International Journal of Antennas and Propagation

Volume 2018, Article ID 5478580, 14 pages

https://doi.org/10.1155/2018/5478580

## Backward Scattering Characteristics of a Reentry Vehicle Enveloped by a Hypersonic Flow Field

^{1}School of Physics and Optoelectronic Engineering, Xidian University, Xi’an 710071, China^{2}School of Electrical Engineering, Xidian University, Xi’an 710071, China

Correspondence should be addressed to Jiajie Wang; nc.ude.naidix@eijaijgnaw

Received 13 April 2018; Accepted 8 July 2018; Published 19 August 2018

Academic Editor: Giuseppe Castaldi

Copyright © 2018 Haoyu Sun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The hypersonic flow field around a reentry vehicle has a significant influence on the ground-vehicle communication as well as on the detection and recognition of the reentry vehicle. Backward scattering characteristics of a reentry vehicle enveloped by a hypersonic flow field are analyzed using a high-order auxiliary differential equation finite difference time-domain (ADE-FDTD) method in this paper. Flow field parameters, including electron density, neutral particle density, and temperature, are obtained by solving the Navier-Stokes (NS) equations numerically. According to the flow field parameters, distributions of the plasma frequency and the collision frequency are then derived. Based on a validity of the physical model and the high-order ADE-FDTD method, backward radar cross sections (RCSs) of a perfect electrical conductor (PEC) sphere enveloped by a hypersonic flow field under different Mach numbers, heights, and incident angles of the electromagnetic (EM) wave are then investigated. Numerical results show that the incident angle of the EM wave exerts noticeable effects on the backward RCS, which is due to an inhomogeneous distribution of the plasma. The flight height and Mach number have significant influences on the distribution of the plasma that they play an important role in the variation of the RCSs. The results presented in this paper provide useful reference data for practical tests in ballistic range or in the high-frequency plasma wind tunnels, where a sphere target is usually used due to its simple shape.

#### 1. Introduction

The development of hypersonic reentry vehicles in the near space, such as shuttles, rockets, and missiles, attracts increasing attention in recent years due to their significant strategic position. When a hypersonic vehicle reenters the atmosphere, severe friction between the aircraft and the ambient air results in a dramatic increase in the local temperature and pressure, which leads to intensified air ionization, and a layer of plasma flow is generated around the reentry vehicle [1]. The plasma flow, which consists of numerous free electrons, ions, and neutral particles, is nonmagnetic, low-temperature, weakly ionized, and quasi-neutral (i.e., electricity neutral on macroscopic-length scales) [2, 3]. It greatly affects the transmission of electromagnetic (EM) waves that it has a very strong interference on the communication between the reentry aircraft and the ground station; it even leads to blackout in certain conditions [4, 5]. Moreover, the reflection, refraction, and absorption of EM waves caused by the plasma sheath or wake change the radar scattering characteristics of the hypersonic vehicle [6–9], which has a significant influence on the detection, tracking, and recognition of the target.

In the past decades, lots of studies have been carried out on the analysis of the formation of plasma flow around a hypersonic vehicle and their interactions with EM waves. Early in the 1960s, a series of hypersonic experiments were performed in the Radio Attenuation Measurements (RAM) program to gain a thorough knowledge of the plasma sheath properties and its effects on the communication systems of the reentry vehicle. Some techniques to alleviate communications blackout were developed [5]. Due to the expensive costs and poor repeatability of the reentry flight experiment, laboratory simulations of hypersonic plasma flows [10], for example, using ballistic range [11] or plasma wind tunnel [12], were developed that the field properties of plasma flow as well as their EM scattering characteristics can be determined [13]. So far, most of the efforts were devoted to the analysis of transmission, reflection, and attenuation of EM waves in the plasma sheath in order to alleviate the interruption of plasma on ground-vehicle communication and to find out an alternative approach to bridge the linkage during the blackout time [14–17]. Limited attention was paid to the analysis of the scattering properties of the vehicle enveloped by a hypersonic plasma flow, which plays an essential role in the detection, tracking, and identification of hypersonic targets.

Due to the lack of experimental data on the plasma flow and the restriction of computing ability, in most of the previous literature, plasma flows with certain electron density profiles were assumed. And the analysis of the scattering by the plasma flow was implemented using approximated approaches, which permit to predict the plasma effects qualitatively. Backscattering cross sections and differential cross sections were calculated for a conducting cylinder coated with an anisotropic and inhomogeneous plasma sheath by Rusch and Yeh [6], where a parabolic electron density profile is chosen such that it approximates the actual profile of the plasma sheath encountered for a reentry vehicle. A spherical model uniformly coated by plasma has been used to calculate the backward cross section of a plasma-clad sphere as a function of the normalized plasma thickness [18]. The scattering characteristics of a blunt cone covered by an inhomogeneous plasma sheath are investigated from S-band to Ku-band frequencies by using the physical optics (PO) method [19], where both the collision frequency and the plasma frequency are assumed to be sine distribution.

