Axial Force Coefficient Research Articles

Aerodynamic characteristics of different configurations of mechanically deployable aerodynamic decelerator in subsonic region

AbstractThe deceleration effect of the deployable aerodynamic decelerator is not as good as a parachute in the subsonic region. This paper proposes a novel concept of using a parachute-like configuration (PLC) to enhance the deceleration performance of the mechanically deployable aerodynamic decelerator (MDAD) through structural transformation. The MDAD turned into the PLC from the sphere cone configuration (SCC) at Ma 0.8. The aerodynamic characteristics of the two configurations are analysed deeply. Compared to the SCC, the results show that the drag coefficient increases effectively, and the maximum increases is about 10% in the PLC. The airflow is altered by the MDAD configuration, which can affect the surface pressure and temperature. During the transformation process, the axial and normal force coefficients tend to stabilise. However, the static stability of the PLC deteriorates sharply compared to the SCC when the angle-of-attack exceeds 45°.

Numerical Study on the Influence of Separation Time Sequence on the Initial Thermal Separation

The process of separating stages is crucial for multistage rockets, directly influencing the success of the launch plan. Different separation timing methods alter the flow field structure within the interlevel zone at separation, influencing the separation of the two-stage rockets. This paper employs the SST k-ω turbulence model to investigate the structure of the flow field and its aerodynamic and motion characteristics under different nozzle baffle opening and separation times, taking into account variable properties, supersonic compressibility, and the upstream–downstream interference. First, we examined the standard flow field structure, considering the engine jet, the lateral jet between stages, and the disturbance from the external supersonic inflow. Then, we discussed the displacement characteristics and axial force coefficient curves of the first and second steps of the separation process. Finally, we explored the impact of baffle opening and separation times on the flow field structure and axial force coefficients of the two stages at the onset of separation. For the flow field structure, a delay in the baffle opening and separation moment led to a gradual increase in downstream and separation regions until they stabilized after a certain range. However, the axial force coefficients displayed different behavior before and after the design point.

A numerical study on the hydrodynamics of a swimming crocodile model

Aiming to uncover the propulsion mechanisms underlying a cruising crocodile, we conduct computational fluid dynamics (CFD) simulations on the flow around a simplified three-dimensional model of the Crocodylus siamensis. The locomotion of the crocodile model is realized through undulating its body and tail, mimicking a crocodile-like swimming pattern. At a cruising speed of U∞ = 0.5 m/s (corresponding to a Reynolds number Re = 9.95 × 105 based on U∞ and the body length L), the hydrodynamics of the crocodile model are investigated, taking into account effects of the undulation parameters (i.e., amplitude A and frequency f). The normalized undulation parameters cover broad ranges of 0.6 ≤ A* = A/W ≤ 1.0 and 0.25 ≤ f * = fW/U∞ ≤ 0.625, where W is the body width. The CFD simulations are conducted in ANSYS Fluent, with the SST k–ω turbulence model and user-defined functions for dynamic mesh being used. Numerical results reveal that A* and f * render profound effects on the hydrodynamic performance of the crocodile model. The time-mean axial force coefficient (CA¯) and power coefficient (C¯Power) exhibit rapid growth with increasing A* and/or f *, while the root mean square lateral force coefficient (Cy,rms) is more dependent on f * than on A*. It is further found that, irrespective of A*, CA¯ and C¯Power can be well scaled with Strouhal number St (= 2fA/U∞) or St2(1 − U∞/c). Furthermore, distinct flow patterns are observed in the wake of the crocodile model undulating at different St, corresponding to the drag, transition (or cruising), and thrust type swimming, respectively. Discussion is made on the wake flow structures and their connections to the generation of the hydrodynamic forces. The findings from this work contribute to the understanding of the propulsion mechanisms of the swimming crocodile, meaningful for the design of efficient biomimetic amphibious robots.

CFD analysis on the aerodynamic coefficients of an ejection seat system at supersonic speed

In the present study, a 3-D study of the aerodynamic coefficients of an ejection seat system is performed. The analysis is performed using the Reynolds Averaged Navier-Stokes equations where an unstructured grid of the polyhedral cells is used. The aerodynamic coefficients are calculated using a density-based solver and the standard k-ε turbulence model. The investigation is performed at Mach number (Ma) = 1.25 by varying the angle of attack (α) from -15° to 15° with the increment of 5° where the yaw angle (β) is fixed at 0°. According to the findings, the magnitude of the axial force coefficient (CX) increases as α decreases whereas the value of the normal force coefficient (CZ) decreases with the increase of α. Similarly, the value of the pitching moment coefficient (Cm) decreases with the increase of α.

