In this chapter
Importance of the Subject Flow Physics o Viscous Drag Laminar Flow Control Compliant Walls Riblets Large-Eddy Breakup Devices Surface Additives o Drag due to Lift o Interference Drag o Wave Drag o Vortex Drag Drag due to Speed o Drag at Very Low Speeds o Drag at Transonic Speeds o Drag at Supersonic Speeds Drag Reduction Approaches Methods of Computation Summary of Drag Data o CD of Various Aerodynamic Systems o CD Levels of Misc. Aircraft o CD Levels of Road Vehicles Selected References
Drag force is a very large topic in aerodynamics. There are books and conferences entirely devoted to it, along with countless specialized publications. From a physical point of view, drag is the resultant of forces acting normally and tangentially to a surface, the former ones being pressure terms, and the latter ones viscous terms. The mechanism under which these forces are created is ultimately related to the formation of vortices and shear layers.
Importance of the Subject
Very narrow gains (1 % or less) can translate into a change of technology. It is widely assumed that the fuel crisis of the 1970s created the need to invest in drag reduction technology for aircraft transport. But the problem is wider than that, since all the aerodynamic systems use external power that is partially dissipated due to drag forces. Effects of Drag Reduction For example, a reduction in the drag coefficient of an ordinary passenger car from CD = 0.4 to CD=0.3 would improve the fuel consumption by 7.5 %. This saving multiplied by the number of road vehicles in Europe and North America yields a figure (at least 10 billion gallons/year) that could affect the price of the crude oil in the world markets. The reduction of 10 % drag on a large military transport aircraft would save over 10 million gallons of fuel over the life time of the aircraft. A 15 % drag reduction on the Airbus A340-300B would yield a 12 % fuel saving, other parameters being constant (Mertens, 1998). See the Table of Drag Data for more details.
Flow Physics The fundamental mechanisms by which drag is produced in steady state conditions can be reduced to the following ones Viscous Drag Viscous drag is produced by the effects of viscosity on the aerodynamic systems, through the thrust that must be applied to overcome the shear layers due to the non slip condition.
Lift-induced Drag Drag due to lift is the result of the downwash (vertical flow) and to the strength of the vortices produced at some particular locations (wing tips or other sharp edges) of many lifting systems.
Vortex Drag Vortex drag can be created by both lifting and non lifting bodies (usually of the bluff variety, ex. road vehicles, airships). Vortices are released during flow separatio and trail downstream to form structured or unstructured wake patterns.
Interference Interference is the effect of the presence of one body on the aerodynamics of a second body. The interference drag is a system drag that is present even in absence of viscous effects (ideal fluid) and non lifting conditions. Since interference occurs in many practical situations interference drag is a separate topic.
Wave Drag Wave drag is created by radiation of disturbances in the fluid by a moving body. This is the case of transonic and supersonic flows; in hydrodynamics waves are produced by several means, the most important of which is probably the pattern of surface waves produced by boats, ships and submerged bodies. The presence of one or more drag components, along with their respective amounts, clearly depends on the aerodynamic arrangement and the system operation.
Speed-induced Drag Another classification sometimes used is that according to speed. The speed (e.g Reynolds and Mach numbers) have, in fact, one of the most important effects on both the drag build-up and the drag level.
Drag Reduction Approaches The most effective approach to drag reduction is to concentrate on the components that make up the largest percentage of the overall drag. Small improvements on large quantities can become in fact remarkable aerodynamic improvements. This is another reason why the drag build-up analysis is always made before attempting to study the drag reduction strategies.
Methods of Computation There are several methods used to compute the drag of a lifting body. For example:
The drag of an airfoil at subsonic speeds can be computed by using the SquireYoung approximation. The method consists in evaluating the drag coefficient by using boundary layer quantities at the trailing edge.
By using the axial momentumbalance on a large control volume (between two planes far upstream and downstream the body).
By integration of the surface forces (CFD approach). There are two contributions: the tangential (due to skin friction) and normal (due to pressure) contributions. This is the approach followed most by the current research.
Other (simplified) methods include: Integration of circulation in the Treffz plane (induced drag of large aspect ratio wings); Hayes formula (for linearized supersonic flow); Munk's stagger theorems (for linearized multi-body lifting systems), etc. A detailed review of CFD capabilities has been recently published by van Dam (1999). Selected References
Hoerner SF. Fluid Dynamic Drag, Hoerner Fluid Dynamics, 1965. AGARD, Special Course on Concepts for Drag Reduction, AGARD Report R654, 1977. AGARD, Special Course on Subsonic/Transonic Aerodynamic Intereference for Aircraft, AGARD Report R-712, 1983. AGARD, Aircraft Drag Prediction and Reduction, AGARD Report R-723, 1985. Clift R, Grace JR, Weber ME. Bubbles, Drops, and Particles, Academic Press, New York, 1978. Sovran G, Morel T, Mason WT. (editors). Aerodynamic Drag Mechanisms of Bluff Bodies and Road Vehicles, Plenum Press, New York, 1978 (ISBN 0-30631119-4).
Viscous drag (or skin friction drag) is due to the stresses on the aerodynamic surfaces and in the boundary layer. The decreased momentum in the flowfield results in a corresponding loss of momentum of the aerodynamic system. Some of the physical aspects involved in the viscous drag loss are: presence of shear layers, turbulent transition, boundary layer separation. The amount of energy losses depends largely on the aero- hydrodynamic system. On a sailing boat it can range between 1/3 and (nearly) the total drag, depending on the speed of the craft (at low speeds the viscous drag is large, in percent, whereas the wave drag is low). Some typical viscous losses are listed below: Table 1: Summary of viscous drag supersonic fighter
25-30 %
large tranport aircraft
40 %
executive aircraft
50 %
VTOL aircraft underwater bodies ships at low/high speed gas pipelines
70-80 % 70 % 90-30 % 90 %
Reduction Methods Methods for viscous drag reduction rely on techniques that alter the turbulence structure and/or the wall characteristics. These methods are both powered (active methods) and unpowered. Active methods widely used include
boundary layer control Wall cooling (air), or heating (water)
The are also the passive methods, such as vortex generators, along with appropriate design of the aerodynamic surfaces, by minimizing the wetted area and the volume. Other sophisticated techniques include:
Laminar Flow Control(LFC) Compliant Walls Riblets Large-Eddy Breakup Devices (LEBU) Surface Additives (polymers, bubbles)
Selected References
Hoerner SF. Fluid Dynamic Drag, Hoerner Fluid Dynamics, 1965. AGARD. Special Course on Concepts for Drag Reduction, AGARD Report R654, 1977. AGARD. Special Course on Subsonic/Transonic Aerodynamic Intereference for Aircraft, AGARD Report R-712, 1983. AGARD. Aircraft Drag Prediction and Reduction, AGARD Report R-723, 1985.
Laminar Flow Control
Laminar Flow Control (LFC) describes technical means to control the boundary layer development. Laminar flow control consists in a boundary layer suction (that is removal of some flow through surface holes), or a wall cooling. A more unusual technique consists in using resonant walls. A boundary layer usually changes from laminar to turbulent, due to disturbances in the viscous layer (Tollmien-Schlichting waves) that amplify. Amplification, though, occurs only if certain stability criteria (depending on Reynolds number, free-stream turbulence, surface conditions, forced vibrations, etc.) are not satisfied. Boundary layer stability is a large topic on its own. We will limit the following considerations to a few practical aspects of LFC. Boundary layer suction requires a propulsion system that consumes energy. The method is effective if the power required to activate the LFC system is less the power saved thanks to the boundary layer control. The normal velocity required to suck part of the boundary layer are very small and have no macroscopic effect on the surface pressure distribution. The surface must be of superior quality and with minimum roughness, the normal suction must be as uniform as possible, to avoid further distortions in the flow structure. Table 1 lists a number of results achieved with LFC wings (Pfenninger, 1977). Table 1: Subsonic/supersonic wing CD with LFC Device
Sweep
Re x
M
CD x
Subsonic Wing
30 deg
6
0.75
8
Subsonic Wing
0.0 deg
10
0.75
5
Supersonic Wing
35 deg
20
3.00
7
Related Material
Riblets Large-Eddy Break-up Devices Compliant Walls Wall Cooling
Selected References
Lachman G.V. (editor),Boundary Layer and Flow Control (2 Vols.), Pergamon Press, 1961.
