# LOW SPEED WIND TUNNEL TESTING BARLOW PDF

Low speed wind tunnel testing I by Jewel B. Barlow, William H. Rae, Alan . Barlow and Alan Pope wish to acknowledge his early contributions to planning for. 1-John Wiley & Sons ().pdf - Ebook download as PDF File .pdf), Text File . txt) or read Low speed wind tunnel testing I by Jewel B. Barlow, William H. 1% Jewel B. Barlow William H. Rae, Jr. Alan Pope A WILEY-MTERSCIENCE Ed. of: Low-speed wind tunnel testing / WiUiam H. Rae, Jr., Alan Pope. 2nd ed.

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new PDF Low-Speed Wind Tunnel Testing Full Online, new PDF Low -Speed Wind Tunnel Testing Full Page, new PDF Abstract: This paper presents low speed wind tunnel tests of a 2D NACA airfoil Keywords: Aerodynamic balance, Wind tunnel test, Low Reynolds . [2] Barlow J.B., Rae W. H., Pope A.: Low-Speed Wind Tunnel Testing, 3rd. 11, November Book Reviews. Low-Speed Wind Tunnel Testing, Third Edition. Jewel B. Barlow, William H. Rae Jr., and Alan Pope, Wiley, New York,

The investigative. The great advances in theory and computational capability notwithstanding, experimental explorations remain the mainstay for obtaining data for designers' refined and final decisions across a broad range of applications. A primary tool of experimental aerodynamics is the wind tunnel. The proper and productive use of experimental investigations in general and wind tunnels in particular requires applications of aerodynamic theory and computational methods in the planning of facilities, the planning of experiments, and the interpretation of resulting data.

Those aspects of aerodynamics will be drawn upon heavily in the course of this book. To answer the question posed above: The most successful attack on virtually any aerodynamic design problem will be based on application of a combination of results from experimental, theoretical, and computational methods appropriately combined and leavened by experience.

Included in those and other texts are discussions of flow similarity in which definitions of similar flows are given. This is a very important concept that leads to significant advantages in experimental work and in theoretical and computational work as well. Knowledge, mathematical model of the processes involved is not required to apply the Pi theorem. A reduction in the number of independent parameters to be manipulated in an investigation is obtained based on the requirement of dimensional homogeneity for any equation expressing a valid relationship among physical variables.

Some of the most important results are those associated with "distorted" models, that is, models in which complete similarity cannot be achieved but that nevertheless are very useful.

Such models are the norm rather than the exception, as becomes apparent when almost any specific wind tunnel program is being planned. Although the application of dimensional analysis has been of great importance in studies in aerodynamics, that approach will not be elaborated at this point.

Motivated by the need to bring theoretical, computational, and experimental methods into closer proximity, dimensionless similarity parameters will be obtained directly from the equations for which solutions are sought in theoretical and computational studies.

Principal Equations of Aerodynamics The fundamental principles from which the equations used to model "low-speed" aerodynamic flows are derived are only three in number. These are 1 mass is conserved, 2 force and motion are related by Newton's Second Law, and 3 energy exchanges are governed by the First Law of Thermodynamics.

In addition to these three principles, certain fluid properties and their variations with pressure and temperature must be described mathematicallv. The equations expressing the three principles provide relationships among various quantities such as density, velocity, pressure, rate of strain, internal energy, and viscosity as they vary in space and time.

The dependence for a particular quantity, say velocity, is indicated as V r, t where r is a three-component position vector and t is time. The details of the function expressing the space and time dependence are strongly affected by the choice of reference frame while the physical phenomena cannot be affected by the choice of reference frame.

It is desirable to choose reference frames that lead to relatively simple forms for the functional descriptions of the various quantities. One relation is between "Lagrangian" and "Eulerian" descriptions of the motion of particles. The other relation is between the time derivatives of quantities when measurements are made from two reference frames that are moving relative to one another.

The Lagrangian and Eulerian perspectives of motion of a field of particles are described in almost every book on aerodynamics. The Lagrangian perspective is based on the idea of "tagging" every particle and subsequently describing the motion of each particle as a function of time with a space coordinate indicating the identity of the particle.

The usual choice would be that the space coordinate indicates the position of the particle at time equal to zero. The Eulerian perspective is based on the idea of focusing on particular points in space and describing the motion of particles passing through each point in space as a function of time.

The time derivatives are related by Equation 1. The derivative from the Lagrangian perspective is referred to as a "total derivative" or "material derivative" and is indicated by the capital D as the derivative symbol. The relation holds for all other such quantities including components of velocity: The relationships that arise when two reference frames are moving relative to one another are important when "noninertial" reference frames become more convenient.

The time derivative is the "total" derivative in the sense used in Equation 1. It can be written as a partial differential equation as follows: In this equation and throughout the book p is the density of the fluid. The surface force for a material element is expressed in terms of the state of stress at the location of the element.

For a particular material the state of stress is. Newton's Second Law. The left-hand side can be written as This last form is convenient for deriving the well-known Bernoulli equation when the appropriate conditions are applied. The body force is frequently neglected in aerodynamic developments but rarely in hydrodynamic applications. The standard notations for divergence operator and dot product are used. Body forces will also arise in cases of noninertial reference frames.

For elastic bodies the relationship between stress and strain is given by Hooke's law. The NavierStokes equation for the case of a viscous compressible fluid with body force of gravitational origin can be written as. For any particular material. These equations are known as the NavierStokes equations. The assumption that the bulk modulus is times the coefficient of viscosity is incorporated in Equation 1. Stokes' law of friction states that the "stress is proportional to the time rate of strain.

The elements of s associated with a Cartesian reference frame are given by the equations -. The two most common forms of the relation are those for elastic bodies and for Newtonianfluids.

