Fundamental of Incomp Flow
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Aerodynamics Material - Taylor & Francis
CopyrightAerodynamics material - Taylor & Francis ______________________________________________________________________ 257 Aerodynamics Symbol List Symbol Definition Units a speed of sound ⁄ a speed of sound at sea level ⁄ A area aspect ratio ‐‐‐‐‐‐‐‐ b wing span c chord length c Copyrightmean aerodynamic material chord- Taylor & Francis specific heat at constant pressure of air · root chord tip chord specific heat at constant volume of air · / quarter chord total drag coefficient ‐‐‐‐‐‐‐‐ , induced drag coefficient ‐‐‐‐‐‐‐‐ , parasite drag coefficient ‐‐‐‐‐‐‐‐ , wave drag coefficient ‐‐‐‐‐‐‐‐ local skin friction coefficient ‐‐‐‐‐‐‐‐ lift coefficient ‐‐‐‐‐‐‐‐ , compressible lift coefficient ‐‐‐‐‐‐‐‐ compressible moment ‐‐‐‐‐‐‐‐ , coefficient , pitching moment coefficient ‐‐‐‐‐‐‐‐ , rolling moment coefficient ‐‐‐‐‐‐‐‐ , yawing moment coefficient ‐‐‐‐‐‐‐‐ ______________________________________________________________________ 258 Aerodynamics Aerodynamics Symbol List (cont.) Symbol Definition Units pressure coefficient ‐‐‐‐‐‐‐‐ compressible pressure ‐‐‐‐‐‐‐‐ , coefficient , critical pressure coefficient ‐‐‐‐‐‐‐‐ , supersonic pressure coefficient ‐‐‐‐‐‐‐‐ D total drag induced drag Copyright material - Taylor & Francis parasite drag e span efficiency factor ‐‐‐‐‐‐‐‐ L lift pitching moment · rolling moment · yawing moment · M mach number ‐‐‐‐‐‐‐‐ critical mach number ‐‐‐‐‐‐‐‐ free stream mach number ‐‐‐‐‐‐‐‐ P static pressure ⁄ total pressure ⁄ free stream pressure ⁄ q dynamic pressure ⁄ R -
CHAPTER TWO - Static Aeroelasticity – Unswept Wing Structural Loads and Performance 21 2.1 Background
Static aeroelasticity – structural loads and performance CHAPTER TWO - Static Aeroelasticity – Unswept wing structural loads and performance 21 2.1 Background ........................................................................................................................... 21 2.1.2 Scope and purpose ....................................................................................................................... 21 2.1.2 The structures enterprise and its relation to aeroelasticity ............................................................ 22 2.1.3 The evolution of aircraft wing structures-form follows function ................................................ 24 2.2 Analytical modeling............................................................................................................... 30 2.2.1 The typical section, the flying door and Rayleigh-Ritz idealizations ................................................ 31 2.2.2 – Functional diagrams and operators – modeling the aeroelastic feedback process ....................... 33 2.3 Matrix structural analysis – stiffness matrices and strain energy .......................................... 34 2.4 An example - Construction of a structural stiffness matrix – the shear center concept ........ 38 2.5 Subsonic aerodynamics - fundamentals ................................................................................ 40 2.5.1 Reference points – the center of pressure..................................................................................... 44 2.5.2 A different -
Potential Flow Theory
2.016 Hydrodynamics Reading #4 2.016 Hydrodynamics Prof. A.H. Techet Potential Flow Theory “When a flow is both frictionless and irrotational, pleasant things happen.” –F.M. White, Fluid Mechanics 4th ed. We can treat external flows around bodies as invicid (i.e. frictionless) and irrotational (i.e. the fluid particles are not rotating). This is because the viscous effects are limited to a thin layer next to the body called the boundary layer. In graduate classes like 2.25, you’ll learn how to solve for the invicid flow and then correct this within the boundary layer by considering viscosity. For now, let’s just learn how to solve for the invicid flow. We can define a potential function,!(x, z,t) , as a continuous function that satisfies the basic laws of fluid mechanics: conservation of mass and momentum, assuming incompressible, inviscid and irrotational flow. There is a vector identity (prove it for yourself!) that states for any scalar, ", " # "$ = 0 By definition, for irrotational flow, r ! " #V = 0 Therefore ! r V = "# ! where ! = !(x, y, z,t) is the velocity potential function. Such that the components of velocity in Cartesian coordinates, as functions of space and time, are ! "! "! "! u = , v = and w = (4.1) dx dy dz version 1.0 updated 9/22/2005 -1- ©2005 A. Techet 2.016 Hydrodynamics Reading #4 Laplace Equation The velocity must still satisfy the conservation of mass equation. We can substitute in the relationship between potential and velocity and arrive at the Laplace Equation, which we will revisit in our discussion on linear waves. -
Introduction to Compressible Computational Fluid Dynamics James S