The Compliant Wall The complaint wall is a relatively recent idea to reduce the drag by using flexible coatings on the aero- hydrodynamic surfaces. The idea of flexible skins comes from observations on swimming dolphins, and more generally on animal propulsion. The compliant wall must interact with the boundary layer and influence its development, laminar or turbulent. If this has to be true, the wavelength of the skin flexibility must be of the same order of magnitude of the boundary layer thickness, while the amplitude must be of the same order as the viscous sublayer. The idea is that, when the surface is affected by fluid flow around it, it will start an interaction surface-boundary layer such that the boundary layer remains attached for a longer length and the drag of the system will be reduced. The problem, however, is not so easy. The properties of the compliant surface must be well understood, else the effect is ... the opposite (that is a compliant surface that triggers boundary layer separation). Some energy conmsiderations are necessary: In the case of a rigid surface, the drag produced serves to dissipate propulsion power into the fluid (by means of of viscosity, radiation, etc.); in the case of a passive compliant surface part of this energy goes into the surface itself and is dissipated through internal damping; with an active compliant surface power would be required to activate the surface-boundary layer interaction (for example, heating of the coating to activate its compliant properties). Therefore, the fundamental question is whether the net energy balance is positive or negative.
Riblets Summary
Drag Reduction Off-Design Performances o Flow Mis-alignment o Surface Contamination o Effects of Pressure Gradients o Effects of Wetted Area Applications o Aircraft Selected References
Scientists have been speculating for many years whether there is any surface having less drag of a flat plate. The drag of a flat plate is reported in the figure below, for both laminar (Blasius) and turbulent flow. Experimental studies in the 1970s showed that small grooves (riblets) aligned with the flow had the property of modifying the near-wall structure of the boundary layer. In particular, the riblets proved to work as a constraint to the production of the Reyonlds stresses associated with the growth and eruption of the eddies in the the low-speed regions of the boundary layers.
Figure 1: common types of riblets
Later research was aimed at investigating the properties of such grooves, by studying the wall boundary conditions and the flow properties at corner regions. A number of studies of zoologic nature was added to the fluid dynamic problem, by studying the characteristics of fast-swimming sharks and dolphins, form where some ideas were derived. On of the main practical concerns was (and it is) the amount of drag reduction that can be achieved, and studies were directed to investigating the optimum ratio fin-height/riblet spacing, physical dimensions of the riblets, along with the optimum shape (L- U- Vgrooves and others, Fig. 1).
Drag Reduction The skin friction drag reduction data published in the technical literature is variable, but converging to a figure of 8 %, with more conservative values of 5 % to the most optimistic figures of 10-11 %, obtained in laboratory conditions. While these numbers do not seem excessively high, they do lead to enourmous savings. Take for example a subsonic jet transport, for which the skin friction drag is of the order of 45 % at cruise conditions. If half of the surface could be covered by efficient riblets that provide an 8 % skin friction saving, the total saving would be just less than 4 %, a remarkable amount.
Off-Design Performances Flow alignment and surface quality are two main concerns, alogn with pressure gradients, three-dimensional flows and effects of the increased wetted area. The results are as follows: Flow Mis-Alignment No practical effects weere measured on flow mis-alignement up to 15 deg ( 0 deg is a flow perfectly aligned with the riblet). At higher flow angles, up to 40 deg, performances deteriorate gradually, and the riblets become ineffective, if not inappropriate, at such angles. For these reasons some investigators have been studying three-dimensional riblets, also called compound riblets, that would be locally optimized to follow the main direction of the flow. Surface Contamination The surface covered with a riblet film may undergo contamination over time, due to deposition of dust, combustion particulate, atmospheric aggression, etc. This can be a major concern for submerged bodies, such as ships and submarines. However, there
seems to be no effects for periods limited to one day, whereas in aircraft applications the effects, if any, occur over a much longer time scale. Pressure Gradients Pressure gradients have a minor effect, probably 1-2 % on the total skin friction drag reduction. Increase of Wetted Area Increase of wetted area is a problem of any riblet geometry (see figure 1 above), therefore useful configurations are those that, besides stabilizing the boundary layer, have a limited increase in wetted area. Obviously, the skin friction works over a larger surface (this is a problem especially with L-grooves.)
Applications Applications are more common in hydrodynamics where the drag reduction possibilities are larger, in particular on sailing boats. Airfoil applications showed a drag reduction rate of about 6-8 %, although in some recent experiments a skin friction drag reduction of 16 % was achieved at an angle of attack of 6 deg. Aircraft Skin friction drag for a large commercial aircraft is of the order of 40 % of the total. This figure is slighty larger for a smaller executive airfract (up to 50 %). Small gains on this numbers translate into major fuel savings and direct operative costs. One can easily speculate with the 10 % drag saving given above, but this is very far from reality. Both Boeing Aircraft and Airbus have tested riblets for this purpose. Data reported for a 1/11 scale model of the Airbus A320 at cruise Mach number M=0.7 was a viscous drag saving of 4.85 %, with about 66 % of the aircraft wetted area covered by Vriblets (s/h=1). Application of riblets is generally done using special films, rather than estruding the grooves directly on the surface. Riblet films have been manifactured by a number of companies, among them, the 3M company. The riblets dimensions most widely tested fall in the range 0.02mm - 0.10 mm height, with optimal h/s ratio of the order 15. Related Material
Large-Eddy Break-up Devices Compliant Walls Laminar Flow Control
Additives Wall Cooling
Selected References 1. Emerging Techniques in Drag Reduction, edited by Choi, K.S., Prasad, K.K. and Truong, T.V. Mechanical Eng. Publ. Ltd, London, 1996 (ISBN 0-08529-8917-2) 2. Drag Reduction in Fluid Flows: Techniques for Friction Control, by Sellin RHJ, Moses RT. Ellis Horwood Ltd, Chichester, 1989 (ISBN 0-7458-0753-X) 3. Bechert DW, Bruse M, Hage W, VanderHoeven JGT, Hoppe G. Experiments on drag-reducing surfaces and their optimization with an adjustable geometry, in J. Fluid Mech., Vol. 338, pp. 59-87 May 10 1997 4. Walsh MJ. Riblets, in Progress in Aeronautics and Astronautics, Vol. 123, 1990. On the Web These sites are not part of the aerodyn.org domain. There is no guarantee nor control over their content and availability.
NASA riblets for Starts and Stripes (engineering) Scientific American Article, Jan. 1997 (general)
Large Eddy Breakup Devices (LEBU)
LEBU, similarly to the surface riblets, produce extensive downstream regions of reduced skin friction coefficients. However, the experimental data gathered over the last twenty years provided widely varying results, which are also depending on the Reynolds number. The overall performance seems to be related to the drag of the devices themselves. The best drag reduction rates (in percentage) are not better than the surface riblets, roughly 7 to 8 percent. Among these, the tapered trailing edge devices have been found among the best. Cases of interest include trailing edge flows, for examples thick flat plates and airfoils, where trailing edge separation is an issue at relatively large Reynolds numbers. Some NACA 0009 LEBU devices were found to provide a local net skin friction reduction in the range of 30 percent. Similar experiments on cambered NACA 4409 gave no benefits, possibly because of boundary layer separation on the devices themselves.
LEBU performance at the higher Reynolds numbers and transonic conditions often required in aeronautics is strongly dependent on the drag of the devices. Their effectiveness is presumably much reduced at these conditions. In some instances the LEBU have been coupled with the riblets, but the optimal combination of these systems requires experimentation. Related Material
Large-Eddy Break-up Devices Compliant Walls Laminar Flow Control Additives Wall Cooling [Top of Page]
Surface Additives
Effects on Viscous Drag Selected References
Surface additives such as polymers, microbubbles and solid particles have been particularly studied in recent years, due to their virtue of reducing the aero/ hydrodinamic drag by inhibiting the fundamental processes that cause turbulent transition (Berman, 1978). Effects on Viscous Drag The effect becomes evident at just a few parts-per- million (ppm), and gradually increases to values that depend on the molecular nature of the dilute suspension. The molecular weight seems to be playing an important part in the drag reduction characteristics. Most of the additives used are polymers of high molecular weight (for ex. polyetylene-oxide). There are reports of as much as 80 % skin friction drag reduction in internal flows, and 60 % in external flows ! - Such values open up fantastic opportunities for both pipelines and marine applications (high speed vehicles, submarines). For example long polymers derived from alfa-olefins are used for drag reduction in commercial pipelines for crude oil and refined oil products (gasoline, diesel, etc.).
