High-Performance Airfoil with Low Reynolds-Number Dependence on Aerodynamic Characteristics
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Convection Heat Transfer
Convection Heat Transfer Heat transfer from a solid to the surrounding fluid Consider fluid motion Recall flow of water in a pipe Thermal Boundary Layer • A temperature profile similar to velocity profile. Temperature of pipe surface is kept constant. At the end of the thermal entry region, the boundary layer extends to the center of the pipe. Therefore, two boundary layers: hydrodynamic boundary layer and a thermal boundary layer. Analytical treatment is beyond the scope of this course. Instead we will use an empirical approach. Drawback of empirical approach: need to collect large amount of data. Reynolds Number: Nusselt Number: it is the dimensionless form of convective heat transfer coefficient. Consider a layer of fluid as shown If the fluid is stationary, then And Dividing Replacing l with a more general term for dimension, called the characteristic dimension, dc, we get hd N ≡ c Nu k Nusselt number is the enhancement in the rate of heat transfer caused by convection over the conduction mode. If NNu =1, then there is no improvement of heat transfer by convection over conduction. On the other hand, if NNu =10, then rate of convective heat transfer is 10 times the rate of heat transfer if the fluid was stagnant. Prandtl Number: It describes the thickness of the hydrodynamic boundary layer compared with the thermal boundary layer. It is the ratio between the molecular diffusivity of momentum to the molecular diffusivity of heat. kinematic viscosity υ N == Pr thermal diffusivity α μcp N = Pr k If NPr =1 then the thickness of the hydrodynamic and thermal boundary layers will be the same. -
Laws of Similarity in Fluid Mechanics 21
Laws of similarity in fluid mechanics B. Weigand1 & V. Simon2 1Institut für Thermodynamik der Luft- und Raumfahrt (ITLR), Universität Stuttgart, Germany. 2Isringhausen GmbH & Co KG, Lemgo, Germany. Abstract All processes, in nature as well as in technical systems, can be described by fundamental equations—the conservation equations. These equations can be derived using conservation princi- ples and have to be solved for the situation under consideration. This can be done without explicitly investigating the dimensions of the quantities involved. However, an important consideration in all equations used in fluid mechanics and thermodynamics is dimensional homogeneity. One can use the idea of dimensional consistency in order to group variables together into dimensionless parameters which are less numerous than the original variables. This method is known as dimen- sional analysis. This paper starts with a discussion on dimensions and about the pi theorem of Buckingham. This theorem relates the number of quantities with dimensions to the number of dimensionless groups needed to describe a situation. After establishing this basic relationship between quantities with dimensions and dimensionless groups, the conservation equations for processes in fluid mechanics (Cauchy and Navier–Stokes equations, continuity equation, energy equation) are explained. By non-dimensionalizing these equations, certain dimensionless groups appear (e.g. Reynolds number, Froude number, Grashof number, Weber number, Prandtl number). The physical significance and importance of these groups are explained and the simplifications of the underlying equations for large or small dimensionless parameters are described. Finally, some examples for selected processes in nature and engineering are given to illustrate the method. 1 Introduction If we compare a small leaf with a large one, or a child with its parents, we have the feeling that a ‘similarity’ of some sort exists. -
Notes on Earth Atmospheric Entry for Mars Sample Return Missions