Detailed derivations of these equations are given by Schlichting9 and Loitsyanskii. The perfect gas equation. It is assumed that air in these regimes is a calorically perfect gas. Viscosity is primarily a function of temperature in the cases of both air and water. Two additional parameters also are present.

First Law of Thermodynamics: The Energy Equation The energy equation is a mathematical representation of the principle of conservation of energy. In the case of air. The energy equation may be written as An additional variable. Equations 1. In such circumstances both density and viscosity can be considered constant.

As stated above. A form is given here that is appropriate for flow of a fluid in which there may be heat transfer by conduction. These parameters are considered to be constants throughout any flow considered in this book. In flows of water. In the case of water. Since there are seven scalar variables. Equation of State and Other Considerations Equations 1. The reader is referred to Anderson2 and LoitsyanskiiIo for detailed derivations of the energy equation. An assumption of constant density is invariably applied for flows of water.

We consider typical cases of air and water because it is common to use lowspeed wind tunnels to investigate hydrodynamic as well as aerodynamic problems. These are the specific heat at constant volume.

Properties of Air Air is a mixture of nitrogen. Equation 1. The seventh relation is a specification of variation of viscosity with temperature. The dependence of viscosity on temperature is frequently approximated by a power law. It is common to idealize their properties. The equation of state is written as Equation 1. For each problem to be investigated there will be an appropriate set of initial and boundary conditions that along with the set of equations 1.

Jones" has given a substantial summary of the models of properties of air. For example Equation 1. For T. Air at "Standard" Condition Temperature. The saturation vapor pressure is related to temperature by Equations 1. T Density. This is small but is definitely not negligible compared to the level of measurement accuracy sought in many wind tunnel experiments.

The temperature should be in the range of TABLE 1. Kinematic viscosity. Jones" gives an extensive development and arrives at Equation 1. An equation for viscosity of air has previously been given as Equation 1. The small variation with temperature at atmospheric pressure is modeled by Jones with Equation 1.

Table 1. This gives density in kilograms per cubic meter for temperature in degrees Celsius. Properties of Water The density of water is nearly constant over common ranges of pressure and temperature. The variation in kinematic viscosity of water with temperature is primarily due to change in the viscosity.

A row showing the reciprocal of the kinematic viscosity is included as this is a value directly proportional to the Reynolds number for a given size of model or prototype and a given speed. For the present discussion. Fresh Water Temperature The complete geometry of the body including any time-dependent motion is required to specify the boundary conditions at the body. Note that this would have to be treated more generally to include aeroelastic phenomena.

Attention is now turned to arriving at a corresponding set of nondimensional equations. The geomeby can be nondimensionalized as a ratio to some reference length. In principle. Sea water will be somewhat more dense and have slightly different viscosity. The fluid speeds will be nondimensionalized by using the ratio to the speed at a selected point far away from the body. This is not a fundamental requirement, but it is the standard practice.

In some experimental arrangements and in many computational problems-the question of whether there is an available point considered to be "far" from the body becomes an important issue. The density will also be nondimensionalized in terns of the ratio to the value at the selected point far from the body.

Pressure will be nondimensionalized by introducing the standard pressure coefficient. The pressure coefficient is the ratio of the change in pressure due to the presence of the body as compared to the pressure at the selected point far from the body to the dynamic pressure at the selected point far from the body. Temperature will be nondimensionalized by its ratio to the value at the selected point far from the body.

The time will be nondimensionalized as a ratio to the time for a fluid particle to travel the reference length at the speed of flow far from the body. To summarize, we will consider the variables in Equations 1.

Including the square root in the definition is not essential, but it is done here to be consistent with common usage. The symbol e, is a unit vector in the direction of the gravitational field. Normally the coordinates would be chosen so that only one element would be nonzero.

The Froude number is important for flows in which there is a free surface, such as will exist for surface ships. A Froude number will also arise as an important similarity parameter if there are unsteady boundary conditions.

The acceleration of the boundaries will play a role similar to the gravitational acceleration. The Froude number is a significant parameter in some cases of dynamic systems such as towed bodies. A complete. The Froude number will not appear if the fluid body forces are neglected.

This is a common assumption introduced in aerodynamics texts. The Froude number will not be considered further in this introductory material. The second coefficient appearing inEquation 1. It is the Reynolds number,. The Reynolds number is the primary similarity parameter of interest in planning experiments for Mach numbers less than The process of developing the nondimensional form of the energy equation leads to the introduction of some additional and some alternative parameters of the fluid.

The nondimensional energy equation can be written as. There are many terms inEquation 1. The important result to be obtained here from this equation is that there are two dimensionless coefficients that did not appear in the nondimensional Navier-Stokes equation. These are the Mach number M.

The Mach number is a flow parameter while the Prandtl number is a property of the fluid that is temperature dependent. The last term of Equation 1. For low-speed flows that do not have heated or cooled boundaries, there is seldom a significant contribution from this term. We will consider that this term is negligible for most circumstances with which we will be dealing in this book. This also implies that the Prandtl number will not be a consideration since it only appears in the heat conduction term.

The net result is that the dimensionless energy equation provides the Mach number as an additional similarity parameter for our present class of problems.

The associated boundary conditions for any particular case must also be obtained in nondimensional form. For the moment consider only cases for which the boundary conditions are not functions of i. This does not mean that the flow is steady throughout the domain. Almost all flows of importance to vehicle aerodynamics are turbulent and therefore unsteady. Most wind tunnel studies involve steady "mean" flow.