Pipeline performance is greatly enhanced with the injection of the polymer at each pumping station. The dilute solution may vary from 1 ppm (part-per-million) to several ppm. Drag savings of 25-30 % (sometimes more) are reported. This means that at constant pumping power, there is a corresponding increase in throughput, or at constant throughput the pumping power can be reduced (by reducing for example the number of pumping stations). In aircraft applications the drawback, though, would be the amount of additives that must be released from the surface and the power required to run the system. Related Material
Riblets Large-Eddy Break-up Devices Compliant Walls Laminar Flow Control Wall Cooling
Selected References
Emerging Techniques in Drag Reduction, edited by Choi KS, Prasad KK, Truong TV. Mechanical Eng. Publ. Ltd, London, 1996 (ISBN 0-08529-8917-2) Drag Reduction in Fluid Flows: Techniques for Friction Control, by Sellin, RHJ, Moses RT. Ellis Horwood Ltd, Chichester, 1989 (ISBN 0-7458-0753-X)
Lift-induced Drag Summary
Drag due to Lift Selected References
This type of drag is due to the vorticity produced by a lifting wing (induced drag or vortex drag) and is expressed as momentum deficiency in the wake. This type of drag can be a drawback of high-lift systems. Typically, a strong vortex is released at the tip. The dissipation of this vortex farther downstream is one of the source of loss, but this is of viscous nature. The inviscid nature of the drag is also due to the downwash created in the slipstream, which on turns is related
to an induced angle of attack. Reduction Methods Methods used for the minimization of the induced drag make use of techniques to diffuse this vortex and redistribute the wing loading. The methods include:
Use of very-large wing spans Use of non-planar lifting systems Load redistribution by wing optimization
For lifting wings some of the devices commonly designed are the following Tip Devices
Winglets Tip sails Hoerner Tips
The methods listed above are used for the reduction of the vortex drag produced at the tip. Selected References
Hoerner SF. Fluid Dynamic Drag, Hoerner Fluid Dynamics, 1965. AGARD. Special Course on Concepts for Drag Reduction, AGARD Report R-654, 1977. AGARD. Special Course on Subsonic/Transonic Aerodynamic Intereference for Aircraft, AGARD Report R-712, 1983. AGARD. Aircraft Drag Prediction and Reduction, AGARD Report R-723, 1985. [Top of Page]
High Aspect-Ratio Wings The use of larger aspect-ratios is a well known means to reduce the induced drag, that is the drag created by the spanwise distribution of circulation, ultimately due to the development of two strong tip vortices. From three-dimensional small disturbance theory it is found that the optimum distribution of circulation is the one that creates a constant downwash velocity if the slipstream (wake). With this distribution of downwash velocity, the spanwise lift distribution is elliptic, and the induced drag is at a minimum. If the wing planform is also elliptic, there is a closed expression relating the lift to the induced drag. Fig. 1 shows the behavior of the induced drag coefficient as a function of the wing aspect-ratio at two lift levels, from the small disturbance theory (Since this theory was developed for large aspect-ratio wings, values of CDi for aspect-ratios less than 5 are rather off.)
Figure 1: Induced drag vs. AR at different lift levels.
Figure 2: Lift curve slope as function of wing AR The actual aspect-ratio is a compromise between conflicting requirements. For example, for a transport aircraft the optimal aspectratio would be around 8 for minimum cost acquisition, and twice as much for minimum fuel consumption. A fighter aircraft has a low aspect-ratio for manouvrability. Sail planes, human powered planes, high altitude airplanes have a very large wing span, but have poor manouvrability characteristics. The table below provides some typical values. Table 1: Some Aspect-Ratios System Supersonic Jet Aircraft
AR 2.0
Racing Cars Wings Fighter Aircraft Subsonic Jet Aircraft Lockeed U-2
2.8 2.5-3.5 7-9 11.3
Sail Planes
20
Solar Powered Centurion
26
Related Material
Low-Aspect Ratio Wings Wing Tip Devices Summary of Aspect-Ratios Planform Optimization Tip Blowing
Related Web material These sites are not part of the aerodyn.org domain. There is no control over their content or availability.
Copyright © A. Filippone (1999-2002). All Rights Reserved.
Interference Drag in Aerodynamics Summary
Overview Roughness Drag Junction Drag Selected References
Interference is the effect of an aerodynamic component on another: wing-body, wing-nacelle (Fig. 1), vertical-horizontal tail, junctions in general, biplane, ground effect, freee surface problems in hydrodynamics, and more. When Interference Occurs Interference occurs when the sum of the drag forces of the single components is larger that the drag of the composite system. In general, interference is a reciprocal effect, although in some cases (such as supersonic flows) it can be unidirectional (downstream propagation only.) Interference at supersonic speeds can be excessively high.
Figure 1: Wing-nacelle-pilon interference at transonic speeds. Aerodynamic interference on wing-body combinations has been widely investigated at subsonic, transonic and supersonic speeds. Recent research on supersonic aircraft (Kharitonov, 1998) has allowed to determine the optimal position of the wing by systematic analysis of the interference coefficients. Interference at Low Speeds Interference at low speed can be computed with some approximate yet powerful methods: Munk's stagger theorem gives the value of the induced drag for an arbitrary system of lifting lines; Prandtl's theory allows to compute the biplane configuration; the inviscid flow models resulting in the panel methods allow the computation of quite general multi-body configurations, including ducted propellers.
Roughness Drag The most common interference effects arise from imperfections, small scale bumps, holes and other irregularities (Fig. 4 below), due to surface finish, accumulated dirt, etc. Roughness/excrescence drag can be virtually eliminated when the surface is hydraucally smooth, e.g. the excrescence height is less than the boundary layer sublayer thickness. Some typical drag values are the following: cylinder excrescence CD=0.76, semi-sphere CD=0.32.
Junction Drag Important data on junction drag have been compiled by Hoerner (1965). Particularly important is the T-strut configuration, for which some technical solutions with fairings yield as much as 94 % drag saving.
Figure 2: common types of interfering imperfections Methods for reducing the interference effects include accurate streamlining, and proper system design. Sometimes it is possible to take advantage of the interference effects (using appropriate strakes, for example) to reduce the system drag to values below the sum of the single components. A typical example taken from the natural world is the birds formation flight. Related Material
Birds Formation Flight
Selected References
AGARD. Special Course on Concepts for Drag Reduction, AGARD Report R-654, 1977. AGARD. Special Course on Subsonic/Transonic Aerodynamic Intereference for Aircraft, AGARD Report R-712, 1983. AGARD. Aircraft Drag Prediction and Reduction, AGARD
Report R-723, 1985. [Top of Page] Copyright © A. Filippone (1999-2002). All Rights Reserved.
Wave Drag Summary
Overview Selected References
Wave drag in aerodynamics is drag associated with the shock wave and shock-induced separation. This type of drag appears at transonic and supersonic speeds. The drag from acoustic waves is always negligible. The problem is more general in hydrodynamics, since wave propagation occurs at all speeds for all types of sailing vessels and for most cases of submerged bodies. There are several ways of dealing with wave drag: use of transonic/supersonic area ruling for wing-body combinations; use of supercritical airfoils, thin wing sections, wing sweep, low-aspect ratio wings, boundary layer control, blunt leading edge (at hypersonic speeds). Less orthodox methods include oblique and anti-symmetric wings (wings never built, in fact). At transonic speeds some of the main concerns are: driving the drag divergence upward, removing the buffeting and the possible shock stall. At supersonic and hypersonic speeds a few peculiar problems appear: namely, aerotherodynamic heating, and structural stiffness compatible with volume distribution and wing thickness. Methods of analysis have long relied on linearized potential theories. At hypersonic speeds Newtonian theories are still common. Related Material
Supercritical Airfoils Oblique Flying Wing Drag at Supersonic Speeds Wave Propagation
Copyright © A. Filippone (1999-2002). All Rights Reserved.
Vortex Drag Summary
Generalities Splitter Plates Ventilated Cavities Tangential Slots Fences Boat-tailed after-bodies Selected References
Vortex drag is due to some form of separation (tip flow separation, separation from a bluff body, etc.). For this reason it is also called form drag or pressure drag. Separation and related effects cannot be avoided on bluff bodies and particular situations of streamlined bodies (most road vehicles, aircraft after bodies). Separation is generally associated with adverse pressure gradients. The pressure field in the separated areas is lower than it would be in presence of a boundary layer. The low pressure field at the base of the body is the origin of the base drag. Specific vortex drag reduction techniques are listed below. The technology presented below is intended for subsonic speeds. Vortex drag reduction at supersonic speeds are far less successful.
