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Verification of calculations for heating the fuselage of an unmanned aerial vehicle with a jet stream of a turbojet engine


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The paper presents the results of heating the fuselage of a small-sized unmanned aerial vehicle by a jet of a turbojet engine in a dense layout. A method for protecting the fuselage from heating is developed. Numerical simulations were conducted using the Ansys CFX software employed for solving gas dynamics problems. A comparison of the conducted calculations with those obtained in a field experiment was carried out. It was found that the propagation of a jet stream and the temperature spot of fuselage heating correspond to the experimental data with a sufficiently high accuracy under the accepted simplifications of the computational geometric model and the accepted boundary conditions of the computational mathematical model. 

For citations:

Degtyarev A.A., Molchanov A.V. Verification of calculations for heating the fuselage of an unmanned aerial vehicle with a jet stream of a turbojet engine. Journal of «Almaz – Antey» Air and Space Defence Corporation. 2020;(3):69-76.


Modern trends in implementation and develop­ment of software-based computational methods for solving the problems related to gas dynamics allow minimisation of the aircraft design stage, from the statement of work (SOW) to end product, including reduction of the amount of full-scale tests to verify aerodynamic characteristics (ADC).

This paper presents a set of computations based on small-sized unmanned aerial vehicle (UAV) and intended to evaluate the convergence of numerical simulation and a full-scale experi­ment. The purpose of the study is to create an ite­ration process showing how geometrical parame­ters of UAV elements change during numerical simulation in order to reduce the number of full- scale experiments. The main task is to assess the impact of the turbojet engine (TJE) jet stream on the surface of the UAV in a dense layout and to find a solution to protect the UAV against this im­pact, with the minimum reduction of UAV ADC.

Task description

The task is to provide a qualitative assessment of the temperature spot propagation area and to ob­tain numerical values of the UAV fuselage heating temperature. The development of a computational method is based on possible reconstruction of outside conditions such as temperature and low velocity of ram airflow during a full-scale experi­ment, i. e. with the UAV placed in a fixed position. Thus, verification of the computation results will allow to use the developed computational method for assessing the impact of the jet stream on the UAV skin for various ram airflow velocities. Be­sides, the developed computational method will allow to find an engineering solution to reduce the fuselage heating temperature in order to pre­vent degradation of its strength properties and destruction.

The object under study is the mock-up of a small-sized UAV fuselage replicating the theo­retical contour under study, as well as the JetCat P220-RXi TJE with known characteristics [5]. General view of the object under study is shown in Figure 1.

Fig. 1. General view of UAV area under study

Simulation problem statement

Aerodynamic forces and moments based on the working medium (gas) flow passing around a solid body can be determined by employing full-scale wind-tunnel experiments and numerical methods. The flow of viscous compressible gas can be de­scribed by a system of the Navier - Stokes equa­tions (2) supplemented by the equation of conti­nuity (1) and the equation of energy (3) [1].

Equation of continuity:


Moment equations:

where  -    stress tensor; δ – Kronecker symbol.

Equation of energy:

where -   total enthalpy; expression  · SM characterises work of external forces; SM, SE – source terms for impulse and energy, respectively.

To close the system of equations, the equation of ideal compressible gas state is used:

where: Δ – Laplace operator; - Hamilton operator; - tensor product; w– molecular weight of gas; p – gas pressure; ρ – gas density; μ – coefficient of gas dynamic viscosity; λ – gas thermal conductivity coefficient; h – enthalpy;  - oncoming flow velocity vector; t – time; R0 – universal gas constant.

Aerodynamic forces and moments affecting an aircraft can be represented as follows [3]:

where:   Fx,y,z - projections of forces affecting UAV on body axes; Mx,y,z - projections of moments of forces affecting UAV on body axes;Cx,y,z - – aerodynamic force coefficients; mx,y,z - aerodynamic
moment coefficients;
  -  ram air pressure; V – ram airflow velocity; S – wing area; l – wing span; bA – mean aerodynamic wing chord.

Most of numerical methods for solving the problems related to gas dynamics are based on the finite volume method, i. e. the computational domain is divided in a finite number of subdo­mains (cells), and differential equations are to be solved in each of the elementary units with regard to boundary conditions.

In order to determine the ADC at the UAV design stage, we used the Ansys CFX software [4] that allows to simulate various hydrodynamic and aerodynamic problems using a wide range of available turbulence models.

Turbulence is assumed based on the Menter’s model (Shear Stress Transport - SST), which combines models к-ω and к-ε with optional auto­matic transition between the models, depending on the gas flow area [2] (where к - turbulence kinetic energy, ε - dissipation rate, ω - vorticity). Giving preference to the SST model is caused by a trade-off of the computation accuracy and the time required to conduct a numerical simulation.

The application of a more accurate turbu­lence model, for instance, a large eddy simula­tion model (LES methods) or a detached eddy simulation (DES) method, is constrained by grid dimensions and is not feasible for this research as it takes more computational power and compu­ting time in case the UAV geometry is subject to iteration variation.

To reduce grid dimensions and computing time, a model is cut by the symmetry plane, with the relevant boundary condition added to the com­putational model. The grid dimension is 7.6 mln cells with 10 prismatic layers and parameter Y+ < 2 (Fig. 2).

