The characteristics and corrections of ventral support interferences in the transonic-speed wind tunnel for the blended-wing-body aircraft

Abstract

For the problem of ventral support interference in a transonic-speed wind tunnel with the blended-wing-body aircraft NPU-BWB-300 installed, the numerical simulation method based on Reynolds-averaged Navier–Stokes (RANS) equations is used to study the influence law of aerodynamic characteristic interference with the variation of Mach numbers and angles of attack. Moreover, the characteristics of ventral support interference for blended-wing-body aircraft and conventional aircraft are compared. The relevant mechanism of the generation and change of ventral support interference is revealed by employing analysis of the body surface pressure, the shock wave of the strut, and the separation area between the strut and the aircraft. The aerodynamic characteristic interference obtained from the numerical simulation is linearized based on the principle of the least square method. Afterward, a numerical simulation correction method of ventral support interference in the transonic-speed wind tunnel for the blended-wing-body aircraft is developed. Finally, the test results after the corrections of ventral support interferences in the transonic-speed wind tunnel for NPU-BWB-300 are obtained, which is significant for the evaluation of current aerodynamic performances and subsequent optimization designs.

1 Introduction

NPU-BWB-300 is a Blended Wing Body (BWB) aircraft concept proposed by the Institute of Aircraft Configuration Design of Northwestern Polytechnical University, the aerodynamic design of which has been subjected to a large number of numerical simulations and optimizations in the early stage, and it is currently in the research stage of wind tunnel tests and flight tests [1]. The wind tunnel test is a bridge between numerical simulation and flight test, and the quality of wind tunnel test data directly affects the aerodynamic characteristic evaluation of NPU-BWB-300 and the flight verification of the aerodynamic design. Accordingly, the selection of appropriate support forms and the deduction of support interference becomes a key issue [2, 3].

Support interference in wind tunnels is usually divided into two parts. One is far-field interference, and the other is near-field interference. In transonic-speed wind tunnel tests, the flow field near the model surface is complex, and the support interference can be transmitted both forward and backward, which has a large impact on the accuracy of the test results [4]. For near-field interference, the presence of struts destroys the model shape, affects the local pressure distribution, and also changes the development of the boundary layer near the surface area. In the transonic-speed wind tunnel test, the influences of shock waves caused by the struts are usually not negligible [5]. If the tail is located in the affected area, besides the drag, there will be a great impact on the lift and the pitch moment, and the wind tunnel test results must be specifically corrected [6]. Furthermore, the central lifting body of BWB is more fused with the wing than conventional configurations, the pressure perturbations of which are more likely to be transmitted in the spanwise direction. Therefore, it is worthwhile to investigate how to analyze and correct the support interference in the BWB transonic-speed wind tunnel test.

Sting support, ventral support, and wire support are several commonly used support forms in transonic-speed wind tunnel tests [7, 8]. The shape of BWB is relatively special, which places great constraints on the support forms in wind tunnel tests: the central lifting body of BWB has a cross-section of the airfoil profile, and the trailing edge is thin, which makes it difficult to provide enough space for the balance; and the rear of the central lifting body is arranged with a V-tail, nacelles, and a beaver-tail elevator. If a conventional sting support is used, it will cause significant shape changes to the tail of the model and affect the consistency between the test model and the prototype model. It is worth noting that the flight Reynolds number of NPU-BWB-300 is high, and only by using a large test model can the similarity of the Reynolds number be realized. The wire support is difficult to withstand the test model of NPU-BWB-300. Therefore, the ventral support is a more suitable choice compared to others [9]. Researchers in earlier wind tunnel tests also chose the ventral support, which was moved forward to the center front fuselage, in order to reduce the impact on the model [10, 11].

