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Modelling & implementation of Aerodynamic Zero-lift Drag into ADAPDT

ABSTRACT

The objective of this project work was to construct and implement an algorithm into the program ADAPDT to calculate the zero-lift drag profile for defined aircraft geometries. ADAPDT, short for AeroDynamic Analysis and Preliminary Design Tool, is a program that calculates forces and moments about a flat plate geometry based on potential flow theory. Zero-lift drag will becalculated by means of different hand-book methods found suitable for the objective and applicable to the geometry definition that ADAPDT utilizes.

Drag has two main sources of origin: friction and pressure distribution, all drag acting on the aircraft can be traced back to one of these two physical phenomena. In aviation drag is divided into induced drag that depends on the lift produced and zero-lift drag that depends on the geometry of the aircraft.

How reliable and accurate the zero-lift drag computations are depends on the geometry data that can be extracted and used. ADAPDT’s geometry definition is limited to flat plate geometries however although simple it has the potential to provide a huge amount of data and also deliver good results for the intended use. The flat plate representation of the geometry proved to be least sufficient for the body while wing elements could be described with much more accuracy.

Different empirical hand-book methods were used to create the zero-lift drag algorithm. When choosing equations and formulas, great care had to be taken as to what input was required so that ADAPDT could provide the corresponding output. At the same time the equations should not be so basic that level of accuracy would be compromised beyond what should be expected from the intended use.

Finally, four well known aircraft configurations, with available zero-lift drag data, were modeled with ADAPDT’s flat plate geometry in order to validate, verify and evaluate the zero liftdrag algorithm’s magnitude of reliability. The results for conventional aircraft geometries provided a relative error within 0-15 % of the reference data given in the speed range of zero to Mach 1.2.

While for an aircraft with more complicated body geometry the error could go up to 40 % in the same speed regime. But even though the limited geometry is grounds forun certainties the final product provides ADAPDT with very good zero-lift drag estimation capability earlier not available. A capability that overtime as ADAPDT continues to evolve has the potential to further develop in terms of improved accuracy.

INTRODUCING DRAG & THE ADAPDT PROGRAM

Skin friction drag arises because of the viscosity in the air that flows in the boundary layer closest to the skin of the object. Viscosity is a molecular resistance that fluids exhibit against displacement relative to each other and with respect to the surface of solid objects. This can roughly be compared to the illustration of the skier in figure 2-4a below.

Figure 2-4a. Illustration showing tangential dynamic friction force acting between the skis and the snow

Figure 2-4a. Illustration showing tangential dynamic friction force acting between the skis and the snow

When the skier slides on the snow the surface of the ski and snow slide along another and give cause to a tangential force, slowing him down, that is skin friction drag. Similar in aviation when air flows in the boundary layer closest to the skin of the wing, or other area, the air is slowed down to a standstill closest to the body, figure 2-4b.

Figure 2-4b. Illustration showing the boundary layer closest to the skin and how, due to skin friction, the air is slowed down.

Figure 2-4b. Illustration showing the boundary layer closest to the skin and how, due to skin friction, the air is slowed down

Interference drag is caused by vortices originating from junctions, at sharp concave angles, between parts of an object, for example wing and fuselage as shown by figure 2-6a. These vortices, caused by the acceleration of air due to higher pressure around these parts, give rise to drag. To minimize interference drag all the sharp junctions need to be smoothed out, this is done by adding fillets between the parts, figure 2-6b.

Figure 2-6a. Vortices originating from sharp junctions between wing and body

Figure 2-6a. Vortices originating from sharp junctions between wing and body

Figure 2-6b Principal sketch of fillets used to reduce interference drag.

Figure 2-6b Principal sketch of fillets used to reduce interference drag

When the flow case is set and saved the next step is to choose a profile for each wing area. To do this scroll down in the “Tools” menu bar and select “Add Profile Camber and Thickness”. Doing this brings up the interface, figure 2-12 left, where profiles can either be loaded or created, leaving only to select which areas the chosen profile is to be imported to giving a result as shown in figure 2-12 right part.

Figure 2-12 Interface to select and add a profile to the geometry, here a Naca 65A004 is selected (left window). The Naca profile has been added, wing now has a thickness and a camber defined (right figure).

