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The use of a transonic airfoil code for analysis, inverse design, and direct optimization of an airfoil immersed in propfan slipstream is described. A summary of the theoretical method, program capabilities, input format, output variables, and program execution are described. Input data of sample test cases and the corresponding output are given.
Two dimensional wind tunnel tests were conducted on a high speed natural laminar flow airfoil in both the Langley 6 x 28 inch Transonic Tunnel and the Langley Low Turbulence Pressure Tunnel. The test conditions consisted of Mach numbers ranging from 0.10 to 0.77 and Reynolds numbers ranging from 3 x 1 million to 11 x 1 million. The airfoil was designed for a lift coefficient of 0.20 at a Mach number of 0.70 and Reynolds number of 11 x 1 million. At these conditions, laminar flow would extend back to 50 percent chord of the upper surface and 70 percent chord of the lower surface. Low speed results were also obtained with a 0.20 chord trailing edge split flap deflected 60 deg.
Development of airfoil sections suitable for high-speed applications has generally been difficult because little was known of the flow phenomenon that occurs at high speeds. A definite critical speed has been found at which serious detrimental flow changes occur that lead to serious losses in lift and large increases in drag. This flow phenomenon, called the compressibility burble, was originally a propeller problem, but with the development of higher speed aircraft serious consideration must be given to other parts of the airplane. Fundamental investigations of high-speed airflow phenomenon have provided new information. An important conclusion of this work has been the determination of the critical speed, that is, the speed at which the compressibility burble occurs. The critical speed was shown to be the translational velocity at which the sum of the translational velocity and the maximum local induced velocity at the surface of the airfoil or other body equals the local speed of sound. Obviously then higher critical speeds can be attained through the development of airfoils that have minimum induced velocity for any given value of the lift coefficient. Presumably, the highest critical speed will be attained by an airfoil that has uniform chordwise distribution of induced velocity or, in other words, a flat pressure distribution curve. The ideal airfoil for any given high-speed application is, then, that form which at its operating lift coefficient has uniform chordwise distribution of induced velocity. Accordingly, an analytical search for such airfoil forms has been conducted and these forms are now being investigated experimentally in the 23-inch high-speed wind tunnel. The first airfoils investigated showed marked improvement over those forms already available, not only as to critical speed buy also the drag at low speeds is decreased considerably. Because of the immediate marked improvement, it was considered desirable to extend the thickness and lift coefficient ranges for which the original forms had been designed before further extending the investigation.
Advances in the fields of electronics, batteries, and electric motors have enabled broad adoption of small-scale aircraft for various terrestrial applications. Numerous Micro Aerial Vehicles (MAVs) and small Unmanned Aerial Vehicles (UAVs), both civil and military, are in use today. Operation at their design flight condition often requires rotors, propellers, or wings to perform at Reynolds numbers significantly below 500,000 [1]. Airfoil performance at low Reynolds numbers is generally characterized by low aerodynamic performance (i.e. the attainable lift-to-drag ratio) compared to performance of airfoils at higher Reynolds numbers. The critical chord-based Reynolds number for conventional airfoils lies around Rec = 100,000 to Rec = 500,000 [2]. Below this critical Reynolds number, laminar separation of the boundary layer is usually the cause for poor performance. Researchers have found that below the critical Reynolds number, flat and cambered plates can outperform smooth airfoils. Circular-arc cambered plates especially have remarkable performance advantages compared to conventional airfoil shapes [3].
A description is presented of a technique for the optimization of airfoil pressure distributions using an interactive inverse boundary-layer program. This program allows the user to determine quickly a near-optimum subsonic pressure distribution which meets his requirements for lift, drag, and pitching moment at the desired flow conditions. The method employs an inverse turbulent boundary-layer scheme for definition of the turbulent recovery portion of the pressure distribution. Two levels of pressure-distribution architecture are used - a simple roof top for preliminary studies and a more complex four-region architecture for a more refined design. A technique is employed to avoid the specification of pressure distributions which result in unrealistic airfoils, that is, those with negative thickness. The program allows rapid evaluation of a designed pressure distribution off-design in Reynolds number, transition location, and angle of attack, and will compute an airfoil contour for the designed pressure distribution using linear theory.
To systematically investigate the potential of advanced airfoils in advance preliminary design studies, empirical relationships were derived, based on available wind tunnel test data, through which total drag is determined recognizing all major aircraft geometric variables. This technique recognizes a single design lift coefficient and Mach number for each aircraft. Using this technique drag polars are derived for all Mach numbers up to MDesign + 0.05 and lift coefficients -0.40 to +0.20 from CLDesign.
Wind tunnel tests were conducted to determine the low speed two dimensional aerodynamic characteristics of a 17 percent thick medium speed airfoil (MS(1)-0317) designed for general aviation applications. The results were compared with data for the 17 percent thick low speed airfoil (LS(1)-0417) and the 13 percent thick medium speed airfoil (MS(1)-0313). Theoretical predictions of the drag rise characteristics of this airfoil are also provided. The tests were conducted in the Langley low turbulence pressure tunnel over a Mach number range from 0.10 to 0.32, a chord Reynolds number range from 2 million to 12 million, and an angle of attack range from about -8 to 20 deg.
This report documents the experimental aerodynamic characteristics of a 14 percent thick supercritical airfoil based on an off design sonic pressure plateau criterion. The design normal force coefficient was 0.7. The results are compared with those of the family related 10 percent thick supercritical airfoil 33. Comparisons are also made between experimental and theoretical characteristics and composite drag rise characteristics derived for a full scale Reynolds number of 40 million.
