A New Design of Variable-Geometry TBCC Inlet Based on an Internal Waverider Concept

The turbine based combined cycle propulsion system, a hopeful air-breathing propulsion system for high speed aircrafts, needs to work in a wide Mach number range. To meet the requirement, the variable-geometry internal waverider inlet based on improved Internal Conical of Flowfield C+ is proposed in this paper. Firstly, the axisymmetric basic flowfield is improved to an Internal Conical of Flowfield C+ with a higher external compression ratio, which befit to relieving the mass flow choke under low Mach number conditions. Secondly, a variable-geometry design method is proposed for the internal waverider and turbine based combined cycle inlet. In order to ensure sealing of variable geometry inlet, a new arrangement of the inlet osculating planes is proposed. And when the inlet geometry varies to expand the throat, the shape of cross-sections always keeps smooth. Such design contributes to a waverider shock structure without corner flows and high efficiency in wide speed range. Finally, CFD results indicate that the internal waverider and turbine based combined cycle inlet exhibits excellent aerodynamic performance characteristics, with high mass flow coefficient and low total pressure loss, thus enabling a great improvement for the turbine based combined cycle system.


Introduction
In recent decades, the demand of military competition and weapons equipment in the aerospace field is growing. And the research on high-speed aircraft has been motivated, such as missiles that can execute remote rapid strikes or penetration, supersonic/hypersonic integrated intelligence fighters, surveillance, reconnaissance, reusable launch vehicles and so on. A propulsion system is crucial for high-speed aircraft to achieve a wide range of flight speeds [1][2][3]. However, there is currently no single type of power propulsion that can cover a wide range of flight Mach numbers. Therefore, the use of a combination of different kinds of propulsion systems is an effective solution, exploiting the advantages of each system in their own optimum speed range. Typical combined propulsion systems include TBCC and RBCC. The TBCC is with large specific impulse, favourable economic performance, repeatable utilization and the capability of taking off/landing horizontally, thus leading to great potential applications in aerospace vehicles. For example, the J58 power propulsion unit [2], which supplies the thrust for the famous "Black Bird" supersonic reconnaissance aircraft, is one kind of air-breathing combined propulsion system.
As a key component for the TBCC system, the inlet should provide an appropriate compressed air flow for the ramjet combustor or turbojet. Thus, high-quality outflows of the inlet are important for improving the overall performance of the TBCC. Typical inlets applied in the TBCC have simple aerodynamic shapes and easily adjustable geometric configurations. For example, the axisymmetric inlet installed in the J58 [4,5] and the two-dimensional inlet installed in X-43B [6,7]. However, the aerodynamic performances of these inlets are still not so excellent to satisfy the requirements of high-speed aircrafts. While the recently proposed inward turning inlet has significant advantages over axisymmetric/planar inlets; for instance, the strong ability to capture the air flow, high compression efficiency and low total pressure loss [8,9]. If this inlet was applied to the TBCC, the aircraft would benefit from the outstanding performance of the inward turning inlet.
Furthermore, some advanced TBCC programs have adopted inward turning inlets, and in order to enable the inlet to start and operate in low Mach number conditions, a variable-geometry design for the inlet is needed. As shown in Figure 1 and Figure 2 [10,11], the FaCET engine uses a variable inward turning inlet. The inlet equips a movable diverter flap to distribute the mass flow into the turbojet and ramjet/scramjet. While the internal contraction of the inward turning inlet is beyond the Kantrowitz starting limits, the inlet incorporates a rotating cowl to associate in starting, but the inlet performance in wide working range cannot be compromised. The "Trijet" TBCC scheme ( Figure 3) proposed by the Aerojet Corporation also utilizes a streamline-tracing inward turning inlet [12][13][14], with part of the air flow guided into the turbojet or ejector ramjet passages by the actuation of forward doors and aft doors in the variable-geometry mechanism. But in this case, the shock structure is complex due to the presence of several sharp corners in the flow passages showed in Figure 4, which has great impact on the inlet performance.  compression surface based on a high-external-compression flow pattern. So the flow structure in compression duct can be improved and the performance of the inlet can be enhanced. This approach As mentioned above, to enable practical use of the inward turning inlet, some improvements are still required for TBCC inlet. This paper proposed a new designed variable-geometry inlet with smooth   The IWRI inlet is obtained on the basis of the axisymmetric osculating theory. As showed in Figure  6, the configuration of the three-dimensional inlet can be simplified into a collection of two-dimensional osculating planes, such as OAa and OBb. If the incident shock is close to the lip in each osculating plane, the full flow capture ability of the inlet can be guaranteed, and in fact, the flow pattern in the osculating plane is similar to the responding basic flow field.
In this paper, the shape of the upwind section is of the square class for favourable matching with the forebody of the aircraft. Since previous research has indicated that a circular combustion chamber can bear a smaller frictional resistance and heat load, the exit shape is either a circle or an ellipse to match with the downstream combustion chamber. In addition, the design Mach number of the IWRI inlet is 4.0 while the design flight height is 22 km. The design mass flow rate of IWRI inlet is 6.5 kg/s, with an aspect ratio of 1.75 for the shape of the upwind section and a contraction ratio of 5.9.