The angles can be given in terms of the components of 9,on a set of body-fixed axes. Let tib, Cb,Gbbe the components of? If we could obtain solutions of the set of equations with the associated boundary conditions, we would have a set of functions:. The values of the pressure coefficient and the shear stresses at the body surface would typically be of particular interest in the present context since the integrals of those quantities over the surface of the body provide the total force coefficients.

To obtain these from the above set of functions, it is necessary to form the combinations representing expressions for the normal and tangential stress components on the body surface and integrate these over the entire body surface.

This process provides dimensionless coefficients for force and moment components that can be represented by.

When the time dependence is averaged out or the actual circumstance of having steady boundary conditions yields steady results, these coefficients are functions only of the dimensionless similarity parameters Reynolds number and Mach number along with the attitude angles.

These are powerful results applying equally to experimental, analytical, and computational studies of fluid flows. Instead of separately varying the density, viscosity, flow speed, body size, and temperature, it is only necessary to vary the combinations represented by the similarity parameters.

Each solution of the nondimensional system for a value of the Reynolds number provides a result that applies for every combination of the four involved quantities that give that particular Reynolds number. Of further significance is that the result shows that different fluids as well as different sizes of bodies in streams of differing speeds and differing coefficients of viscosity can be used when it is convenient to do so as long as the similarity parameters are matched.

For bodies completely immersed in a single fluid as is always the case in wind tunnels and that are rigid and held in a fixed position, the results will not be dependent on the Froude number, as has been stated previously. One interpretation of "low speed" as applied to wind tunnels is the speed below which the Mach number dependence is small enough to be neglected.

In such cases, which are our primary concern, the results will be dependent on only one similarity parameter, the Reynolds number. We find that for a body of fixed shape held rigidly in a "low-speed" stream, the time averages of the force and moment coefficients are functions of a single parameter, the Reynolds number, and two angles that are required to specify the body attitude relative to the free stream.

This result holds for flows of water when cavitation is not present and for flows of air at speeds up to a Mach number of With the assumption of constant density, Equation 1. In cases in which dehsity is nearly constant, there are many situations in which the temperature variation is negligible. Such problems are entirely mechanical without any thennodynamic phenomena.

The force and moment coefficients in such cases will, of course, not be dependent on Mach number. Classical Bernoulli Equation For an idealized case of steady flow with viscosity equal to zero and a uniform velocity field far from any object that may be in the flow, we will have the time derivatives equal to zero, the Reynolds number will be infinity, and the curl of the velocity field must be everywhere equal to zero. This is the classical Laplace equation that arises in many applications in classical physics.

The study of its solutions is sometimes called potential theory due to its application in determining the gravitational field potential associated with distributions of mass. With the same assumptions as above for arriving at the Bemoulli equation except that time dependence is still allowed, Equation 1. Real flows in wind tunnels and elsewhere are always unsteady. For sufficiently small values of the Reynolds number, flows can be established that are very nearly steady based on observations.

In a small set of circumstances, there are known solutions to the NavierStokes equations. None of these are of direct value to vehicle designers, although they serve as an aid to aerodynamicists in trying to understand basic issues in fluid flow. A vast majority of aerodynamic problems associated with vehicle design and wind engineering efforts involve flows that can be considered to have an incoming free stream that can be characterized by a time-independent mean flow with a superimposed additive fluctuating contribution most often characterized in terms of a "turbulence level.

The interaction with the body of interest creates a spatial modification of the mean flow and in general creates fluctuating motions in the flow in addition to those present in the incoming stream. Landahl and Mollo-Christenseni4give a good treatment of methods and summaries of aspects of turbulence.

## Low-Speed Wind Tunnel Testing, 3rd Edition

Issues associated with modeling effects of turbulence, both experimentally and computationally, are the most difficult issues with which aerodynamicists must grapple. There are important classes of problems frequently studied in wind tunnels for which the assumption that the boundary conditions on the fluid are independent of time is not valid. Examples are studies that involve propellers or rotors, towed devices suspended on thin cables, significant elastic deflections such as occur for flutter models, fabric structures such as parachutes or sails, forced or "free" motion of complete models, and manipulation of the incoming flow.

Incoming flow may be manipulated to produce essentially deterministic large-scale variations in the flow or, as in the case of wind engineering studies, the incoming stream may be passed over roughness elements or otherwise processed to produce high levels of large-scale turbulence.

In addition, the presence of significant acoustic signals can in some situations produce significant macroscopic effects. Aeroacoustic effects in low-speed flows have been receiving increasing attention in the s. The most influential paper on this topic is that of Lighthill," who derived an equation containing the same assumptions as those required in deriving the Navier-Stokes equations for compressible flow.

It has become known as Lighthill's equation. We show it here and discuss some general properties because these proper-. Lighthill's equation is given as. The right-hand side contains Tfi,the celebrated Lighthill stress tensor. Direct solution of aeroacoustic problems using this formulation has not been achieved for technically important problems.

But it is the basis for much understanding of aeroacoustics, especially generation and propagation of sound from jet engines. A subsequent development by Ffowcs-Williams and HawkingsI6is most important to currently ongoing efforts to develop methods of direct solution to aeroacoustic problems and to understanding of mechanisms of generation.

They derived what has become known as the FfowcsWilliams-Hawkings equation, and a formal solution is given here as Equations 1. There are a large number of variables. On the right-hand sides the variables are as follows: This is the time at each source element for which the emitted signal will reach the observer at time t.

Very important descriptive interpretations have been given for the three terms, and they are found to scale very differently with flow speed. The "monopole" term is identified with a vibrating solid surface or an oscillating mass source. Examples are loudspeaker cones, vibrating sheet metal or glass, or the pulsating gas emitted from an automobile exhaust pipe.

These are the most efficient generators of sound. The associated intensities increase as the fourth power of the fluid velocity. The "dipole" term is identified with an oscillating pressure on a solid surface that then acts as a sound radiator.

