Numerical Investigation on Aerodynamic Characteristics of an Active Jets-Matrix Serving as Pitch Control Surface

Abstract

To facilitate future Hypersonic Flight Vehicle (HFV) implementation with high maneuverability throughout its reentry trajectory, an Active Jets-Matrix (AJM) is designed to serve as the flapless pitch control surface. The AJM consists of four control groups composed in total of 48 supersonic nozzles. The AJM aims to utilize the jet flow-interaction-induced additional control moment to improve the control efficiency during atmospheric entry. A comparative research method is employed to study the eight simulation cases for three different HFV configurations (baseline, mechanical control surface with 30° deflection, and the AJM configuration) and two AJM control moment adjustment strategies (nozzle chamber pressure regulation and discretized nozzle group on–off control). A conventional in-house computational fluid dynamics (CFD) solver with the two-equation SST turbulence model is employed to undertake the simulation tasks. Simulation results indicate that: (a) only the AJM configuration is capable of trimming the HFV in pitch channel; (b) nonlinearity exists between the augmentation moment and the specific control variable from respective adjustment strategies; (c) the chamber pressure regulation strategy bears higher overall efficiency, while the discretized control strategy induces more intense local jet-flow interaction. With a maximum control moment augmentation of 1.58, the AJM presents itself as a competitive candidate for future HFV flapless control methods.

1. Introduction

A conventional flight control surface adjusts its control force output by altering the surface aerodynamic force through changes in geometry and adaption of the external flow on the new curvature [1]. However, conventional geometry-varying control surfaces rely excessively on external flow properties. If the freestream lacks sufficient density or dynamic pressure, i.e., at a high altitude or large angle of attack (AoA), such a control surface will experience a significant control efficiency drop. In addition, a mechanical control surface with moving parts requires more maintenance effort and additional space inside the wing for actuators. The gaps between the moving and static components will also increase the vehicle’s radar signature. All these characteristics stand against the requirements of future flight vehicles. In contrast, a flapless flight control system is capable of overcoming such drawbacks through the removal of geometrically changing parts. It can also smooth the surface of the vehicle and simplify the trailing edge design. In this study, an Active Jets-Matrix-(AJM)-based concept of the flapless flight control system is proposed to offer an alternative control method for HFVs, which need to maneuver in and out of the atmospheric environment.

To understand the significance and difference of the AJM concept compared with other flapless flight control systems, a literature review is provided herein regarding three primary categories of the existing flapless flight control systems, i.e., circulation control (CC), fluidic thrust vectoring (FTV), and direct thrust employment (Reaction Control System and lateral jet).

Circulation control is based on the Coanda Effect, which was patented by Coanda [2] and describes the tangential movement of secondary flow into the primary flow. The injected secondary flow then redirects the main flow and functions as a variable trailing edge. Englar [3] applied this effect to high-lift airfoil design starting in the 1970s. Englar and Huson [4] mounted their circulation-control-boosted airfoil onto a Grumman A6 aircraft and tested it in-flight in 1983. Various researchers continued with their work over the following decades. However, it was later considered that depending on the Coanda Effect for lift generation was not quite practical owing to high implementation difficulties and cost-inefficiency. Researchers turned to consider applying the Coanda Effect to build novel flight control systems [1]. Numerous research activities have been reported since then. The subsequent body of research on the DEMON flight vehicle [5,6,7,8,9,10] and the MAGMA aerial vehicle [1,11,12,13,14] presents remarkable examples regarding these research activities. DEMON successfully tested a subsonic CC trailing edge control method in a wind tunnel as reported by Crowther et al. [9]. Though the scheduled flight test in 2009 was interrupted by poor weather conditions [10], roll channel CC control was finally tested inflight in 2010 [15]. Recently, MAGMA from BAE systems completed a roll channel fluidic controlled flight in 2019 with supersonic CC units [16]. Meanwhile, SACCON is also under development [17]. Other works include Santos UAV [18] and JAVA UAV from [19,20,21]. Ref. [1] summarized the flight-tested vehicles equipped with various kinds of CC units. Despite fruitful research and experimental efforts, the physical nature of the CC has restricted it to low-speed aircrafts, and researchers are still struggling to migrate it from subsonic to transonic flight vehicles [1].

Fluidic Thrust Vectoring is a group of thrust vector control methods based on secondary flow injection, which alters the primary flow direction and structure [22]. Relevant methods include the shock-vector control method, throat shifting, and counterflow. The shock-vector control method introduces the secondary fluid into the supersonic flow after the high-speed mainstream flows pass the nozzle throat, thus creating an oblique shock downstream of the nozzle throat and forcing the mainstream to make a turn after passing the shock. The resulting total thrust vector is therefore redirected. Related literature includes Wing et al. [23,24]. The throat shifting method distinguishes itself from shock-vector control by the injection of jet flow precisely at the nozzle throat, i.e., the original sonic plane. The injected flow will cause the sonic plane to be skewed compared with its initial orientation and subsequently the supersonic flow direction. Related research can be found in Deere et al. [25] and Miller et al. [26]. The concept of counterflow as a method of vectoring the thrust force from the nozzle could be explained as: the creation of a reverse-flowing secondary fluid layer adjacent to the primary flow by vacuum suction and the subsequent establishment of a shear layer between the flows which entrains mass. The asymmetric creation of this secondary flow will bend the primary jet towards it and therefore change the direction of the thrust vector. Strykowski and Krothapalli [27] put forward this concept in 1993 and provided first-hand experimental results showing that the method could at least achieve a continuous vectoring range of 0–20°. A similar study was published by Flamm [28]. The JAVA and DEMON UAVs are also implemented with FTV using tangential-injected flows [1]. The MAGMA demonstrative flight vehicle employed FTV with normal secondary flow injection to realize pitch control in its 2019 flight test. In the same paper, Shearwood et al. [16] also confirmed the possibility of a full three-axis fluidic flight control system involving FTV, CC, and wingtip reaction jet for MAGMA using MATLAB Simulink. Other studies concerning fluidic thrust vectoring can be found in publications from Deere et al. [22,29,30], Waithe [31] and Chambers [32]. However, the FTV methods are used within the nozzles of the vehicle’s main engine, which means that the vehicle should have an engine at first. Secondly, the vectoring angle of the FTV is limited by the dimensions of the engine nozzle. Furthermore, the control force from FTV is always coupled with the main thrust. All these characteristics have bounded the application and control performance of FTV.

