3. Drag: an Introduction
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Glossary Physics (I-Introduction)
1 Glossary Physics (I-introduction) - Efficiency: The percent of the work put into a machine that is converted into useful work output; = work done / energy used [-]. = eta In machines: The work output of any machine cannot exceed the work input (<=100%); in an ideal machine, where no energy is transformed into heat: work(input) = work(output), =100%. Energy: The property of a system that enables it to do work. Conservation o. E.: Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes. Equilibrium: The state of an object when not acted upon by a net force or net torque; an object in equilibrium may be at rest or moving at uniform velocity - not accelerating. Mechanical E.: The state of an object or system of objects for which any impressed forces cancels to zero and no acceleration occurs. Dynamic E.: Object is moving without experiencing acceleration. Static E.: Object is at rest.F Force: The influence that can cause an object to be accelerated or retarded; is always in the direction of the net force, hence a vector quantity; the four elementary forces are: Electromagnetic F.: Is an attraction or repulsion G, gravit. const.6.672E-11[Nm2/kg2] between electric charges: d, distance [m] 2 2 2 2 F = 1/(40) (q1q2/d ) [(CC/m )(Nm /C )] = [N] m,M, mass [kg] Gravitational F.: Is a mutual attraction between all masses: q, charge [As] [C] 2 2 2 2 F = GmM/d [Nm /kg kg 1/m ] = [N] 0, dielectric constant Strong F.: (nuclear force) Acts within the nuclei of atoms: 8.854E-12 [C2/Nm2] [F/m] 2 2 2 2 2 F = 1/(40) (e /d ) [(CC/m )(Nm /C )] = [N] , 3.14 [-] Weak F.: Manifests itself in special reactions among elementary e, 1.60210 E-19 [As] [C] particles, such as the reaction that occur in radioactive decay. -
Drag Force Calculation
DRAG FORCE CALCULATION “Drag is the component of force on a body acting parallel to the direction of relative motion.” [1] This can occur between two differing fluids or between a fluid and a solid. In this lab, the drag force will be explored between a fluid, air, and a solid shape. Drag force is a function of shape geometry, velocity of the moving fluid over a stationary shape, and the fluid properties density and viscosity. It can be calculated using the following equation, ퟏ 푭 = 흆푨푪 푽ퟐ 푫 ퟐ 푫 Equation 1: Drag force equation using total profile where ρ is density determined from Table A.9 or A.10 in your textbook A is the frontal area of the submerged object CD is the drag coefficient determined from Table 1 V is the free-stream velocity measured during the lab Table 1: Known drag coefficients for various shapes Body Status Shape CD Square Rod Sharp Corner 2.2 Circular Rod 0.3 Concave Face 1.2 Semicircular Rod Flat Face 1.7 The drag force of an object can also be calculated by applying the conservation of momentum equation for your stationary object. 휕 퐹⃗ = ∫ 푉⃗⃗ 휌푑∀ + ∫ 푉⃗⃗휌푉⃗⃗ ∙ 푑퐴⃗ 휕푡 퐶푉 퐶푆 Assuming steady flow, the equation reduces to 퐹⃗ = ∫ 푉⃗⃗휌푉⃗⃗ ∙ 푑퐴⃗ 퐶푆 The following frontal view of the duct is shown below. Integrating the velocity profile after the shape will allow calculation of drag force per unit span. Figure 1: Velocity profile after an inserted shape. Combining the previous equation with Figure 1, the following equation is obtained: 푊 퐷푓 = ∫ 휌푈푖(푈∞ − 푈푖)퐿푑푦 0 Simplifying the equation, you get: 20 퐷푓 = 휌퐿 ∑ 푈푖(푈∞ − 푈푖)훥푦 푖=1 Equation 2: Drag force equation using wake profile The pressure measurements can be converted into velocity using the Bernoulli’s equation as follows: 2Δ푃푖 푈푖 = √ 휌퐴푖푟 Be sure to remember that the manometers used are in W.C. -
Chapter 4: Immersed Body Flow [Pp
MECH 3492 Fluid Mechanics and Applications Univ. of Manitoba Fall Term, 2017 Chapter 4: Immersed Body Flow [pp. 445-459 (8e), or 374-386 (9e)] Dr. Bing-Chen Wang Dept. of Mechanical Engineering Univ. of Manitoba, Winnipeg, MB, R3T 5V6 When a viscous fluid flow passes a solid body (fully-immersed in the fluid), the body experiences a net force, F, which can be decomposed into two components: a drag force F , which is parallel to the flow direction, and • D a lift force F , which is perpendicular to the flow direction. • L The drag coefficient CD and lift coefficient CL are defined as follows: FD FL CD = 1 2 and CL = 1 2 , (112) 2 ρU A 2 ρU Ap respectively. Here, U is the free-stream velocity, A is the “wetted area” (total surface area in contact with fluid), and Ap is the “planform area” (maximum projected area of an object such as a wing). In the remainder of this section, we focus our attention on the drag forces. As discussed previously, there are two types of drag forces acting on a solid body immersed in a viscous flow: friction drag (also called “viscous drag”), due to the wall friction shear stress exerted on the • surface of a solid body; pressure drag (also called “form drag”), due to the difference in the pressure exerted on the front • and rear surfaces of a solid body. The friction drag and pressure drag on a finite immersed body are defined as FD,vis = τwdA and FD, pres = pdA , (113) ZA ZA Streamwise component respectively. -