NASA/TP–2006-213486 Notes on Earth Atmospheric Entry for Mars Sample Return Missions Thomas Rivell Ames Research Center, Moffett Field, California September 2006 The NASA STI Program Office . in Profile Since its founding, NASA has been dedicated to the • CONFERENCE PUBLICATION. Collected advancement of aeronautics and space science. The papers from scientific and technical confer- NASA Scientific and Technical Information (STI) ences, symposia, seminars, or other meetings Program Office plays a key part in helping NASA sponsored or cosponsored by NASA. maintain this important role. • SPECIAL PUBLICATION. Scientific, technical, The NASA STI Program Office is operated by or historical information from NASA programs, Langley Research Center, the Lead Center for projects, and missions, often concerned with NASA’s scientific and technical information. The subjects having substantial public interest. NASA STI Program Office provides access to the NASA STI Database, the largest collection of • TECHNICAL TRANSLATION. English- aeronautical and space science STI in the world. language translations of foreign scientific and The Program Office is also NASA’s institutional technical material pertinent to NASA’s mission. mechanism for disseminating the results of its research and development activities. These results Specialized services that complement the STI are published by NASA in the NASA STI Report Program Office’s diverse offerings include creating Series, which includes the following report types: custom thesauri, building customized databases, organizing and publishing research results . even • TECHNICAL PUBLICATION. Reports of providing videos. completed research or a major significant phase of research that present the results of NASA For more information about the NASA STI programs and include extensive data or theoreti- Program Office, see the following: cal analysis. -
1 Fluid Flow Outline Fundamentals of Rheology
Fluid Flow Outline • Fundamentals and applications of rheology • Shear stress and shear rate • Viscosity and types of viscometers • Rheological classification of fluids • Apparent viscosity • Effect of temperature on viscosity • Reynolds number and types of flow • Flow in a pipe • Volumetric and mass flow rate • Friction factor (in straight pipe), friction coefficient (for fittings, expansion, contraction), pressure drop, energy loss • Pumping requirements (overcoming friction, potential energy, kinetic energy, pressure energy differences) 2 Fundamentals of Rheology • Rheology is the science of deformation and flow – The forces involved could be tensile, compressive, shear or bulk (uniform external pressure) • Food rheology is the material science of food – This can involve fluid or semi-solid foods • A rheometer is used to determine rheological properties (how a material flows under different conditions) – Viscometers are a sub-set of rheometers 3 1 Applications of Rheology • Process engineering calculations – Pumping requirements, extrusion, mixing, heat transfer, homogenization, spray coating • Determination of ingredient functionality – Consistency, stickiness etc. • Quality control of ingredients or final product – By measurement of viscosity, compressive strength etc. • Determination of shelf life – By determining changes in texture • Correlations to sensory tests – Mouthfeel 4 Stress and Strain • Stress: Force per unit area (Units: N/m2 or Pa) • Strain: (Change in dimension)/(Original dimension) (Units: None) • Strain rate: Rate -
Chapter 5 Dimensional Analysis and Similarity
Chapter 5 Dimensional Analysis and Similarity Motivation. In this chapter we discuss the planning, presentation, and interpretation of experimental data. We shall try to convince you that such data are best presented in dimensionless form. Experiments which might result in tables of output, or even mul- tiple volumes of tables, might be reduced to a single set of curves—or even a single curve—when suitably nondimensionalized. The technique for doing this is dimensional analysis. Chapter 3 presented gross control-volume balances of mass, momentum, and en- ergy which led to estimates of global parameters: mass flow, force, torque, total heat transfer. Chapter 4 presented infinitesimal balances which led to the basic partial dif- ferential equations of fluid flow and some particular solutions. These two chapters cov- ered analytical techniques, which are limited to fairly simple geometries and well- defined boundary conditions. Probably one-third of fluid-flow problems can be attacked in this analytical or theoretical manner. The other two-thirds of all fluid problems are too complex, both geometrically and physically, to be solved analytically. They must be tested by experiment. Their behav- ior is reported as experimental data. Such data are much more useful if they are ex- pressed in compact, economic form. Graphs are especially useful, since tabulated data cannot be absorbed, nor can the trends and rates of change be observed, by most en- gineering eyes. These are the motivations for dimensional analysis. The technique is traditional in fluid mechanics and is useful in all engineering and physical sciences, with notable uses also seen in the biological and social sciences. -