Improvement of the starting ability of the internal waverider inlet
Generally, TBCC inlets need to amplify the throat to ensure the starting performance of the inlet, when the working Mach number is lower than design Mach number. But in fact, if the throat is extend to rather larger, it will increase the weight and the structure complexity of the inlet. Therefore, it enables a fundamental solution for problems such as the complex shock structure in the Trijet inlet, while simultaneously maintaining the high mass flow capture characteristics.

Design method of internal waverider inlet
Based on our group's previous studies reported in [15,16], the ICFC flow field showed in Figure 5 is adopted as the basic flow field for IWRI. And it is acknowledged that the aerodynamic performance of a three-dimensional inward turning inlet is closely  The characteristic line displayed in Figure 8 is the corresponding Mach line at the emitting point of the compression curve, and the line spacing reflects the degree of airflow compression (the lines gathering means compression) or expansion (the lines dispersing means expansion). Comparison of the improved ICFC+ flow field and the original ICFC flow field shows that the local expansion region following the initial shock is decreased. And the characteristic lines generated from the compression curve are gathered as close as possible to the cowl lip point, thus raising the external compression ratio. Besides, the compressing ability of the basic flow field is improved within a shorter length as the Mach number after the reflected shock is reduced from 1.60 to 1.55 for the same upstream speed. In summary, the improved ICFC+ flow field with a higher external compressing ratio is beneficial for relieving the mass burden under low Mach num-is desired that the inlet can spill the needless flow under lower flight speed.
The IWRI inlet is with good mass flow capture ability, the mass flow coefficient is high with value 0.87 even in Mach 2.0 [17]. Unfortunately, excessive capture mass flow of IWRI inlet will result in a bad starting ability in lower Mach status. One of the methods is to improve the starting ability of the IWRI inlet to push down the Busemann compression curve of the original ICFC flow field [9]. And six different functions are given in [9] to improve the basic ICFC flow field.
Considered that the gradient of the starting and ending positions of inverse tangent function is small which ensures the smooth transition of the compression curve. So here a new function used inverse tangent is proposed: The initial Busemann compression curve is generated to offset a certain distance Two-dimensional variable inlet always rotates a selected movable surface around a single axis to enlarge the throat area. As the throat area of the IWRI inlet should be enlarged by 4.8 times in Mach 2.0 conditions, the traditional geometric transformation method is not sufficient to ensure that the inlet can be started.
So, this work presented a new geometric trans-formation method. The IWRI compression surface is divided into two parts along the symmetry plane [15] (the blue surface shows in Figure 10) and rotate the two compression surfaces around each axis to expand the throat. The enlarged IWRI inlet can obtain the starting ability in low Mach conditions. As showed in Figure 5, the cut position of the movable compression surface is a distance from the inlet entrance. So that a rotation of the inlet surface would not change the depend surface which generates the first incident shock wave of the IWRI inlet.
Over the full range of Mach number conditions, the boundary between the fixed and movable com-pression surfaces requires special attention to en-sure a smooth shape of the throat section. As pre-sented in Figure 11, the rotation axes (l and l') are both in the YOZ plane with an angle θ to the OZ axis. According to the one-dimensional flow analysis, θ is equal to 30° to enlarge the throat area as much bers by larger spilling flow.
Based on the improved ICFC+ flow field, the os-culating axisymmetric theory mentioned in section of Design method of internal waverider inlet is used to generate the IWRI inlet with a higher external compression ratio. The three-dimensional configu-ration of the IWRI inlet is showed in Figure 9.