In recent years, the investigations for analyzing and correcting support interference mainly involve experimental methods, numerical simulation methods, and engineering estimation methods [9]. The experimental studies are practicable but time-consuming and expensive. The engineering estimation methods are inapplicable to the unconventional aircrafts. The numerical simulation methods are advantageous in terms of revealing the flow mechanism and avoiding secondary interference, which is of great significance for the correction of aerodynamic characteristics in wind tunnel engineering applications [12]. At present, for the transonic-speed wind tunnel test, the research work focuses on the numerical simulation method to correct the interference of the sting support for the conventional aircraft, which has formed a complete analysis system [13,14,15,16]. However, for the wind tunnel test of the BWB configuration, most of the research focuses on the low-speed ventral support model [17,18,19], whose cross-section shape and interference characteristics are quite different from those of the transonic-speed ventral support model [20,21,22]. Although the focuses of the articles mentioned above are not entirely identical to this paper, the research methods involved are still worth learning from. There are many works about wind tunnel experiments related to BWB. Wind tunnel measurements indicate that the tail-mounted engine layout produces the minimum drag penalty, while the fuselage-mounted engine layout increases drag the most [23]. The flange balance has high measurement accuracy and good correlation with the traditional cone balance. Flange balance meets the requirement of BWB layout aircraft high speed wind tunnel test and has a broad application prospect, so that it could be popularized in the future [24]. The current study presents a combination of experimental and computational investigations of a scaled-down Blended Wing Body (BWB) Unmanned Aerial Vehicle (UAV) model. The flow around the BWB scaled-down model is modeled by adopting four turbulence models, three of them based on the concept of eddy viscosity and one on the Reynolds-stress transport equation modeling [25]. The research on the characteristics and corrections of ventral support interference in transonic-speed wind tunnels for blended-wing-body aircraft in the open literature is rarely seen, and those relevant ones are summarized below.

The COMAC Beijing Aircraft Technology Research Institute [26] conducted numerical simulation and analysis using the RANS solver based on a multi-block structured mesh for the support interference problem, encountered in the transonic wind tunnel for the force and pressure test of a large wide BWB civil aircraft. The computational analysis was carried out for the BWB configuration with ventral struts, and the results and mechanism of the changes in the lift and drag characteristics of the whole aircraft caused by the ventral support were investigated. The study only focused on the design point condition, and the location of the ventral strut was close to the nose. The interference characteristics were manifested as a reduction in lift, a decrease in drag at small angles of attack, an increase in drag at large angles of attack, and an increase in pitch-up moment.

China Aerodynamics Development and Research Center [27, 28], for a ventral-supported BWB aircraft in transonic-speed wind tunnel tests, to begin with, used numerical simulation methods to study the support interference characteristics, especially for the variation law of interference when the blade inclination angle, expansion angle, and chord length were changed within a certain range. Afterward, the blade with an inclination angle of 60°, an expansion angle of 0°, and a chord length of 170 mm, considered to minimize the ventral support interference, was selected to correct the interference of the BWB transonic-speed ventral support in an experimental method, with the help of a V-shaped dummy struct. Eventually, it was found that, for the test condition of Ma = 0.75, the interference of the ventral support presented an increase in the lift and the pitch-up moment of the BWB aircraft, an increase in drag when angles of attack are negative and a decrease in drag when angles of attack are positive. The change in the geometry parameters of the ventral support blade affected the adverse pressure area near the trailing edge to a different degree, which was the main reason for the change in the longitudinal aerodynamic coefficients.

The complexity of the aerodynamic problems with ventral support interferences in the transonic-speed wind tunnels is multiple and is interconnected and intertwined. Some results showed that support creates a gradient of pressure on the rear body, giving rise to the drag force. Especially, bent sting produces changes of pressure on the lower surface of the horizontal tail, changing the aerodynamic force and the pitching moment on the tail. The interference cannot be physically eliminated and its effects will have to be allowed for in the planning of test experiments in the wind tunnel [29]. The influence of Reynolds and Mach numbers is not negligible, which contribute to the greatest extent to the inaccuracy and diversity of measuring results of the lift-curve slope [30]. Aerodynamicists have struggled with “Reynolds number gap”. At all times of the wind tunnel utilization, the Reynolds number achieved in the wind tunnel was far below the full-scale Reynolds number [31]. So the scaling of the wind tunnel is also important. For a successful contribution of the wind tunnel tests in the development of aeronautical vehicles, it is essential that the level of quality of measurements and the uncertainties involved are assessed and understood [32]. Taking VTI T-38 as an example, forces and moments on the models were measured using several six-component strain-gauge balances. The accuracy of the assembled balances was between 0.1% FS and 0.2% FS, and the accuracy of the monolithic balances was slightly better than 0.1% FS, except for the axial force component [33].