Splitter Plates The mechanism by which the device works is the movement of the
separation vortex downstream, away from the body. Fig. 1. below shows the artrangement of a 3D bluff body. Splitter plates have also been applied to airfoils and wings.
Figure 1: Splitter plate behind a bluff body
Ventilated cavities These are thin surfaces mounted at the edge of the base. Regular slots are cut through, that allow for ventilation of the low pressure separated field. Horizontal vented cavities are sometimes applied to passenger cars.
Figure 2: Vertical and horizontal vented cavities
Tangential slots
As shown in Fig. 4, they are used to accelerate slow air flow behind a corner (they are used on commercial vehicles of all sizes.)
Figure 3: Corner slot for vortex drag reduction; velocity field shown. The acceleration of the slot flow serves to push flow that has been slowed down by the abrupt change of direction.
Fences The use of fences on after-bodies is sometimes justified by the need to redirect the flow streamlines. The effect is to remove the flow separation. An example is shown in the figure below, that is an aircraft after-body.
Figure 4: Fences to reduce after-body drag on C-17. Fences are also used on the main wing to redirect the boundary layer flow. These devices can be found in most of the 1st generation of commercial jets (for example, Vickers VC-10, BAC 1-11, Trident) and in some early military aircraft (MiG-17). Fig. 5 below shows the large fence on the wing of the Hawker-Siddeley Trident 2.
Figure 5: Wing fences on Hawker-Siddeley Trident 2 (Duxford Air Museum, England).
Boat-tailed afterbodies Such afterbodies are streamlined and designed for optimal shape. Base drag reduction rates of 50 % (at subsonic speeds) can be achieved with the devices listed above. For lifting wings some of the devices commonly designed are the following:
Vortex Generators Wall Suction Wall jets
Concave Surface Cavities As dimples on sports ball, used to promote turbulent transition, which shifts the drag crisis of the bluff body to a lower speed. There is an amount of research available on this particular topic (for ex. Metha, 1985).
Related Material
Bluff Body problems in road vehicles
Selected References
Lachmann GV(editor). Boundary Layer and Flow Control, Pergamon Press, 1961. Hoerner SF. Fluid Dynamic Drag, Hoerner Fluid Dynamics, 1965. Tanner M. "Reduction of Base Drag", in Progress in Aerospace Sciences, Vol. 16, No. 4, 1975. Chang PK. Separation of Flow, Pergamon Press, 1966. [Top of Page]
Copyright © A. Filippone (1999-2002). All Rights Reserved.
Speed-related Drag Summary
Drag of Well Known Bodies o Flat Plate Drag o Cylinder Drag o Sphere Drag Drag at Very Low Speeds Drag at Transonic Speeds Drag at Supersonic Speeds Typical Drag Coefficients Selected References
Speed is related to the flow regime: laminar, transitional, and turbulent. This is a major problem in all aerodynamic systems. Laminar boundary layers are characterized by minimum skin friction drag. Laminar boundary layers are generally assumed to keep laminar at Reynolds numbers , to be transitional at about , and turbulent above this value. The actual transitional Reynolds numbers may depend on the specific case and several side constraints.
Drag of Well Known Bodies Flat plate, circular cylinder, sphere and cones have been widely studied over the years, and the amount of data collected is staggering: in particular drag data are available from the smallest Reynolds numbers (unity and below), to the largest Mach numbers (hypersonic speeds). The data witness the importance of this set of bodies as a limiting case of real life problems. Flat Plate Drag The effect of the velocity (or Reynolds number) on the behavior of the drag coefficient of a flat plate for both laminar and turbulent incompressible flow is shown in the figure below. The turbulent drag has been computed with various theories (von Kármán-Schoenerr, PrandtlSchlichting, White).
Figure 1: Computed flat plate CD at subsonic speeds Current laminar wings have drag coefficients closer to the laminar curve (Blasius theory) than to the turbulent curve. The problem is, however, far more complex, since real-life flows involve a range of Reynolds numbers with transitional boundary layers. The laminar curve in Fig. 1, though, can be considered a practical barrier of the skin friction drag. The effect of turbulent transition on the flat plate drag coefficient is shown schematically in Fig 2. (incompressible flow)
Figure 2: Real flat plate CD at subsonic speeds At transonic and supersonic speeds the problem is complicated by the temperature gradient in the boundary layer. Semi-empirical correlations of the type shown above have been proposed (Green, Hoerner, WinterGaudet, etc.) to reduce the compressible skin friction coefficient to an incompressible one by using the free stream Mach number. Flat plate drag calculations at supersonic Mach numbers were first performed by van Driest, 1952. For details on high speed drag on a flat plate see White, 1974. Circular Cylinder There is a large body of investigations on cylinders at all speeds and all aspect ratios, with fixed or rotating bodies. The infinite cylinder (e.g. cylinder of very large L/D) is one of the most amusing problems in fluid dynamics. Its rational study was first performed by von Kármán (1911), who investigated the appearance of the so called vortex trail (or vortex street), while studying the advantages of streamlined bodies for drag reduction. The following considerations will be restricted to the drag characteristics as function of the Reynolds number. Fig. 3 below shows a classic summary of cylinder drag coefficients, from the creeping flow domain (see below) to large Reynolds numbers. Speeds are intended as subsonic at all cases. The data show a drag crisis at about Re=500,000.
Figu re 3: Cylinder CD at subsonic speeds The technical literature reports a large number of semi-empirical formulas for the CD. The experimental drag of Fig. 3 can be fitted with a simple equation. The finite cylinder is not less interesting. Actually, it features a great variety of wake flow patterns, instabilities and drag coefficients (Williamson, 1996). Sphere Drag Fig. 4 shows the behavior of the drag coefficient for a sphere at subsonic speeds. The surface finish has been found of extreme importance in imparting aerodynamic characteristics. The two curves on the graphic refer to two different surface conditions. When the surface is rough, turbulent transition occurs earlier, and so does the drag drop. This feature is fully exploited in golf balls (Metha, 1985).
Figure 4: CD of a sphere at subsonic speeds Experiments on spheres have been perfomed up to M=12.15 in freon (to the author's knowledge.) The figure below shows the CD behavior at supersonic and hypersonic speeds (data elaborated from Cox-Crabree, 1965).
Figure 5: CD of a sphere at supersonic speeds
Drag at Very Low Speeds Very low speeds are characteristic of flows at Reynolds numbers less than a 50,000. Some airfoils still work as at Reynolds numbers as low as
30,000. Yet they become increasingly inefficient at lower speeds. This range is also that of the model airplanes, micro-propellers, and micro-air vehicles (MAV). Creeping Flows At lower speeds we find many insects. Flows at Re < 10 are also called creeping flows, which are not considered properly aerodynamic. The drag characteristics at low speeds are strongly affected by the laminar separation and by viscous skin friction, according to a physics explained in the low speed chapter. The drag coefficient can take very unusually high values, that are approximated with the Oseen formula at Re < 1 and by the Klaycho formula at Re < 400. For extensive low Reynolds data consult Clift et. al, 1978. Drag reduction at low speeds is a very open problem in aerodynamics, that only recently has become object of analysis, mainly spurred by technological advances in solar powered flight, high altitude flight, unmanned vehicles, model airplains, and more.
Drag at Transonic Speeds At transonic speeds there are local buckets of supersonic flow delimited by shock waves. Shock waves and shock-induced boundary layer separation are a consistent source of drag at these speeds. A typical example of how the drag increases is given by the divergence Mach number for a airfoil section (below)
Figure 6: Transonic drag rise
At a certain Mach number that depends on the airfoil and the angle of attack, a wave drag starts to build up because of the increasing effect of the shock wave. Once the flow is fully supersonic, the drag coefficient falls. The climb shown in Fig. 6 can be pushed toward higher Mach numbers with supercritical airfoils. Airfoils at Transonic Speeds A case of particular interest is that of the airfoil section, whose transonic drag rise is dependent on the angle of attack. An example is shown in Fig. 7 below.