Introduction to Compressible Computational Fluid Dynamics James S. Sochacki Department of Mathematics James Madison University [email protected] Abstract This document is intended as an introduction to computational fluid dynamics at the upper undergraduate level. It is assumed that the student has had courses through three dimensional calculus and some computer programming experience with numer- ical algorithms. A course in differential equations is recommended. This document is intended to be used by undergraduate instructors and students to gain an under- standing of computational fluid dynamics. The document can be used in a classroom or research environment at the undergraduate level. The idea of this work is to have the students use the modules to discover properties of the equations and then relate this to the physics of fluid dynamics. Many issues, such as rarefactions and shocks are left out of the discussion because the intent is to have the students discover these concepts and then study them with the instructor. The document is used in part of the undergraduate MATH 365 - Computation Fluid Dynamics course at James Madi- son University (JMU) and is part of the joint NSF Grant between JMU and North Carolina Central University (NCCU): A Collaborative Computational Sciences Pro- gram. This document introduces the full three-dimensional Navier Stokes equations. As- sumptions to these equations are made to derive equations that are accessible to un- dergraduates with the above prerequisites. These equations are approximated using finite difference methods. The development of the equations and finite difference methods are contained in this document. Software modules and their corresponding documentation in Fortran 90, Maple and Matlab can be downloaded from the web- site: http://www.math.jmu.edu/~jim/compressible.html. -
INCOMPRESSIBLE FLOW AERODYNAMICS 3 0 0 3 Course Category: Programme Core A
COURSE CODE COURSE TITLE L T P C 1151AE107 INCOMPRESSIBLE FLOW AERODYNAMICS 3 0 0 3 Course Category: Programme core a. Preamble : The primary objective of this course is to teach students how to determine aerodynamic lift and drag over an airfoil and wing at incompressible flow regime by analytical methods. b. Prerequisite Courses: Fluid Mechanics c. Related Courses: Airplane Performance Compressible flow Aerodynamics Aero elasticity Flapping wing dynamics Industrial aerodynamics Transonic Aerodynamics d. Course Educational Objectives: To introduce the concepts of mass, momentum and energy conservation relating to aerodynamics. To make the student understand the concept of vorticity, irrotationality, theory of air foils and wing sections. To introduce the basics of viscous flow. e. Course Outcomes: Upon the successful completion of the course, students will be able to: Knowledge Level CO Course Outcomes (Based on revised Nos. Bloom’s Taxonomy) Apply the physical principles to formulate the governing CO1 K3 aerodynamics equations Find the solution for two dimensional incompressible inviscid CO2 K3 flows Apply conformal transformation to find the solution for flow over CO3 airfoils and also find the solutions using classical thin airfoil K3 theory Apply Prandtl’s lifting-line theory to find the aerodynamic CO4 K3 characteristics of finite wing Find the solution for incompressible flow over a flat plate using CO5 K3 viscous flow concepts f. Correlation of COs with POs: COs PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11 PO12 CO1 H L H L M H H CO2 H L H L M H H CO3 H L H L M H H CO4 H L H L M H H CO5 H L H L M H H H- High; M-Medium; L-Low g. -
Overview of Pressure Coefficient Data in Building Energy Simulation and Airflow Network Programs
PREPRINT: Costola D, Blocken B, Hensen JLM. 2009. Overview of pressure coefficient data in building energy simulation and airflow network programs. Building and Environment. In press. Overview of pressure coefficient data in building energy simulation and airflow network programs D. Cóstola*, B. Blocken, J.L.M. Hensen Building Physics and Systems, Eindhoven University of Technology, the Netherlands Abstract Wind pressure coefficients (Cp) are influenced by a wide range of parameters, including building geometry, facade detailing, position on the facade, the degree of exposure/sheltering, wind speed and wind direction. As it is practically impossible to take into account the full complexity of pressure coefficient variation, Building Energy Simulation (BES) and Air Flow Network (AFN) programs generally incorporate it in a simplified way. This paper provides an overview of pressure coefficient data and the extent to which they are currently implemented in BES-AFN programs. A distinction is made between primary sources of Cp data, such as full- scale measurements, reduced-scale measurements in wind tunnels and computational fluid dynamics (CFD) simulations, and secondary sources, such as databases and analytical models. The comparison between data from secondary sources implemented in BES-AFN programs shows that the Cp values are quite different depending on the source adopted. The two influencing parameters for which these differences are most pronounced are the position on the facade and the degree of exposure/sheltering. The comparison of Cp data from different sources for sheltered buildings shows the largest differences, and data from different sources even present different trends. The paper concludes that quantification of the uncertainty related to such data sources is required to guide future improvements in Cp implementation in BES-AFN programs. -