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 -
UNIT – 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 total force (FR) can be resolved in two components: 1. Drag (FD): Component of the total force in the direction of motion of fluid. 2. Lift (FL): Component of the total force in the perpendicular direction of the motion of fluid. It occurs only when the axis of the body is inclined to the direction of fluid flow. If the axis of the body is parallel to the fluid flow, lift force will be zero. Expression for Drag & Lift Forces acting on the small elemental area dA are: i. Pressure force acting perpendicular to the surface i.e. p dA ii. Shear force acting along the tangential direction to the surface i.e. τ0dA (a) Drag force (FD) : Drag force on elemental area = p dAcosθ + τ0 dAcos(90 – θ = p dAosθ + τ0dAsinθ Hence Total drag (or profile drag) is given by, Where �� = ∫ � cos � �� + ∫�0 sin � �� = pressure drag or form drag, and ∫ � cos � �� = shear drag or friction drag or skin drag (b) Lift0 force (F ) : ∫ � sin � ��L Lift force on the elemental area = − p dAsinθ + τ0 dA sin(90 – θ = − p dAsiθ + τ0dAcosθ Hence, total lift is given by http://www.rgpvonline.com �� = ∫�0 cos � �� − ∫ p sin � �� 2 The drag & lift for a body moving in a fluid of density at a uniform velocity U are calculated mathematically as 2 � And �� = � � � 2 � Where A = projected area of the body or�� largest= � project� � area of the immersed body. -
Drag Bookkeeping
Drag Drag Bookkeeping Drag may be divided into components in several ways: To highlight the change in drag with lift: Drag = Zero-Lift Drag + Lift-Dependent Drag + Compressibility Drag To emphasize the physical origins of the drag components: Drag = Skin Friction Drag + Viscous Pressure Drag + Inviscid (Vortex) Drag + Wave Drag The latter decomposition is stressed in these notes. There is sometimes some confusion in the terminology since several effects contribute to each of these terms. The definitions used here are as follows: Compressibility drag is the increment in drag associated with increases in Mach number from some reference condition. Generally, the reference condition is taken to be M = 0.5 since the effects of compressibility are known to be small here at typical conditions. Thus, compressibility drag contains a component at zero-lift and a lift-dependent component but includes only the increments due to Mach number (CL and Re are assumed to be constant.) Zero-lift drag is the drag at M=0.5 and CL = 0. It consists of several components, discussed on the following pages. These include viscous skin friction, vortex drag due to twist, added drag due to fuselage upsweep, control surface gaps, nacelle base drag, and miscellaneous items. The Lift-Dependent drag, sometimes called induced drag, includes the usual lift- dependent vortex drag together with lift-dependent components of skin friction and pressure drag. For the second method: Skin Friction drag arises from the shearing stresses at the surface of a body due to viscosity. It accounts for most of the drag of a transport aircraft in cruise. -
Fluid Mechanics, Drag Reduction and Advanced Configuration Aeronautics
NASA/TM-2000-210646 Fluid Mechanics, Drag Reduction and Advanced Configuration Aeronautics Dennis M. Bushnell Langley Research Center, Hampton, Virginia December 2000 The NASA STI Program Office ... in Profile Since its founding, NASA has been dedicated to CONFERENCE PUBLICATION. Collected the advancement of aeronautics and space papers from scientific and technical science. The NASA Scientific and Technical conferences, symposia, seminars, or other Information (STI) Program Office plays a key meetings sponsored or co-sponsored by part in helping NASA maintain this important NASA. role. SPECIAL PUBLICATION. Scientific, The NASA STI Program Office is operated by technical, or historical information from Langley Research Center, the lead center for NASA programs, projects, and missions, NASA's scientific and technical information. The often concerned with subjects having NASA STI Program Office provides access to the substantial public interest. NASA STI Database, the largest collection of aeronautical and space science STI in the world. TECHNICAL TRANSLATION. English- The Program Office is also NASA's institutional language translations of foreign scientific mechanism for disseminating the results of its and technical material pertinent to NASA's research and development activities. These mission. results are published by NASA in the NASA STI Report Series, which includes the following Specialized services that complement the STI report types: Program Office's diverse offerings include creating custom thesauri, building customized TECHNICAL PUBLICATION. Reports of databases, organizing and publishing research completed research or a major significant results ... even providing videos. phase of research that present the results of NASA programs and include extensive For more information about the NASA STI data or theoretical analysis. -