The preliminary design of high-altitude, long-endurance RPVs is complicated by the paucity of data concerning airfoils with high lift coefficients at low Re numbers. Attention is presently given to a generic airfoil of this type for the design Re number range of 700,000 to 2 million. Low drag is predicted for lift coefficients from 0.4 (for high speed dashes) to 1.5 (for maximum mission endurance). The airfoil is such that its maximum lift coefficient, at 1.8, is unaffected by the surface contamination that would be encountered during takeoffs and landings in rain or over insect-infested runways.
A new inverse method for aerodynamic design of airfols is presented for subcritical flows. The pressure distribution in this method can be prescribed as a function of the arc length of the as-yet unknown body. This inverse problem is shown to be mathematically equivalent to solving only one nonlinear boundary value problem subject to known Dirichlet data on the boundary. The solution to this problem determines the airfoil, the freestream Mach number, and the upstream flow direction. The existence of a solution to a given pressure distribution is discussed. The method is easy to implement and extremely efficient. A series of results for which comparisons are made with the known airfoils is presented.
The low speed aerodynamic characteristics of a 14 percent thick supercritical airfoil are documented. The wind tunnel test was conducted in the Low Turbulence Pressure Tunnel. The effects of varying chord Reynolds number from 2,000,000 to 18,000,000 at a Mach number of 0.15 and the effects of varying Mach number from 0.10 to 0.32 at a Reynolds number of 6,000,000 are included.
A body-fitted grid embedment technique applicable to inviscid transonic airfoil flow field analysis was developed and verified through a series of tests. Test cases used to verify the technique show that the accuracy of the solution was increased by grid embedding. This enhancement of the solution is especially true when small supercritical zones occur which cannot be adequately described using the main grid only. Results obtained with the SKANFP full potential program are considered with regard to the massive separated flow and high lift and the undesirable unrealistic 'bump' in the vicinity of the separation point due to a mismatch between the unseparated and separated pressure distributions. Techniques used to eliminate this feature are discussed.
The development and incorporation into TRANDES of a fully conservative analysis method utilizing the artificial compressibility approach is described. The method allows for lifting cases and finite thickness airfoils and utilizes a stretched coordinate system. Wave drag and massive separation studies are also discussed.
Despite the fact that the flow over a rotor blade is strongly influenced by locally three-dimensional and unsteady effects, practical experience has always demonstrated that substantial improvements in the aerodynamic performance can be gained by improving the steady two-dimensional charateristics of the airfoil(s) employed. The two phenomena known to have great impact on the overall rotor performance are: (1) retreating blade stall with the associated large pressure drag, and (2) compressibility effects on the advancing blade leading to shock formation and the associated wave drag and boundary-layer separation losses. It was concluded that: optimization routines are a powerful tool for finding solutions to multiple design point problems; the optimization process must be guided by the judicious choice of geometric and aerodynamic constraints; optimization routines should be appropriately coupled to viscous, not inviscid, transonic flow solvers; hybrid design procedures in conjunction with optimization routines represent the most efficient approach for rotor airfroil design; unsteady effects resulting in the delay of lift and moment stall should be modeled using simple empirical relations; and inflight optimization of aerodynamic loads (e.g., use of variable rate blowing, flaps, etc.) can satisfy any number of requirements at design and off-design conditions.
The use of mathematical models to study physical problems of current interest to aeronautical engineers has been made possible by the development of numerical techniques to compute solutions of the differential equations of transonic aerodynamics. These advances have encouraged the improvement of supercritical wing technology. A method to determined steady, shockless flow of an inviscid, compressible fluid past a cascade of airfoils in the (x,y)-plane is considered, taking into account also the case of an isolated airfoil. The method of complex characteristics solves the equations in the hodograph plane by extending all variables into the complex domain, where the notion of type is no longer significant. Attention is given to the mathematical background, the method of complex characteristics, and numerical calculations.
A practical procedure for optimum design of aerodynamic shapes is demonstrated. The proposed procedure uses an optimization program based on the method of feasible directions coupled with an analysis program that uses a relaxation solution of the inviscid, transonic, small-disturbance equations. Results are presented for low-drag, nonlifting transonic airfoils. Extension of the method to lifting airfoils, other speed regimes, and to three dimensions if feasible.
Tests were conducted in the Langley low-turbulence pressure tunnel to determine the aerodynamic characteristics of climb, cruise, and landing configurations. These tests were conducted over a Mach number range from 0.10 to 0.35, a chord Reynolds number range from 2.0 x 1 million to 20.0 x 1 million, and an angle-of-attack range from -8 deg to 20 deg. Results show that the maximum section lift coefficients increased in the Reynolds number range from 2.0 x 1 million to 9.0 x 1 million and reached values of approximately 2.1, 1.8, and 1.5 for the landing, climb, and cruise configurations, respectively. Stall characteristics, although of the trailing-edge type, were abrupt. The section lift-drag ratio of the climb configuration with fixed transition near the leading edge was about 78 at a lift coefficient of 0.9, a Mach number of 0.15, and a Reynolds number of 4.0 x 1 million. Design lift coefficients of 0.9 and 0.4 for the climb and cruise configurations were obtained at the same angle of attack, about 6 deg, as intended. Good agreement was obtained between experimental results and the predictions of a viscous, attached-flow theoretical method.
This report covers the period 1 September 1983 to 31 January 1984. The primary task during this reporting period was the continued development of the massive separation model and computer code (SKANSEP). In particular, detailed investigations were conducted with the boundary layer displacement surface correction technique discovered near the end of the last reporting period. This report will present detailed results using this technique and show comparisons with experimental data.