From the above literature review, it can be seen that the interference characteristics of the transonic-speed wind tunnel ventral support mounted for BWB aircraft are mainly focused on the design point. The research on the variation of interference characteristics when Mach numbers change has not yet been investigated, and the correction method based on numerical simulations is still immature. This paper intends to, learning from the correction method of the interference of the ventral support mounted for conventional configurations, calculate and analyze the interference characteristics of the ventral support in the transonic-speed wind tunnel mounted for NPU-BWB-300 based on numerical simulations. For NPU-BWB-300, the transonic-speed wind tunnel test has been conducted before. The Mach number ranges from 0.4 to 0.9, and the angle of attack ranges from −2° to 6°. These test results are modified in this paper, with the longitudinal aerodynamics coefficient correction of ventral support taken into account. The main practical applications of this paper can be summarized into three aspects: 1) The characteristics of the ventral support interference for the blended-wing-body aircraft are obtained in this paper. When conducting similar wind tunnel tests, designers can get the corrected results more quickly. 2) The relevant mechanism of the generation and change of ventral support interference is revealed. It can be used for optimizing the shape and position of the support, which is beneficial for reducing the support interference. 3) Combined with subsequent flight test results, the corrected wind tunnel results can help investigate ground-to-flight correlations for the blended-wing-body aircraft.

2 Test model and equipment

The test model is designed and manufactured by AVIC Huiyang Aviation Propeller Co., Ltd., and is fixed in the test section by using the form of ventral support. The test model consists of a basic BWB airframe and removable flow-through nacelles, V-tails, winglets, Kruger flaps at the leading edge, a rudder at the trailing edge, four simple flap rudder surfaces arranged from the wing root to the wing tip, and spoilers installed above the rudder surfaces, as shown in Fig. 1.

Fig. 1

The test model and component installation [1]

2.1 Scaled model

Based on the consideration of the size of the test section and the blockage requirement, an all-metal model scaled down to 1:72.222 relative to the size of the real aircraft is used in the transonic-speed wind tunnel test, and the measurements of the scaled model and the real aircraft are shown in Table 1. It should be noted in particular that the length of the wing span and the reference area in Table 1 do not take the winglets into account.

Table 1 The measurements of the scaled model for wind tunnel tests and the real aircraft

2.2 Ventral support

The ventral support is manufactured by AVIC Aerodynamics Research Institute. Relative to the length of the fuselage, the installation position of the ventral support is shown in Fig. 2. The support part is near the center of gravity position of the aircraft. The inclination angle of the ventral support is 45°, and the trailing edge does not have an expansion angle. The cross-section profile of the ventral support is a certain symmetric airfoil, shown in Fig. 3, which is applied in the ventral support blade of the transonic-speed wind tunnel, effectively avoiding strong shock waves. Between the two cases for the presence and absence of the ventral support, the reference areas for calculating the lift and drag coefficients are slightly different. The former is 0.165 m², while the latter is 0.181 m². The interface is approximately equal to the cross-section of the ventral support, shown in Fig. 3, the area of which is 0.016 m².

Fig. 2

The installation position of the ventral support

Fig. 3

The cross-section of the ventral support

2.3 Wind tunnel

This test was conducted in the FL-3 wind tunnel of AVIC Aerodynamics Research Institute, which is a direct current intermittent blow-down wind tunnel, shown in Fig. 4, with a test section size of 4.2 m × 1.5 m × 1.6 m (length × width × height). The operating range of the test angle of attack is 0° to 30°, and the operating range of the sideslip angle is −12° to 12°. The Mach number range corresponding to the used nozzle is 0.3 to 1.2.