Chapter 4: Immersed Body Flow [Pp
MECH 3492 Fluid Mechanics and Applications Univ. of Manitoba Fall Term, 2017 Chapter 4: Immersed Body Flow [pp. 445-459 (8e), or 374-386 (9e)] Dr. Bing-Chen Wang Dept. of Mechanical Engineering Univ. of Manitoba, Winnipeg, MB, R3T 5V6 When a viscous fluid flow passes a solid body (fully-immersed in the fluid), the body experiences a net force, F, which can be decomposed into two components: a drag force F , which is parallel to the flow direction, and • D a lift force F , which is perpendicular to the flow direction. • L The drag coefficient CD and lift coefficient CL are defined as follows: FD FL CD = 1 2 and CL = 1 2 , (112) 2 ρU A 2 ρU Ap respectively. Here, U is the free-stream velocity, A is the “wetted area” (total surface area in contact with fluid), and Ap is the “planform area” (maximum projected area of an object such as a wing). In the remainder of this section, we focus our attention on the drag forces. As discussed previously, there are two types of drag forces acting on a solid body immersed in a viscous flow: friction drag (also called “viscous drag”), due to the wall friction shear stress exerted on the • surface of a solid body; pressure drag (also called “form drag”), due to the difference in the pressure exerted on the front • and rear surfaces of a solid body. The friction drag and pressure drag on a finite immersed body are defined as FD,vis = τwdA and FD, pres = pdA , (113) ZA ZA Streamwise component respectively. -
Hydraulics Manual Glossary G - 3
Glossary G - 1 GLOSSARY OF HIGHWAY-RELATED DRAINAGE TERMS (Reprinted from the 1999 edition of the American Association of State Highway and Transportation Officials Model Drainage Manual) G.1 Introduction This Glossary is divided into three parts: · Introduction, · Glossary, and · References. It is not intended that all the terms in this Glossary be rigorously accurate or complete. Realistically, this is impossible. Depending on the circumstance, a particular term may have several meanings; this can never change. The primary purpose of this Glossary is to define the terms found in the Highway Drainage Guidelines and Model Drainage Manual in a manner that makes them easier to interpret and understand. A lesser purpose is to provide a compendium of terms that will be useful for both the novice as well as the more experienced hydraulics engineer. This Glossary may also help those who are unfamiliar with highway drainage design to become more understanding and appreciative of this complex science as well as facilitate communication between the highway hydraulics engineer and others. Where readily available, the source of a definition has been referenced. For clarity or format purposes, cited definitions may have some additional verbiage contained in double brackets [ ]. Conversely, three “dots” (...) are used to indicate where some parts of a cited definition were eliminated. Also, as might be expected, different sources were found to use different hyphenation and terminology practices for the same words. Insignificant changes in this regard were made to some cited references and elsewhere to gain uniformity for the terms contained in this Glossary: as an example, “groundwater” vice “ground-water” or “ground water,” and “cross section area” vice “cross-sectional area.” Cited definitions were taken primarily from two sources: W.B. -
10. Supersonic Aerodynamics
Grumman Tribody Concept featured on the 1978 company calendar. The basis for this idea will be explained below. 