Upwind Sail Aerodynamics : a RANS Numerical Investigation Validated with Wind Tunnel Pressure Measurements I.M Viola, Patrick Bot, M
Upwind sail aerodynamics : A RANS numerical investigation validated with wind tunnel pressure measurements I.M Viola, Patrick Bot, M. Riotte To cite this version: I.M Viola, Patrick Bot, M. Riotte. Upwind sail aerodynamics : A RANS numerical investigation validated with wind tunnel pressure measurements. International Journal of Heat and Fluid Flow, Elsevier, 2012, 39, pp.90-101. 10.1016/j.ijheatfluidflow.2012.10.004. hal-01071323 HAL Id: hal-01071323 https://hal.archives-ouvertes.fr/hal-01071323 Submitted on 8 Oct 2014 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. I.M. Viola, P. Bot, M. Riotte Upwind Sail Aerodynamics: a RANS numerical investigation validated with wind tunnel pressure measurements International Journal of Heat and Fluid Flow 39 (2013) 90–101 http://dx.doi.org/10.1016/j.ijheatfluidflow.2012.10.004 Keywords: sail aerodynamics, CFD, RANS, yacht, laminar separation bubble, viscous drag. Abstract The aerodynamics of a sailing yacht with different sail trims are presented, derived from simulations performed using Computational Fluid Dynamics. A Reynolds-averaged Navier- Stokes approach was used to model sixteen sail trims first tested in a wind tunnel, where the pressure distributions on the sails were measured. -
Shallow-Water Equations and Related Topics
CHAPTER 1 Shallow-Water Equations and Related Topics Didier Bresch UMR 5127 CNRS, LAMA, Universite´ de Savoie, 73376 Le Bourget-du-Lac, France Contents 1. Preface .................................................... 3 2. Introduction ................................................. 4 3. A friction shallow-water system ...................................... 5 3.1. Conservation of potential vorticity .................................. 5 3.2. The inviscid shallow-water equations ................................. 7 3.3. LERAY solutions ........................................... 11 3.3.1. A new mathematical entropy: The BD entropy ........................ 12 3.3.2. Weak solutions with drag terms ................................ 16 3.3.3. Forgetting drag terms – Stability ............................... 19 3.3.4. Bounded domains ....................................... 21 3.4. Strong solutions ............................................ 23 3.5. Other viscous terms in the literature ................................. 23 3.6. Low Froude number limits ...................................... 25 3.6.1. The quasi-geostrophic model ................................. 25 3.6.2. The lake equations ...................................... 34 3.7. An interesting open problem: Open sea boundary conditions .................... 41 3.8. Multi-level and multi-layers models ................................. 43 3.9. Friction shallow-water equations derivation ............................. 44 3.9.1. Formal derivation ....................................... 44 3.10. -
Lattice Boltzmann Modeling for Shallow Water Equations Using High
Louisiana State University LSU Digital Commons LSU Doctoral Dissertations Graduate School 2010 Lattice Boltzmann modeling for shallow water equations using high performance computing Kevin Tubbs Louisiana State University and Agricultural and Mechanical College, [email protected] Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_dissertations Part of the Engineering Science and Materials Commons Recommended Citation Tubbs, Kevin, "Lattice Boltzmann modeling for shallow water equations using high performance computing" (2010). LSU Doctoral Dissertations. 34. https://digitalcommons.lsu.edu/gradschool_dissertations/34 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Doctoral Dissertations by an authorized graduate school editor of LSU Digital Commons. For more information, please [email protected]. LATTICE BOLTZMANN MODELING FOR SHALLOW WATER EQUATIONS USING HIGH PERFORMANCE COMPUTING A Dissertation Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The Interdepartmental Program in Engineering Science by Kevin Tubbs B.S. Physics , Southern University, 2001 M.S. Physics, Louisiana State University, 2004 May, 2010 To my family ii ACKNOWLEDGMENTS I want to acknowledge the love and support of my family and friends which was instrumental in completing my degree. I would like to especially thank my parents, John and Veronica Tubbs and my siblings Kanika Tubbs and Keosha Tubbs. I dedicate this dissertation in loving memory of my brother Kendrick Tubbs and my grandmother Gertrude Nicholas. I would also like to thank Dr. -