This will occur on a surface under a turbulent boundary layer or on the surface of a fixed circular cylinder that is undergoing the periodic shedding of the Karman vortex street phenomena. The efficiency of the dipole source type is intermediate between that of a monopole and a quadropole. The intensity increases as the sixth power of the velocity.

The "quadropole" term is a volume source associated with fluctuating gradients. It is more difficult to visualize but is associated with highly sheared turbulent flow volumes like the shear layers bounding rocket and jet engine exhausts.

The intensity increases as the eighth power of the velocity. This can be the dominant type of source for jet and rocket engines. For low-speed wind tunnel studies, there will be monopole-type sources if there are vibrating surfaces. Variations in noise generation due to shape changes are generally associated with the dipole type of source. We will give some additional brief sections on aeroacoustics at other points in the book as it is being met at low-speed wind tunnels.

Blake" has written one of the most useful technical treatments. The term aerodynamics as used here and throughout this book is intended in a broad sense as being synonymous with fluid dynamics. Anderson, J. Shames, I. Buckingham, E. See also: ASME, 37,, Karamcheti, K. Sedov, L. David, F.

Baker, W. Theory and Practice of Scale Modeling, rev. Schlichting, H. Loitsyanskii, L. Jones, F. Handbook of Chemistry and Physics, 61st ed. Landahl, M. Lighthill, M. I General Theory," Proc. Society, , , Blake, W. Wind Tunnels Experimental information useful for solving aerodynamic and hydrodynamic problems may be obtained in a number of ways: Each device has its own sphere of superiority, and no one device can be called "best. Because they make it possible to use models that can be prepared early in design cycles, because they include the full complexity of real fluid flow, and because they can provide large amounts of reliable data, wind tunnels are often the most rapid, economical, and accurate means for conducting aerodynamic research and obtaining aerodynamic data to support design decisions.

Their use saves both money and lives. The nations and industries of the world support aerodynamic research and development, of which conducting wind tunnel experiments is a major item, according to their needs, abilities, and desires.

In many countries there is a separate national research organization that augments the activities of the armed services. A substantial amount of work is contracted from national agencies to universities and industry. There is a considerable and growing volume of aerodynamic research and development done by corporations for civil purposes in the development of aircraft, automobiles, marine vehicles, and architectural structures. In Chapter 1 we have given the equations for fluid motion in nondimensional form.

These equations provide a foundation for designing scale experiments and interpreting the resulting data. For present purposes, the results of principal interest are the dimensionless coefficients that appear in the nondimensional form of the fluid dynamics equations as derived in Chapter 1.

The three coefficients are the. Reynolds number, the Mach number, and the Froude number. The coefficients as developed in Chapter 1 were obtained by introducing nondimensional variables into the conservation equations. We will now consider a more heuristic approach. When a body moves through a fluid, forces arise that are due to the viscosity of the fluid, its inertia, its elasticity, and gravity.

These forces are represented directly by the various terms in the Navier-Stokes equation. The inertia force, corresponding to the left-hand side of the Navier-Stokes equation, is proportional to the mass of air affected and the acceleration given that mass.

Thus, while it is true that a very large amount of air is affected by a moving body and each particle of air a different amount , we may say that the inertia force is the result of giving a constant acceleration to some "effective" volume of air.

Let this effective volume of air he kl', where I is a characteristic length of the body and k is a constant for the particular body shape. Then we may write Inertia force. Substituting IIV for t, we get Inertia force.

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The gravity force is proportional to the volume of the body, which in turn is proportional to the cube of the reference length. The gravity force may be written Gravity force. Keep in mind that the gravity force term in the Navier-Stokes equation is the force on the fluid.

It is not the gravity force on the body. As mentioned in Chapter I, it is necessary to introduce the equations of motion of the body along with the equations of motion of the fluid to carry out a formal nondimensionalization for the case of a fully coupled system of the motion of the body moving under the influence of the fluid and gravitational forces. However, in the present heuristic consideration, we may consider the gravity force on the body to have the same form as the gravity force on the fluid but with a different constant of proportionality.

Dividing the inertia force by each of the others gives three force ratios that, as can be seen in Equations 2. The last equation, it will be noted, uses the square root of the ratio rather than the ratio itself.

For wind tunnel experiments, the Froude number is an important similarity parameter only for dynamic tests in which model motion as well as the aerodynamic forces are involved.

Although such experiments are very important, they constitute a minority of the experimental program in most wind tunnels. Such experiments will be treated in more detail later in the book. For experiments in which the model is held stationary during data gathering, the Reynolds number and Mach number are the significant similarity parameters. If a model experiment has the same Reynolds and Mach numbers as the full-scale application, then the model and the full-scale flows will be dynamically similar.

The nondimensional functions for fluid velocity components, pressure coefficient, density, viscosity, and temperature will then be the same for the model and the fullscale flows. In turn the force and moment coefficients will be the same for the model and full-scale flows. The moments developed by'the model can.

In practice it is seldom possible to match both Reynolds number and Mach number to full scale in a model experiment. In fact, it is frequently the case that neither Reynolds number nor Mach number can be matched. Choices must then be made on the basis of which parameter is known to be most important for the type of flow situation under consideration. The matching of Mach number usually applies only to flight vehicles in the high-speed flight region as Mach number effects predominate and the matching of Reynolds number effects is not as critical.

In the low-speed flight region Reynolds number effects predominate and matching of Mach number is not as critical. However, for any experiment a careful evaluation of the effect of Reynolds and Mach numbers should be made to ensure that the results can be applied to the full-scale problem. Many wind tunnel experiments are seriously sensitive to Reynolds number effects, and no experiment should be attempted without knowledge of material like that found in Chapter 8 and a discussion with the experienced operators of the tunnel to be used.