Figure 7: Transonic drag rise, with alfa as parameter Military Aircraft Military aircraft feature external stores and weapons systems that can change dramatically the performance of the aircraft. Here only a comparative effect will be shown for some selected configurations, Fig. 8.
Figure 8: Transonic drag rise, with alfa as parameter Methods for reducing the drag at transonic speeds include the use of
Wing Sweep Back Thin Airfoils Supercritical Airfoils Boundary Layer Control Transonic Area Rule
Drag at Supersonic Speeds As in the case of lower speeds, drag is produced by viscosity and vorticity release. There is one more component, called wave drag, peculiar to supersonic flows. In general the total drag will consists of the skin friction (viscous) drag, the induced drag (as in subsonic flows), the (supersonic) drag due to volume, and the (supersonic) wave drag due to lift. Supersonic flows are considered well behaved and more stable, as compared with transonic flows, because the problem of the shock at the wall is eliminated. Effect of Nose Bluntness Bodies of minimum drag at supersonic and hypersonic speeds have a blunted nose. The radius of a blunt body is an essential parameter in determining the heat flux.
Figure 9: Hypersonic CD for sphere and cone Supersonic Area Rule The problem of computing and minimizing the wave drag is fairly complicated, because of several different sources (listed above), and because of conflicting constraints. A general practice is the supersonic area ruling: The wave drag is minimized if the distribution of cross-sectional area along the longitudinal axis is a smooth function. The combination of wing-body interference, in fact, can be reduced to a slender body optimum drag problem, for which the solution is known (Sears-Haack, 1947; von Kármán, 1948). Elliptic Wings The wave drag due to lift is minimized when the loading on each oblique plane is elliptical. The wave drag due to volume is at a minimum when each equivalent body of revolution (opportunely defined) is a SearsHaack body. Overall minimum induced drag can be obtained with an oblique wing of elliptical planform having elliptical loading (R.T. Jones, von Kármán). Elliptical loading distribution can be obtained by twisting the wing. Another approach to drag minimization is the use of flow-reversal theorems ( von Kármán, Hayes, Jones, Graham et. al.). See AshleyLandhal, 1965, for details.
Related Material
The Oblique Flying Wing Bodies of Minimum Wave Drag Theodore von Kármán
Selected References
White FM, Viscous Fluid Flow , McGraw-Hill, New York, 1974. Hoerner SF, Fluid Dynamic Drag, Hoerner Fluid Dynamics, 1965. AGARD, Aircraft Drag Prediction and Reduction, AGARD Report R-723, 1985. Ashley H, Landhal M, Aerodynamics of Wings and Bodies, Addison-Wesley, Reading, MA, 1963. Clift R, Grace JR, Weber ME, Bubbles, Drops, and Particles, Academic Press, New York, 1978. [Top of Page]
Copyright © A. Filippone (1999-2002). All Rights Reserved.
Copyright © A. Filippone (1999-2002). All Rights Reserved.
Summary
Importance of the Subject Flow Phenomena Maximum Lift o Boundary Layer Control Vortex Lift High-Lift Systems o Powered vs. Unpowered Systems High-Lift Airfoils
Pressure Distribution Multi-element Airfoils Design Issues for High-Lift Trailing- and Leading Edge Devices Computational Methods Tables of Maximum CL Selected References o
Lift is a force in a direction normal to the velocity. It is due to both pressure and viscous contributions. The weight of the pressure component is generally far more important; when the viscous component is effective, it works as to reduce the total amount of lift obtainable by an aerodynamic system.
Importance of the Subject High lift systems are required in aeronautics to produce higher maneuverability, for higher endurance under engine failure, for lower take-off and landing speed, higher pay-load, for aircraft weight constraints, maximum engine power limits, etc. High lift systems are of the utmost importance in human powered flight, unpowered gliding, etc. High lift systems are also used (differently) in racing cars and competition sailing boats. The picture below shows the cargo plane C-17 Globemaster with high lift system in operation during a slow landing phase.
Figure 1: McDonnell Douglas C-17 Full Image (102K)
Flow Phenomena Flow phenomena of multi-element wings include: wakes from upstream elements merging with fresh boundary layers on downstream elements; flow separation in the the cove regions; flow separation on the downstream elements, especially at high angles (landing configurations); confluent boundary layers; high- curvature wakes; high flow deflection; possible supercritical flow in the upstream elements, see figure below.
Figure 2: Multi-element wing Two boundary layers are confluent when they develop on different solid surface and come together (generally at a different stage of development). Confluent boundary layers can be identified by studying the local velocity field. Flow separation occurs in cove regions because of the high curvature associated with locally high speed. High speed can also be the reason of supercritical regimes in aircraft configurations.
Maximum Lift The maximum lift obtainable by a single/multi element wing (or by more complicated devices) is generally attributed to flow separation on the suction side, and on the maximum suction peak. The two problems are somewhat dependent. Airfoil characteristics that have a strong effect on the maximum lift coefficient are: camber and thickness distributions, surface quality, leading edge radius, trailing edge angle. CLmax also depends on the Reynolds number. At a fixed Reynolds
number, the operation on the above parameters must remove or delay the flow separation, and delay the pressure recovery on the suction side, along with a number of other details. Prediction of Maximum Lift Accurate prediction of the maximum lift coefficient for an airfoil or wing is still considered an open problem in computational aerodynamics. This difficulty is due to the approximation of the boundary layer conditions at various stages of turbulent transition and separation, besides the proper modeling of the turbulent separated flows. An empirical formula correlating wing CLmax of a swept wing to the main geometric parameters of the high-lift system was derived at the Research Aeronautical Establishment (RAE, UK) in the late 1970s. More recent work was done at McDonnell- Douglas (Valarezo-Chin, 1994).
Vortex Lift The lift force from a wing can be augmented by appropriate manipulation of separation vortices. Basically, this can be done in two ways: with highly swept wings (delta wings) and strakes. The longitudinal vortex has the effect of shifting the stagnation point on the suction surface of the wing (Pohlamus, 1971).
Figure 3: Vortex Lift
High-Lift Systems High lift can be produced by aerodynamic design of single components, design of entire systems, integration of already existing systems, ad hoc technical solutions. The most important methods are the following:
High-lift wing design Multi-element lifting systems Boundary Layer Control Propulsive Lift Other Technical Solutions
Powered vs Unpowered Systems There is a broad classification among all high lift systems: that is between powered and unpowered. The range of applications in aviation is discussed below. The data collected in the figure below have been elaborated from Airbus research (Flaig and Hilbig, 1993). Performances of the C-17 and the YC-14 have been guessed.
Figure 4: Powered vs unpowered high-lift systems Nomenclature SSF=single-slotted flap; DSF=double-slotted flap; TSF=triple-slotted flap; LED=leading-edge device.
High-Lift Airfoils In order to obtain high lift from an airfoil the designer must increase the area enclosed by the pressure coefficient (Cp), that is: the pressure on the lower side must be as high as possible (pressure side), the pressure on the upper side must be as low as possible (suction side). The latter requirement is in fact the most difficult to fulfill, because low pressure is
created through high speed, and high speed triggers flow separation. Flow separation can be limited at high speed by turbulent transition. Pressure Distribution One idea commonly used in design is to control the pressure distribution on the upper side as to maintain the flow at the edge of separation. The more separation is delayed the higher the lift coefficient. This is obtained through a flat top and a gradual pressure recovery (Stratford recovery). Airfoils designed with this approach can exhibit aerodynamic efficiencies L/D of up to 300 !
Multi-Element Airfoils Generally speaking, a multi-element airfoil consists of a main wing and a number of leading- and trailing-edge devices. The use of multi-element wings is a very effective method to increase the maximum lift of an aerodynamic system. The Slat The first element to be added to a main wing was a leading edge slat (Handley-Page, Lachmann, 1917). The solution worked, but it was not clear how. For many years is was assumed that the leading-edge slat was a boundary layer control device (Betz, 1920). Smith (1972) proved that the slat is so effective because of its strong effect on the inviscid pressure distribution. The leading-edge slot deviates the streamlines, creates a downwash on the main element and modifies markedly the leading edge suction peak. Later on, more elements were added to the main wing. A three-element configuration (with leading-edge slat and trailing-edge flap) is classic, but the technology has improved, and 4 or more element are not uncommon, ex. in Fig. 2. A system with increasing number of elements provides an increasing amount of lift. This increase is however associated with an increase in drag.