Fig. 4

The test model and the wind tunnel

3 Numerical methods and validation

The RANS equations are used to solve the flow field. The control equation is discretized using the finite volume method, and the turbulent viscosity term is calculated using the shear stress transport (SST) two-equation model. The spatial discretization follows the high-resolution format, and the time marching strategy is an implicit second-order upwind form. Local time steps are used to accelerate convergence.

The flow field control equation used in the numerical simulation is as follows:

$$\frac{\partial }{\partial t}{\iiint }_{V}\vec{Q}dV+{\iint }_{S}\left(\vec{F}-{\vec{F}_{v}}\right)\cdot \vec{n}dS=0.$$

(1)

In Eq. (1), $V$ is the control volume, and $S$ is the surface area of the control volume. $\vec{Q}$ stands for the conservative variables. $\vec{F}$ and ${\vec{F}_{v}}$ are the convective flux vector and the diffusion flux vector, respectively. $\vec{n}$ represents the unit outward normal vector of surface elements.

The detailed equations of the SST turbulence model are shown below:

$$\frac{{\partial \left( {\rho k} \right)}}{\partial t} + \frac{{\partial \left( {\rho u_{j} k} \right)}}{{\partial x_{j} }} = \tau_{ij} S_{ij} - \rho \beta^{*} \omega k + \frac{\partial }{{\partial x_{j} }}\left[ {\left( {\mu + \sigma_{k} \mu_{t} } \right)\frac{\partial k}{{\partial x_{j} }}} \right],$$

(2)

$$\frac{\partial \left(\rho \omega \right)}{\partial t}+\frac{\partial \left(\rho {u}_{j}\omega \right)}{\partial {x}_{j}}=\frac{\gamma }{{\nu }_{t}}{\tau }_{ij}{S}_{ij}-\rho \beta {\omega }^{2}+\frac{\partial }{\partial {x}_{j}}\left[\left(\mu +{\sigma }_{\omega }{\mu }_{t}\right)\frac{\partial \omega }{\partial {x}_{j}}\right]+2\left(1-{F}_{1}\right)\cdot \frac{\rho {\sigma }_{\omega 2}}{\omega }\cdot \frac{\partial k}{\partial {x}_{j}}\cdot \frac{\partial \omega }{\partial {x}_{j}},$$

(3)

$${\mu }_{t}={\rho {{\nu}_{t}}}=\frac{{\rho a}_{1}k}{{\text{max}}\left({a}_{1}\omega ,\Omega {F}_{2}\right)}.$$

(4)

In the formulas above, $k$ is the turbulent kinetic energy, and $\omega$ is the specific turbulent dissipation rate. ${\tau }_{ij}$ is the shear stress tensor. ${S}_{ij}$ is the strain rate tensor. $\mu$, ${\mu }_{t}$, and ${\nu}_{t}$ are the dynamic viscosity, the turbulent kinematic viscosity, and the turbulent dynamic viscosity, respectively. The definitions of other functions and parameters are detailed in Ref. [34].

3.1 Verification of grid convergence

The grid used for the calculation is shown in Fig. 5. The density of the near-wall area of the aircraft and engine is increased. The nose, nacelle lip, V-tail leading edge, fuselage leading edge, and the leading edge of the ventral support are fined. The first prism layer has a height of ${{y}^{ + }} \le 1$, and there are 20 prism layers, which meets the computational requirements of the near-wall turbulence model. The grid for the configuration without the ventral support is similar to this one, and the grid scales are kept at the same precision. The total number of the grid is about 70% of that of the model with the ventral support since the area of the fine grid is reduced due to the absence of the ventral support.

Fig. 5

Grid for the configuration with the ventral support

Before carrying out the numerical study, the convergence of the grids in Fig. 5 needs to be verified, as shown in Table 2. A grid series containing six sets of grids is formed, and the total number of grids is gradually increased from 30.5 million to 54.5 million by decreasing the scale of the surface grid cells. The aerodynamic coefficients of each set of grids are calculated separately for a Mach number of 0.4 with an angle of attack of 4° and for a Mach number of 0.8 with an angle of attack of 4°.