Numerical investigation on the wake and energy dissipation of tidal stream turbine with modified actuator line method

This study evaluates correction methods for the actuator line method in tidal stream turbine calculations. Findings indicate that three-dimensional Gaussian distribution coefficients align closely with experimental results when ε = 2dr. Tip loss correction addresses abnormal axial force coefficient elevation at the blade tip, while stall delay correction minimally impacts standard turbine operation. Root loss correction slightly affects the root vortex but notably delays the disappearance of the nacelle after tail flow's bimodal region to 4D, contrary to observations. Using a cylinder correction at the blade root improves the root vortex representation. Enhanced ALM, combined with LES, simulates wake and energy loss across varying turbulence intensities. At low turbulence, the spiral vortex structure is clearer, with fewer stray vortices and a more regular circular shape. Increasing turbulence blurs the structure, introducing more turbulent vortices and losing regularity. Entropy production concept represents energy losses as total, direct, and turbulence entropy production. Direct entropy production is minimal, localized at blade tip, nacelle, and support structures due to significant velocity gradients. Indirect entropy production causes substantial energy loss, resembling wake flow's vortex pattern due to turbulent pulsation. With higher turbulence, EPR, EPDD, and EPTD decline as wake vortices are disrupted, reducing energy loss.

Aerodynamic Coefficients of a Microspoiler for Spin-Stabilized Projectiles

In this paper, the aerodynamic coefficients of a microspoiler for a spin-stabilized projectile are studied using a computational fluid dynamics (CFD) simulation. To guarantee an effective study, the CFD simulation methodology is validated by the current literature and a wind-tunnel test. As a result, the additional axial force coefficient, additional normal force coefficient, and normal moment coefficient are obtained and varied with a wide range of Mach numbers (from 0.6 to 2.0), angles of attack (from 0 to 30°), and aerodynamic roll angles (from 0 to 180°). The numerical simulation results show that, in addition to the freestream Mach number and the angle of attack, the effect of the aerodynamic roll angle on the additional axial force and normal force coefficients cannot be negligible. By observing and analyzing a series of pressure field plots around the uncontrolled and controlled projectiles, some important phenomena are reasonably discussed. It was found that the complicated variation in the aerodynamic coefficients of the microspoiler is induced by flow modifications, such as the pressure distribution around the projectile. The results of this research are expected to be supplementary to those concerning the aerodynamic characteristics of spin-stabilized projectiles with microspoilers, as concluded in the current literature.

Data maps for material identification in helical milling by spindle power monitoring

Hole making on stacked aerospace materials is a major operation during aircraft assembly which poses significant challenges during manufacturing because of different material machinability. Strategies involving smart machining including adapting proper cutting conditions using real time monitoring can lead to significant improvements. This paper is a continuation of our research that uses data map methodology characterized by different specific force regions for workpiece material identification. In this article, spindle power is monitored utilizing CNC machine internal sensor during helical milling of Aluminium and Titanium alloys in a aerospace stack for estimating cutting coefficients. Our previous research addressed the material detection in circular milling of Aluminium and Titanium alloys independently using a force dynamometer. The result shows the applicability of data map technique consisting of axial force coefficients for material identification in helical milling and highlights the significance of stack sequence .

On wind turbine loading induced by non-uniform approaching flow at high Reynolds numbers