Introduction to Aerodynamics < 1.7. Dimensional Analysis > Physical
Introduction to Aerodynamics < 1.7. Dimensional analysis > Physical parameters Q: What physical quantities influence forces and moments? V A l Aerodynamics 2015 fall - 1 - Introduction to Aerodynamics < 1.7. Dimensional analysis > Physical parameters Physical quantities to be considered Parameter Symbol units Lift L' MLT-2 Angle of attack α - -1 Freestream velocity V∞ LT -3 Freestream density ρ∞ ML -1 -1 Freestream viscosity μ∞ ML T -1 Freestream speed of sound a∞ LT Size of body (e.g. chord) c L Generally, resultant aerodynamic force: R = f(ρ∞, V∞, c, μ∞, a∞) (1) Aerodynamics 2015 fall - 2 - Introduction to Aerodynamics < 1.7. Dimensional analysis > The Buckingham PI Theorem The relation with N physical variables f1 ( p1 , p2 , p3 , … , pN ) = 0 can be expressed as f 2( P1 , P2 , ... , PN-K ) = 0 where K is the No. of fundamental dimensions Then P1 =f3 ( p1 , p2 , … , pK , pK+1 ) P2 =f4 ( p1 , p2 , … , pK , pK+2 ) …. PN-K =f ( p1 , p2 , … , pK , pN ) Aerodynamics 2015 fall - 3 - < 1.7. Dimensional analysis > The Buckingham PI Theorem Example) Aerodynamics 2015 fall - 4 - < 1.7. Dimensional analysis > The Buckingham PI Theorem Example) Aerodynamics 2015 fall - 5 - < 1.7. Dimensional analysis > The Buckingham PI Theorem Aerodynamics 2015 fall - 6 - < 1.7. Dimensional analysis > The Buckingham PI Theorem Through similar procedure Aerodynamics 2015 fall - 7 - Introduction to Aerodynamics < 1.7. Dimensional analysis > Dimensionless form Aerodynamics 2015 fall - 8 - Introduction to Aerodynamics < 1.8. Flow similarity > Dynamic similarity Two different flows are dynamically similar if • Streamline patterns are similar • Velocity, pressure, temperature distributions are same • Force coefficients are same Criteria • Geometrically similar • Similarity parameters (Re, M) are same Aerodynamics 2015 fall - 9 - Introduction to Aerodynamics < 1.8. -
Aerodynamic Force Measurement on an Icing Airfoil
AerE 344: Undergraduate Aerodynamics and Propulsion Laboratory Lab Instructions Lab #13: Aerodynamic Force Measurement on an Icing Airfoil Instructor: Dr. Hui Hu Department of Aerospace Engineering Iowa State University Office: Room 2251, Howe Hall Tel:515-294-0094 Email:[email protected] Lab #13: Aerodynamic Force Measurement on an Icing Airfoil Objective: The objective of this lab is to measure the aerodynamic forces acting on an airfoil in a wind tunnel using a direct force balance. The forces will be measured on an airfoil before and after the accretion of ice to illustrate the effect of icing on the performance of aerodynamic bodies. The experiment components: The experiments will be performed in the ISU-UTAS Icing Research Tunnel, a closed-circuit refrigerated wind tunnel located in the Aerospace Engineering Department of Iowa State University. The tunnel has a test section with a 16 in 16 in cross section and all the walls of the test section optically transparent. The wind tunnel has a contraction section upstream the test section with a spray system that produces water droplets with the 10–100 um mean droplet diameters and water mass concentrations of 0–10 g/m3. The tunnel is refrigerated by a Vilter 340 system capable of achieving operating air temperatures below -20 C. The freestream velocity of the tunnel can set up to ~50 m/s. Figure 1 shows the calibration information for the tunnel, relating the freestream velocity to the motor frequency setting. Figure 1. Wind tunnel airspeed versus motor frequency setting. The airfoil model for the lab is a finite wing NACA 0012 with a chord length of 6 inches and a span of 14.5 inches. -
Anomalous Viscosity, Resistivity, and Thermal Diffusivity of the Solar