Design Issues for High-Lift
A fundamental problem involved in high-lift design is the evaluation of the computational tools. There is always the possibility of failing to meet the design target. Optimization and design cannot be approached by using the wind tunnel alone, because extensive parametric testing is time consuming and economically unaffordable. In fact, only the final design is generally build and tested in a wind tunnel at the design conditions. The design is complicated by the mutual interaction (interference) among the aerodynamic components. Industry is in fact interested in integrating each component into a more complex aerodynamic system (aircraft design, turbomachinery, etc.), besides optimizing a single device. With the improvement of the computational capabilities a more rational approach to design and optimization has become possible. The use of wind tunnel techniques is complementary and now in a process of closer integration. Examples from the real world include the design multi-stage turbines for aircraft and power generation, aircraft design, internal flows in pipes and channels for pumps, compressors and exhaust gas.
Computational Methods In the past few years the computational methods for high lift have been converging toward Navier-Skotes solvers (unstructured, and multi-block structured), although methods including strongly interactive boundary layers have proven to be almost as successful. The method of computation depends on the complexity of the problem (2D, 3-D, number of high-lift bodies, precision requirements, turbulence modeling, etc.). The figure below shows the pressure field around an inverted 2-element wing for racing applictions. The flow field was computed with a structured multi-block Navier-Stokes code.
Figure 4: pressure field around multi-element inverted wing. Related Material
Aerodynamic Design of airfoils and wings Strakes Delta Wings Computational Methods for high lift
On the Web These sites are not part of the aerodyn.org domain. There is no control over their content or availability.
Airfoil Data Site, at the University of Illinois
Selected References
Hoerner SF. Fluid Dynamic Lift, Hoerner Fluid Dynamics, 1965 Clancy JC. Aerodynamics, John Wiley, New York, 1975. AGARD. High-Lift System Aerodynamics, AGARD CP-515, Banff, Oct. 1993 McCormick BW. Aerodynamics, Aeronautics and Flight Mechanics, John Wiley, New York, 1994. Betz A.Theory of the Slotted Wing, NACA TN-100, 1922. [Top of Page]
Copyright © A. Filippone (1999-2002). All Rights Reserved.
Copyright © A. Filippone (1999-2002). All Rights Reserved.
In this Chapter
Importance of the Subject o Oscillatory Flows o Non Oscillatory Flows o Dimensionless Parameters Dynamic Stall High Angle of Attack Unsteady Wakes behind Bluff Bodies o Flow Past Cylinder o Flow Past Sphere o Other Bluff Bodies Unsteady Boundary Layers Computed Examples Selected References
Aircraft agility depends on the control of the unsteady flow field
Although most aerodynamic flows are treated as steady ones, many others are non stationary. The variety of non stationary flows is large, and includes transient regimes, impulsive starts, maneuvering, periodic flows, and flows that are intrinsically unsteady because of the mechanism of
vortex shedding from bluff bodies.
Importance of the Subject The ability to control general three-dimensional unsteady flows could open new possibilities in the performance of many aerodynamic systems, including aircraft, helicopter and wind energy conversion systems. Other aspects of unsteady flows include: hydrodynamic propulsion (propeller-hull interaction), flapping wing propulsion, a number of cavity flows, and many heat transfer problems. The flows that will be considered are:
Oscillatory Flows Non Oscillatory Flows o Vortex dynamics at high angle of attack o Unsteady wakes behind bluff bodies
Oscillatory Flows The unsteady problems of oscillatory type have been widely studied for airfoils and wings since the 1930s, when the first theories have been formulated (Theodorsen, 1932). Dynamic stall affects helicopter rotor blades in forward flight, maneuvering and descent (because of the asymmetric loads created by the flight dynamics); wind turbine rotors (because of the unsteady nature of the wind, along with the atmospheric boundary layer, the presence of the tower, the topography of the terrain, etc.). Dynamic stall on airfoils is a particular case of the above. At the highest speed of a helicopter rotor another peculiar aspect appears: the unsteady shock wave on the blade. Other unsteady flows of practical importance include flows past circular cylinders (von Karman, 1930s), and past spheres. These phenomena are oscillatory only at very low Reynolds numbers and become fully turbulent and aperiodic at higher speeds. The largest Reynolds number at which the von Karman vortex street is observed is Re=400, that corresponds to a Strouhal number St=0.21.
Dimensionless Parameters The non dimensional parameter defining the similitude of periodic flows is the Strouhal number St=fL/V (f=frequency; L=characteristic length; V = characteristic speed), or the reduced frequency k=2 St. The two non-
dimensional groups are equivalent within a constant. The reduced frequency is used more often for dynamic stall problems.
Dynamic Stall Periodic flows on airfoils and wings (plunging, pitching and a combination of the two) lead to a peculiar effect called dynamic stall. The main reason why dynamic stall appears is the finite response time of the flow to an incoming disturbance (for ex. change in angle of attack, free stream turbulence effects, etc.). The response time (sometimes called time-lag) is dependent on the viscous effects, which ultimately lead to energy dissipation. The latter is proportional to the integral of the hysteresis loop. The first to provide a mathematical description of airfoils in flutter was Theodorsen (1932). His theory was based on linearized small perturbation equations.
Non Oscillatory Flows Besides the cylinder and the sphere at relatively high Reynolds numbers, there is a number of flows that are unsteady and aperiodic, although they can be treated as steady. These include airfoils and wings at high angle of attack. Delta wings, pointed cylinders and prolate spheroids are some examples of technological interest (fighter aircraft, missile aerodynamics, etc.) Their behavior is related to the dynamics of the vortices released from the body surface. Unsteady flows developing in the wakes of bluff bodies, particularly on road vehicles and aircraft after bodies, are of interest from the point of view of the base drag that is produced at the rear end. Similar interest in reported for some cavity flows.
High Angle of Attack Aerodynamics Fundamental studies are available for the flat plate at all speeds (up to hypersonic) and all angle of attacks (up to 90 degrees). This is by itself a sign of the importance of this simple device to the understanding of basic fluid dynamic problems, besides airfoils (Fig. below).
Other systems at angle of attack include blunt and pointed bodies (prolate spheroids, pointed cylinders), delta wings and low aspect-ratio wings. At the other end of the technology there is the full aircraft (Lamar, 1992). Flow separation on these systems is quite complex. On low aspect-ratio wings and delta wings the flow separation produced a substantial augmentation of lift (besides drag).
Unsteady Wakes behind Bluff Bodies Wakes behind bluff bodies are unsteady (and sometimes periodic) at any realistic Reynolds number. Simple geometries like the circular cylinder and the sphere have been investigated for a long time, in order to understand the physics of flow separation and vortex formation in 3-D. These bodies also present a technical interest from the point of view of base drag reduction on cars, trucks, aircraft after bodies and other vehicles. Flow analysis around bluff bodies such as suspension bridges, tall buildings, and towers is nowdays an essential element in the engineering process.
Flow Past a Cylinder The circular cylinder, along with the flat plate, is the body most widely studied in fluid dynamics and aerodynamics. Drag data for the cylinder are known from very low Reynolds numbers all the way to hypersonic speeds. Vortex Shedding. Systematic vortex shedding analysis was first due to
von Karman, who analyzed the breakdown of the symmetric flow. The von Karman vortex street has become one of the most well known unsteady problem. Impulsive start was already known to Prandtl (1904), and the rotating cylinder was known to Tollmien (1931). Drag data are tabulated for all Reynolds numbers, flow visualizations are available up to Mach numbers M=12.1 (to the author's knowledge). Although the unsteady wake behind the cylinder has been considered for a long time as purely two dimensional, there are spanwise vortex structures that appear at some Reynolds numbers. These structures are a function of the cylinder aspect ratio L/D. References on the circular cylinder can be found in any text of fluid dynamics. Related Material
Navier-Stokes computations at very low Re
Flow Past a Sphere Wakes behind spheres are observed to be steady for Reynolds numbers below 300-400. Above this limit (which also depends on the surface finish) vortices break off and are periodically released to form vortex loops that are connected like in a chain. At Re above 6000 the vortex shedding is very periodic, with Strouhal number ranging from 0.125 to 0.20, the largest figure being a limit at high Reynolds numbers (Achenbach, 1974). Similar wakes can be observed behind particles falling in water. Effects of the surface geometry have been studied for the evaluation of the aerodynamic performances of sports balls (Metha, 1985).
