# Numerical Analysis and Verification of the Gas Jet from Aircraft Engines Impacting a Jet Blast Deflector

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## Abstract

The process of the gas jet from aircraft engines impacting a jet blast deflector is not only a complex fluid–solid coupling problem that is not easy to compute, but also a safety issue that seriously interferes with flight deck environment. The computational fluid dynamics (CFD) method is used to simulate numerically the impact effect of gas jet from aircraft engines on a jet blast deflector by using the Reynolds-averaged Navier-Stokes (RANS) equations and turbulence models. First of all, during the pre-processing of numerical computation, a sub-domains hybrid meshing scheme is adopted to reduce mesh number and improve mesh quality. Then, four different turbulence models including shear-stress transport (SST) *k-w*, standard *k-w*, standard *k-ε* and Reynolds stress model (RSM) are used to compare and verify the correctness of numerical methods for gas jet from a single aircraft engine. The predicted values are in good agreement with the experimental data, and the distribution and regularity of shock wave, velocity, pressure and temperature of a single aircraft engine are got. The results show that SST *k*-*w* turbulence model is more suitable for the numerical simulation of compressible viscous gas jet with high prediction accuracy. Finally, the impact effect of gas jet from two aircraft engines on a jet blast deflector is analyzed based on the above numerical method, not only the flow parameters of gas jet and the interaction regularity between gas jet and the jet blast deflector are got, but also the thermal shock properties and dynamic impact characteristics of gas jet impacting the jet blast deflector are got. So the dangerous activity area of crew and equipments on the flight deck can be predicted qualitatively and quantitatively. The proposed research explores out a correct numerical method for the fluid–solid interaction during the impact process of supersonic gas jet, which provides an effective technical support for design, thermal ablation and structural damage analysis of a new jet blast deflector.

## Keywords

Aircraft engine Gas jet Computational fluid dynamics Jet blast deflector Impact effect## 1 Introduction

The high-temperature and high-speed gas jet from aircraft engines is in an over expansion state when the aircraft engines are in full afterburner state to takeoff, which has a serious impact on the flight deck due to the complicated physical phenomena such as shock wave, noise and gas tempering caused by the interaction between gas jet and the jet blast deflector [1, 2]. The gas jet from aircraft engines has basic characteristics of supersonic flow and complex wave system. When the gas jet impacts a jet blast deflector, the thermal shock and dynamic impact will lead to thermal ablation and structure damage. The safety limits for pressure and temperature of the gas jet need to be considered due to the relatively small flight deck for carrying and taking off. Therefore, accurate analysis and control of the gas jet from aircraft engines are key steps for the design and layout of new jet blast deflectors.

At present, domestic and foreign scholars mainly use experimental method, analytical method and numerical method to carry out impact effect research of gas jet. The experimental method mainly uses a small scale model as the experimental object based on the similarity principle. The ideal results can be obtained by testing techniques such as PIV and LDV. However, it is difficult to obtain accurate data in the case of complicated geometry and the contradiction between geometric similarity and dynamic similarity. Furthermore, the experimental method has the problem of long cycle and high cost, which is also easy to be affected by scale effect, external interference and other factors. It is difficult to reflect the true situation of gas jet [3, 4]. At present, the widely used analytical method like one-dimensional/quasi one-dimensional is to establish a physical model and a mathematical model of gas jet by simplifying and assuming the limits of solid boundary. It ignores turbulent effect, flow viscosity and wall interference of gas jet, which makes a large deviation between computational results and experimental data [5, 6, 7]. In contrast, using a numerical method based on RANS equations to compute the impact effect of gas jet is more effective, and more detailed flow field information can be obtained [8].