Influences of non-uniform incoming flow on the wind turbines blades forces and root bending moments (RBMs) are not fully understood. To advance our current understanding, numerical studies of a three-bladed horizontal axis wind turbine with cylinders placed in front of it to produce non-uniform flow approaching the turbine with different non-uniformity levels have been carried out to examine the variations of blade and rotor loading due to the non-uniform incoming flow. The phase-averaged predicted blade forces reveal that the blade tangential force, in-plane RBM, and power coefficient are much more sensitive to the upstream streamwise velocity variations and are much more strongly affected than the blade axial force, out-of-plane RBM, and thrust coefficient. It also shows that for non-uniform incoming flows the blade axial force to the blade tangential force ratio fluctuates significantly during one rotor revolution, resulting in large variations of the blade elastic torsion and that the total blade force (magnitude and direction) undergoes a non-linear change in the circumferential and radial directions, which will likely lead to the reduction in the turbine operational life significantly, especially for long lightweight blades of large size wind turbines. This study also shows different behaviors of the blade forces along the blade span under non-uniform upstream flows in terms of the amplitudes and standard deviations of their oscillations. For the blade tangential force, λ and σ increase monotonously along the blade span up to near the blade tip, whereas those of the blade axial force increase up to approximately 0.6 blade span and show an opposite trend behind that.

Mars Entry, Descent, and Landing Instrumentation 2 Trajectory, Aerodynamics, and Atmosphere Reconstruction

On February 18th, 2021, the Mars 2020 entry system successfully delivered the Perseverance rover to the surface of Mars at Jezero Crater. The entry capsule carried a set of instrumentation installed on the heat shield and backshell, named the “Mars Entry, Descent, and Landing Instrumentation 2.” The instruments include pressure transducers, thermocouples, heat flux gauges, and radiometers to measure the aerodynamic and aerothermodynamic performance of the entry vehicle. This paper describes the trajectory and atmosphere reconstruction results based on the pressure sensor measurements. The process uses a Kalman filter approach to estimate the freestream atmospheric properties from the pressure measurements combined with a model of the pressure distribution of the heatshield and other sensor inputs, including an inertial measurement unit and other on-board navigation sensors, and several external atmospheric observations. The results indicate that the upper altitude density was up to 150% higher than nominal, which is consistent with the observed early entry guidance start time. The density below 40 km was within 12% of the preflight predictions. The reconstructed axial force coefficient was approximately 2% lower than the preflight prediction across the flight range.

Generic Cutting Force Modeling with Comprehensively Considering Tool Edge Radius, Tool Flank Wear and Tool Runout in Micro-End Milling.

Accurate cutting force prediction is crucial in improving machining precision and surface quality in the micro-milling process, in which tool wear and runout are essential factors. A generic analytic cutting force model considering the effect of tool edge radius on tool flank wear and tool runout in the micro-end milling process is proposed. Based on the analytic modeling of the cutting part of the cutting edge in the end face of the micro-end mill bottom, the actual radius model of the worn tool is established, considering the tool edge radius and tool flank wear. The tool edge radius, tool wear, tool runout, trochoidal trajectories of the current cutting edge, and all cutting edges in the previous cycle are comprehensively considered in the instantaneous uncut chip thickness calculation and the cutter-workpiece engagement determination. The cutting force coefficient model including tool wear is established. A series of milling experiments are performed to verify the accuracy and effectiveness of the proposed cutting force model. The results show that the predicted cutting forces are in good agreement with the experimental cutting forces, and it is necessary to consider tool wear in the micro-milling force modeling. The results indicate that tool wear has a significant influence on the cutting forces and cutting force coefficients in the three directions, and the influences of tool wear on the axial cutting force and axial force coefficient are the largest, respectively. The proposed cutting force model can contribute to real-time machining process monitoring, cutting parameters optimization and ensuring machining quality.

Analysis of the axial force distribution characteristics of multistage pumps and its correlation with hydraulic property

As the centrifugal pump is running, the fluid usually flows into the impeller along pump shaft, and the fluid flows out radially by the force of the impeller. The force is mutual, so the impeller is also subjected to the reaction force of the fluid, but the distribution of this force on the blades is uneven. In addition, the front and rear shrouds of the impeller are asymmetric, which are the main causes of axial force. This paper adopts numerical calculation method studying the mechanism of axial force of impeller at all stages of multistage pump at various working conditions, and exploring the formation mechanism of shroud pressure differential force and blade twisting axial force and its variation laws of similarities and differences, analyzing the steady state and transient characteristics between axial force and hydraulic property of double-casing multistage pump. The results show that the rotational angular velocity of the fluid in the front and rear pump chamber at each stage impeller is distributed along the axial direction in three regions, the regions are pump body boundary layer, core region, and impeller boundary layer. The working surface and back surface of the blade twist have the high and low axial force area, and its distribution is staggered, at the same number of stages, the greater the flow rate, the smaller the blade twisting axial force. The shroud pressure differential force with the increase of impeller stages presents a linear increasing trend, conforms to the principle of linear superposition of cover pressure differential force. The total axial force pulsation of multi-stage pump is related to the number of secondary impeller blades, its primary frequency coincides with the secondary impeller blade frequency, increasing the flow rate can reduce the multi-stage pump axial force pulsation amplitude. The pulsation period of single-stage impeller head and efficiency are related to the number of impeller blades, the smaller the number of impeller stages, the stronger the pressure dynamic, and static interference effect of the impeller inlet and outlet. Rotation of the secondary impeller causes dynamic and static interference, which is the main reason for the pulsation of the axial force coefficient in double-casing multistage pumps, the pulsation intensity is related to the periodic generation and shedding of the blade vortex. The results of the study can be used as a reference for optimizing the axial force of double-casing multistage pumps.