Flow Past other Bluff Bodies Bluff bodies other than cylinder and sphere include a wide variety of configurations. Squared cylinders, elliptic cylinders and parallelepipeds of various aspect-ratios are used to simulate more complex real-life objects. We will limit this discussion to road vehicles. Passenger cars, buses and trucks have blunt trailing edges, and various cavities. Streamlining has been applied (successfully) to both cars and trucks (on a lesser degree to buses). However, streamlining on fore bodies has little influence on flow separation and drag. The after body is instead critical. Among the extensive studies performed by the car industry it is interesting to report the effect of the slant angle on both lifting and non
lifting bluff bodies.
Unsteady Boundary Layers The amount of research available for unsteady boundary layer is a tiny thing compared with the body of work carried out on steady, incompressible boundary layers. Typical cases available in the literature include flows past flat plates and circular cylinders, flows started from rest, colliding shear layers, and periodic oscillations. Oscillating boundary layers are the basis of dynamic stall behavior, and therefore are studied from the point of view of unsteady separation. Boundary layer separation is related to the amplitude of the oscillations. For a review of recent work see Cousteix, 1986. Related Material
Computed Examples
Selected References
Theodorsen T. General Theory of Aerodynamic Instability and the Mechanism of Flutter, NACA TR 496, 1935. AGARD. Unsteady Aerodynamics - Fundamentals and Applications to Aircraft Dynamics, AGARD CPP-386, May 1985. Smith FT. Steady and Unsteady Boundary Layer Separation, in Ann. Rev. Fluid Mech, Vol 18, pages 197-220, 1986. [Top of Page]
Copyright © A. Filippone (1999-2002). All Rights Reserved.
Copyright © A. Filippone (1999-2002). All Rights Reserved.
In this Chapter
Aerodynamics of Streamlined Bodies o Laminar Separation Bubble o Turbulent Transition o Lift-Drag Characteristics Aerodynamics of Bluff Bodies Current Research Topics Selected References
Flow phenomena at low Reynolds numbers are more complicated than those occurring at high Reynolds numbers (flow regimes typical of flight), and to some extent poorly understood. It is particularly interesting to report that it is not quite clear how a low Reynolds number airfoil section should look like (Lissaman, 1983). The aerodynamics of bluff bodies, instead, seems more advanced, and the technical literature reports cases at Reynolds number as low as a small fraction of unity. Reynolds numbers for lifting bodies are in the range 50,000 to 500,000. For bluff bodies they are much lower. Both streamlined and bluff bodies are reported.
Figure 1: Low Reynolds Number Aerodynamics
Aerodynamics of Streamlined Bodies The low Reynolds number regime leads to some peculiar features, namely:
Low resistance of a laminar boundary layer to adverse pressure gradients; Appearance of limited areas of flow separation (bubbles) Turbulence transition triggered by boundary layer instability Effects of free stream disturbances and surface conditions 3-D effects in otherwise 2-D flows non linear lift/drag characteristics lift and drag hysteresis at static conditions bifurcations of boundary layer states
Bifurcation of boundary layer states yields non unique and un-symmetric solutions even for symmetric conditions. Theories of slender body aerodynamics at low Reynolds number have been developed by several authors, including Burgers (1938), Taylor (1969), Lighthill (1975). At very low Reynolds number the inertial forces are negligible.
Separation Bubble A separation bubble is a region of locally separated flow on the airfoil. The extent of this region depends on the operational parameters (Reynolds number, angle of attack, free stream turbulence), and airfoil geometry (thickness, camber, surface quality). Depending on a complicated
combination among the above quantities the bubble can be short or long, it can contract or extend with the increasing angle of attack.
Figure 2: Laminar Separation Bubble A long separation bubble usually starts far behind the leading edge, causes a collapse of the leading edge pressure peak and modifies the total pressure distribution on the upper side of the airfoil. This type of bubble is associated with a large loss in lift. A short bubble is just behind the leading edge, does not alter macroscopically the surface pressure distribution, and changes only slightly the lift coefficient.
Figure 3: Cp characteristics
Turbulent Transition Bubble reattachment and airfoil characteristics are strongly dependent on turbulent transition. A bubble reattaches as turbulent, transition occurring at some location within the bubble. At very low Reynolds number a delayed transition may prevent bubble reattachment, and thus cause a premature stall and a consistent loss of lift. For this reason accurate knowledge of transition is necessary. Factors affecting Transition The most general physical causes that trigger turbulent flow transition on a solid wall are the following:
External pressure gradients Temperature Surface roughness External disturbances and acoustic waves
Forced Transition If transition does not occur by natural means, it can be forced by operating of the surface roughness or adding transition trips of appropriate size and shape. One simple criterion sometimes applied to predict bubble reattachment is the Owen-Klanfer criterion, that consists in evaluating the Reynolds number based on boundary layer thickness. Predicting Transition There are several theoretical methods for predicting turbulent transition. Some methods commonly used in aerodynamics include the Michel method, the eN method. The accuracy of these methods (or any other methods currently known) is not always sufficient for computing airfoil characteristics as those reported below.
Lift/Drag Characteristics Lift and drag characteristics are affected by the Reynolds number in a way that is unknown at the speeds proper of commercial flight. The extent of the viscous flow and the separated region (e.g. the size and behavior of the separation bubble).
Fig. 4 and Fig. 5 show two different, albeit typical, lift curves at Reynolds numbers below 100,000.
Figure 4: Airfoil Lift characteristics In the figure above the lift curve is dominated by the laminar separation bubble (B). When the bubble contracts with the increasing incidence, the bubble lift decreases slightly, then increases again and the airfoil finally stalls with a trailing edge separation.
Figure 5: Airfoil Lift characteristics The case above shows a a hysteresis loop (I), that occurs when the airfoil flow at increasing angle of attack features different characteristics of those
at decreasing angle of attack. This result
Figure 6: Drag characteristics
Aerodynamics of Bluff Bodies The bluff bodies considered at low Reynolds number are almost exclusively of spheric shape, since they include the motion of liquid drops bubbles and particulate in air, that are of general technical interest (for example, cavitation problems, combustion, fluidized beds, magnetohydrodynamics; diffusion problems, etc.). At the limit of zero Reynolds number the Navier-Stokes equations are reduced to a condition of equilibrium for the pressure, whose fundamental solution is a point force called stokeslet (Hancock, 1953). In practice the Reynolds number cannot be zero, so small inertia forces are present. The drag coefficient of solid particles and bubbles has been widely investigated, and often some correlations are given: Oseen's equation for Re < 1; For reference, the drag coefficient of a bubble is CD = 10 at Re = 1; CD = 2.6 at Re = 42. Data are also available for slender cylinders.
Current Research Topics For streamlined bodies (airfoils and wings) there is ongoing research in the fields of wind tunnel testing, airfoil design, turbulent transition studies for gliding, human-powered flight, solar-powered flight, wind turbine blades, micro air vehicles. For bluff bodies the field of research includes a wide array of industrial
multi-phase flows, wherein at least one phase is a solid particulate (exhaust gases, fluidized beds, combustion problems), or a bubble (cavitation), dynamics of sprays and jets. Transition prediction is an interesting topic for the most advanced CFD methods. The traditional Reynolds averaged Navier-Stokes equations deal with ensemble averaged equations, and therefore is unable to resolve the large scale eddies. The large eddy simulation (LES) methods model the turbulence in the sub-grid scale. As an alternative, direct Navier-Stokes solution (DNS) may be used. This approach requires very fine grids and small steps to resolve the Kolmogoroff scale. Both LES and DNS are still at a development stage to predict how well they can predict turbulent transition at small Reynolds numbers. Related Material
Navier-Stokes Equations
On the Web These sites are not part of the aerodyn.org domain. There is no control over their content or availability.
Low Speed Airfoils at the University of Illinois
Selected References
Proceedings of the Conference on Low Reynolds Number Airfoil Aerodynamics, UNDAS-CP-77B123, Notre Dame, Indiana, June 1985. Proceedings of the Aerodynamics at Low Reynolds Number 10^4 < Re < International Conference, The Royal Aeronautical Society, London, Oct. 1986. AGARD, Low Reynolds Number Vehicles , AGARDograph AG288, 1985. Selig M, Lyon C, Giguere P, Ninham C, and Guglielmo J., Summary of Low-Speed Airfoil Data, Vol. 2, SoarTech Publ., Virginia Beach, VA, 1996. [Top of Page]
Copyright © A. Filippone (1999-2002). All Rights Reserved.