Despite the fact that it is difficult, if not impossible, to match both Reynolds and Mach numbers in most wind tunnel experiments, the wind tunnel still is one of the most useful tools an aerodynamics engineer has available to him or her. Skillful use of the wind tunnel can make strong contributions to the aerodynamics engineer's goal of quickly and efficiently optimizing his or her design. The more complex the flow phenomena involved, the more important will be the role of the wind tunnel.

An interesting and useful fact that follows from the scaling relations is that the force on a body of a particular shape for which the flow characteristics are a function only of Reynolds number is the same regardless of the combination of size and speed that is used to produce the particular Reynolds number if the fluid, its temperature, and the free-stream pressure are unchanged.

This can be seen by writing the expression for a particular force component. Choosing drag, we have. This indicates that the drag on a particular shape with length of 10 ft at 20 rnph is the same as the drag on the same shape with a length of 1 ft at mph if the fluid temperature and pressure are unchanged. Or the force on a b-scale truck model at mph is the same as the force on the full-scale vehicle at 25 mph. This would certainly start with a sound basis in the current state of aerodynamic theory.

Appropriate results, if such exist, from previous experiments and from previous computational studies are typically of great value. The aerodynamics engineer must then choose approaches to develop the specific information required to meet the objectives of the immediate program. Three broad categories are commonly recognized: The analytical approach plays a vital role in the background studies and in gaining an appreciation for possibilities, but it never suffices for a vehicle development program.

All development programs from the time of the Wright Brothers to the s were based on a combination of analytical and experimental approaches. During the s the evolution of the digital computer reached a point where solutions to approximate forms of the fluid dynamic equations could be obtained for vehiclelike geometries.

The development of methods and computing machinery have advanced rapidly and have led to many predictions that "computers will replace wind tunnels. It has turned out, however, that the continuing dizzy pace of development of computers notwithstanding, the complexity of real flows has only partially been tamed by the computational approach.

Practical computations for complete vehicles for the foreseeable future will require "turbulence models" that up to now at least must be tailored for specific types of flow. Hammond' presented a review of progress in application of computers to engineering development in both structural mechanics and fluid dynamics. In the case of fluid dynamics he gave three aspects of development as pacing items for increasing the effectiveness of applications of the computer: The f i s t two continue to advance at a rapid rate.

In the case of turbulence models, Hamrnond asserted that while many have been developed it is not clear that there has been progress in terms of achieving generality or significantly improved performance in the period from to Ockendon and OckendonZ assert that "modeling turbulence is the major unsolved problem of fluid dynamics. According to Speziale, the direct numerical simulations of complex turbulent flows that are of technological importance could require the generation of databases with upward of loZonumbers.

This is unlikely to be possible in the near future, and even should it become feasible, it is not clear how this would result in a technologically useful result.

The next line of attack that has been expected to minimize requirements for modeling turbulence is large eddy simulation LES. Speziale discusses the failure of LES to live up to its earlier promise and is proposing. Advances in computing power have contributed greatly to the capabilities and cost effectiveness of wind tunnels and other experimental facilities.

The most important parts of the matrix or conditions to be included in an experiment will be those parts that are most at variance with the analytical or computational predictions.

It has never been shown that the Navier-Stokes equations. The process of model design and construc-. Computational methods are now an important tool to be applied in aerodynamic development programs. If this occurs. So what may appear to applied scientists to be mathematical formalities.

In addition. Even small wind tunnels today will commonly have a dedicated computer to manage data gathering and presentation and possibly provide control of the experiment. The availability of increased computing power has contributed in other ways to the effectivenessof wind tunnel programs. According to Doering and Gibbon! This is an issue of far greater importance to analytical and computational efforts than to experimental work of the nature undertaken to support vehicle design.

It is possible that the equations produce solutions which exhibit finite-time singularities. Whether or not the equations actually do display these pathologies remains an open problem: It's never been proved one way or the other. This is true of all large wind tunnels. This enables the aerodynamics engineer both to check the predicted results and.

The air flowing in a closed return wind tunnel. This can shorten the time required to prepare for an experiment provided the wind tunnel facility is intimately involved with the model design so that tunnel mounting features are included in the initial model realization. This is a role that is likely to become more important as project teams are increasingly diversified and information must be delivered with the absolute minimum time delay to a cross section of the development team who may be geographically dispersed.

In general. Figure 2. Virtually every wind tunnel with a test section larger than 2 s ft2 is one of a kind. As with any engineering design. The air flowing through an open circuit tunnel follows an essentially straight path from the entrance through a contraction to the test section. Many of these will be discussed later in this book. The tunnel may have a test section with no solid boundaries open jet or Eiffel type or solid boundaries closed jet or National Physical Laboratory NPL type.

The two basic types are open circuit and closed circuit. Emerging communication technology such as the World Wide Web when linked to the highly computerized wind tunnel of today and tomorrow offers a possibility of the wind tunnel as a virtual laboratory for people for whom physical presence is not convenient or cost effective.

There are new measurement methods that have been enabled by the availability of powerful dedicated computers and the potency of old methods has been amplified greatly. The great majority of the closed circuit tunnels have a single return. The two basic testsection configurations are open test section and closed test section. An example of a closed circuit tunnel is shown in Figure 2. Closed Return W i d Tunnels The following are advantages and disadvantages of a closed return tunnel: Advantages 1.

If used extensively for smoke flow visualization experiments or running of internal combustion engines.

Disadvantages 1. For a given size and speed the tunnel will require more energy to run. Construction cost is typically much less. If located in a room. There is less environmental noise when operating. If one intends to run internal combustion engines or do extensive flow visualization via smoke. Less energy is required for a given test-section size and velocity. For larger tunnels test sections of 70 ft2 and more noise may cause environmental problems.

