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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. -
Lecture 18 Ocean General Circulation Modeling
Lecture 18 Ocean General Circulation Modeling 9.1 The equations of motion: Navier-Stokes The governing equations for a real fluid are the Navier-Stokes equations (con servation of linear momentum and mass mass) along with conservation of salt, conservation of heat (the first law of thermodynamics) and an equation of state. However, these equations support fast acoustic modes and involve nonlinearities in many terms that makes solving them both difficult and ex pensive and particularly ill suited for long time scale calculations. Instead we make a series of approximations to simplify the Navier-Stokes equations to yield the “primitive equations” which are the basis of most general circu lations models. In a rotating frame of reference and in the absence of sources and sinks of mass or salt the Navier-Stokes equations are @ �~v + �~v~v + 2�~ �~v + g�kˆ + p = ~ρ (9.1) t r · ^ r r · @ � + �~v = 0 (9.2) t r · @ �S + �S~v = 0 (9.3) t r · 1 @t �ζ + �ζ~v = ω (9.4) r · cpS r · F � = �(ζ; S; p) (9.5) Where � is the fluid density, ~v is the velocity, p is the pressure, S is the salinity and ζ is the potential temperature which add up to seven dependent variables. 115 12.950 Atmospheric and Oceanic Modeling, Spring '04 116 The constants are �~ the rotation vector of the sphere, g the gravitational acceleration and cp the specific heat capacity at constant pressure. ~ρ is the stress tensor and ω are non-advective heat fluxes (such as heat exchange across the sea-surface).F 9.2 Acoustic modes Notice that there is no prognostic equation for pressure, p, but there are two equations for density, �; one prognostic and one diagnostic. -
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. -
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. -
Airfoil Boundary Layer Separation Prediction [Pdf]
Airfoil Boundary Layer Separation Prediction A project present to The Faculty of the Department of Aerospace Engineering San Jose State University in partial fulfillment of the requirements for the degree Master of Science in Aerospace Engineering By Kartavya Patel May 2014 approved by Dr. Nikos Mourtos Faculty Advisor ABSTRACT Airfoil Boundary Layer Separation Prediction by Kartavya Patel This project features a MatLab complied program that predicts airfoil boundary layer separation. The Airfoil Boundary Layer Separation program uses NACA 4 series, 5 series and custom coordinates to generate the airfoil geometry. It then uses Hess-Smith Panel Method to generate the pressure distribution. It will use the pressure distribution profile to display the boundary layer separation point based on Falkner-Skan Solution, Stratford’s Criterion for Laminar Boundary Layer and Stratford’s Criterion for Turbulent Boundary Layer. From comparison to Xfoil, it can be determined that for low angle of attacks the laminar flow separation point can be predicted from Stratford’s LBL criterion and the turbulent flow separation point can be predicted from Stratford’s TBL criterion. For high angle of attacks, the flow separation point can be predicted from Falkner-Skan Solution. The program requires MatLab Compiler Runtime version 8.1 (MCR) which can be downloaded free at http://www.mathworks.com/products/compiler/mcr/ . ACKNOWLEDGEMENTS I would like to thank Dr. Nikos Mourtos for his support and guidance throughout this project. I would also like to thank Hai Le, Tommy Blackwell and Ian Dupzyk for their contribution in previous project “Determination of Flow Separation Point on NACA Airfoils at Different Angles of Attack by Coupling the Solution of Panel Method with Three Different Separation Criteria”. -
Turbulent Boundary Layer Separation (Nick Laws)
NICK LAWS TURBULENT BOUNDARY LAYER SEPARATION TURBULENT BOUNDARY LAYER SEPARATION OUTLINE ▸ What we know about Boundary Layers from the physics ▸ What the physics tell us about separation ▸ Characteristics of turbulent separation ▸ Characteristics of turbulent reattachment TURBULENT BOUNDARY LAYER SEPARATION TURBULENT VS. LAMINAR BOUNDARY LAYERS ▸ Greater momentum transport creates a greater du/dy near the wall and therefore greater wall stress for turbulent B.L.s ▸ Turbulent B.L.s less sensitive to adverse pressure gradients because more momentum is near the wall ▸ Blunt bodies have lower pressure drag with separated turbulent B.L. vs. separated laminar TURBULENT BOUNDARY LAYER SEPARATION TURBULENT VS. LAMINAR BOUNDARY LAYERS Kundu fig 9.16 Kundu fig 9.21 laminar separation bubbles: natural ‘trip wire’ TURBULENT BOUNDARY LAYER SEPARATION BOUNDARY LAYER ASSUMPTIONS ▸ Simplify the Navier Stokes equations ▸ 2D, steady, fully developed, Re -> infinity, plus assumptions ▸ Parabolic - only depend on upstream history TURBULENT BOUNDARY LAYER SEPARATION BOUNDARY LAYER ASSUMPTIONS TURBULENT BOUNDARY LAYER SEPARATION PHYSICAL PRINCIPLES OF FLOW SEPARATION ▸ What we can infer from the physics TURBULENT BOUNDARY LAYER SEPARATION BOUNDARY LAYER ASSUMPTIONS ▸ Eliminate the pressure gradient TURBULENT BOUNDARY LAYER SEPARATION WHERE THE BOUNDARY LAYER EQUATIONS GET US ▸ Boundary conditions necessary to solve: ▸ Inlet velocity profile u0(y) ▸ u=v=0 @ y = 0 ▸ Ue(x) or Pe(x) ▸ Turbulent addition: relationship for turbulent stress ▸ Note: BL equ.s break down -