Grid Generation Summary
Importance of the Subject Conceptual Problems Visualization Problems o Algebraic Methods o Elliptic Methods o Hyperbolic Methods o Unstructured Methods o Adaptive Methods o Other Methods Surface Control State-of-the-Art Examples Selected References
Grid generation is an essential aspect of all numerical methods that employ finite differences, finite volumes and finite elements for the solution of partial differential equations (PDE). Shortly, it consists in dividing bounded or unbounded flow domains into elements (triangles, quadrilaterals, polygons in 2-D; tetraedrons, parallelepipeds, n-edrons,
etc.) called cells. The problem is a non-trivial one, and requires a considerable amount of time. Development of a grid generation system requires years of work.
Figure 1: 3-D structured grid for external aerodynamics
Importance of the Subject The topic of grid generation has become a field on its own in the increasigly vast field of computational fluid dynamics (CFD). A short selection of publications for reference is given below. Some general considerations regarding suitable methods and their role in CFD are the following:
Almost any method works on a good grid, whereas the bad methods only work on good grids; If one had enough resolution (e.g. enough points), then the grid quality would be of minor importance, provided that some basic requirements are satisfied; if the grid is necessarily coarse, then its quality becomes essential; A good grid can accelerate the convergence of the solution, while a bad grid can even lead to a divergent iteration history.
Conceptual Problems There are a number of conceptual problems that must be addressed when choosing a grid generation system for a particular problem:
Open or closed flow domain
Domain topology (C, H, O, and combinations therein) Single or multiple (single- of multi-block) o block-interface type for multi-block (continuous ?) Overlapping (ex. chimera type) or non-overlapping Algebraic or from differential equations Structured or unstructured Fixed or fully-adaptive Two- or three dimensional
Fig. 2. below shows some typical multi-block interfaces (for structured grids). The most common interface is the full matching (top left). The other systems require interpolation of fluid dynamic quantities at nonmatching points.
Figure 2: Some common multi-block interface structures
Visualization Issues Once the grid has been generated, it must be visualized to check for errors (they come in an infinite variety). For 3-D grids this is a particular difficult stage, where a computer animated image, or a CAD-based system is absolutely essential, and this is proven by the fact that the most sophisticated systems currently available come with visualization facilities. Minor errors can be fixed with ad hoc post- processing, going under the definition of grid smoothing.
Input Requirements Given the complexity of the problem just outlined, one can argue also on the amount of user input required. Some methods excel for the amount of data that must be set (for example a multi-block structured grid, requiring
point bunching on all sides). Unstructured grids have been sometimes preferred on the structured counterparts because grids - also in complex domains - can be generated more automatically. How about the grid quality then ? - If the code runs, do not fix it, otherwise repeat the fundamental steps.
Grid Generation Methods Below it is described a set of algebraic and differential methods that makes up the bulk of the available methods. Algebraic Methods Algebraic methods are based on coordinate transformation equations in a physical domain. In their most simple form they are Lagrange and Hermite transformations (are called shearing transformations). Some methods are based on interpolation schemes in multi-dimensions. Transfinite interpolation (Eriksson, 1982), and multi- surface transformation (Eiseman, 1985) produce good grids for closed domains. Integration of the methods with additional control on the boundary values and elliptic smoothing (see further down) give efficient grid generation systems (for example ICEM/CFD, GridPro) These methods in their most developed form allow some control on the values of the derivatives at the boundary. Elliptic Methods Elliptic methods are based on the solution of elliptic partial differential equations with some conditions (called forcing terms) to force point bunching. The problem is formulated via a set of Poisson equations (Thompson, 1977) with forcing terms usually defined by the ThomasMiddlecoff terms (Thomas-Middlecoff, 1982), or by other appropriate control functions (Sorenson, 1995). The solution of the system is iterative, for example with a Successive Over- Relaxation (SOR) method. For large grids the computing time is considerable. Elliptic systems produce very smooth grids (sometimes too smooth) and they can be used to smooth out metric discontinuities in the transfinite interpolation systems (for this purpose also a Laplace smoother will
suffice). Hyperbolic Methods Hyperbolic methods are based on the solution of partial differential equations of hyperbolic type, that are solved marching outward from the domain boundaries. The idea of using hyperbolic PDEs is very effective for external flows where the wall boundaries (airfoil, wing, wing-body, etc.) are well defined, whereas the far field boundary is left arbitrary. This situation also eliminates the need to specify point distribution on some of the edges of the flow domain, and makes it more handy than for example the transfinite interpolation methods. In its basic formulation (Steger- Chaussee, 1980) the hyperbolic grid generator is based on a condition of orthogonality, and a condition on the cell area. The method can be integrated with grid line smoothing and orthogonality checks. Unstructured Methods There are several algorithms for generating unstructured grids. The Delauney triangulation method other Voronoi methods and the advancing front method are the most popular, also among solution-adaptive systems, and they are the basis of some commercial fluid dynamic codes (for example Star-CD, Rampant). The field is in rapid expansion, and there are schools of thought whether the unstructured approach is better or worse than the structured approach to the solution of PDEs in fluid dynamics. Briefly, unstructured grids can be generated faster on most complex domains, and exists for all domains. Mesh refinement can be done without difficulties, also on a local basis and adaptively. Storage of the grid data is no easy (it requires information on which node is neighbor to which), it takes far more memory than in a structured sense, and therefore hinders parallelizarion of computer codes. Adaptive Grids All the methods described above make use of some empirical knowledge about the form of the solution of the PDEs. This knowledge makes us force many points in regions of large field gradients (for ex. boundary
layers). Better solutions could be obtained if a first guess grid could be adapted in a time-marching numerical scheme to follow exactly the evolution of the field gradients (a particular difficult problem is the position of the shock wave in a transonic flow.) Methods that can be used to follow the solution include: weight functions, Poisson smoothing, electro-dynamic analogy. The major problem of the adaptivity systems is that they must be built in the solver of the PDEs, and cannot be left out as in the most popular approach. Other Methods For some problems of particular difficult nature scientists have developed hybrid methods that feature both structured and unstructured zones. These methods are the chimera technique and the hybrid structured/ unstructured technique. The chimera approach consists in building partially overlapping blocks. Boundary conditions need to be exchanged at the interface between domains and this is usually done through some form of interpolation. The hybrid scheme takes advantage of both unstructured and structured methods by applying structured body fitted coordinates to the body and unstructured networks in the outer boundaries. Problems that require such a complex CFD approach include rotor/fuselage interaction in a full rotorcraft simulation, propeller to fixed wing analysis, etc.
Surface Control All grid generation processes (especially 3-D problems) start with a surface definition. This definition is seldom an easy task. The input may consist of points, lines, curves, splines, surface patches, etc. All these items can be defined through a CAD system. Sometimes it is necessary to spline, smooth and re-patch the input data. Some examples for 2-D airfoil problems are shown in theexamples. Some grid generation systems come with their own facilities (for ex. ICEM/Surf, widely used in automotive industry).
State-of-the-Art
Presently there is no one method that fits all. Most still depends on the quality of the CFD solution that can be achieved. The characteristics of the block boundaries depend on the capabilities of the flow solver. In the structured domain, algebraic methods have been preferred because faster. Multi-Disciplinary Strategies The most up-to-date methods have been embedded in sophisticated multidisciplinary tools that come with CAD/CAE interface, surface treatment techniques, complex visualization tools, post-processing, etc. These tools allow multi-block structured. Problem Size The number of cells that can are necessary depends on the particular problem. Usually a minimum number is easy to figure out. Most practical aerodynamic problems can be solved with several million cells. The 10 million mark is current practical bound. More on
Examples of calculation
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Mesh Generation: Web Authority
Selected References
AGARD, Application of Mesh Generation to Complex 3-D Configurations, AGARD CP-464, Aug. 1989. NASA, Surface Modeling, Grid Generation, and Related Issues in Computational Fluid Dynamic Solutions, NASA CP-3291, May 1995. Thompson JF, Warsi ZUA, Mastin CW. Numerical Grid Generation, North Holland, 1985. Eiseman P. Grid Generation for Fluid Mechanics, Ann. Rev. Fluid Mech, Vol 17, pages 487-522, 1985. AGARD, Three-Dimensional Grid generation for Complex
Configurations - Recent Progress, AGARDograph AG-309, 1988. [Top of Page] Copyright © A. Filippone (1999-2002). All Rights Reserved.