Simple Airfoil Research Articles

Self-sustained oscillations and bifurcations of transonic flow past simple airfoils

A turbulent flow past two symmetric airfoils, whose bow and aft portions are circular arcs, whereas midparts are flat, is studies numerically. The amplitude of lift coefficient oscillations versus the free-stream Mach number M∞ is analyzed at zero angle of attack. Ranges of M∞ in which there exist flow bifurcations are determined.

Fabrication and Performance of a Pin Fin Micro Heat Exchanger

Nickel micro pin fin heat exchangers can be electroplated directly onto planar or non-planar metal surfaces using a derivative of the LIGA micromachining process. These heat exchangers offer the potential to more effectively control the temperature of surfaces in high heat flux applications. Of particular interest is the temperature control of gas turbine engine components. The components in the gas turbine engine that require efficient, improved cooling schemes include the gas turbine blades, the stator vanes, the turbine disk, and the combustor liner. Efficient heating of component surfaces may also be required (i.e., surfaces near the compressor inlet to prevent deicing). In all cases, correlations providing the Nusselt number and the friction factor are needed for such micro pin fin heat exchangers. Heat transfer and pressure loss experimental results are reported for a flat parallel plate pin fin micro heat exchanger with a staggered pin fin array, with height-to-diameter ratios of 1.0, with spacing-to-diameter ratios of 2.5 and for Reynolds numbers (based on the hydraulic diameter of the channel) from 4000 to 20,000. The results are compared to studies of larger scale, but geometrically similar, pin fin heat exchangers. To motivate further research, an analytic model is described which uses the empirical results from the pin fin heat exchanger experiments to predict a cooling effectiveness exceeding 0.82 in a gas turbine blade cooling application. As a final point, the feasibility of fabricating a relatively complex micro heat exchanger on a simple airfoil (a cylinder) is demonstrated.

The Contact of a Cuspidal Crack

A simplified airfoil mapping is used to define a cuspidal crack. The objective is to investigate the effects of compressive loads on an infinite solid containing crack-like flaws. Such an objective cannot be achieved by using the conventional line crack to characterize the flaws. The associated contact problem is solved exactly by assuming that the contact region is small in comparison to the crack length. It is shown that the well-known Barenblatt model is just the present contact problem in reverse. Moreover, a specific functional form is determined to describe the so-called cohesive force which was assumed to be a material function by Barenblatt.

Shock Tube as a Device for Testing Transonic Airfoils at High Reynolds Numbers

A performance analysis of gas-driven shock tubes shows that transonic airfoil flows with chord Reynolds numbers in the range of 100 million can be generated behind the primary shock in a large shock tube. A study of flow over simple airfoils has been carried out at low and intermediate Reynolds numbers to assess the testing technique. Results obtained from schlieren photos and airfoil pressure measurements show that steady transonic flows similar to those observed for the airfoils in wind tunnels can be generated within the available testing time in a shock tube with either properly-contoured test section walls or a properly-designed slotted-wall test section. The study indicates that the shock tube is a useful facility for studying two-dimensional high Reynolds number transonic airfoil flows.

The use of higher-order surface singularity distributions to obtain improved potential flow solutions for two-dimensional lifting airfoils

This paper analyzes and tests the ability of the surface source singularity method to calculate flow about two-dimensional lifting airfoils using the relatively small element numbers typical of three-dimensional cases. The aim is to discover improved calculation techniques for both two and three dimensions. The body of the paper presents a series of test airfoils about which the flow has been calculated by various refinements of the method. Conclusions are drawn from the results. The original form of the method, which uses flat surface elements, piecewise constant source density, and a constant surface vorticity distribution, is found to be satisfactory for ‘ordinary’ simple airfoils with finite trailing edges. For airfoils with very thin and/or highly loaded aft portions the original form of the method experiences difficulty, generally due to the fact that a singularity of the source density is required at the trailing edge. By using a parabolic surface vorticity the difficulty is largely alleviated, and satisfactory results are obtained. This modification is very easy to implement numerically. Further refinements consisting of curved surface elements, piecewise-parabolic source density, and the Kutta condition extrapolated to the trailing edge improve the solution sill further and produce extremely accurate pressure distributions on rather extreme airfoils with surprisingly small element numbers.

Comment on "Turbulent Skin Friction for Tapered Wings"

Table 1 compares the ratio of Cf/Cf(Rr) obtained for Reynolds numbers of 10 and 10 by using Simpson's rule to evaluate the integral with C/(£) given by Eq. (1) with the values obtained by using Eqs. (5) and (9). The small differences have no practical significance. The last column using Eq. (5) with n = l/l shows that this is quite adequate for this Reynolds number range. The use of Eq. (5) allows more accurate evaluations of Cf(Rr) than simple skin friction laws such as Eq. (1) or Eq. (3) to be employed. Collar's expression which takes the laminar contribution into account or simple airfoil methods such as the one given by Thwaites can be applied. Also, it is possible to obtain analytic results for other planforms.

Surface Dipole Strength for Flow Past Airfoils

A new correlation technique enables the determination of local acoustic source strength on the surface of flat plates and simple airfoil shapes. The method is based on Curle's equation for surface generated noise and involves cross correlation between local surface pressure and the farfield acoustic pressure. Flat plate airfoils of circular planform were positioned in a quiet open jet airflow. The distribution of dipole strength was obtained by moving the point of surface pressure measurement around on the surface. Distinctively different distributions were obtained for cases of vortex shedding (airfoil at zero angle of attack in core of jet), separated flow (airfoil at 16° angle of attack in core of jet), and incident turbulence (airfoil in turbulent mixing layer). The popular notion that noise comes dominantly from the edges of a plate was not strongly supported. In some cases, however, definite localized source regions were identified. The technique also enabled estimates of correlation area for the surface pressure pattern to be made. These were generally a small fraction of the plate area (1%–10%). [Facilities and support for this work were provided by the Trane Company Research Department, LaCrosse, Wisconsin.]

On the motion of thin airfoils in fluids of finite electrical conductivity

A two-dimensional, small-perturbation theory for the steady motion of thin lifting airfoils in an incompressible conducting fluid, with the uniform applied magnetic field perpendicular to (and in the plane of) the undisturbed, uniform flow field, is described. The conductivity of the fluid is assumed to be such that the magnetic Reynolds number,Rm, of the flow is large but finite. Within this assumption, a theory based on superposition of sinusoidal modes is constructed and applied to some simple thin airfoil problems.It is shown that with this particular field geometry the Alfvén wave mechanism is important in making possible very deep penetration into the flow field of currents and their associated vorticity. It is also shown that the current penetration for an airfoil is much larger than for a wavy wall of wavelength equal to the airfoil chord.A value ofRm= 5 is found to be a good approximation to infinity in this study; in fact, use of the present technique for values ofRmof the order of unity is permissible. These results provide an indication of what is meant by ‘large’ magnetic Reynolds number in two-dimensional magneto-aerodynamics.