Under direct thrust employment, there is the reaction control system (RCS) and lateral jet (LJ). RCS is commonly used in launch vehicles and terminal stage payloads, such as satellites, space ships, and space shuttles. Due to the extremely thin atmosphere or near-vacuum environment it operates in, only direct thrust from RCS is of major use, while conventional control surface is not applicable [33]. Distinct from aerial control surfaces, the RCS is usually arranged in pairs to be able to provide pure torque to the flight vehicle, or pure translational maneuverability. As a rather matured technology used for spacecraft, recent research activities focus mostly on innovative control methods and advanced high-impulse propulsion systems [34,35,36], etc. Few have considered the optimization of RCS systems in an atmospheric environment, where the usage of the RCS direct thrust becomes expansive.

The lateral jet is used widely in advanced interceptor missiles for high maneuverability. The jets used here provide large lateral control moments to enable the missiles to make sharp turns. Brandeis and Gill [37,38] conducted experiments on missile configurations regarding LJ and investigated the augmentation effect induced by the jet-flow interaction. They also considered preserving and maximizing the amplification control effect through further interaction with fins. Graham et al. [39,40] completed numerical investigations of the above experiments. Wu et al. [41], Li et al. [42] and Jia et al. [43] also investigated the topic numerically based on experimental results from [37]. Among them, Jia et al. further studied the force augmentation effect of multiple lateral jets using exhaust gas as working fluid. Current LJ usually comes in the form of a group of solid rocket motors. By controlling the ignition state of each motor, the desired control thrust can be obtained. However, the single-fire and single-use nature of the LJ is its largest drawback.

In this study, the targeted wing-body Hypersonic Flight Vehicle (HFV) operates at an altitude of 60 km and reaches Mach 15 with a 20° angle of attack (AoA). The thin atmosphere and low freestream dynamic pressure have ruled out the utilization of conventional mechanical control surfaces and CC. Meanwhile, FTV cannot provide a sufficiently wide range of the vectoring angle. Straightforward employment of the RCS or LJ is probably quite inefficient at such dilemmatic altitude, while a hybrid system as equipped on space shuttles or X-37B is far too complicated [44]. A novel solution is thus necessary.

Therefore, an Active Jets-Matrix-based flapless flight control system is proposed to tackle the dilemma. The AJM consists of multiple supersonic nozzles and employs both direct thrust and jet-flow interaction-induced additional force for overall control force/moment generation. It functions as an RCS system in space and works efficiently with the help of interaction force at lower altitudes. The objective of this study is to investigate the feasibility and performance of the AJM concept in comparison with a conventional mechanical control surface. Different AJM working states and pitch control moment adjustment strategies are also researched and their performance compared.

Section 2 of the paper provides details of the configurations used in this study, which includes a baseline configuration, a mechanical control surface supported configuration and an AJM supported configuration. Relative performance and efficiency indicators in addition to eight comparative simulation cases design are also introduced in Section 2. Section 3 offers some details of the numerical method regarding the CFD solver and the corresponding validation case. Boundary conditions and the computational mesh can also be found in this section. Computational results of the AJM aerodynamic performance and knowledge gained are analyzed in Section 4. Section 5 summarizes all the key findings and inspirations from this study.

2. Configuration and Methodology

2.1. Hypersonic Flight Vehicle

To study the pitch control performance of the AJM, a hypersonic flight vehicle model has been selected. The model bears a wing-body baseline configuration. Its aerodynamic characteristics have already been analyzed during the design phase. Three kinds of configuration have been studied in this research: the baseline configuration, the mechanical control surface configuration, and the AJM configuration. The latter two configurations have taken relative pitch control measures.

2.1.1. Baseline Configuration

The baseline model (Figure 1) has no control surfaces. The origin is set at the nose tip and the x-axis travels through the symmetry plane ($xoy$) pointing backward. The y-axis is in the vertical direction pointing upward, while the z-axis represents spanwise direction. All geometric parameters mentioned in the paper are normalized against the HFV body length l. Therefore, the total HFV length is $l=1$ with a wingspan of $d=0.702$. The maximum height h of the vehicle is 0.124.

The center of gravity ($CG$) is located around ($x,y$) = (0.716, 0.035). The baseline configuration is not trimmed in the pitch channel under the studied flight condition (altitude of 60 km, $Ma$ = 15 and 20° AoA). The imbalanced pitch moment tends to raise its nose up. Therefore, a suitable pitch control surface is necessary to maintain the designed flight angle of attack.

2.1.2. Mechanical Control Surface Configuration

A set of conventional mechanical control surfaces in the form of two body flaps (see Figure 2) is designed for the HFV as the counterpart for comparison with the unconventional AJM. The hinge of the body flap is placed on the lower surface of the HFV. The center of the hinge rests at $z=0.112$ to the $xoy$ plane, 0.953 in x direction to the origin. The dimensions of the body flap are $0.033\times 0.105\times 0.003$. All edges are rounded off to 0.0015. The deflection angle is 30° downward.

2.2. Active Jets-Matrix Configuration

While current RCS and LJ both lay little emphasis on the jet-flow interaction effect, the AJM aims to effectively employ such additional “disturbance” to achieve the control objective with reduced direct thrust demand, and consequently lower jet mass amount. A straightforward inline distribution simply reduces the chance of free flow interaction with the downstream jets. Therefore, the current design employs a staggered distribution of the nozzles to avoid the hindrance effect of the nozzles in the front rows. Further optimization of the current AJM nozzle distribution is another interesting topic which will not be covered in this paper.

The AJM is placed at a similar location to the body flap. The HFV is equipped with two AJMs. Each AJM consists of 48 supersonic nozzles, i.e., 8 staggered rows with 6 nozzles each. The AJM nozzles are assumed to be installed vertically inside the HFV, which means the jet will be exhausted in the $-y$ direction.