10. Supersonic Aerodynamics 10.1 Introduction There have actually only been a few truly supersonic airplanes. This means airplanes that can cruise supersonically. Before the F-22, classic “supersonic” fighters used brute force (afterburners) and had extremely limited duration. As an example, consider the two defined supersonic missions for the F-14A: F-14A Supersonic Missions CAP (Combat Air Patrol) • 150 miles subsonic cruise to station • Loiter • Accel, M = 0.7 to 1.35, then dash 25 nm - 4 1/2 minutes and 50 nm total • Then, must head home, or to a tanker! DLI (Deck Launch Intercept) • Energy climb to 35K ft, M = 1.5 (4 minutes) • 6 minutes at M = 1.5 (out 125-130 nm) • 2 minutes Combat (slows down fast) After 12 minutes, must head home or to a tanker. In this chapter we will explain the key supersonic aerodynamics issues facing the configuration aerodynamicist. We will start by reviewing the most significant airplanes that had substantial sustained supersonic capability. We will then examine the key physical underpinnings of supersonic gas dynamics and their implications for configuration design. Examples are presented showing applications of modern CFD and the application of MDO. We will see that developing a practical supersonic airplane is extremely demanding and requires careful integration of the various contributing technologies. Finally we discuss contemporary efforts to develop new supersonic airplanes. 10.2 Supersonic “Cruise” Airplanes The supersonic capability described above is typical of most of the so-called supersonic fighters, and obviously the supersonic performance is limited. -
7. Transonic Aerodynamics of Airfoils and Wings
W.H. Mason 7. Transonic Aerodynamics of Airfoils and Wings 7.1 Introduction Transonic flow occurs when there is mixed sub- and supersonic local flow in the same flowfield (typically with freestream Mach numbers from M = 0.6 or 0.7 to 1.2). Usually the supersonic region of the flow is terminated by a shock wave, allowing the flow to slow down to subsonic speeds. This complicates both computations and wind tunnel testing. It also means that there is very little analytic theory available for guidance in designing for transonic flow conditions. Importantly, not only is the outer inviscid portion of the flow governed by nonlinear flow equations, but the nonlinear flow features typically require that viscous effects be included immediately in the flowfield analysis for accurate design and analysis work. Note also that hypersonic vehicles with bow shocks necessarily have a region of subsonic flow behind the shock, so there is an element of transonic flow on those vehicles too. In the days of propeller airplanes the transonic flow limitations on the propeller mostly kept airplanes from flying fast enough to encounter transonic flow over the rest of the airplane. Here the propeller was moving much faster than the airplane, and adverse transonic aerodynamic problems appeared on the prop first, limiting the speed and thus transonic flow problems over the rest of the aircraft. However, WWII fighters could reach transonic speeds in a dive, and major problems often arose. One notable example was the Lockheed P-38 Lightning. Transonic effects prevented the airplane from readily recovering from dives, and during one flight test, Lockheed test pilot Ralph Virden had a fatal accident. -
SIMULATION of UNSTEADY ROTATIONAL FLOW OVER PROPFAN CONFIGURATION NASA GRANT No. NAG 3-730 FINAL REPORT for the Period JUNE 1986
SIMULATION OF UNSTEADY ROTATIONAL FLOW OVER PROPFAN CONFIGURATION NASA GRANT No. NAG 3-730 FINAL REPORT for the period JUNE 1986 - NOVEMBER 30, 1990 submitted to NASA LEWIS RESEARCH CENTER CLEVELAND, OHIO Attn: Mr. G. L. Stefko Project Monitor Prepared by: Rakesh Srivastava Post Doctoral Fellow L. N. Sankar Associate Professor School of Aerospace Engineering Georgia Institute of Technology Atlanta, Georgia 30332 INTRODUCTION During the past decade, aircraft engine manufacturers and scientists at NASA have worked on extending the high propulsive efficiency of a classical propeller to higher cruise Mach numbers. The resulting configurations use highly swept twisted and very thin blades to delay the drag divergence Mach number. Unfortunately, these blades are also susceptible to aeroelastic instabilities. This was observed for some advanced propeller configurations in wind tunnel tests at NASA Lewis Research Center, where the blades fluttered at cruise speeds. To address this problem and to understand the flow phenomena and the solid fluid interaction involved, a research effort was initiated at Georgia Institute of Technology in 1986, under the support of the Structural Dynamics Branch of the NASA Lewis Research Center. The objectives of this study are: a) Development of solution procedures and computer codes capable of predicting the aeroelastic characteristics of modern single and counter-rotation propellers, b) Use of these solution procedures to understand physical phenomena such as stall flutter, transonic flutter and divergence Towards this goal a two dimensional compressible Navier-Stokes solver and a three dimensional compressible Euler solver have been developed and documented in open literature. The two dimensional unsteady, compressible Navier-Stokes solver developed at Georgia Institute of Technology has been used to study a two dimensional propfan like airfoil operating in high speed transonic flow regime.