Because supersonic gas jet has the characteristics of high temperature, high pressure and high speed, there are two main difficulties in numerical computation. One is that the numerical computation of supersonic gas jet with complicated geometric model and flow characteristics is sensitive to initial field. The initial deviation from actual physical field will cause difficulty of convergence, even divergence at the beginning of computation. The other is that a high-precision discrete format, appropriate turbulence model and boundary conditions are needed to capture shock wave and expansion wave of the flow field, which leads to a long computation time and large memory usage. Therefore, domestic and foreign scholars usually use two-dimensional numerical simulation model to carry out the research [9, 10, 11]. But the flow information of two-dimensional numerical results is limited, which is unable to analyze the anisotropic impact effect of gas jet on a jet blast deflector. Three-dimensional numerical model was used by some scholars to simulate the impact process of gas jet, but the thermal shock effect of gas jet was not considered [12, 13]. According to the geometry of a single aircraft engine and the characteristics of gas jet, numerical simulation of the gas jet is made combined with different turbulence models. The high-precision results with SST *k*-*w* turbulence model are analyzed and verified. Then a scheme of sub-domains hybrid mesh is designed based on three-dimensional numerical model with coupling aircraft engines and a jet blast deflector. The parameters such as shock wave, velocity, pressure and temperature are got, and impact effect of the gas jet from aircraft engines on a jet blast deflector and the surrounding environment is analyzed.

## 2 Numerical Computation Model

### 2.1 Mathematical Model

*ρ*is the gas density,

*t*is the computation time,

*u*

_{i}and

*u*

_{j}are velocities in the Cartesian coordinate system, \(\overline{{u^{\prime}_{i} u^{\prime}_{j} }}\) is Reynolds stresses,

*μ*is the molecular viscosity,

*p*is the static pressure,

*f*

_{i}is the unit mass force,

*δ*

_{ij}is Kronecker delta,

*h*

_{i}is the static enthalpy,

*H*is the total enthalpy,

*J*

_{ij}is the diffusion mass flux,

*S*

_{a}is the external heat source caused by surface reaction and radiation,

*τ*

_{ij}is the viscous stress tensor,

*q*

_{j}is the heat flux.

*k*-

*ε*,

*k*-

*w*and RSM turbulence models are used for turbulence closure, which express \(- \rho \overline{{u^{\prime}_{i} u^{\prime}_{j} }}\)with low-order correlative term or time-average expression [14, 15]. The

*k*-

*ε*and

*k*-

*w*models based on isotropic turbulence assume that the change rate of Reynolds stress and time-averaged velocity field is linear. Moreover, the concept of eddy viscosity or turbulent viscosity is introduced, so there is a big error in the computation of inhomogeneous turbulence like swirling. SST

*k*-

*w*model has different turbulence constants, which not only increases a horizontal dissipation derivative but also takes into account the transport process of turbulent shear stress in the definition of turbulent viscosity compared with standard

*k*-

*w*model. These features make SST

*k*-

*w*model have a wider applicable scope such as the flow with adverse pressure gradient, aerofoil, transonic shock wave, etc. [16]. RSM should have better potential to predict the key features of rotating flows than other models in theory as it considers the convection and diffuse effect of Reynolds stresses based on turbulence anisotropy, but its precision is limited to closed form so that RSM does not show the advantages in numerical computation of gas jet [17]. According to the Boussinesq’s assumption, The SST

*k*-

*w*turbulence model can be written in Cartesian tensor form as

*k*is the turbulence kinetic energy,

*w*is the specific dissipation rate,

*Γ*

_{k}is the effective diffusivity of

*k*,

*Γ*

_{w}is the effective diffusivity of

*w*,

*G*

_{k}is the generation of

*k*due to mean velocity gradients,

*Y*

_{k}is the dissipation of\(k\)due to turbulence,

*Y*

_{w}is the dissipation of\(w\)due to turbulence,

*D*

_{w}is the cross-diffusion term.

*σ*

_{k}is the turbulent Prandtl number for

*k*,

*σ*

_{w}is the turbulent Prandtl number for

*w*,

*μ*

_{t}is the turbulent viscosity,

*S*is the strain rate magnitude,

*F*

_{1}is the blending function,

*β*

^{*},

*β*

_{i},

*σ*

_{w,2}are constants.