Anomalous Viscosity, Resistivity, and Thermal Diffusivity of the Solar Wind Plasma Mahendra K. Verma Department of Physics, Indian Institute of Technology, Kanpur 208016, India November 12, 2018 Abstract In this paper we have estimated typical anomalous viscosity, re- sistivity, and thermal difffusivity of the solar wind plasma. Since the solar wind is collsionless plasma, we have assumed that the dissipation in the solar wind occurs at proton gyro radius through wave-particle interactions. Using this dissipation length-scale and the dissipation rates calculated using MHD turbulence phenomenology [Verma et al., 1995a], we estimate the viscosity and proton thermal diffusivity. The resistivity and electron’s thermal diffusivity have also been estimated. We find that all our transport quantities are several orders of mag- nitude higher than those calculated earlier using classical transport theories of Braginskii. In this paper we have also estimated the eddy turbulent viscosity. arXiv:chao-dyn/9509002v1 5 Sep 1995 1 1 Introduction The solar wind is a collisionless plasma; the distance travelled by protons between two consecutive Coulomb collisions is approximately 3 AU [Barnes, 1979]. Therefore, the dissipation in the solar wind involves wave-particle interactions rather than particle-particle collisions. For the observational evidence of the wave-particle interactions in the solar wind refer to the review articles by Gurnett [1991], Marsch [1991] and references therein. Due to these reasons for the calculations of transport coefficients in the solar wind, the scales of wave-particle interactions appear more appropriate than those of particle-particle interactions [Braginskii, 1965]. Note that the viscosity in a turbulent fluid is scale dependent. -
Active Control of Flow Over an Oscillating NACA 0012 Airfoil
Active Control of Flow over an Oscillating NACA 0012 Airfoil Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By David Armando Castañeda Vergara, M.S., B.S. Graduate Program in Aeronautical and Astronautical Engineering The Ohio State University 2020 Dissertation Committee: Dr. Mo Samimy, Advisor Dr. Datta Gaitonde Dr. Jim Gregory Dr. Miguel Visbal Dr. Nathan Webb c Copyright by David Armando Castañeda Vergara 2020 Abstract Dynamic stall (DS) is a time-dependent flow separation and stall phenomenon that occurs due to unsteady motion of a lifting surface. When the motion is sufficiently rapid, the flow can remain attached well beyond the static stall angle of attack. The eventual stall and dynamic stall vortex formation, convection, and shedding processes introduce large unsteady aerodynamic loads (lift, drag, and moment) which are undesirable. Dynamic stall occurs in many applications, including rotorcraft, micro aerial vehicles (MAVs), and wind turbines. This phenomenon typically occurs in rotorcraft applications over the rotor at high forward flight speeds or during maneuvers with high load factors. The primary adverse characteristic of dynamic stall is the onset of high torsional and vibrational loads on the rotor due to the associated unsteady aerodynamic forces. Nanosecond Dielectric Barrier Discharge (NS-DBD) actuators are flow control devices which can excite natural instabilities in the flow. These actuators have demonstrated the ability to delay or mitigate dynamic stall. To study the effect of an NS-DBD actuator on DS, a preliminary proof-of-concept experiment was conducted. This experiment examined the control of DS over a NACA 0015 airfoil; however, the setup had significant limitations. -
Aerodynamics of Small Vehicles
Annu. Rev. Fluid Mech. 2003. 35:89–111 doi: 10.1146/annurev.fluid.35.101101.161102 Copyright °c 2003 by Annual Reviews. All rights reserved AERODYNAMICS OF SMALL VEHICLES Thomas J. Mueller1 and James D. DeLaurier2 1Hessert Center for Aerospace Research, Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, Indiana 46556; email: [email protected], 2Institute for Aerospace Studies, University of Toronto, Downsview, Ontario, Canada M3H 5T6; email: [email protected] Key Words low Reynolds number, fixed wing, flapping wing, small unmanned vehicles ■ Abstract In this review we describe the aerodynamic problems that must be addressed in order to design a successful small aerial vehicle. The effects of Reynolds number and aspect ratio (AR) on the design and performance of fixed-wing vehicles are described. The boundary-layer behavior on airfoils is especially important in the design of vehicles in this flight regime. The results of a number of experimental boundary-layer studies, including the influence of laminar separation bubbles, are discussed. Several examples of small unmanned aerial vehicles (UAVs) in this regime are described. Also, a brief survey of analytical models for oscillating and flapping-wing propulsion is presented. These range from the earliest examples where quasi-steady, attached flow is assumed, to those that account for the unsteady shed vortex wake as well as flow separation and aeroelastic behavior of a flapping wing. Experiments that complemented the analysis and led to the design of a successful ornithopter are also described. 