Through the use of comer turning vanes and screens. The initial cost is higher due to return ducts and comer vanes. This can be important for a tunnel used for developmental experiments with high utilization two or three shifts. Open Return Wind Tunnels The following are advantages and disadvantages of an open return tunnel: Open circuit designs are also frequently used by science fair participants who build their own wind tunnels.

Because of the low initial cost. This is usually a factor only if used for developmental experiments where the tunnel has a high utilization rate. For closed return tunnels of large size with an external balance. The most common geometry is a closed test section.

The cost of building a model. Open or Closed Test Section? An open test section in conjunction with an open circuit tunnel will require an enclosure around the test section to prevent air being drawn into the tunnel from the test section rather than the inlet. Slotted wall test sections are becoming more common as are test sections that can be converted among two or more configurations.

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If tunnel has high utilization. If one uses the rule of thumb that the model span should be less than 0. In fact. Many open test-section. It is also noted that in larger size tunnels a rectangular test section is preferable because it is easier to change a model when working off a flat surface. A number of tunnels are available in which full-scale automobiles are routinely used as test articles. This is an anomaly for aircraft experiments other than takeoff and landing.

The cost of building and operating a tunnel of this size is staggering to contemplate. Consideration of this goal is given in the following. Recalling the earlier discussions of flow similarity. Necessary compressor equipment will add to the cost for pressurized tunnels. Despite these problems. In practice most development experiments are done in tunnels with widths from 10 to 20 ft. A second approach is to change the working fluid.

These tunnels used an annular return duct. High-Reynolds-Number lhnnels It is often not practicable to obtain full-scale Reynolds numbers by use of a fullscale vehicle in an experimental facility. Operation of pressurized facilities involves additional time to change the pressure condition and to access the model. There are an increasing number of wind tunnels in use exclusively for other than aeronautical applications.

The VDT. We provide synopses of a number of specialized classes of facilities. The shell cost for a given size will be greater but the proper comparison is the shell cost for equal Reynolds number. For high-speed tunnels capable of sonic speeds or more. If one increases the pressure by a factor of One of the oldest methods is to build a tunnel that can be pressurized.

For a given power input the use of Freon 12 can increase the Mach number by a factor of 2. Some basic issues related to cost of construction and cost of operation of pressurized tunnels must be considered. There will be. Low productivity of the NTF due to the long times required to cycle and stabilize the temperature has prevented it from being useful as a development facility. By this technique it is possible to operate over a range of dynamic pressures and Reynolds numbers at a constant temperature to the tunnel's stagnation pressure limit.

The range of unit Reynolds number and Mach number is impressive. The working fluid is nitrogen. A drawing of the circuit is shown in Figure 2. The Lockheed low-speed wind tunnel has tandem test sections with two contractions.

Recent recognition of detrimental effectson the environment from the use of Freon has led to plans to use a different heavy gas. Since power varies with the cube of velocity. This was the solution in both the Boeing Helicopter Co.

This sort of facility is very expensive both to build and to operate. The second test section has a cross section of ft2 and speeds from 58 to mph. Flight velocities in the transition region are low. The NTF tunnel combines the ability to operate at cryogenic temperatures with the ability to change pressure up to 9 atm.

This design avoids the high installed power required to drive the larger. The first. The European Transonic Facility at Cologne. The length of the tunnel is increased by this solution. These test sections may suffer from poorer flow quality than a tunnel built for the purpose. Lockheed Martin Aeronautical Systems tunnel in Marietta. The United Technologies Research Center has a large wind tunnel with interchangeable test sections.

The McDonnell-Douglas low-speed tunnel actually has three legs. This is attractive. This could be the settling area ahead of the contraction cone or. With this arrangement. The speed available will also be determined by the original tunnel dimensions. A number of spin. NASA Langley has performed a considerable number of free-flight experiments in the 30 X 6 0 4 tunnel" with powered models. The recovery from a spin is studied in a spin tunnel.

These tunnels were of the open return type and were arranged so that dimensionally and dynamically scaled models could be flown under the influence of gravity. At present. In this way spin modes can be predicted from the measurements without the restrictive requirement of dynamic scaling of the model. In the design and construction of the tunnel.

These few examples show that there are many ingenious and practical solutions to adapting an existing facility for new experiments. The tunnels could be tilted to set the angle of the air stream to match the glide path of the model.

The dynamic behavior of the model could be studied in these tunnels. A dynamically similar model is inserted into the tunnel by an operator in a spinning attitude. An example is shown in Figure 2. Free-Flight Tunnels In the s several "free-flight" tunnels were built.

Spin lhnnels or Vertical Wind k n e l s The tendency of some aircraft to enter a spin after a stall and the subsequent need to determine actions to achieve recovery from the spin have been perennial problems of the aircraft designer. Some spin tunnels use an annular return with turning vanes while others are open circuit with the air drawn in at the bottom and emitted at the top.

Rotary balances have also been installed in horizontal wind tunnels to carry out similar experimental programs. Germany tunnels have been built in several countries. This tunnel was moved to the Virginia Polytechnic Institute and State University in where it continues to serve as both a general.

Propeller lhnnels Propeller tunnels are similar to conventional tunnels with the exception that they usually have an open test section and a round cross section see Chapter 3.

Bihrle Applied Research Tunnel. Similar results are obtained by using oscillating model techniques or free-flight experiments in conventional tunnels. The second test section was curved to simulate turning flight. This tunnel had two interchangeable test sections about 6 ft in size. The altitude requirement necessitates pumps to provide the low density.