The area expansion ratio (nozzle exit area $A_{j,e}$ over throat area $A_{j,t}$) of the nozzle is 46. The arrangement of the AJMs is shown in Figure 3. The geometric center of the AJM is 0.113 to the $xoy$-plane and 0.972 to the $xoz$-plane.

The distributed nozzle matrix delivers more flexibility for the precise control of the total control force, which is critical for Hypersonic Flight Vehicles. Moment adjustment of the AJM can be achieved through: total pressure regulation and discretized on–off control down to each AJM nozzle. Single nozzle control offers the highest adjustment accuracy, but requires too many valves and may exceed the HFV structural weight limit. Hence, the AJMs are grouped into 4 control sets, namely B1–B4 (see Figure 3). Each group consists of two rows of nozzles.

In this paper, performance analysis of total pressure regulation and different working groups from B1 to B4 have also been conducted.

2.3. AJM Parameter Design and Performance Evaluation

2.3.1. Parameter Design

As the geometry of the AJMs are pre-defined, the AJM nozzle performance characteristics can theoretically be estimated based on the assumption of isentropic and ideal nozzle flow theory. Accordingly, the area expansion ratio $A_{j,e}/A_{j,t}$ can be related to nozzle exit Mach number $M{a}_j$ through the following equation.

$$\frac{A_{j,e}}{A_{j,t}}=\frac{1}{M{a}_j}{\left[(1+\frac{\gamma -1}{2}M{a_j}^2)\frac{2}{\gamma +1}\right]}^{\frac{\gamma +1}{2(\gamma -1)}}$$

(1)

where the subscript j stands for jet, e stands for the nozzle exit plane, and t denotes the throat plane.

For the sonic nozzle as in the validation case, $M{a}_j=1$ and the right-hand side of the above equation will be reduced to 1. In the case of supersonic nozzles, the above equation cannot be solved directly. A Matlab function vpasolve is used to obtain the numerical solution in the range from 1 to $+\infty$ with the given area expansion ratio.

As soon as $M{a}_j$ is solved, the flow parameters at the nozzle exit can be obtained through the following relationships.

$$\frac{T_j}{T_{j,0}}={\left(1+\frac{(\gamma -1)}{2}M{a_j}^2\right)}^{-1}$$

(2)

$$\frac{P_j}{P_{j,0}}={\left(1+\frac{(\gamma -1)}{2}M{a_j}^2\right)}^{-\frac{\gamma }{\gamma -1}}$$

(3)

$$q_j=K\frac{P_{j,0}}{\sqrt{T_{j,0}}}{A}_{j,t}$$

(4)

$$K=\sqrt{\frac{\gamma }{R}{\left(\frac{2}{\gamma +1}\right)}^{\frac{\gamma +1}{\gamma -1}}}$$

(5)

where T and P are static temperature and pressure, q represents mass flow rate and R is the gas constant. $\gamma$ here is the ratio of specific heats. Subscript 0 denotes the stagnation parameter.

Theoretical thrust $F_{Th\_th}$ of the AJM nozzle can be estimated using the equation below.

$$F_{Th\_th}=K{P}_{j,0}{A}_{j,t}M{a}_j\sqrt{\gamma R{\left(1+\frac{(\gamma -1)}{2}M{a_j}^2\right)}^{-1}}+A_{j,e}{P}_j$$

(6)

Subscript $th$ indicates that the value is theoretical.

Here, the total pressure is used as the independent variable to control the theoretical thrust of the AJM, and the total temperature to optimize the total mass flow rate with a given thrust.

The above equations stand only when the flow inside the nozzle is under critical condition and no normal shock exists inside the nozzle’s expansion section. Thus, it is necessary to check whether the ambient pressure exceeds the maximum allowed back pressure $P_{max\_b}$ for critical operation of the nozzle. Static pressure $P_s$ behind the vehicle’s leading bow shock is taken as the ambient pressure outside the jets, which is no doubt much higher than the actual ambient pressure. Normal shock relation is employed here to obtain $P_{max\_b}$ and $P_s$.

$$\frac{P_{s(max\_b)}}{P_{f\left(j\right)}}=\frac{2\gamma }{(\gamma +1)}M{a_{f\left(j\right)}}^2-\frac{\gamma -1}{\gamma +1}$$

(7)

where subscript s denotes after shock value and f stands for freestream.

2.3.2. Performance Evaluation

Regarding the performance evaluation of the AJM, coefficients of force and moment are used. Reference dynamic pressure is calculated from the freestream condition, the reference area is the HFV surface projection in the $xoz$-plane and the reference length is the HFV body length.

Coefficient $C_M$ denotes the original pitch moment coefficient of the HFV obtained from the CFD simulation, $C_{M\_ref}$ is the result of the baseline/reference cases. $\Delta C_M$ is the change of the pitch control moment coefficient with respect to the corresponding reference case:

$$\Delta C_M=C_M-C_{M\_ref}={C_M}_{\_d}+{C_M}_{\_i}$$

(8)

The pitch moment coefficient $\Delta C_M$ in fact contains two parts. The $C_{M\_d}$ (with the subscript d denoting direct) considers only the moment established from the surface pressure on the body flap alone and from the direct thrust produced by the nozzles in the case of AJM configuration. Meanwhile, the interaction between the freestream and the body flap or the AJM will change the HFV surface pressure distribution and lead to a change in the pitch moment coefficient. This change is then described by the $C_{M\_i}$ (with the subscript i denoting interaction). The $C_{M\_i}$ could be obtained by subtracting $C_{M\_d}$ from $\Delta C_M$.

The moment augmentation coefficient $K_M$ is defined as the ratio between $\Delta C_M$ and $C_{M\_d}$. In the AJM configuration case, the $C_{M\_d}$ could be estimated with Equation (6).

$$K_M=\frac{\Delta C_M}{C_{M\_d}}$$

(9)

$$C_{M\_d}=\sum _{k=1}^n{C}_{T\_th,k}{L}_k$$

(10)

where n is the number of the nozzles in the AJM, $C_{T\_d\_th,k}$ is the theoretical thrust of the kth nozzle and $L_k$ is the length of the pitch moment arm. The CFD computed thrust will be evaluated against the theoretical value.

