# MATHEMATICAL DYNAMIC MODEL OF THERMAL AND HYDRAULIC PROCESSES IN AIRCRAFT FUEL SYSTEM TANKS

S.D. Vynnychuk

Èlektron. model. 2022, 44(6):03-20

https://doi.org/10.15407/emodel.44.06.003

### ABSTRACT

A generalized mathematical model of dynamic thermal processes in fuel system tanks and hydraulic processes in the supercharging and drainage system is proposed. In the model of dynamic temperature changes in the CB, the idea of forming a parametric dependence is laid down, which, due to the selection of the values of the model parameters, would take into account the influence of the main factors at different stages of the flight and allow the adjustment of the model. 9 such parameters are highlighted and illustrated how each of them separately affects the temperature change in the tank. The given calculation data show that the change in their values has a different effect on the shape of the graph of the temperature change in the CB for the analyzed flight. Therefore, due to their selection, it is possible to obtain temperature values in the CB close to the experimental ones. The found values of the coefficients change little for different variants of flights, which indicates the acceptability of model (4) - (6) for use in preliminary analysis for a number of flights based on one of them. Such a model, perhaps in a somewhat simplified form, can be used in assessing the flammability of fuel in aircraft tanks. For the model of hydraulic processes, a universal algorithm for determining the flow distribution for 10 variants of boundary conditions for the network is proposed, which describes the calculation scheme of the supercharging and drainage system, where part of the boundary conditions can be set implicitly, provided that the pressure drops on the branches of the network are linear functions of the flow rate in the corresponding branch. This model complements the general model of dynamic hydraulic processes in the supercharging and drainage system, including tanks, which was proposed by the author earlier.

### KEYWORDS

aircraft fuel system, hydraulic network, average fuel temperature, tank pressure, mathematical model

### REFERENCES

1. Advisory Circular № 25.981-2А (2008), «Fuel Tank System Flammability Reduction Means», (available at: http://www.fire.tc.faa.gov/systems/fueltank/FTFAM.stm)
2. S. Department of Transportation FAA DOT/FAA/AR-05/8 (2008), Fuel Tank Flammability Assessment Method. User’s Manual, (available at: http://www.fire.tc.faa.gov/systems/fueltank/FTFAM.stm)
3. Vynnychuk, S.D. (2022), “Mathematical model of hydraulic processes in the supercharging and drainage system”, Elektronne modelyuvannya, Vol. 44, no. 2, pp. 3-14, available at: https://doi.org/10.15407/emodel.44.02.003.
4. Vynnychuk, S.D., Kolomiiets, Y.A. and Koziuk, O.I. (2022), “Model and algorithm for calculating flow distribution in the central tank of the supercharging system and drainage without drainage and bypass”, Elektronne modelyuvannya, Vol. 44, no. 4, pp. 21-27, available at: https://doi.org/10.15407/emodel.44.04.021
5. Vynnychuk, S.D. (2016), “Definition of flow distribution in networks with a tree graph”, Elektronne modelyuvannya, Vol. 38, n 4, pp. 65-80, DOI: https://doi.org/10.15407/emodel.
6. Abramovich, G.N. (1969), Prikladnaya gazovaya dinamika. 3-ye izd., pererab. [Applied gas dynamics. 3rd ed., revised], Nauka, Moscow, Russia.

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