The shell of this tunnel is heavily insulated to help keep the tunnel cold. Low-Turbulence Tunnels These tunnels usually have a wide-angle diffuser just ahead of the settling chamber in order to increase the size of the settling chamber without a corresponding increase in the overall circuit dimensions.

Some low-turbulence tunnels of the closed return type have used " curved corners rather than the usual two 90' turns. Among the largest and most powerful experimental facilities in existence is the propulsion test facility at the U.

They have been built both as open circuit and closed return types. The large settling chamber has honeycombs and a larger than usual number of screens to damp out turbulence.

Two-Dimensional Tnnnels Two-dimensional tunnels are used primarily for evaluation of airfoil sections. These tunnels have. A novel aspect of this facility is that the fan must be run at idle speed during model changes to prevent it from freezing. The formation of ice on aircraft continues to be a serious safety problem for aircraft and helicopters that operate at low to medium altitudes.

Besides propeller experiments. Propulsion 'hnnels Experimental evaluation of aircraft engines. Since the engine must be operated in the tunnel. External Flows There are two distinct classes of wind tunnels involved in aerodynamic experiments on automobiles. Unlike the case of aircraft. Usually these tunnels are of the nonreturn type. The tunnels are usually of the low-turbulence type and may be pressurized to increase the Reynolds numbers. The one that is the main focus of this book is concerned first and foremost with the external aerodynamic flow and'with internal flow to the extent it has a significant interaction with the external flow characteristics.

For smoke sources current practice seems to favor vaporized light oils.

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For research tunnels. The General Motors Research Laboratory operates both model. Smoke is used for flow visualization in many general-purpose tunnels. It is also advantageous to use moderate scale such as 0.

Both two. Smoke tunnels used for research rather than demonstration purposes tend to have very large contraction ratios up to The Lockheed low-speed wind tunnel in Marietta. Smoke has been injected both just before the model and at the tunnel inlet. In North America there are several wind tunnels used extensively for automobile aerodynamic experiments. All of the major automobile manufacturers worldwide either own or have regular access to wind tunnels for such experiments of both model.

In Europe. Martin wind tunnel GLMWT at the University of Maryland has worked extensively on automobile aerodynamics as well as heavy truck aerodynamics beginning in The primary manufacturers in Japan. The Chrysler Corp. The Glenn L. Every manufacturer has several climatic wind tunnels. Vehicle Entrance An automotive "environmental" wind tunnel. The size that - h- 6. Movable Corner Turning Vane These facilities have capability to heat and cool the airstream. Ford Motor Co. They are typically very heavily scheduled for their environmental purposes.

The auto industry frequently refers to wind tunnels. Control Room An example of such a wind tunnel is shown in Figure 2. Steam Lances Lamps Section Courtyard Cooling Tower 7. The use of a wide-angle diffuser to permit a contraction ratio of Wind tunnels for automotive experiments are increasingly required to have low-flow noise levels so that wind noise associated with flow around the vehicle can be measured with sufficient accuracy to allow assessment of proposed design variations.

This permitted the length needed for the fan noise suppressors. A major point concerning wind tunnel experiments on automobiles is the question of ground simulation. Most automobiles are considered to be aerodynamically bluff bodies. This and other issues will be addressed in more detail later in the book. To provide a strict simulation. A considerable amount of work has been carried out to address thequestionof when this is necessaryand when this conditioncan be relaxed. This leads tointeractions between the flow about the model and the wind tunnel walls or free jet boundary that are somewhat more complex than is the case for bodies with fully attached flow.

Generally speaking.

Realizing the advantages of holding the model and the measuring instrumentation still and letting the fluid move. Special features include: The principal difference is the clearance between the bottom of the car and the ground.

And the flow quality is generally less than is thought proper for external aerodynamic studies. One result is that understanding these types of flow in wind tunnels continues to engage research personnel. While basically a singlereturn wind tunnel with a closed test section upstream of an open one. A sketch of the tunnel is shown in Figure 2. The wedges used for reflection cancellation are evident in the background. Increased understanding of aeroacoustic principles.

There is also a need to integrate directly the outcomes of experiments with the outcomes of computational simulations as each progresses. This is a capability that continues to be a work in progress at many laboratories.

Nevertheless, as stated in the preface to the previous edition, the basic methods and theory have remained unchanged over several decades. The scope of the book remains the same: to help students taking a course in wind tunnel experimentation and to furnish a reference source to wind tunnel engineers and others who use wind tunnels to solve problems of fluid flow or vehicle development.

Considerable new material has been added in this edition. Some material has been added to the treatment of fundamental issues, including a more extensive theoretical introduction to help relate experimental work to computational simulations and a chapter on the design of experiments and data quality.

The most obvious additions are separate chapters on ground vehicle experiments, marine vehicle experiments, and wind engineering, with the material on aircraft divided into two chapters.

Because of the wide scope, we continue to include material on tunnel design, calibration, and simple as well as more sophisticated instrumentation. All the material in the book is directed to low-speed experiments. Pope and K. We note the absence of a table of wind tunnel facilities that has appeared in previous editions. The substantial additions of material have resulted in a rather large book.

We believe this represents a readily available resource and that it is likely to be maintained with up-to-date information. The untimely death of Bill Rae in cut short his work on this edition. Jewel Barlow and Alan Pope wish to acknowledge his early contributions to planning for the revisions leading to the current form. Jewel Barlow is pleased that Alan Pope saw fit to substantially entrust this endeavor to him and hopes that the result is worthy of that trust.

## J. B. Barlow, W. H. Rae, Jr, A. Pope-Low Speed Wind Tunnel Testing. 1-John Wiley & Sons (1999).pdf

Several students at the University of Maryland have made substantial contributions. First among those is Daniel "Rick" Harris, who drafted the chapter on marine vehicles, with Rui Guterres, who drafted the chapter on ground vehicles, and Molly Simmons, who did yeoman duty in many ways in close array.