2.4. Comparative Simulation Cases Design

A total of 8 cases are designed in this study. Starting from the baseline case computation to different moment adjustment strategies, their results are compared to acquire in-depth knowledge of the AJM. Computation cases and notes are given below in

Table 1. Computational Cases and Notes.

Case	Body Flap	AJM	Note
1	None	None	Baseline Model
2	30° Downward Deflection	None	Mechanical CS Model
3	None	Inactive	No-Jet Baseline Model
4	None	B1 to B4 active	$P_{j0}$ = 10 MPa 1
5	None	B1 to B4 active	$P_{j0}$ = 5 MPa 2
6	None	B1 to B2 active	$P_{j0}$ = 10 MPa
7	None	B2 to B3 active	$P_{j0}$ = 10 MPa
8	None	B3 to B4 active	$P_{j0}$ = 10 MPa

¹ Case 4 is noted as the maximumly operational state since it has the largest F_Th and q_j. ² Cases 5–8 are noted as the half operational states, as the total F_Th and q_j in these cases are reduced by 50% with respect to Case 4 the maximumly operational state.

.

1.

Common Basis for Comparison

As the results from different kinds of control surface configuration and meshes are to be compared, it is important to guarantee that their $C_M$ and $\Delta C_M$ are referenced to the same reference values. Therefore, a common basis for comparison should be established before the comparison of the computational results.

Case 1 is set to be a baseline reference for all other study cases. Its mesh is constructed completely on the baseline configuration mentioned in Section 2.1. Case 1 is used as a direct reference point for the mechanical control surface configuration (Case 2). As the original design of the HFV bears no consideration of mechanical control surface, any installation of components that protrude from the HFV surface is recognized as a disturbance to the baseline configuration.

Case 3 is the No-Jet baseline case for all cases employing the AJM configuration. The results from Case 3 need to be compared with Case 1 at first, this will clarify the influence of the refined mesh around the AJM. With the discrepancy in the key result between both cases laying within the acceptable range, Case 1 and Case 3 then form the common basis, which enables and justifies the direct comparison of computational results from different configurations and meshes.

All key performance indicators are also subsequently computed after the common basis for comparison to be established.

2.

Performance Comparison between the Body Flap and the AJM

To better understand the performance and capabilities of the AJM, the computation of the body flap configuration in Case 2 provides a pitch control performance reference of the conventional control surface, while the counter-part Case 4 gives the result of the unconventional AJM in the maximumly operational state.

A qualitative analysis of flow characteristics is conducted for both cases at first. Then, the aerodynamics coefficients from both configurations are evaluated against each other. The pitch moment coefficient is a director indicator of the pitch-trimming capability. Additionally, the coefficients of lift and drag, as well as their ratio are used to reflect the overall influence of different configurations on the aerodynamic HFV performance. The moment augmentation coefficient depicts the extra gain of effective pitch moment from the interaction of respective control surface with the free flow.

3.

Performance Comparison between Different Working States

To achieve the goal of effective attitude control throughout the flight trajectory, study of the AJM under different working states is essential. Cases 5 to 8 are referred to as the half operational state, as the total $F_{T}h$ and $q_j$ in these cases are reduced by 50% with respect to Case 4 (the maximumly operational state). Case 5 is an example of the pressure regulation strategy of the AJM moment. The total nozzle pressure has been reduced to 5 MPa, other parameters remained unchanged. Cases 6–8 group the AJM nozzles into B1–B4 and has them functioning in pairs, representing a discretized control strategy. All other flow parameters remained unchanged, only the number of working AJM groups has been reduced by half and active groups moved further downstream from case to case.

The results are compared with Case 4 to reveal the difference in flow pattern. Aerodynamic characteristics are then evaluated against the baseline Case 3 and Case 4 to study the change in AJM performance. Patterns of pressure and working group location influence on moment coefficient are inspected.

4.

Performance Comparison between Different Moment Adjustment Strategies

The last topic aims to understand the difference between different moment adjustment strategies. The chamber pressure adjustment of the AJM nozzles is intuitively simple and direct, yet large-scale pressure regulation is associated with complicated devices and systems. The number of valves related to the discretized moment adjustment strategy of the AJM nozzles may pose problems attributed to increased structural weight. Therefore, an investigation regarding the efficiency of both strategies is indispensable.

Case 5 is comparatively studied with Cases 6–8. Their flow field contour, streamlines, and sectional surface pressure distribution are analyzed in-depth against each other. The information gained from this topic will serve the future AJM moment adjustment strategy optimization well.

3. Numerical Method and Computation

3.1. Numerical Method

A conventional in-house CFD solver undertakes the computational tasks in this study. The Reynolds-averaged Navier–Stokes equations with the two-equation SST turbulence model [45] are utilized to simulate the hypersonic flow field. All working fluid in the simulations is set as air. Equation of state for ideal gas without chemical reactions is taken. The spatial discretization of the convective flux term is supported by a multi-dimensional total variation diminishing polynomial interpolation method [46] with second-order accuracy. An implicit time integration method is used in the steady-state simulation. Solutions are considered converged when the residual drops at least four orders of magnitude and the oscillation of pitch moment coefficient is much less than 0.1%.

3.2. Validation

The experimental result from Brandeis and Gill [37] is used to validate the numerical method. The $l/d=4$ ogive body model has a circular nozzle measuring 8 mm in diameter. The distance from the nose tip to the nozzle center (also the origin) is 225 mm. The computational mesh for the validation case is provided below in Figure 4, the height of the first mesh layer is 0.001 mm. The nozzle boundary condition is modified from the original parameters according to the method described in Section 2.2. Complete boundary conditions for the $Ma=3.3$ experiment are listed below in

Table 2. Boundary Conditions of the Validation Case.

Boundary	Parameter	Value
freestream	$P_f$	19,496.98 Pa
	$T_f$	84 K
	$V_f$	612.634 m/s
	Angle of Attack (AoA)	0°
Model Surface	$T_w$	295 K
Sonic Nozzle	$P_j$	2,640,000 Pa
	$T_j$	295.11 K
	$V_j$	344.38 m/s

.

Here, the subscript w represents the wall.

