**ABSTRACT**

The purpose of the present master thesis is to optimize the current fuel tank simulations procedure for the next generation of JAS 39 Gripen ghters developed by SAAB AB. The current simulation process involves three different steps performed in three different computer environments.

While the procedure works reasonably well on the fuel tank models of the previous version of the aircraft, it is too slow for the new Gripen tank models and their high level of detail. An optimized version of the procedure is put forward, which allows for tank analysis and fuel system simulation within reasonable time frames. Suggestions are made for future improvements.

**BACKGROUND**

**Problem Definition**

Behind most regulations lies an accident where people got injured or killed. Some events were completely unforeseeable, but others could have easily been avoided with better safety procedures, better maintenance, and, more often than desirable, better engineering. Testing and verification of each system and of the complete aircraft should not come as a last phase in the design project; on the contrary, they should accompany every stage in the aircraft design process.

The relevancy of the situation to the fuel system of the Gripen can be described by a simplified example of engine flameout. The high maneuverability of combat aircraft unavoidably leads to fuel moving around in fuel tanks. We assume the aircraft does not have much fuel left, and performs a sharp nose-down manoeuver. This leads to negative Gs acting on the aircraft, and the fuel moving in the tanks accordingly, away from the pipe port corresponding to engine fuel feed. The aircraft then experiences a flame-out, i.e. the extinction of the flame in the combustion chamber of the engine, a potentially deadly occurance.

**METHOD**

The data generated from the previous 2 steps is inserted into the tank model in Dymola. This model, in turn, is included in a simplified fuel system model consisting of pipes, a source and a sink, as well as of environment settings saved in the “system” component, as shown in Fig. 3.1. The Dymola simulation helps to better understand the dynamic movement of fuel within the tanks during aircraft maneuvering. Among other data, it provides accurate information on the hydrostatic pressures at the pipe inlets within the system.

Radial Basis Functions (RBF) Networks are one of the best ways of approximation of multi-variate scattered data, due to their excellent approximation properties. In short, they can be visualized as an “input – process – output” system. The input is the data generated from CATIA – the x,y,z components of the acceleration vector, the fuel volume, the x,y,z coordinates of the fuel surface and the corresponding ones of the center of gravity of the fuel in the tank.

The output is a function, s, which can give a good approximation of the data for inputs different than the ones where the value of the exact function is known. The approximating function is defined using fewer points than the ones available in the input data (points which will be called centers). A representation of the network is shown in Fig. 3.10.

The acceleration problem can be modeled by considering two rotating frames: the inertial frame of the Earth (denoted by the superscript i), and the rotating frame fixed to the body of the aircraft (denoted by the superscript r). The two frames are illustrated in Fig. 3.27.

**RESULTS**

Figure 4.1: A simplified fuel system model with one tank, two pipes, a source and a sink; the system component is modified in order to allow for the calculation of the local acceleration acting on the tank’s center of gravity. The acceleration component feeds the values for the linear and angular acceleration of the aircraft, and the tank model performs the calculation.

**DISCUSSION**

The oscillations are difficult to spot with the naked eye; they appear in the 3^{rd} or 4^{th} decimal, and can only be seen after several zoom-ins. Fig. 5.1 shows how the approximation of the x-coordinate of a point on the fuel surface looks like (as a function of volume), and Fig. 5.2-5.3 show how they look like at a zoom-in. The high oscillations result in the long Dymola computations time.

As mentioned before, the Runge phenomenon appears for all RBF functions, and increases in influence with the degree of the polynomial (thus making Wendland’s functions not suitable) and with the degree of accuracy of the approximation. This is due to the fact that the peaks appear for the kernel functions around each center point; the higher the accuracy, the more center points there are for an approximation, and therefore the more oscillations are included in the final approximation.

**CONCLUSIONS**

The goal of the thesis was to improve the existing tank analysis procedures in order to be applicable for the Gripen NG new fuel tanks. This has been accomplished, by reducing the analysis time to around 35 h from hundreds of hours, and by removing the memory problems encountered in CATIA. The fuel system model was extended to include the calculation of the local acceleration acting on each fuel tank, rather than the global acceleration acting on the aircraft’s center of gravity.

As for the function giving the approximation to be used in Dymola, the inverse multiquadric seems to offer the best approximation with the settings of Simulation 39. However, since the Runge phenomenon influences all the simulations executed for this thesis, a second comparison needs to be performed when the oscillation source is identified and removed.

Source: KTH

Author: Alexandra Oprea

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