Computational and Experimental Study on Performance of Sails of a Yacht
Available online at www.sciencedirect.com SCIENCE DIRECT" EIMQINEERING ELSEVIER Ocean Engineering 33 (2006) 1322-1342 www.elsevier.com/locate/oceaneng Computational and experimental study on performance of sails of a yacht Jaehoon Yoo Hyoung Tae Kim Marine Transportation Systems Researcli Division, Korea Ocean Research and Development Institute, 171 Jang-dong, Yuseong-gu, Daejeon 305-343, South Korea ^ Department of Naval Architecture and Ocean Engineering, Chungnam National Un iversity, 220 Gung-doiig, Yuseong-gu, Daejeon 305-764, South Korea Received 1 February 2005; accepted 4 August 2005 Available online 10 November 2005 Abstract It is important to understand fiow characteristics and performances of sails for both sailors and designers who want to have efhcient thrust of yacht. In this paper the viscous fiows around sail-Hke rigid wings, which are similar to main and jib sails of a 30 feet sloop, are calculated using a CFD tool. Lift, drag and thrust forces are estimated for various conditions of gap distance between the two sails and the center of effort ofthe sail system are obtaiaed. Wind tunnel experiments are also caiTied out to measure aerodynamic forces acting on the sail system and to validate the computation. It is found that the combination of two sails produces the hft force larger than the sum of that produced separately by each sail and the gap distance between the two sails is an important factor to determine total hft and thrust. © 2005 Elsevier Ltd. AU rights reserved. Keywords: Sailing yacht; Interaction; Gap distance; CFD; RANS; Wind tunnel 1. Introduction The saihng performance of a yacht depends on the balance of hydro- and aero-dynamic forces acting on the huU and on the sails. -
Vortex Stretching in Incompressible and Compressible Fluids
Vortex stretching in incompressible and compressible fluids Esteban G. Tabak, Fluid Dynamics II, Spring 2002 1 Introduction The primitive form of the incompressible Euler equations is given by du P = ut + u · ∇u = −∇ + gz (1) dt ρ ∇ · u = 0 (2) representing conservation of momentum and mass respectively. Here u is the velocity vector, P the pressure, ρ the constant density, g the acceleration of gravity and z the vertical coordinate. In this form, the physical meaning of the equations is very clear and intuitive. An alternative formulation may be written in terms of the vorticity vector ω = ∇× u , (3) namely dω = ω + u · ∇ω = (ω · ∇)u (4) dt t where u is determined from ω nonlocally, through the solution of the elliptic system given by (2) and (3). A similar formulation applies to smooth isentropic compressible flows, if one replaces the vorticity ω in (4) by ω/ρ. This formulation is very convenient for many theoretical purposes, as well as for better understanding a variety of fluid phenomena. At an intuitive level, it reflects the fact that rotation is a fundamental element of fluid flow, as exem- plified by hurricanes, tornados and the swirling of water near a bathtub sink. Its derivation from the primitive form of the equations, however, often relies on complex vector identities, which render obscure the intuitive meaning of (4). My purpose here is to present a more intuitive derivation, which follows the tra- ditional physical wisdom of looking for integral principles first, and only then deriving their corresponding differential form. The integral principles associ- ated to (4) are conservation of mass, circulation–angular momentum (Kelvin’s theorem) and vortex filaments (Helmholtz’ theorem). -
Studies on Blood Viscosity During Extracorporeal Circulation
Nagoya ]. med. Sci. 31: 25-50, 1967. STUDIES ON BLOOD VISCOSITY DURING EXTRACORPOREAL CIRCULATION HrsASHI NAGASHIMA 1st Department of Surgery, Nagoya University School of Medicine (Director: Prof Yoshio Hashimoto) ABSTRACT Blood viscosity was studied during extracorporeal circulation by means of a cone in cone viscometer. This rotational viscometer provides sixteen kinds of shear rate, ranging from 0.05 to 250.2 sec-1 • Merits and demerits of the equipment were described comparing with the capillary viscometer. In experimental study it was well demonstrated that the whole blood viscosity showed the shear rate dependency at all hematocrit levels. The influence of the temperature change on the whole blood viscosity was clearly seen when hemato· crit was high and shear rate low. The plasma viscosity was 1.8 cp. at 37°C and Newtonianlike behavior was observed at the same temperature. ·In the hypothermic condition plasma showed shear rate dependency. Viscosity of 10% LMWD was over 2.2 fold as high as that of plasma. The increase of COz content resulted in a constant increase in whole blood viscosity and the increased whole blood viscosity after C02 insufflation, rapidly decreased returning to a little higher level than that in untreated group within 3 minutes. Clinical data were obtained from 27 patients who underwent hypothermic hemodilution perfusion. In the cyanotic group, w hole blood was much more viscous than in the non cyanotic. During bypass, hemodilution had greater influence upon whole blood viscosity than hypothermia, but it went inversely upon the plasma viscosity. The whole blood viscosity was more dependent on dilution rate than amount of diluent in mljkg. -