1. INTRODUCTION Interest in the design and development of small unmanned aerial vehicles (UAVs) has increased dramatically in the past two and a half decades. -
Low Reynolds Number Effects on the Aerodynamics of Unmanned Aerial Vehicles
Low Reynolds Number Effects on the Aerodynamics of Unmanned Aerial Vehicles. P. Lavoie AER1215 Commercial Aviation vs UAV Classical aerodynamics based on inviscid theory Made sense since viscosity effects limited to a very small region near the surface True because inertial forces 2 1 Ul 6-8 Re = = ⇢U (µU/l)− = 10 viscous forces ⌫ ⇠ AER1215 - Lavoie 2 Commercial Aviation vs UAV Lissaman (1983) AER1215 - Lavoie 3 Commercial Aviation vs UAV For most UAV 103 Re 105 As a result, one can expect the flow to remain laminar for a greater extent flow field. This has fundamental implications for the aerodynamics of the flow. AER1215 - Lavoie 4 Low Reynolds Number Effects Lissaman (1983) AER1215 - Lavoie 5 Low Reynolds number effects At high Re, the drag is fairly constant with lift As low to moderate Re, large values of drag are obtained for moderate angles of attack What is going on? How to explain all this? Lissaman (1983) AER1215 - Lavoie 6 The Boundary Layer To understand what is going on, let us investigate the boundary layer a bit more closely. First, governing equations @ (⇢u) @ (⇢v) Mass conservation + =0 @x @y x-momentum conservation @u @u @p @ 4 @u 2 @v @ @v @u ⇢u + ⇢v = + µ + µ + @x @y −@x @x 3 @x − 3 @y @y @x @y ✓ ◆ ✓ ◆ AER1215 - Lavoie 7 Boundary Layer Equations After some blackboard magic… @ (⇢u) @ (⇢v) Mass conservation + =0 @x @y x-momentum conservation @u @u dp @ @u ⇢u + ⇢v = e + µ @x @y − dx @y @y ✓ ◆ AER1215 - Lavoie 8 Flow Separation What is the momentum equation at the surface (assume constant viscosity)? Blackboard magic… Fluid is doing work against the adverse pressure gradient and loses momentum, until it comes to rest and is driven back by the pressure. -
Arxiv:1903.08882V2 [Physics.Flu-Dyn] 6 Jun 2019
Lattice Boltzmann simulations of three-dimensional thermal convective flows at high Rayleigh number Ao Xua,∗, Le Shib, Heng-Dong Xia aSchool of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China bState Key Laboratory of Electrical Insulation and Power Equipment, Center of Nanomaterials for Renewable Energy, School of Electrical Engineering, Xi'an Jiaotong University, Xi'an 710049, China Abstract We present numerical simulations of three-dimensional thermal convective flows in a cubic cell at high Rayleigh number using thermal lattice Boltzmann (LB) method. The thermal LB model is based on double distribution function ap- proach, which consists of a D3Q19 model for the Navier-Stokes equations to simulate fluid flows and a D3Q7 model for the convection-diffusion equation to simulate heat transfer. Relaxation parameters are adjusted to achieve the isotropy of the fourth-order error term in the thermal LB model. Two types of thermal convective flows are considered: one is laminar thermal convection in side-heated convection cell, which is heated from one vertical side and cooled from the other vertical side; while the other is turbulent thermal convection in Rayleigh-B´enardconvection cell, which is heated from the bottom and cooled from the top. In side-heated convection cell, steady results of hydrodynamic quantities and Nusselt numbers are presented at Rayleigh numbers of 106 and 107, and Prandtl number of 0.71, where the mesh sizes are up to 2573; in Rayleigh-B´enardconvection cell, statistical averaged results of Reynolds and Nusselt numbers, as well as kinetic and thermal energy dissipation rates are presented at Rayleigh numbers of 106, 3×106, and 107, and Prandtl numbers of arXiv:1903.08882v2 [physics.flu-dyn] 6 Jun 2019 ∗Corresponding author Email address: [email protected] (Ao Xu) DOI: 10.1016/j.ijheatmasstransfer.2019.06.002 c 2019.