Introduction
CHAPTER 1 Introduction "For some years I have been afflicted with the belief that flight is possible to man." Wilbur Wright, May 13, 1900 1.1 ATMOSPHERIC FLIGHT MECHANICS Atmospheric flight mechanics is a broad heading that encompasses three major disciplines; namely, performance, flight dynamics, and aeroelasticity. In the past each of these subjects was treated independently of the others. However, because of the structural flexibility of modern airplanes, the interplay among the disciplines no longer can be ignored. For example, if the flight loads cause significant structural deformation of the aircraft, one can expect changes in the airplane's aerodynamic and stability characteristics that will influence its performance and dynamic behavior. Airplane performance deals with the determination of performance character- istics such as range, endurance, rate of climb, and takeoff and landing distance as well as flight path optimization. To evaluate these performance characteristics, one normally treats the airplane as a point mass acted on by gravity, lift, drag, and thrust. The accuracy of the performance calculations depends on how accurately the lift, drag, and thrust can be determined. Flight dynamics is concerned with the motion of an airplane due to internally or externally generated disturbances. We particularly are interested in the vehicle's stability and control capabilities. To describe adequately the rigid-body motion of an airplane one needs to consider the complete equations of motion with six degrees of freedom. Again, this will require accurate estimates of the aerodynamic forces and moments acting on the airplane. The final subject included under the heading of atmospheric flight mechanics is aeroelasticity. -
How Do Airplanes
AIAA AEROSPACE M ICRO-LESSON Easily digestible Aerospace Principles revealed for K-12 Students and Educators. These lessons will be sent on a bi-weekly basis and allow grade-level focused learning. - AIAA STEM K-12 Committee. How Do Airplanes Fly? Airplanes – from airliners to fighter jets and just about everything in between – are such a normal part of life in the 21st century that we take them for granted. Yet even today, over a century after the Wright Brothers’ first flights, many people don’t know the science of how airplanes fly. It’s simple, really – it’s all about managing airflow and using something called Bernoulli’s principle. GRADES K-2 Do you know what part of an airplane lets it fly? The answer is the wings. As air flows over the wings, it pulls the whole airplane upward. This may sound strange, but think of the way the sail on a sailboat catches the wind to move the boat forward. The way an airplane wing works is not so different. Airplane wings have a special shape which you can see by looking at it from the side; this shape is called an airfoil. The airfoil creates high-pressure air underneath the wing and low-pressure air above the wing; this is like blowing on the bottom of the wing and sucking upwards on the top of the wing at the same time. As long as there is air flowing over the wings, they produce lift which can hold the airplane up. You can have your students demonstrate this idea (called Bernoulli’s Principle) using nothing more than a sheet of paper and your mouth. -
Introduction to Aerospace Engineering
Introduction to Aerospace Engineering Lecture slides Challenge the future 1 Introduction to Aerospace Engineering Aerodynamics 11&12 Prof. H. Bijl ir. N. Timmer 11 & 12. Airfoils and finite wings Anderson 5.9 – end of chapter 5 excl. 5.19 Topics lecture 11 & 12 • Pressure distributions and lift • Finite wings • Swept wings 3 Pressure coefficient Typical example Definition of pressure coefficient : p − p -Cp = ∞ Cp q∞ upper side lower side -1.0 Stagnation point: p=p t … p t-p∞=q ∞ => C p=1 4 Example 5.6 • The pressure on a point on the wing of an airplane is 7.58x10 4 N/m2. The airplane is flying with a velocity of 70 m/s at conditions associated with standard altitude of 2000m. Calculate the pressure coefficient at this point on the wing 4 2 3 2000 m: p ∞=7.95.10 N/m ρ∞=1.0066 kg/m − = p p ∞ = − C p Cp 1.50 q∞ 5 Obtaining lift from pressure distribution leading edge θ V∞ trailing edge s p ds dy θ dx = ds cos θ 6 Obtaining lift from pressure distribution TE TE Normal force per meter span: = θ − θ N ∫ pl cos ds ∫ pu cos ds LE LE c c θ = = − with ds cos dx N ∫ pl dx ∫ pu dx 0 0 NN Write dimensionless force coefficient : C = = n 1 ρ 2 2 Vc∞ qc ∞ 1 1 p − p x 1 p − p x x = l ∞ − u ∞ C = ()C −C d Cn d d n ∫ pl pu ∫ q c ∫ q c 0 ∞ 0 ∞ 0 c 7 T=Lsin α - Dcosα N=Lcos α + Dsinα L R N α T D V α = angle of attack 8 Obtaining lift from normal force coefficient =α − α =α − α L Ncos T sin cl c ncos c t sin L N T =cosα − sin α qc∞ qc ∞ qc ∞ For small angle of attack α≤5o : cos α ≈ 1, sin α ≈ 0 1 1 C≈() CCdx − () l∫ pl p u c 0 9 Example 5.11 Consider an airfoil with chord length c and the running distance x measured along the chord.