Table 2 Number of the grid sequence

As shown in Fig. 6, for the case of Ma = 0.4 and α = 4°, all the aerodynamic coefficients change slightly with the increase of the number of grids, and the relative errors are kept in a reasonable range compared with the experimental values (the lift coefficient is around 5%, and the drag coefficient and the pitch moment coefficient are around 10%). For the case of Ma = 0.8 and α = 4°, the lift coefficient and the drag coefficient change slightly and are close to the experimental values (the relative errors are all within 10%). The fluctuation of the pitch moment coefficient is relatively obvious, and the range of relative errors is between 8% and 18%. For the case of Ma = 0.8 and α = 4°, there are no obvious convergence trends in the drag and moment coefficients, which seems to be a common phenomenon for unstructured grids in some cases. Therefore, for choosing an appropriate grid, we still need to consider the proximity to experimental results. The calculated results of grid No. 4 is the closest to the experimental results, as shown in Fig. 6b. Dashed lines represent for the experiment results of the drag and moment coefficients. Considering the proximity to experimental results and the consumption of computational resources, grid No. 4 in Table 2 is used in the following calculations.

Fig. 6

Computed results for the mesh convergence

3.2 Comparison with experimental results

Based on grid No. 4, the lift, drag, and pitch moment coefficients at a low subsonic speed (Ma = 0.4) and a high subsonic speed (Ma = 0.8) are calculated respectively, and compared with the FL-3 wind tunnel test results. As shown in Fig. 7, the range of the angles of attack for the low subsonic condition is about 20°, and that for the high subsonic condition is about 12°. For most of the ranges of the calculated angles of attack, it can be seen that the numerical calculation results are in good agreement with the test results, which can verify that the numerical method, turbulence model, and grid generation strategy chosen in this paper are reasonable, and can be used to calculate and analyze the interference of the ventral support in the transonic-speed wind tunnel of the BWB aircraft.

Fig. 7

Comparisons between computational results and experimental results

4 Analysis and discussions

Based on the numerical method, turbulence model, and grid generation strategy established in Section 3, numerical simulations of the flow fields of the scaled test model of NPU-BWB-300 with and without the ventral support were carried out, respectively. The calculation conditions are consistent with the test conditions, where the Mach number ranges from 0.4 to 0.9 and the angle of attack ranges from −2° to 6°.

4.1 Interference characteristics

As shown in Fig. 8, the curve labeled with “w” in the legend is the calculation result of the test model with ventral support, and the curve labeled with “w/o” in the legend is the calculation result of the test model without ventral support. It is worthy of note that the unit length of the longitudinal axis of the lift coefficients represents 0.1, and that of the drag and pitch moment coefficients is 0.01.

Fig. 8

Comparisons of aerodynamic characteristics

For the lift characteristic in Fig. 8a, the influence of ventral support represents an increase in lift when the Mach number is small, but a decrease in lift when the Mach number is large. For the drag characteristic in Fig. 8b, the influence of ventral support is manifested as a reduction in drag for the majority of all the conditions. For the pitch moment characteristic in Fig. 8c, the ventral support interference shows no regular patterns, sometimes causing an increase in the pitch-up moment, and sometimes causing a decrease in the pitch-up moment, for which a more in-depth quantitative analysis is needed.

Assume the aerodynamic coefficient is $V$, which can represent any one of the lift coefficient $C_{L}$, the drag coefficient $C_{D}$, or the pitch coefficient $C_{m}$.

$$\delta V = V_{w} - V_{w/o}.$$

(5)

In Eq. (5), $\delta V$ is the interference of $V$ caused by the ventral support. $V_{w}$ is the $V$ calculated for the case with the ventral support. $V_{w/o}$ is the $V$ calculated for the case without the ventral support.