With the rapid development of high-performance computers, various efficient algorithms were proposed that they enable us to solve the Navier-Stokes (NS) equations in the computational fluid dynamics (CFD) and the Maxwell equations in the computational electromagnetics (CEM) numerically. EM wave scattering characteristics in time-varying and spatially nonuniform plasma sheaths was investigated by Chen et al. [20] using the finite-difference time-domain (FDTD) method. Nevertheless, the collision frequency of the plasma sheath in [20] was calculated empirically and the variation of RCS is only summarized at the L and S wave bands. RCSs of a 10 cm diameter and 30 cm height metal cone with and without plasma were studied by Chung [21] for the S band and X band using FDTD. However, the simulation parameters were not chosen strictly and a simplified physical model was applied that limited its application in practical cases. Based on the hypersonic flow field data obtained in the repeatable laboratory simulations using ballistic range [11] or plasma wind tunnel [12], more practical physical models of hypersonic flow field can be established using the CFD technique [17]. By adopting a CFD tool to derive the distributions of electron density and atmospheric temperature around the targets, backscattering RCS of a hypersonic perfect electrical conductor (PEC) cone with a plasma sheath were investigated by Qian et al. [22, 23] using the volume-surface integral equation method incorporated with the multilevel fast multipole algorithm (MLFMA). However, only the properties at certain frequencies in the L-band were predicted. To reveal the effects of hypersonic flow field on the scattering characteristics of a reentry vehicle in wide wave bands, backward RCSs of a reentry vehicle enveloped by a hypersonic flow field are analyzed using a high-order auxiliary differential equation finite-difference time-domain (ADE-FDTD) method in this paper, where the hypersonic flow field is established by solving the NS equations numerically under different flight conditions.

The rest of the paper is organized as follows. In Section 2, descriptions of the modeling of a hypersonic flow field and the high-order ADE-FDTD method are briefly revisited. Numerical analysis of EM scattering properties of a PEC sphere enveloped by a hypersonic flow field under different flight conditions is presented in Section 3. Section 4 serves as a conclusion.

#### 2. Method and Theoretical Treatments

##### 2.1. Modeling of the Hypersonic Flow Field

Without any assumption on the distributions of the plasma parameters, the flow field around a hypersonic vehicle is established by numerically solving the NS equations in this paper. The flow field around the hypersonic vehicle is thermochemical nonequilibrium, governed by NS equations with chemical reaction source terms, accounting for the mass, momentum, and energy conservation laws. The Park two-temperature chemical-kinetic model [24] is applied in our simulations, where one temperature is assumed to characterize the translational and rotational energies of neutral, and another temperature for the molecular vibrational, electron translational, and electronic excitation energies. Concerning the chemistry model, the seven-species air model is applied, where the gas in the flow field is chemically regarded as a mixture of partially ionized air with seven species (, , , , , , and ).

The 3D nondimensional Navier-Stokes (NS) equations that include thermochemical nonequilibrium-related terms can be written in the following form:

The vector of conserved quantity is described by where and are the density of species and the density of mixed gas, respectively. , , and denote velocity components in , , and directions. and are the total internal energy per unit mass and vibrational energy per unit mass, respectively.

The inviscid flux vectors , , and in , , and directions are given, respectively, as where and are the pressure and enthalpy.

The viscous flux vectors , , and in , , and directions are expressed, respectively, as where is the Lewis number, is the Prandtl number, and , , and are the heat conductivity coefficient, specific heat capacity, and species mass fraction, respectively. represent the components of the stress tensor, denote the translational-rotational heat in , , and directions, and describe the vibrational heat flux terms in , , and directions.

The source vector has the following form in Park’s two-temperature model: where is the individual species mass formation rate and is the vibrational source term.

The NS equations are solved by the Advection Upstream Splitting Method by Pressure-Based Weight function [25] (AUSMPW+) based on the finite volume method. The diffusion terms are the central difference. The implicit lower-upper symmetric Gauss-Seidel relaxation [26] (LU-SGS) is taken as the time marching algorithm.

In the 1960s, a series of hypersonic experiments were performed to study the communications blackout in the RAM program. Among these flights, a large amount of data was collected during the reentry of the RAM-C II flight. The RAM-C II vehicle was a spherically blunted cone with a 9-degree cone half-angle, 0.1524 m nose radius, and a total length of 1.3 m, whose geometry is shown in Figure 1(a).