, 2-6 March 2015
1 FAST a Pre-Design Tool for the Atmospheric Re-entry of Space Vehicles and Debris F. Sourgen (*) Y. Prévereaud J-L. Vérant E. Laroche J-M. Moschetta (*) frederic.sourgen@onera.fr Onera Midi Pyrénées Center
More informationMAE 101A. Homework 7 - Solutions 3/12/2018
MAE 101A Homework 7 - Solutions 3/12/2018 Munson 6.31: The stream function for a two-dimensional, nonviscous, incompressible flow field is given by the expression ψ = 2(x y) where the stream function has
More informationPrinciples of Convection
Principles of Convection Point Conduction & convection are similar both require the presence of a material medium. But convection requires the presence of fluid motion. Heat transfer through the: Solid
More informationPHYS 390 Lecture 23 - Photon gas 23-1
PHYS 39 Lecture 23 - Photon gas 23-1 Lecture 23 - Photon gas What's Important: radiative intensity and pressure stellar opacity Text: Carroll and Ostlie, Secs. 9.1 and 9.2 The temperature required to drive
More information21st International Symposium on Rareed Gas Dynamics half-angle cone forebodies, while Stardust and Microprobe have forebody cone half-angles of 60 and
Rareed Transitional Bridging of Blunt Body Aerodynamics R. G. Wilmoth, R. C. Blanchard, J. N. Moss NASA Langley Research Center, Hampton, VA, USA 1 Introduction Bridging relations are frequently used to
More informationUNIT 4 FORCES ON IMMERSED BODIES. Lecture-01
1 UNIT 4 FORCES ON IMMERSED BODIES Lecture-01 Forces on immersed bodies When a body is immersed in a real fluid, which is flowing at a uniform velocity U, the fluid will exert a force on the body. The
More informationExperiments at the University of Minnesota (draft 2)
Experiments at the University of Minnesota (draft 2) September 17, 2001 Studies of migration and lift and of the orientation of particles in shear flows Experiments to determine positions of spherical
More informationAA210A Fundamentals of Compressible Flow. Chapter 5 -The conservation equations
AA210A Fundamentals of Compressible Flow Chapter 5 -The conservation equations 1 5.1 Leibniz rule for differentiation of integrals Differentiation under the integral sign. According to the fundamental
More information2 Navier-Stokes Equations
1 Integral analysis 1. Water enters a pipe bend horizontally with a uniform velocity, u 1 = 5 m/s. The pipe is bended at 90 so that the water leaves it vertically downwards. The input diameter d 1 = 0.1
More informationThe Simulation of Wraparound Fins Aerodynamic Characteristics
The Simulation of Wraparound Fins Aerodynamic Characteristics Institute of Launch Dynamics Nanjing University of Science and Technology Nanjing Xiaolingwei 00 P. R. China laithabbass@yahoo.com Abstract:
More informationBallistic Atmospheric Entry (Part II)
Ballistic Atmospheric Entry (Part II) News updates Straight-line (no gravity) ballistic entry based on altitude, rather than density Planetary entries (at least a start) 1 2010 David L. Akin - All rights
More informationPart A: 1 pts each, 10 pts total, no partial credit.
Part A: 1 pts each, 10 pts total, no partial credit. 1) (Correct: 1 pt/ Wrong: -3 pts). The sum of static, dynamic, and hydrostatic pressures is constant when flow is steady, irrotational, incompressible,
More information( ) A i,j. Appendices. A. Sensitivity of the Van Leer Fluxes The flux Jacobians of the inviscid flux vector in Eq.(3.2), and the Van Leer fluxes in
Appendices A. Sensitivity of the Van Leer Fluxes The flux Jacobians of the inviscid flux vector in Eq.(3.2), and the Van Leer fluxes in Eq.(3.11), can be found in the literature [9,172,173] and are therefore
More informationA New Aerial Shell Ballistic Model Experimentally Verified
An earlier version appeared in: 11 th International Symposium on Fireworks (29). A New Aerial Shell Ballistic Model Experimentally Verified L. Weinman Schneier/Weinman Consultants Austin, TX, USA Lawrence@Weinman.Net
More informationAEROSPACE ENGINEERING DEPARTMENT. Second Year - Second Term ( ) Fluid Mechanics & Gas Dynamics
AEROSPACE ENGINEERING DEPARTMENT Second Year - Second Term (2008-2009) Fluid Mechanics & Gas Dynamics Similitude,Dimensional Analysis &Modeling (1) [7.2R*] Some common variables in fluid mechanics include:
More informationAS3010: Introduction to Space Technology
AS3010: Introduction to Space Technology L E C T U R E S 8-9 Part B, Lectures 8-9 23 March, 2017 C O N T E N T S In this lecture, we will look at factors that cause an orbit to change over time orbital
More informationDay 24: Flow around objects
Day 24: Flow around objects case 1) fluid flowing around a fixed object (e.g. bridge pier) case 2) object travelling within a fluid (cars, ships planes) two forces are exerted between the fluid and the
More informationDetermining the Drag Coefficient from PITCHf/x Data
Determining the Drag Coefficient from PITCHf/x Data Isaac N. Hall Michigan State University, East Lansing, Michigan 48824 Alan M. Nathan Department of Physics, University of Illinois, Urbana, IL 61801
More information