Lift Forces in External Flows
• DECEMBER 2019 Lift Forces in External Flows Real External Flows – Lesson 3 Lift • We covered the drag component of the fluid force acting on an object, and now we will discuss its counterpart, lift. • Lift is produced by generating a difference in the pressure distribution on the “top” and “bottom” surfaces of the object. • The lift acts in the direction normal to the free-stream fluid motion. • The lift on an object is influenced primarily by its shape, including orientation of this shape with respect to the freestream flow direction. • Secondary influences include Reynolds number, Mach number, the Froude number (if free surface present, e.g., hydrofoil) and the surface roughness. • The pressure imbalance (between the top and bottom surfaces of the object) and lift can increase by changing the angle of attack (AoA) of the object such as an airfoil or by having a non-symmetric shape. Example of Unsteady Lift Around a Baseball • Rotation of the baseball produces a nonuniform pressure distribution across the ball ‐ clockwise rotation causes a floater. Flow ‐ counterclockwise rotation produces a sinker. • In soccer, you can introduce spin to induce the banana kick. Baseball Pitcher Throwing the Ball Soccer Player Kicking the Ball Importance of Lift • Like drag, the lift force can be either a benefit Slats or a hindrance depending on objectives of a Flaps fluid dynamics application. ‐ Lift on a wing of an airplane is essential for the airplane to fly. • Flaps and slats are added to a wing design to maintain lift when airplane reduces speed on its landing approach. ‐ Lift on a fast-driven car is undesirable as it Spoiler reduces wheel traction with the pavement and makes handling of the car more difficult and less safe. -
Studies of Mast Section Aerodynamics by Arvel Gentry
Studies of Mast Section Aerodynamics By Arvel Gentry Proceedings of the 7th AIAA Symposium on the Aero/Hydronautics of Sailing January 31, 1976 Long Beach, California Abstract This paper summarizes the studies that were conducted with the objective of obtaining a mast-section shape with improved aerodynamic flow properties for use on the 12-Meter Courageous. TheDecember project 1999 consisted of a theoretical study defining the basic aerodynamics of the mast-mainsail combination followed by both analytical and experimental studies of various mast-section shapes. A new 12-Meter mast-section shape evolved from these studies that demonstrated significantly improved airflow patterns around the mast and mainsail when compared directly with the conventional 12-Meter elliptical section. This new mast shape was used in constructing the mast for Courageous used in the successful 1974 defense of the America's cup against the Australian challenger Southern Cross. 1. Introduction The mast has always been thought of as being an Bill Ficker, who skippered Intrepid in the 1970 defense, was undesirable but necessary appendage on a sailboat. It slated to be the skipper of the new aluminum Courageous. holds the sails up but contributes considerable drag and Ficker and David Pedrick (S&S project engineer on disturbs the airflow over the mainsail so that its efficiency Courageous) wondered if a new mast-section shape might is greatly reduced. This popular belief has led to a number lead to improved boat performance. This paper describes of different approaches in improving the overall efficiency the work done in attempting to answer that question. of a sailing rig. -
Adaptive Separation Control of a Laminar Boundary Layer Using
J. Fluid Mech. (2020), vol. 903, A21. © The Author(s), 2020. 903 A21-1 Published by Cambridge University Press doi:10.1017/jfm.2020.546 Adaptive separation control of a laminar https://doi.org/10.1017/jfm.2020.546 . boundary layer using online dynamic mode decomposition Eric A. Deem1, Louis N. Cattafesta III1,†,MaziarS.Hemati2, Hao Zhang3, Clarence Rowley3 and Rajat Mittal4 1Mechanical Engineering, Florida State University, Tallahassee, FL 32310, USA 2Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA https://www.cambridge.org/core/terms 3Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA 4Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA (Received 18 November 2019; revised 13 April 2020; accepted 22 June 2020) Adaptive control of flow separation based on online dynamic mode decomposition (DMD) is formulated and implemented on a canonical separated laminar boundary layer via a pulse-modulated zero-net mass-flux jet actuator located just upstream of separation. Using a linear array of thirteen flush-mounted microphones, dynamical characteristics of the separated flow subjected to forcing are extracted by online DMD. This method provides updates of the modal characteristics of the separated flow while forcing is applied at a rate commensurate with the characteristic time scales of the flow. In particular, online DMD provides a time-varying linear estimate of the nonlinear evolution of the controlled , subject to the Cambridge Core terms of use, available at flow without any prior knowledge. Using this adaptive model, feedback control is then implemented in which the linear quadratic regulator gains are computed recursively. This physics-based, autonomous approach results in more efficient flow reattachment compared with commensurate open-loop control.