Geometric transformation method of internal waverider inlet with smooth compression surface
For the IWRI inlet with a design Mach number of M4.0, the mass flow coefficient of the IWRI at M2.0 is up to 0.87 [15]. In order to prevent choking of the airflow, the method of enlarging the throat is adopted in this paper. And the throat area in lower Mach numbers can be estimated according to the one-dimensional flow analysis method based on formula (1). The formula is assumed that the air compression process is steady, adiabatic and isen-tropic from the entrance to the throat. According to the previous researches of our group, the total pressure recovery is approximately 0.85 and the Mach number of the throat is in the range of M1.1-1.2 in Mach 2.5 condition. So the throat area is ap-proximately 4.8 times larger than the area of the design point. ensure sealing the hot compressed air in low Mach conditions, it is necessary to add sealing surface to the IWRI inlet. The sealing surface is also showed in Figure 11 while CC'/DD' at the side walls is fixed and EF at topside is movable. In the process of variable geometry, the throat shape changes from the design elliptic line OCD to the enlarged curve OCC'EFD'DO which still keep continuous.
The three-dimensional variable geometry of IWRI inlet is showed more clearly in Figure 12. The grey parts are fixed compression surfaces and the blue parts are movable compression surfaces. When the inlet geometry changes, the sealing surfaces are added to prevent high-speed airflow run-ning away. The orange parts (CC' and DD' in Figure as possible with the same rotation angle. The com-pression surface of the variable-geometry IWRI inlet in this paper keeps smooth and its actuation can been seen from the cross section showed in Figure   11. The movable throat section in design condition is divided at points C/D by the straight lines CC' and DD' which are perpendicular to the rotation axes.
The moveable throat profiles are always tangent to CC'/DD', so the cross sections along the flow direc-tion can keep smooth when the IWRI inlet geome-try changes.
As Figure 11 shows, the movable profile CD changes to profiles C'F and D'E after varying the inlet geometry. Obviously, there are gaps between the moveable surfaces and the fixed surfaces. To

Modification design for the sealing of topside surface gap
As mentioned in last section there is a gap in the topside of the inlet compression surface during 11) are fixed sealing surfaces which are obtained by rotating the side-edge lines of the movable compression surface around the axes. The green part (EF in Figure 11) is movable sealing surface which is placed on the topside to cover the gap between two separate movable compression parts. Therefore, the variable-geometry IWRI inlet can be ob-  sition surface is showed as the red part in Figure 15. And the aspect ratio of the new inlet is 1.8. In this way, the profile of the gap in the back face of the IWRI inlet maintains flat surfaces in the case of arbitrary freestream Mach numbers, and the gap can be sealed well by the corresponding planes.
The variable-geometry design method does not change the upstream part of compression surface which is required by the IWRI inlet to generate the initial shock at the entrance. Thus, a high mass flow coefficient is maintained over a wide range of freestream Mach numbers. Furthermore, the enlarged throat resulting from the variable-geometry actuation can ensure a successful start ability of the IWRI TBCC inlet, and keep the throat Mach number in the range of M1.1-M1.5. In addition, the cross-sectional shape of the enlarged throat is smooth and maintains a continuous curvature, giving rise to excellent flow quality due to the absence of corner flow phenomena.