The comparison of the pressure coefficient from the experiment and CFD simulation is depicted below in Figure 5. It can be seen from the plot that the CFD result corresponds well to the experimental result. Furthermore, the jet-flow interaction induced control force augmentation factor K from the experiment is 0.935, while the current solver produced a very close result of 0.963. Other research works, such as Graham and Weinacht [39], Wu et al. [41], Li et al. [42] and Jia et al. [43], have also obtained comparable validation results (K as well as pressure distributions) with different solvers. Therefore, the solver employed in this study is considered validated.

3.3. Boundary Conditions

For computation cases in this study, the boundary conditions for the freestream and the nozzle exit are directly specified using primitive variables including pressure P, temperature T, and velocity V. Isothermal no-slip wall condition is imposed on the surface of the model. As the HFV model is symmetric with respect to the $xoy$-plane, only half of the models are numerically investigated. Therefore, a symmetry boundary condition is necessary. The outlet of the computational domain is defined as the supersonic outflow condition.

All cases have the same freestream boundary condition (

Table 3. List of Boundary Conditions.

Boundary	Parameter	Value
freestream	$P_f$	21.96 Pa
	$T_f$	247.02 K
	$V_f$	4727.16 m/s
	Angle of Attack (AoA)	20°
Model Surface	$T_w$	300 K
AJM	$P_j$ (Case 4,6,7,8)	7794.08 Pa
	$P_j$ (Case 5)	3897.04 Pa
	$T_j$	103.52 K
	$V_j$	1183.01 m/s

). The surface of the HFV is 300 K. The boundary conditions of the AJM nozzles are specified using $P_j$, $T_j$, and $V_j$.

Since the AJM operates at two different total pressure levels, two $P_j$ values have been listed above for the AJM boundary. The static temperature and exit velocity remain the same. As said before, the turbulence model used is the k-$\omega$ SST model.

3.4. Grid Independence Study

To determine the height of first prism layer for the final computational mesh, a grid independence study has been conducted. A section of the HFV lower surface containing the AJM is taken and modeled. The section model utilized the same boundary conditions as those in Case 4 (refer to Table 1 and Table 3), therefore sufficient to simulate the free flow behind the leading shock and the jet-flow interaction with low computational cost. Three grids with different first layer height are considered, among which the cell height of 0.001 mm used in the Moderate grid is also employed by Hoholis et al. [17] and Chen et al. [47]. Grid specifications and the calculation results are listed in

Table 4. Grid Specifications and Results.

Grid	Number of Cells	First Layer Height	${\mathit{C}}_{\mathit{L}}$	${\mathit{C}}_{\mathit{D}}$	${\mathit{C}}_{\mathit{M}}$
Fine	1.9 Million	0.0001 mm	0.5247	0.2164	0.364454
Moderate	1.6 Million	0.001 mm	0.5244	0.2163	0.364204
Coarse	1.3 Million	0.01 mm	0.5241	0.2161	0.363888

.

From Table 4 and Figure 6 above, it can be seen that the moderate mesh with first layer height of 0.001 mm provides results with minimum discrepancies (less than 0.07%) to the fine mesh. Meanwhile, the computational effort of the moderate mesh is also economic. Therefore, the first layer height of 0.001 mm is selected to mesh the HFV geometries.

3.5. Computational Mesh

The final computational meshes for Case 1, Case 2, and Case 3 are given below. Figure 7a provides an overview of the mesh in Case 1. The meshes of different configurations are similar generally. Differences exist on the lower surface of the HFV. Enlarged views of the control surface installation place in the same point of view and scale are given in Figure 7b for Case 1, in Figure 7c for Case 2 and Figure 7d for Case 3.

Due to the symmetric geometry of the HFV, mesh for only half of the model is generated. All of the computational meshes are unstructured with the height of the first prism layer being 0.001 mm. The total number of cells ranges from 19 to 22 million.

4. Results and Discussion

4.1. Common Basis for Comparison

Table 5. Computational Results of Aerodynamic Characteristics.

Case	${\mathit{C}}_{\mathit{L}}$	${\mathit{C}}_{\mathit{D}}$	$\mathit{L}/\mathit{D}$	${\mathit{C}}_{\mathit{M}}$1	$\Delta {\mathit{C}}_{\mathit{M}}$
1	0.2645	0.1206	2.193	0.013891	-
2	0.2892	0.1549	1.866	0.004088	−0.009802
3	0.2644	0.1206	2.193	0.013907	-
4	0.3418	0.1479	2.310	−0.006832	−0.020739
5	0.3095	0.1363	2.270	0.001821	−0.012086
6	0.3087	0.1360	2.269	0.002430	−0.011477
7	0.3070	0.1355	2.266	0.002487	−0.011420
8	0.3054	0.1350	2.263	0.002492	−0.011415

¹ Positive for nose-up and negative for nose-down.

below summarizes the results of the basic aerodynamic coefficients from all cases. These parameters are used to characterize the aerodynamic performance of the HFV configurations.

As stated in Section 2.4, the influence of differences in baseline configuration mesh should be ruled out at first to set a common comparison basis for the study.

It can be seen from the table that the baseline configuration Case 1 has an $L/D$ of 2.193 and the $C_M$ is 0.013891, which means that the HFV has a nose-up tendency. Case 3 sets a new reference for Cases 4–8. It differs from Case 1 with refined mesh around the AJM. From Table 5, it can be concluded that the aerodynamic coefficients are generally the same in these two cases. The $C_L$ from both cases differ from each other by only 0.0001, which is less than 0.05%. The $C_M$ exhibits a slightly higher discrepancy with a relative error of around 0.1%.

Hence, the influence of mesh density can be ruled out from both cases, and a cross configuration comparison of force/moment coefficients could be conducted. The $\Delta C_M$ of the cases are then calculated to study the pitch control capability and are also shown in Table 5 for convenience.

Figure 8 displays the Mach number (symmetry and the outlet plane) and static temperature (section plane x = 0.612, range shown 200 to 2000 K) contour lines of the flow field, and also the surface pressure contour (range shown 0 to 1500 Pa) of the HFV lower surface of the baseline case and the maximumly operating AJM case (Case 4). The leading shock is easily identified. The operating AJM hardly affects the upstream flow field. Thus, the flow parameters behind the leading shock remain the same in front of the jet-flow interaction region.