As shown in Fig. 9, the variation of $\delta V$ with the change of Mach numbers and angles of attack is the interference characteristic of the ventral support in the transonic-speed wind tunnel for NPU-BWB-300. Generally speaking, the interference characteristics for the lift coefficient represent an increase in lift when $Ma \le 0.85$ and a reduction in lift when $Ma = 0.90$. The overall variation of $\delta C_{L}$ is between −0.02 and 0.01. The interference characteristics for the drag coefficient are manifested as a reduction in drag for most of the test conditions, and only when $Ma = 0.90$ and $\alpha \le 2^{ \circ }$, show an increase in drag. The overall variation of $\delta C_{D}$ is practically between −0.002 and 0.002. The interference characteristics for the pitch moment coefficient present as a decrease in the pitch-up moment when $Ma \le 0.60$ and an increase in the pitch-up moment when $Ma = 0.80$ and $\alpha \ge 3^{ \circ }$, and show no regular patterns when $Ma \ge 0.85$. The overall variation of $\delta C_{m}$ is between −0.004 and 0.004 for most test conditions.

Fig. 9

Comparisons of interference characteristics

From the perspective of quantitative analysis, the interference characteristics of the transonic-speed wind tunnel ventral support of the BWB aircraft can be summarized in Table 3. Quoted from Ref. [9], the interference characteristics of the transonic-speed wind tunnel ventral support of the aircraft with the conventional configuration are further compared in Table 3. Substantially, $\delta C_{L}$ of both are basically identical. $\delta C_{D}$ and $\delta C_{m}$ of the BWB aircraft are relatively smaller.

Table 3 Interference characteristics of the ventral support

4.2 Flow field analysis for ventral support

In the transonic-speed wind tunnel, due to the presence of the ventral support, the detailed characteristics of the flow field present some changes, which are closely related to the formation of the interference characteristics. In this section, the flow field analysis of NPU-BWB-300 with/without the ventral support is carried out at an angle of attack of 4° and Mach numbers of 0.6, 0.8, and 0.9, and the typical changes in the flow field under the influence of the ventral support are explained in terms of the surface pressure of the fuselage, the shock wave caused by the strut, and the separation at the junction of the fuselage and the strut.

Figure 10 shows the pressure coefficient curves of three spanwise positions at different Mach numbers, which are the symmetry ($\eta = 0$), the wing-body blended section ($\eta = 33\%$), and the mid-wing section ($\eta = 67\%$). In the figure, the horizontal coordinates are dimensionless based on the chord length of the local airfoil, and the directions of all the longitudinal coordinates are from top to bottom, indicating the increasing pressure. For the symmetry position, all three Mach numbers show similar characteristics. The upper airfoil is almost unaffected, and the pressure increases in most areas of the lower airfoil due to the station point caused by the strut, which is not weakened until after x/c = 0.8. For the position of $\eta = 33\%$, the pressure coefficient curves are almost overlapped when the Mach number is 0.6, and the influence of the ventral support is negligible at this time. When the Mach number is 0.8, the surface pressures of both upper and lower airfoils are slightly reduced. Nevertheless, when the Mach number is increased to 0.9, the surface pressures of both upper and lower airfoils are significantly reduced. For the upper airfoil, the influenced region is mainly concentrated in the vicinity of the leading edge, and for the lower airfoil, the influenced region is located between x/c = 0.4 and x/c = 0.8. For the position of $\eta = 67\%$, the pressure coefficient curves are almost consistent at all three Mach numbers, indicating that the influence of the ventral support is negligible at this place.