- (1)
Pressure inlet: on the inlet of twin engines, total pressure (371425 Pa) and total temperature (2200 K) based on Boussinesq’s assumption are imposed with considering the influence of wind speed. Moreover, on the section outside the outlet of engine nozzles, environmental pressure (101325 Pa) and environmental temperature (300 K) are imposed.

- (2)
Pressure outlet: on the radial section of the computational domain and the axial section that 25 m away from the outlet of engine nozzles, static pressure distribution (101325 Pa) and environmental temperature (300 K) are imposed.

- (3)
Wall boundary: on the double engine nozzles, jet blast deflector and flight deck, no slip wall is imposed with considering viscous effect, and heat transfer coefficient is given.

The definition of the coordinate system is that *X* axis points downstream, *Y* axis points upwards and *Z* axis accords with the right hand principle. The coordinate origin is the intersection of engine nozzles’ outlet section, flight deck and starboard side of computational domain.

### 2.2 Computational Model

*X*axis of 5 m,

*Y*axis of 0 m, and

*Z*axis from 13.497 m to 22.495 m.

## 3 Mesh Generation and Numerical Method

### 3.1 Mesh Generation Scheme

### 3.2 Numerical Computation Method

The mathematical model of gas jet is a series of nonlinear equations, which employs a cell-centered finite volume method that allows the adoption of computational elements with arbitrary polyhedral shape. The flow equation, turbulent kinetic energy equation and turbulent dissipation rate equation are discretized with second-order upwind scheme. The coupled implicit algorithm is used to solve the continuity equation, momentum equation and energy equation synchronously during the discrete process. The discrete algebraic equations are solved by Gauss-Seidel method [23]. According to the linear stability theory, Courant number is adjusted from 0.5 to 4 continuously with iterative number increasing. Algebraic Multi-Grid (AMG) method is used to accelerate the speed of convergence, and the convergence criterion is set as 0.0001.

The supercomputer in National University of Defense Technology was used to complete the numerical simulation due to large size computational model, too much mesh and large memory occupied by coupled implicit algorithm. A total of 9 nodes including 72 cores were used in each computational process, which took 9 hours to get each converged result.

## 4 Numerical Computation Results and Analysis

### 4.1 Verification of Numerical Method for the Gas Jet from an Aircraft Engine

*k*-

*w*, standard

*k*-

*ε*, standard

*k*-

*w*and RSM are used to solve numerically impact effect of the gas jet from a scramjet nozzle in full afterburner state. The generated sub-domains hybrid mesh is shown in Figure 5. The comparison of computational results with available experimental data is shown in Figure 6, which shows the velocity values at different distances from the axial center of single engine nozzle’s outlet section. It can be seen that the computational results are in good agreement with the experimental data. The relative error of the computational results increases with the distance increasing, and the computational results are slightly larger than the experimental data. The predicted values of SST

*k*-

*w*model are much closer to the experimental data by comparison, whose maximum error is 5.55%. While the maximum error of standard

*k*-

*w*, standard

*k*-

*ε*and RSM model are 7.25%, 8.63% and 8.94% respectively. It shows that the numerical method used in this paper is suitable for solving impact effect of the gas jet from an aircraft engine, and the SST

*k*-

*w*turbulence model can obtain higher prediction accuracy.

### 4.2 Impact Characteristics Analysis of Gas Jet Based on Fluid-Solid Coupling Effect

*X*axis of 146077 N and −

*Y*axis of 411957 N, which causes a torque of 562597 Nm around the rod fulcrum on back of the jet blast deflector. The high-temperature areas mainly concentrate on upward 2/3 part of the jet blast deflector. The highest temperature areas are facing the twin scramjet nozzles, which produce thermal shock effect of above 1400 K, as shown in Figure 18. In addition, due to block effect of the jet blast deflector on gas jet, the temperature of the flight deck in front of the jet blast deflector is relatively high, which will cause a threat to crew and equipments on the flight deck. So it is necessary to determine dangerous areas around the jet blast deflector.