Table 6. Force and Moment Coefficients on Control Surface.

Case	${\mathit{C}}_{\mathit{T}\_\mathit{d}\_\mathbf{th}}$	${\mathit{C}}_{\mathit{M}\_\mathit{d}\_\mathbf{th}}$	${\mathit{C}}_{\mathit{T}\_\mathit{d}\_\mathbf{CFD}}$	${\mathit{C}}_{\mathit{M}\_\mathit{d}\_\mathbf{CFD}}$	${\mathit{K}}_{\mathit{M}}$
1	-	-	-	-	-
2	-	-	-	0.01039	0.94
3	-	-	-	-	-
4	0.06243	0.01602	0.05979	0.01534	1.35
5	0.03122	0.00801	0.02990	0.00767	1.58
6	0.03122	0.00769	0.02988	0.00736	1.56
7	0.03122	0.00801	0.02994	0.00768	1.49
8	0.03122	0.00833	0.02991	0.00798	1.43

below lists the comparison between theoretical force/moment prediction and CFD results. As mentioned in Section 2.3, the change in y directional force and pitch moment coefficients can be decomposed into two parts: direct generation and interaction. Since the direct generation could be estimated theoretically, they are extracted from the CFD results and compared with the theoretical values. The coefficients $C_{T\_d\_th}$ and $C_{M\_d\_th}$ are theoretical direct thrust and moment, respectively. The $C_{T\_d\_CFD}$ and $C_{M\_d\_CFD}$ are the force and pitch moment obtained from the CFD computations. In Case 2, $C_{M\_d\_CFD}$ is the moment integrated from the surface of the body flap alone. In the last column, parameter $K_M$ indicates the scale of augmentation on the control moment induced by the jet-flow interaction. The theoretical values correspond well with the CFD computed results as shown in Table 6, the relative errors of the force and moment coefficients are all less than 5%. The small discrepancy between the prediction and simulation results has proved the validity of the AJM parameters design method.

4.2. Comparison between Body Flap and AJM

This section provides the analysis of both flow and aerodynamic characteristics of both configurations. Case 2 provides the result of the body flap configuration with 30° downward deflection. Case 4 gives the result for a maximumly operating AJM.

Figure 9 gives the HFV surface pressure contour of Case 2 and Case 4. It can be seen that the body flap undertakes most of the high-pressure and generates a majority of the control force, while the pressure rise on the HFV surface is relatively small. In Case 4, the interaction-induced high-pressure in front of the AJM is quite obvious. Though the overall pressure around the AJM is much less than that on the body flap, the induced high-pressure area is much larger.

Figure 10 shows the comparison of the flow field from different cases with streamlines. In Figure 10a, a large leeside vortex is visible behind the body flap in Case 2. Such a separation vortex decreases the surface pressure of both the leeside of the body flap and the sheltered section of the lower HFV surface. A smaller separation bubble can be seen in front of the body flap leading-edge. The narrow gap existing between the flap and the main body leaks some flow and therefore reduces the leading-edge separation range. Thus, most of the body flap’s control force is generated on the high-pressure windward side. Altogether, the size of these two separation bubbles could provide the main explanation for $K_M<1$ in Case 2.

Figure 10b shows the pressure contour and streamlines of the maximum operating AJM case. Massive separation vortex ahead of the first row of AJM can be identified and is beneficial to the HFV surface pressure. The jet flows form several shear layers, a high-pressure spot can be seen at the location where the first jet confronts the freestream. Both the freestream and jet flow streamlines are highly curved. Apparent jet expansion exists between jets. Pressure rise (light blue) between the first few rows of jets are also noticeable, which indicates that the jet-flow interaction also occurred here. The large high-pressure interaction region and the intensive upstream separation vortex contribute significantly to the high $K_M$ in Case 4.

The separation caused the high-pressure region to extend approximately 6 cm in front of the flap in Case 2, while in Case 4 the region stretched approximately 19 cm. From the streamline comparison, it can be concluded that the AJM-occupied surface area is akin to a “thicker flap”. On the “thicker flap” (AJM area), there is constant presence of useful high-pressure. The low-pressure region behind this “thicker flap” lies mostly outside the computation domain. In contrast, the separation vortex on the leeside of the body flap inevitably reduces the HFV surface pressure. All these differences sculpt the significant $K_M$ gap between the two cases.

In Case 2, $C_L$ and $C_D$ coefficients are both larger than that of Case 1, yet $C_D$ increases larger. The $L/D$ ratio of Case 2, the body flap case, thus drops to 1.866 (14.9% drop). $C_M$ decreases to only 29.4% of the baseline result (Case 1) and fails to balance the HFV in pitch channel. While in Case 4 the AJM case, $C_L$ has grown from 0.2644 in Case 3 to 0.3418, which is 18.2% larger than that in the body flap case. $C_D$ experiences an increase as that in Case 2, but the increment is 5.8% less. The resulting $L/D$ ratio in Case 4 increases to 2.310, which is 5.4% larger than the baseline case and 20.3% more than that in Case 2.

The $C_M$ now in Case 4 measures −0.006832, i.e., −49.1% with respect to the baseline case. A change of sign can be noticed, which means that a maximumly operating AJM is more than capable of pitch trimming the HFV. Furthermore, the $\Delta C_M$ is approximately twice that of the body flap configuration (Case 2).

The body flap configuration also bears no extra gain from any interaction. Figure 9 shows that there is a high-pressure region just in front of the flap hinge, but this pressure rise could be easily neutralized by the flap leeward separation pressure drop. Therefore, its $K_M$ coefficient is only 0.94. In contrast, the AJM Case 4 produces a $K_M$ of 1.35.

On the system cost of the two control strategy: conventional flap systems are usually heavy, but have a long working duration. Larger flap size and deflection angle can be realized to improve the pitch control performance with the cost of increased power demand on the actuator, installation space, thermal protection measures and system weight. In addition, the flap strategy can deteriorate the HFV aerodynamic performance. On the other hand, the AJM is supposed to possess a simple supply system similar to a small thruster. It could share part of the pipeline and the pressurized tank of the main engine to further reduce the system complexity. However, the working duration is limited by the amount of working fluid, which is also a weight constraint for the vehicle design. Therefore, the comparison here could prove that the AJM concept is a feasible alternative for HFV flight control. However, whether it represents the optimum solution depends on the application scenario and further system optimization.