Nonlinear deformation and instability of a dielectric elastomer tube actuator

The mechanical response and electromechanical instability (EMI) of a dielectric elastomer tube actuator (DETA) under the coupling loadings of voltage, internal pressure and axial force are studied in this paper. Based on the Gent model and considering the nonlinear relationship between dielectric permittivity and stretches, two different loading conditions are discussed: force tuning and voltage tuning. For the force tuning, it is found that the radius of the DETA first decreases, then increases and finally decreases due to the competition between the axial force and voltage as well as the strain-stiffening property of the Gent model under the large deformation. For the voltage tuning, the effects of axial force, internal pressure and electrostrictive coefficient on the electromechanical response are explored. The electrical breakdown (EB) during the nonlinear deformation of DETA is also analyzed. The stress distribution along the thickness of the DETA is given by the analytical solution, and the two failure modes including EMI and loss of tension for the DETA are studied with axial constraints. It is found that the EMI can be eliminated by changing the stretch in the z-direction and internal pressure, which may also lead to the failure of loss of tension. The competitive relations of the two failure modes are discussed in detail. This work can contribute to the design of DETAs with a large actuation.

Türbülans Yoğunluğunun Geçiş Yer Tahminine Etkisinin Bölgesel Korelasyon Geçiş Modeli ile İncelenmesi

Aerodynamic parameters are among the most important parameters in flight performance analyses of air/sea vehicles. Free stream turbulence intensity has significant importance on aerodynamic parameters obtained with computational fluid dynamic analyses and wind tunnel tests measurements. In this study, the effect of free stream turbulence intensity on the transition locations of spheroid geometry using with the widely accepted local correlation transition model. The computations are performed at 6.5 x 106 Reynolds number with 0 and 5 degree angle of attacks. The computations at 5 degree angle of attack are compared with an available experimental study. The effect of free stream turbulence intensity is investigated with axial force coefficient, normal force coefficient, and surface friction coefficient distributions. It is seen that axial and normal force coefficients increase with increasing free stream turbulence intensity. The differences in force coefficients obtained with the free stream intensity range used in the study shall create noteworthy effects in flight performance analyses. When surface friction coefficients are investigated, the transition model estimates the transition locations earlier while free stream turbulence intensity increases as expected. However, the transition front geometry is obtained significantly different with respect to the experimental results.

Estimation of Discretization Uncertainty Using the γ−Reθ Transition Model for Transitional Flows on 6:1 Spheroid

Abstract This paper aims to estimate the surface mesh size related discretization uncertainties using the γ−Reθ transition model combined with the shear stress transport (SST) k–ω turbulence model. For comparison, this work employs an available experimental study performed with a 6:1 prolate spheroid. The grid convergence index (GCI) study is performed for axial force, surface skin friction, and pressure coefficients with three levels of meshes. The transition model estimates the axial force coefficients (CX), approximately half of which are obtained using fully turbulent calculations with higher GCI values. The GCI values around the axial force coefficients for the level-2 mesh are less than 1% based on fully turbulent calculations. However, with the transition model, these values for the same mesh level increase to 10%. While the GCI values of surface pressure coefficients are very small based on both fully turbulent and transition model calculations, these coefficients show differences at the trailing part of the spheroid. Significant differences are also observed in the surface friction coefficients. While the model captures drastic changes in terms of transition in the surface friction coefficients at the suction side of the spheroid, such drastic change is not observed in fully turbulent calculations. On the other hand, there is no sign of any transition phenomenon at the pressure side, contrary to the observations of experimental measurements. The transition model is not able to estimate the transition front geometry correctly. The GCI values of the surface friction coefficients increase dramatically, up to 765% around the transition regions.