Fig. 10

Pressure coefficient curves at some spanwise positions

For Fig. 10a, when the Mach number is 0.6, the ventral support interference only affects the pressure distribution at the symmetry, and it can be presumed that the ventral support interference makes the pressure increase in a small area near the symmetry of the lower surface of the aircraft. Thus, $\delta C_{L} > 0$, which is identical to the result presented in Fig. 9a. For Fig. 10b, the ventral support interference affects a larger area when the Mach number is 0.8, and the lift increases first and then decreases from the symmetry to the wing-body blended section, which slightly reduces the lift of the aircraft. For Fig. 10b, focusing on the left figure, we take the pressure coefficient for the case of absence of the ventral support as a reference, and the presence of the ventral support reduces the pressure on the lower surface of the fuselage, indicating an increase in lift. For Fig. 10b, focusing on the middle figure, the presence of the ventral support increases the pressure on the lower surface of the fuselage, indicating a decrease in lift. For Fig. 10c, when the Mach number is 0.9, the pattern of ventral support interference is similar to that of Ma = 0.8. However, the influence of decreasing pressure is wider and stronger, and the combined influence of each region is manifested as $\delta C_{L} < 0$. This is consistent with the result in Fig. 9a, but it is not known why the pressure field changes in this way, and we will try to analyze the mechanism of this change in the following section.

Figure 11 shows the wall shear stress contours at different Mach numbers and the Mach number contours at three spanwise positions corresponding to Fig. 10. It can be seen that the velocity field under the fuselage is significantly changed due to the presence of the ventral support, and the viscous effect of the solid wall decelerates the airflow. The wall shear stress in the figure can be considered as a characterization of the surface friction coefficient. For the case of Ma = 0.8 and α = 4°, the Mach number contours of the cross section located 0.3 m below the nose are shown in Fig. 12. The ventral support also acts like a “guide vane”, which makes the airflow underneath the fuselage pass more smoothly, thus reducing the friction drag, which is considered to be the reason why $\delta C_{D} < 0$ for most of the test conditions.

Fig. 11

Contours of wall shear stress and Mach number

Fig. 12

The Mach number contours below the fuselage

From Fig. 11d and f, it can be seen that when the Mach number is 0.8 and 0.9, there is an obvious separation area at the trailing edge of the strut, which is considered to be caused by the shock wave. The separation is caused by the sudden decrease of the pressure after the shock wave. The interference to the flow field can be propagated both forward and backward within the range of the transonic speed, and the separation area is close to the wing in the flow direction. Therefore, it can be assumed that its influence on the flow field is not negligible, and the separation flow is often accompanied by the appearance of vortical flow, which leads to the emergence of a low-pressure region and shows the induced effect of pressure reduction on the surrounding flow field.

In general, when the Mach number is 0.6, the separated flow induced by the strut is not significant, and the viscous deceleration effect of the solid wall dominates. For the lower surface, the ventral support interference is manifested as an increase in pressure. When the Mach number is increased to 0.8, or even 0.9, with the expansion of the separation region, the influence of the vortex low-pressure is dominant, which leads to the decrease of the pressure of the lower surface. Subsequently, the ventral support interference is changed from increasing the lift to decreasing it. This explains why the pressure of the lower surface increases first and then decreases from the symmetry to the wing-body blended section in the spanwise direction.

In this paper, it is believed that $\delta C_{m}$ are mainly related to the relative positions of the ventral support and the center of gravity of the aircraft, while the fluctuation characteristics of $\delta C_{m}$ are related to the separated flow. The separated flow is naturally unsteady. When the separated flow appears, the aerodynamic coefficient calculated by numerical simulations will show fluctuating characteristics. Considering that the fluctuating characteristics are also shown in Fig. 9, it is assumed that the fluctuation characteristics of $\delta C_{m}$ are related to the separated flow. Taking the example of the junction between the fuselage and the strut as shown in Fig. 13, we will explore the changes in the separated flow field with the Mach number increasing, and explain why there are incremental fluctuations with the increase of the Mach number.

Fig. 13

The junction of the aircraft and the support

The separated flow field in the vicinity of the junction is illustrated in Fig. 14. As the Mach number increases, the separation area increases gradually, and the separation area here is close to the lower surface of the fuselage, which has a direct impact on the pitch moment coefficient. The larger the Mach number, the larger the separation area is, and the more obvious the fluctuation characteristics represent.