4.3. Performance Comparison between Different AJM Working States

4.3.1. Pressure Regulation Strategy

In Figure 11, the flow pattern of Case 5 can be distinguished from Case 4 with the smaller separation vortex, additional vortex near the first jet and larger jet deflection angle. As the total pressure of the jet in Case 5 has dropped by 50%, the momentum and exit pressure of the jet are also reduced. It is therefore easier for the freestream to circumvent the jet-formed obstacle, resulting in a smaller separation and flow deflection angle. As the smaller nozzle exit pressure gives the jet little pressure allowance for further expansion, an additional vortex is formed over the first row of nozzles.

Figure 12 provides the comparison of lower surface pressure distribution from Case 4 and Case 5. Though the distribution is similar, the pressure peak is significantly lower in Case 5. The positions of local pressure peaks move downstream for roughly one row in Case 5. Further notice should be made to the low-pressure regions. In Case 4, the nozzles on both flanks of the AJM achieve little or even no jet-flow interaction. Though these regions in Case 5 also present significantly lower pressure than that near the center of the AJM, their pressure level is still higher than that in case 4. A relatively more even pressure distribution is obtained in Case 5. The edge of the interaction area in x-direction shrinks by around 6 cm and the region behind the AJM experiences a gradual pressure recovery. All of these phenomena could be explained as: due to the pressure drop inside the AJM, freestream tends to penetrate into the AJM further instead of bypassing the jets from flanks.

Observations on the surface pressure distribution along the x-axis are conducted to the spanwise section plane 0.085, 0.116 and 0.121. Figure 13 provides the comparison of the surface pressure distribution plots from Case 4 and Case 5. It can be read from the plots that the nozzle exit pressure of the AJM in Case 5 dropped exactly by half, the interaction-induced surface pressure boost is generally at the same level in both cases. The part of the curves ahead of the first row of jets from both cases have a similar pressure level, but different pressure rise starting points. Pressure peaks between rows of nozzles appear as the free flow is trapped among the staggered jets matrix. The maximum pressure peak near the first jet in Case 4 at Section 0.121 has much larger values (roughly 1500 Pa higher than that in Case 5) and a more forward position compared with that in Case 5 as the jets are stronger in Case 4. Another point worth mentioning is that such high-pressure peaks do not go down as much when nozzle exit pressure drops by half, as if there were a hysteresis effect. At section plane 0.085 and 0.116, the first interaction pressure peak between rows (around x = 0.96) has a similar pressure level in both cases, but the pressure peaks between the following rows in Case 5 are higher levels than that in case 4. This explains the origin of $K_M$ in Case 5 being the highest among all simulation cases.

Figure 14 offers a 3D visualization of the surface pressure distribution on the lower surface of the HFV. The y-axis is assigned to the surface pressure. The interaction influenced area is significantly larger in Case 4. The first row of peaks in Case 4 bear a much higher pressure level, while the pressure peaks seem more uniform within the AJM. The jets form a matrix of bars that hinders the movement of free flow.

The $C_L$, $C_D$ and the $L/D$ ratio in Case 5 all experience a slight drop compared with that in Case 4. However, the aerodynamic performance boost is maintained, as the $L/D$ ratio is 3.5% higher than that in Case 3.

$C_M$ of Case 5 is again positive 0.001821, meaning that the HFV is not balanced. However, the $\Delta C_M$ shrinks less than 50% of that from Case 4, which implies that the interaction-induced augmentation moment changes nonlinearly with the nozzle chamber pressure $P_{j,0}$.

Meanwhile, the $K_M$ rises to 1.58, 16.6% higher than that in Case 4 ($K_M$ = 1.35). The computational result for AJM $C_T$ and $C_M$ dropped exactly by half compared with that in Case 4 as shown in Table 6.

With such results, one can confidently state that the jet-flow interaction-induced augmentation effect does not move linearly with AJM moment. Such non-linearity provides opportunities for high-efficiency design and will be a powerful tool for flow rate optimization.

Short conclusions in this subsection are: (a) higher nozzle exit pressure leads to a higher interaction pressure peak; (b) the jet-flow interaction-induced augmentation moment behaves nonlinearly with nozzle pressure; (c) a lower nozzle exit pressure allows the flow to penetrate the AJM deeper, and therefore more intense interaction occurs between the jets and free flow. In this context, further study should be made into the arrangement of pressure levels inside the AJM to optimize the interaction distribution.

4.3.2. Discretized Control Strategy

An alternative method to control the AJM force and moment is by changing the number of working AJM nozzles. Cases 6–8 adopt this concept and are used to study the influence of different working groups on actual performance.

When keeping the jet total pressure unchanged, i.e., 10 MPa, and reducing the number of working nozzles by half, the flow field in front of the second row of nozzles in Case 6 is identical to that in Case 4 as shown in Figure 15. The pressure peak and the frontal separation vortex shrink slightly. The absence of jets in the downstream removes the support for the frontal jets. Consequently, the jets are deflected toward the HFV surface even further downstream, reaching an extent similar to that in Case 5.

With the information from Figure 12 and Figure 16, the surface pressure distribution of Case 4 and Cases 6–8 can be compared. It can be noticed from the figures that the surface pressure peaks in Case 6 are at similar levels, and their positions move slightly backward. The high interaction pressure displayed in Case 4 is generally retained in Case 6 within the operational AJM groups. All working AJM nozzles interact well with the free flow and achieve considerable pressure augmentation. Therefore, the $K_M$ is largely increased.

Similar results can be retrieved from Cases 7 and 8 with the main difference resting in the position of the pressure peaks and the pressure level behind the AJM. Pressure peaks move further downstream as the operational AJM groups travel backward. As the AJM groups approach close to the bottom of the HFV, there is less space and chance for the pressure to recover. The surface behind the AJM is gradually dominated by low pressure.