Robert Ranzenbach, Ahmad Kassaee, and Mark Dresser as leaders of the technical staff along with June Kirkley as the right-hand person in the office and her able assistant, Zenith Nicholas, have done much to keep the Glenn L.

Martin Wind Tunnel laboratory on an even keel while allowing Jewel Barlow to focus on preparation of the manuscript. Jewel Barlow also wishes to express his gratitude to the many representatives of member facilities of the SATA with whom he has had the privilege and pleasure of sharing meetings, information, and experiences that have enriched his knowledge of wind tunnel experiments and more.

Very special thanks from Jewel Barlow are expressed to Diane Barlow, his wife, who has given unwavering support as well as good advice. The concepts to be treated are applicable to higher speed tunnels and to water tunnels as well. However, before launching into the main topics, it is worthwhile to set the stage for wind tunnels in general by asking the question: What has motivated the invention, development, and continuing uses of wind tunnels?

Our planet, Earth, is completely enveloped by oceans of air and water. Humans and almost all the other creatures spend their lives immersed in one or the other of these fluids. Naturally produced motions from gentle breezes and currents to storms and floods have profound impact on human existence. Winds and currents have been harnessed for moving about by boat and sail since before the earliest existing recorded history. Today, less than years after the first successful airplane, there exists a vast array of aircraft tailored for many specific uses with corresponding variety in their shapes.

The shapes of airplanes are determined by considerations of aerodynamics with varying degrees of attention to performance, agility, stealth, procurement cost, operational cost, time to delivery, and any other aspect that a customer may require for intended missions.

There are millions of automobiles in routine use whose shapes attest to the influence of external aerodynamics on the decisions of the designers. The main focus for production automobiles has been on aerodynamic drag, although lift has received considerable attention as well. Aerodynamic down load is most often the main objective for racing automobiles.

Automobile companies are also keenly interested in knowing how to choose details of external shapes - to reduce exterior and interior noise. Racing- yacht. Architects routinely require aerodynamic evaluations of any prominent building almost anywhere.

Nearly every building component is being subjected to aerodynamic evaluation if it is to be accepted for use in hurricane-prone areas such as Florida. The shapes of submarines and the details of their propulsion systems are evaluated as designers attempt to maximize speed, minimize energy requirements, and minimize noise generation.

Aerodynamic influences are substantial in the design of large bridges.

Yet the veil covering the secrets of the forces involved in the dynamic interactions of fluids and solid objects has only begun to be lifted and only in relatively recent times and continues to refuse all efforts to tear it cleanly away.

The great advances in theory and computational capability notwithstanding, experimental explorations remain the mainstay for obtaining data for designers' refined and final decisions across a broad range of applications. A primary tool of experimental aerodynamics is the wind tunnel. The proper and productive use of experimental investigations in general and wind tunnels in particular requires applications of aerodynamic theory and computational methods in the planning of facilities, the planning of experiments, and the interpretation of resulting data.

Those aspects of aerodynamics will be drawn upon heavily in the course of this book. The most successful attack on virtually any aerodynamic design problem will be based on application of a combination of results from experimental, theoretical, and computational methods appropriately combined and leavened by experience. Included in those and other texts are discussions of flow similarity in which definitions of similar flows are given.

This is a very important concept that leads to significant advantages in experimental work and in theoretical and computational work as well. Knowledge, mathematical model of the processes involved is not required to apply the Pi theorem.

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A reduction in the number of independent parameters to be manipulated in an investigation is obtained based on the requirement of dimensional homogeneity for any equation expressing a valid relationship among physical variables. Some of the most important results are those associated with "distorted" models, that is, models in which complete similarity cannot be achieved but that nevertheless are very useful.

Such models are the norm rather than the exception, as becomes apparent when almost any specific wind tunnel program is being planned. Although the application of dimensional analysis has been of great importance in studies in aerodynamics, that approach will not be elaborated at this point. Principal Equations of Aerodynamics The fundamental principles from which the equations used to model "low-speed" aerodynamic flows are derived are only three in number.

These are 1 mass is conserved, 2 force and motion are related by Newton's Second Law, and 3 energy exchanges are governed by the First Law of Thermodynamics. In addition to these three principles, certain fluid properties and their variations with pressure and temperature must be described mathematicallv.

The equations expressing the three principles provide relationships among various quantities such as density, velocity, pressure, rate of strain, internal energy, and viscosity as they vary in space and time. The dependence for a particular quantity, say velocity, is indicated as V r, t where r is a three-component position vector and t is time.

The details of the function expressing the space and time dependence are strongly affected by the choice of reference frame while the physical phenomena cannot be affected by the choice of reference frame. It is desirable to choose reference frames that lead to relatively simple forms for the functional descriptions of the various quantities. One relation is between "Lagrangian" and "Eulerian" descriptions of the motion of particles. The other relation is between the time derivatives of quantities when measurements are made from two reference frames that are moving relative to one another.

The Lagrangian and Eulerian perspectives of motion of a field of particles are described in almost every book on aerodynamics.For example Equation 1.

Show related SlideShares at end. As stated above, it is also assumed that the thermal conductivity is constant, in which case it can be factored to the leading position in the last term of Equation 1. This is either impossible or very costly for many vehicles. The untimely death of Bill Rae in cut short his work on this edition.

The time derivative is the "total" derivative in the sense used in Equation 1. To be most useful. This factor, now known as the Reynolds number , is a basic parameter in the description of all fluid-flow situations, including the shapes of flow patterns, the ease of heat transfer, and the onset of turbulence.

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