*X*axis, including center of left engine (Point 1), midpoint of center line between twin engines (Point 2) and isometric point of left engine (Point 3). Due to the existence of shock wave, the initial stage of Point 1’s static temperature and velocity is a decay pulse curve. With the distance from scramjet nozzle increasing, the static temperature and velocity decay slowly. After the jet blast deflector, static temperature and velocity drop to the same parameters with surrounding environment. The temperature and velocity of Point 2 and Point 3 only increase suddenly in front of the jet blast deflector, which are the same parameters with surrounding environment in other areas. Due to interaction of the gas jet from twin engines on the jet blast deflector, the temperature and velocity of Point 2 increase faster than that of Point 3.

*X*axis from 0 m to 16.2 m and

*Z*axis from 6.8 m to 29.2 m.

*X*axis from 0 m to 18.9 m and

*Z*axis from 4.6 m to 29.6 m.

In short, the jet blast deflector can well deflect high-speed, high-pressure and high-temperature gas jet, and main harm of the gas jet from twin engines on crew and equipments on the flight deck is greatly weakened. According to the dangerous area of high-temperature and high-speed gas jet, it is recommended to determine the dangerous area of gas jet as *X* axis from 0 m to 19.8 m and *Z* axis from 4.0 m to 30.2 m based on the safety factor of 5%. It can ensure that crew and equipments outside this rectangular area on the flight deck will not be affected by the gas jet.

## 5 Conclusions

- (1)
In the pre-processing of numerical simulation of the supersonic gas jet from aircraft engines, the sub-domains hybrid meshing scheme applied can adapt to the complex geometry of the jet blast deflector, not only reducing the mesh number, but also improving the ability to capture complex wave system interference with higher mesh accuracy.

- (2)
In numerical computation of the supersonic gas jet from a single aircraft engine, the good agreement between computational results with four different turbulence models and experimental data validates the correctness of the numerical method and shows that SST

*k*-*w*turbulence model is more suitable for the numerical simulation of compressible viscous gas jet with high prediction accuracy. - (3)
The formation and evolution of shock wave and the parameters such as velocity, pressure and temperature are got through the numerical analysis of the gas jet from a single aircraft engine, which provides a theoretical basis for layout of the jet blast deflector.

- (4)
The numerical method of fluid-solid coupling problem that the gas jet from aircraft engines impacting a jet blast deflector is explored out with CFD technique. The dangerous activity area of crew and equipments on the flight deck is predicted qualitatively and quantitatively based on the thermal shock properties and dynamic impact characteristics.

## Notes

### Authors’ Contributions

F-DG was in charge of the whole trial; F-DG wrote the manuscript; D-XW, H-DW and M-MJ assisted with sampling and laboratory analyses. All authors read and approved the final manuscript.

### Authors’ Information

Fu-Dong Gao, born in 1982, is currently a lecturer at *Department of Carrier Aviation Security and Station Management, Naval Aeronautical University, China*. He received his PhD degree from *National University of Defense Technology, China*, in 2012. His research interests include computational fluid dynamics, design and performance prediction of the fluid machinery.

De-Xin Wang, born in 1968, is currently an associate professor at *Department of Carrier Aviation Security and Station Management, Naval Aeronautical University, China*. He received his master degree on electrical engineering and automation from *Beihang University, China*, in 1993.

Hai-Dong Wang, born in 1974, is currently an associate professor at *Department of Carrier Aviation Security and Station Management, Naval Aeronautical University, China*.

Ming-Ming Jia, born in 1982, is currently a lecturer at *Department of Carrier Aviation Security and Station Management, Naval Aeronautical University, China*.

### Competing Interests

The authors declare that they have no competing interests.

### Funding

Supported by National Natural Science Foundation of China (Grant No. 51505491), and Shandong Provincial Natural Science Foundation of China (Grant No. ZR2014EEP019).

### Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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