The plots in Figure 17 confirm the above analysis, as they are identical in most of their paths except for the post-AJM region. This part of the curves in Case 6 rises apparently and extensively, while in Case 7 they are cut shorter, and in Case 8 with almost no chance for pressure recovery. Figure 18 gives a more vivid illustration of the pressure distribution. The sudden drop in pressure is quite straightforward compared with that in Figure 14.

Quantitatively speaking, the resulting $C_L$ in Case 6 is reduced to 0.3087, 9.7% lower than that in Case 4. The $C_D$ experiences a similar change (8.0%), while $C_M$ has a noticeable increase compared to Case 4. Key aerodynamic characteristics from Cases 7 and 8 are close to those in Case 6.

The theoretical pitch moment in Case 6 is the smallest as the moment arms are the shortest. However, from the previous analysis and Figure 12, the region where the most significant interaction occurs is well preserved and enough space for pressure recovery is provided. Therefore, the augmentation moment $C_{M\_i\_CFD}=\Delta C_M-C_{M\_d\_CFD}$ drops only by 23.7% in Case 6 and the $K_M$ for Case 6 increases to 1.56, while $K_M$ in Case 4 is only 1.35.

In Case 7, the theoretical thrust and moment produced should be exactly half of that in Case 4, due to the geometric similarity. However, the computed $\Delta C_M$ is 55.1% of that in Case 4, which again indicates the non-linearity of jet-flow interaction with respect to the number of jets. With the longest nozzle moment arms, Case 8 produces yet the lowest $C_M$ result among all AJM cases. As mentioned above, without much chance for post-AJM region pressure recovery, the $K_M$ values of Case 7 and 8 go straight down to 1.49 and 1.43.

The knowledge gained here indicates that: (1) non-linearity exists between the number of active nozzles and the augmentation moment; (2) conventional mechanical control surfaces have no concern nor potential to leeward surface pressure utilization, and are hence usually placed in the way to obtain the longest moment arm. The AJM, on the contrary, is more selective to the positioning as a balanced or optimized position exists, which could make the best advantage of long nozzle moment arms and the AJM leeward pressure recovery. Thus, a guideline needs to be proposed for the placement of the AJM.

4.4. Performance Comparison between Different Moment Adjustment Strategies

From Figure 11 and Figure 15 it can be seen that the frontal separation vortex in Case 5 is significantly smaller than that in Case 6. As the jet flow is distributed into 48 nozzles in Case 5 and into 24 nozzles in Case 6, the exhaust jet is less concentrated in Case 5, resulting in a wider spread but an even higher pressure area over the AJM. The pressure peak over the AJM is also much smaller in Case 5. However, the jet streamlines are deflected to a similar extent in both cases.

Comparing all cases with reduced theoretical thrust, i.e., Cases 5–8, it is clear that Case 5, the pressure regulation candidate, captured the highest $K_M$ = 1.58, which is 1.1 times higher than that from Case 8 (with the lowest $K_M$ = 1.43). This result may sound astonishing as in the cases representing discretized nozzle control, the most intensive jet-flow interaction pressure peaks are actually preserved.

From Figure 13 and Figure 17, Figure 14 and Figure 18, one can understand the hidden mechanism: the interaction intensity changes non-linearly with nozzle exit pressure. The interaction pressure peak level drops by around 1500 Pa in Case 5 compared with that in Cases 6–8 (as they both bear full AJM working groups). The surface pressure distribution plots show pressure jumps around AJM nozzles in Cases 6–8. The high nozzle exit pressure seems wasteful or excessive to achieve a certain level of surface pressure boost, which can also be produced with a halved exit pressure as in Case 6. The most significant effect a high nozzle exit pressure can exert is a high-intensity first-row surface pressure peak, whose upper limit seems exclusively dependent on the nozzle exit pressure.

The benefit obtained from the non-linearity of the interaction pressure level on nozzle exit pressure thus easily surpasses the enhancement gained from the retention of high-intensity interaction regions in Cases 6–8. Based on this information, the next research topic could be proposed: AJM moment adjustment strategy based on combined pressure regulation and discretized nozzle control. Such a strategy should be able to control the working state and the chamber pressure at the same time. Thus, every jet has the opportunity to achieve a high-level jet-flow interaction with suitable exit pressure.

5. Conclusions

A comparative numerical study of the aerodynamic characteristics of a Hypersonic Flight Vehicle (HFV) with conventional mechanical control surface and Active Jets-Matrix (AJM) is carried out in this study. The purpose is to acquire first-hand information regarding the performance, flow characteristics and possible optimization guidelines of the AJM design. The employed numerical method is validated against experimental data. In total, eight computational cases are conducted and comparatively studied. The pitch control performance and the effect of different AJM moment adjustment strategies are investigated. The following conclusions are reached:

1.

The maximumly operating AJM is capable of producing a sufficiently large control moment to trim the HFV in pitch channel under the investigated flight condition, while a 30° downward deflecting body flap fails to balance the HFV. The AJM has also effectively utilized the jet-flow interaction with a minimum $K_M$ of 1.35.

2.

Nonlinearity exists between the AJM nozzle chamber pressure as well as the number of active nozzles and the interaction-induced augmentation moment. Thorough understanding and utilization of this nonlinearity could render the AJM an efficient and attractive flapless flight control method.

3.

Excessive high-pressure becomes an obstacle to further jet-flow interaction inside the AJM and thus reduces the control efficiency.

4.

Pressure recovery in the post-AJM region is also beneficial and warrants consideration when placing the AJM.

5.

A combined AJM moment adjustment strategy based on pressure regulation and discretized nozzle control could be the optimal moment adjustment method.

This study proves that the AJM concept is an effective option for HFV flight control. However, the system cost compared with the conventional flap system is a flight-mission-specific question. The selection between the conventional flap method and the AJM as well as other alternatives should be made upon the overall consideration of HFV volumetric efficiency, main engine type, flight trajectory, etc. The engineering application of AJM still requires much study and systematic optimization of the HFV.

6. Patents

Attitude control system of cross-domain aircraft, CN212515478U (https://patents.google.com/patent/CN212515478U/en?oq=CN212515478U, accessed on 15 August 2022).