Figure 2-12 Interface to select and add a profile to the geometry, here a Naca 65A004 is selected (left window). The Naca profile has been added, wing now has a thickness and a camber defined (right figure)

THEORY

Figure 3-1. Overall principle layout of the zero-lift drag curve buildup

Figure 3-1. Overall principle layout of the zero-lift drag curve buildup

The most important factor when modeling drag is to have a very good defined geometry of the aircraft to be studied. Otherwise assumptions need to be made in order to describe an equivalent geometry bringing with it lots of uncertainties about the results. Unfortunately due to the limited geometry definition in ADAPDT many simplifications and assumptions had to be made in order for the algorithm to be able to deliver results. Therefore only clean aircraft geometries consisting of: wings, bodies, stabilizers and fin combinations should be modeled. This section is divided into three subsections that compose the total drag curve, shown below in figure 3-1: Subsonic, Transonic and Supersonic Drag.

Figure 3-2. Transonic zero-lift drag slope build-up

Figure 3-2. Transonic zero-lift drag slope build-up

Transonic flight is defined as, in theory, spanning from about Mach 0,7 to 1,2 depending on the aircraft configuration. But in reality transonic airspeed begins at the critical Mach number, which is when some local airflow over the aircraft exceeds Mach 1, and then ends when the entire flow around the aircraft is supersonic. At this stage if speed is further increased only a small amount of drag rise will occur due to very weak shock waves. If speed continues to increase past Mcrit it will eventually reach the Mach drag divergence number, MDD, where the drag will rise significantly, refer to figure 3-2.

Figure 3-4. Non-linear model by Gersten and Bollay.

Figure 3-4. Non-linear model by Gersten and Bollay

The linear method described above is unable to correctly account for nonlinearities such as vortices from wing leading edges and tips. One solution to this is to make it so that the vortices aren’t bound to following the surface. According to and experiments done by Gersten and Bollay during 1940:s observations during wind tunnel testing where made that the tip vortices not bound to the surface left the plane with the angle α/2 shown by figure 3-4. Alpha is the angle between the free stream and the surfaces x-axis. This model has proven to give sufficiently good resemblance with experiments performed, especially for plates with a low aspect ratio.

RESULTS

Figure 4-1. Scheme describing the basic overall interlinking between ADAPDT and the Zero-drag algorithm

Figure 4-1. Scheme describing the basic overall interlinking between ADAPDT and the Zero-drag algorithm

Figure 4-1 presents an overview of the algorithm and how the functions work together to present the results to the user when gui_CalcZeroDrag is called. The schematic of the PlotZeroDrag algorithm is included in the appendix

Figure 4-7. F-4e drawings (to the left), F-4e in ADAPDT (to the right)

Figure 4-7. F-4e drawings (to the left), F-4e in ADAPDT (to the right)

Figure 4-7 shows the aircraft drawings and recreation in ADAPDT. This aircraft has a complex end section thanks to the twin engine outlets placed a bit inward under the tail section. Also a slightly complex wing design with different wing profiles at the inner section and outer section. The aircraft is designed for supersonic flight therefore the empirical efficiency factor EWD was set to 1,7.

Figure 4-11. F-104G drawings (left) and F-104G in ADAPDT (right).

Figure 4-11. F-104G drawings (left) and F-104G in ADAPDT (right)

Figure 4-11 shows the aircraft drawings and recreation in ADAPDT. The F-104G Starfighter is an old aircraft entirely designed and optimized for supersonic flight. The empirical wave drag efficiency factor for this aircraft, although optimized for supersonic flight, was set to 2,3 which gave the best agreeing results.

DISCUSSION & CONCLUSION

When adding new algorithms and parts to an already existing and working program lots of difficulties arise. One is to gain enough knowledge about the code to understand its structure and how different parts affect one another. The reason for this is that the new and existing code should have similar structures to not create confusion for successive developers of the code. Another huge difficulty is to extract the correct data and use the already existing tools when creating the new parts of the program. Therefore before embarking on modification and addition of new modules, the workings of the existing code needs to be understood thoroughly.

In conclusion ADAPDT’s code is very well structured and written. The code was fairly easy to track and get to understand which is extremely valuable and appreciated when developing a new module for the program. The zero-lift drag algorithm is far from complete and many modifications can and will be done to improve it over time as ADAPDT continues to develop.

The zero-lift drag calculations depend entirely upon how well the geometry of the aircraft can be defined in the program and how much of this that can be extracted. ADAPDT’s body geometry definition is very limited and therefore lots of approximations, assumptions and simplifications had to be done so that the zero-drag code could collect a sufficient amount of information to perform its calculations. Meanwhile all the wing areas can be very well defined making it possible to receive very reliable drag data from the algorithm.

Source: Malardalen University
Author: David Bergman

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