Flow Characteristic Analysis of the Turbine-Based Combined Cycle Inlet
To analyse the IWRI TBCC inlet, CFD simulations for 3-D inlet model are performed by commercial software, CFX. The structured grid is generated by ANSYS ICEM, and the total number of mesh points is 1.5 million. The standard K-E turbulence model is adopted for numerical simulation, and the verification and validation of the numerical method are described in [8,18]. From the reference [8], this CFD method is accurate for the inlet which work Mach number is of the range of M2.0-4.0.
The results of the IWRI inlet at the design point (M4.0) are displayed as follows. In Figure 16, the Mach contours on the typical osculating planes reveal that the flow characteristics of the three-di-variable-geometry actuation, and it requires to add a movable sealing surface. As the edge of the movable compression surface is a curve and required movable sealing surface is with different geometry shape in different Mach conditions. So it is difficult to design the movable sealing surface to guarantee air tightness over the full range of inlet's transformation (responding to all range of flight speed). In this paper, a movable folded plate in the topside is used to seal the gap in different operational conditions.
As Figure 13 shows, the edge line of the movable compression surface can be displayed as the compression line at the symmetry plane. And we change the curve line of the symmetry to polyline firstly. The curve compression line gkh is modified to two straight lines gh' and h'k on the symmetry plane. In order to ensure that the two compression lines are as close as possible, gh' is tangent to the curve gkh at the point g and h'k is tangent to the curve gkh. The detailed parameters of the compression lines are showed in Figure 13.   Figure  18) and the O 2 Q plane (showed in Figure 19) indicates that an oblique shock will be generated at point k' (shown in Figure 13) and there are almost same shock-wave structures as the upper diagram in Figure 13, when the compressing curve of the symmetric surface is changed to a straight line. Fortunately, this phenomenon does not have a significant effect on the flow or shock structures of other osculating planes.
mensional inlet (such as the shock structure and flow pattern), are similar to the two-dimensional basic flow field. The incident shock of the inlet is circularly shaped at every cross-section along the flow direction, as showed in Figure 17, and it covers the entrance of the inlet to capture 100% of the upstream airflow. The high mass flow coefficient favours a low drag of external flows and provides sufficient thrust for the aircraft. Figure 18 shows that there exists a shock/boundary interaction near the position of the shoulder because the reflected shock is influenced by the viscosity, causing little shown in Figure 20, with two fixed sealing plates (orange parts) added in the side-walls and a movable sealing plate (green part) on the top-wall (as mentioned in Figure 11 and Figure 12). Figure 21 Mach: 0.2 0.6 1 1.4 1.8 2.2 2.6 2.9 3.05 3.15 3.25 3.6 3.98  off-design points, this shock gradually moves away from the cowl lip to the upstream and the spillage flow increases with Mach number decreasing. Nevertheless, the side walls of the inlet can still achieve an on-lip shock, which is the key factor guaranteeing its high mass coefficient characteristics. The Mach number distribution at the throat sections shows that the profiles of the Mach contour lines are smooth. There is no corner flow at the throat sional compressing ability and does not appear any corner flow.

Numerical simulation results show that the var-
iable-geometry Turbine-Based Combined Cycle inlet exhibits multiple advantages, such as high mass flow capture ability, low total pressure loss and strong compressing ability, which are highly significant for improving the overall per-section, and the exit flow of inlet is relatively good considering the exit flow of typical other type inlets (such as two-dimensional planar inlet).

Aerodynamic Performance Analysis of the Turbine-Based Combined Cycle Inlet
As the flight speed decreases, the rotation angle of the movable compression walls is increased to enlarge the throat area for starting the inlet under low Mach number conditions, and the rotation angle shows a nonlinear relationship with the flight speed. The aerodynamic performance based on numerical simulation results under different typical Mach numbers (presented in Table 2) indicates that the variable-geometry TBCC inlet exhibits the advantages of a high mass flow coefficient and a low total pressure loss with strong compressing ability, which arise from the IWRI inlet.
Compared to the IMX inlet, a typical binary inlet mentioned in [7], the new designed variable-geometry IWRI inlet is with higher compression efficiency at Mach 4.0 condition. And compared to the ATREX inlet, a variable geometry axisymmetric inlet mentioned in [5,19], the variable-geometry IWRI inherits high mass airflow capture coefficient even in off-design conditions and maintains a rather higher total pressure recovery. Such excellent performances result from the new design method of geometry transforming without any convex part or corner. It is obvious that these advantages are beneficial for increasing the engine thrust, which is of great significance for improving the overall performance of the TBCC.

Conclusion
In this paper, an appropriate variable-geometry inlet design without any convex part or corner is proposed for a Turbine-Based Combined Cycle system, based on the Internal Waverider Inlet with a high external compression ratio. Using CFD numerical simulations, the flow field characteristics and aerodynamic performances of different operation- 16. You Y (2011) An overview of the advantages and con-formance of the Turbine-Based Combined Cycle system. 5. Although there are errors in calculations in this article, the CFD turbulence model adopted in calculations has been checked, and the errors are within the tolerable range. So the results of calculations are reliable.