Fig. 2. Computational grid with prismatic layers in the TJE area

To develop a mathematical model, we use the technique for computing UAV ADC related to variation of ram airflow velocity (V, m/s), angle of attack (α, °), and angle of slip (β, °). The air at the temperature of 25 °C and density of ρ = 1.18 kg/m3 is selected as a medium; the ram airflow velocity varies from zero to the maximum flight velocity value. A gas mixture consisting of nitrogen and carbon dioxide (70 % N2, 30 % CO2) with probable compete fuel combustion is used as an operating fluid at the TJE nozzle exit. The known values [5] of mass flow rate (0.45 kg/s), nozzle exit gas velocity (1760 km/h used as the reference value for computation) and nozzle exit gas temperature (750 °С) are selected as boundary conditions for the TJE. The heat is transferred from the efflux to the fuselage surface with the help of the convection model without heat absorp­tion by the surface.

Computation results

As a result, we can represent the distribution of the TJE jet stream heat wake over the UAV fuse­lage surface. The maximum rated UAV surface temperature is 157 °C (430 K); the heat wake dis­tribution is shown in Figure 3.


Fig. 3. Temperature distribution over fuselage surface

Besides, as the ram airflow velocity increases, the jet stream is attracted to the fuselage surface, resulting in fuselage temperature rise. The tem­perature variation is shown in Figure 4.

Fig. 4. Temperature distribution over fuselage surface

To protect the fuselage surface from the thermal effect caused by the TJE jet stream, we developed a thermal protection shield (Fig. 5), the sizes and position of which were determined iteratively.

Fig. 5. General view of the UAV area under study with thermal protection shield

The development of a thermal protection shield resulted in a considerable drop in the heat­ing temperature bot at zero velocity of ram airflow and at increased velocity. The maximum tempera­ture reached 63 °C (336 K). The computation re­sult is shown in Figures 6 and 7.

Fig. 6. Temperature distribution over fuselage surface at ram airflow velocity V = 1 m/s


Fig. 7. Temperature distribution over fuselage surface at ram airflow velocity V = 70 m/s

Herewith, a thermal protection shield on the UAV under study does not affect lift force coefficient Cya within the entire range of operating angles of attack, slightly changes the longitudinal stability (Fig. 8, 9), and reduces the maximum rated velocity by no more than 5 km/h.

Experiment results

The full-scale experiment intended to prove the results of fuselage heating computations at zero ram airflow velocity without a thermal protection shield shows the heating temperature numeric values that almost reach the rated ones, as well as represents the behaviour of fuselage temperature variations over its area. The experiment result is shown in Figure 10.

Fig. 10. Temperature distribution over fuselage surface during experiment

According to specifications, degradation of the composite material’s strength properties begins at 80 °С, and material destruction occurs at 120 °C.

The maximum temperature measured during the experiment was 121 °C followed by destruc­tion (melting) of the composite material binder as shown in Figure 11.

Fig. 11. Boiling of binding composite material and bulging of paint coating

Taking into account low ambient temper­ature, which is minus 6 °C in comparison with the rated value of 25 °C (Δ = 31 °C), the resulted temperature of 121 °С can be normalized to the rated value and reach 152 °C.


Computations performed in the Ansys CFX soft­ware environment allow to obtain the model showing the distribution of the TJE jet stream for the aircraft in a dense layout with the fuselage, as well as to develop several model-based variants of thermal protection. One of the variants was proposed.

At the same time, we managed to minimize an increase in the drag force and variation of UAV longitudinal stability caused by installation of a thermal protection shield. The sizes and position of the latter were selected iteratively until the tole­rable fuselage heating temperature was reached and the impact on the UAV ADC was minimized.

In development of the computational mo­del, parameters of fuselage surface roughness and microroughness naturally formed during manu­facturing were not considered, but, despite these assumptions, the computation results prove high convergence with the experimental data. There­fore, this model can be used in aircraft design, including aircraft layout.


Conducted computations and obtained experimen­tal data prove the implemented computation method suitable for analysing the impact of the turbojet stream on the UAV surface at various flight speeds and altitudes with a considerably high degree of convergence. The difference between the calculated and experimental temperature values is 5 °С, or less than 5 %.

Such an approach allows to minimise the end product design stage, skipping milestones for obtaining experiment results, thereby reducing material losses in case of failed experiments.


1. Ansys CFX-Solver Theory Guide. Release 2019 R3. Canonsburg: ANSYS, Inc., 2019. 350 p.

2. Menter F.R. Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applica-tions // AIAA Journal. 1994. Vol. 32. № 8.

3. Бюшгенс Г.С., Студнев Р.В. Аэродинамика самолета. Динамика продольного и бокового движения. М.: Машиностроение, 1979. 352 с.

4. Пугачев П.В., Свобода Д.Г., Жарковский А.А. Расчет вязкого течения в лопастных гидромашинах с использованием пакета Ansys CFX. СПб: Изд-во Политехн. ун-та, 2016. 120 с.

5. Каталог «JetCat». 2019. URL: (дата обращения: 27.05.2020).

About the Authors

A. A. Degtyarev
Central Scientific Research Institute of Chemistry and Mechanics
Russian Federation

Degtyarev Alexander Alexandrovich – Cand. Sci. (Phys.-Math.), Head of the Special Design Bureau, Deputy General Director. Research interests: dynamics of complex technical systems.


A. V. Molchanov
Central Scientific Research Institute of Chemistry and Mechanics
Russian Federation

Molchanov Andrey Viktorovich – Researcher, Department of Control Systems, Special Design Bureau. Research interests: aerodynamics, mechanics of liquids and gases, automatic control systems, aircraft design.



For citations:

Degtyarev A.A., Molchanov A.V. Verification of calculations for heating the fuselage of an unmanned aerial vehicle with a jet stream of a turbojet engine. Journal of «Almaz – Antey» Air and Space Defence Corporation. 2020;(3):69-76.

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ISSN 2542-0542 (Print)