Fig. 14

Area of the separated flow

4.3 Corrected results for ventral support

In this section, based on the analysis of the interference characteristics and flow field of ventral-supported NPU-BWB-300 in the transonic-speed wind tunnel, the calculated data of the interference of the aerodynamic coefficient obtained by numerical simulations and the aerodynamic coefficient of the original test data are used as the preparatory data. Then, the least-squares method is used to linearize these data. Finally, the corrected test data of the ventral-supported NPU-BWB-300 in the transonic-speed wind tunnel is obtained.

As described above, in Eq. (5), $V$ is the aerodynamic coefficient obtained in the wind tunnel test, which can represent any one of the lift coefficient $C_{L}$, the drag coefficient $C_{D}$, or the pitch coefficient $C_{m}$. $\delta V$ is the interference of $V$ calculated in the numerical simulation. For $V$ and $\delta V$, the processing steps are as follows:

• 1) linear fitting of ${{\delta V} \mathord{\left/ {\vphantom {{\delta V} V}} \right. \kern-0pt} V}$, and obtain $\left( {{{\delta V} \mathord{\left/ {\vphantom {{\delta V} V}} \right. \kern-0pt} V}} \right)^{ * };$

• 2) calculate $\left( {\delta V} \right)^{ * } = \left( {{{\delta V} \mathord{\left/ {\vphantom {{\delta V} V}} \right. \kern-0pt} V}} \right)^{ * } \times V;$

• 3) calculate $V^{ * } = V - \delta V^{ * }.$

Figure 15 shows the results after linear fitting of ${{\delta V} \mathord{\left/ {\vphantom {{\delta V} V}} \right. \kern-0pt} V}$, and this step means to correct the amount of aerodynamic coefficient interference obtained from the numerical simulation. Drawn lessons from Ref. [6, 9, 10], the linearization processing makes the law more significant and eliminates unnecessary disturbances. It is worth mentioning that the unit of the longitudinal axis is expressed as a percentage.

Fig. 15

Linear fitting of the relative quantity of aerodynamic coefficient interference

Figure 16 shows the corrected test data of the ventral-supported NPU-BWB-300 in the transonic-speed wind tunnel. The most corrections appear when the Mach number is up to 0.85 or higher. For the pitch moment coefficient, when $Ma = 0.90$ and $\alpha \le 2^{ \circ }$, the corrections significantly increase the pitch-up moment, which eliminates the impact of shock waves. Compared with Fig. 8, the transonic-speed wind tunnel ventral support interference characteristics are more prominently reflected in the corrected test results.

Fig. 16

Corrected test data and original test data

5 Conclusions

• 1) Using numerical methods, the interference characteristics of the ventral-supported NPU-BWB-300 in the transonic-speed wind tunnel are obtained. The interference characteristics for the lift coefficient represent an increase in lift when $Ma \le 0.85$ and a reduction in lift when $Ma = 0.90$. The interference characteristics for the drag coefficient are manifested as a reduction in drag for most of the test conditions, and only when $Ma = 0.90$ and $\alpha \le 2^{ \circ }$, show an increase in drag. The interference characteristics for the pitch moment coefficient present as a decrease in the pitch-up moment when $Ma \le 0.60$ and an increase in the pitch-up moment when $Ma = 0.80$ and $\alpha \ge 3^{ \circ }$, and show no regular patterns when $Ma \ge 0.85$.

• 2) The influence of the ventral support on the lift is caused by the viscous effect of the solid wall of the strut and the separated flow induced by the shock wave after the strut. The ventral support acts like a “guide vane”, which makes the airflow underneath the fuselage pass more smoothly, thus reducing the friction drag. The fluctuation is related to the separation flow field near the junction between the fuselage and the strut, especially for the pitch moment coefficient. The larger the Mach number, the more obvious the fluctuation characteristics represent.

• 3) A numerical simulation correction method for the transonic-speed wind tunnel ventral support of the BWB aircraft NPU-BWB-300 is developed. The amount of aerodynamic characteristic interference obtained from numerical simulations is linearized. The interference characteristic of the ventral-supported NPU-BWB-300 in the transonic-speed wind tunnel is more prominently reflected in the corrected test results.