A rectangular strut on the expansion ramp of a scramjet thruster for thrust vector control

Cold flow experiments were conducted on a laboratory model of a scramjet thruster consisting of a rectangular strut spanning the width of the expansion ramp of the model. The cross section of the strut was square. The strut was placed at halfway of the ramp length. The experiments were conducted at six different thruster pressure ratios (TPR) i.e., the ratio of inlet total pressure to ambient pressureranging from 5 to 10 at each of six strut heights. The internal wall pressure distributions of the thruster and schlieren images of the flow obtained from experiments were examined. The possibility of using the strut as a supplementary device in the thruster for the control of a hypersonic vehicle which normally employs aerodynamic control was studied. The inlet Mach number of the combustor was 1.8. The thruster model consisted of an isolator, a diverging area combustor and a single expansion ramp. The inlet flow to the thruster was provided by a supersonic nozzle with a rectangular exit of matching dimensions to the rectangular isolator. The diverging combustor was of rectangular cross section, the bottom wall being flat and the upper wall making an inclination of 2.44oto the bottom wall. From the top and bottom wall pressure distributions, two-dimensional internal force coefficients and pitching moment coefficients were calculated and variation of these coefficients with strut height were studied. Larger strut heights caused an increase in side force coefficient at all expansion levels of the ramp nozzle i.e., for all the TPRs employed in the present work (5–10). The variation of pitching moment coefficient with strut height exhibited the similar behavior as that of the side force coefficient. Shifting of strut position from expansion ramp tail end to the ramp mid position did not affect the nature of these variations. These variations were in general nonlinear in nature but the degree of non-linearity varied based on the value of TPR. Larger non linearity in side force coefficient variation was observed at TPRs 5,9 and 10. Larger moment coefficients resulted at lower TPR for the mid ramp position of the strut when compared to ramp tail end position. Large strut heights caused noticeable downward deflection of ramp surface flow. Calculations using the experimental data on wall pressure in the range of strut height variation employed in the present experiments indicate that increments up to 12% in moment coefficient, 20% in side force coefficient and 4% in axial force coefficients were achieved when the strut height was increased to its maximum value (12% of combustor entry section hydraulic diameter). Schlieren images show that the exhaust flow over the expansion ramp suffered a downward deflection and the strut position & height affected the magnitude of the deflection.

Thermo-Hydro-Mechanical Numerical Analysis of Energy Pile in Saturated Clay

In order to study the mechanical properties of energy piles under long-term heat injection-heat extraction cycle loading conditions, the influence of temperature on the mechanical properties of foundation soils needs to be considered. The subroutine of an elastic-plastic constitutive model of soil considering the influence of temperature is developed in Abaqus. Finally, the changes of additional pile top displacement, lateral friction resistance and axial force of energy pile under long-term heat injection-pumping cyclic loading under different loads and different soil parameters under the same load are discussed. The results show that: (1) The soil around the pile is subjected to plastic deformation due to the expansion and contraction of the pile. The higher the load on the pile top is, the greater the additional temperature settlement generated at the pile top is. (2) Under 0.5PU load, the increase of OCR, swelling index or permeability coefficient of foundation soil will cause the decrease of additional settlement of pile top. And the additional side friction and axial force, plastic parameters or soil permeability coefficient increases will produce greater additional side friction and axial force. This study has certain significance for the long-term use of energy piles.

Multi-objective optimization of a multi-cellular aluminum extruded crush rail subjected to dynamic axial and oblique impact loading conditions

This work presents a multi-objective shape optimization study of a multi-cellular aluminum extrusion subjected to dynamic axial and oblique (20° angled) impact loading conditions. Finite element models are developed, validated with experimental data, parameterized, and used to exhaust the design space using a full factorial design of experiments. An analysis of different energy absorption characteristics, such as axial and oblique mean crush force, crush efficiency, and oblique impact coefficient, are presented. A multi-objective optimization problem is defined to generate new solutions that dominate a baseline profile in all aspects of performance, which produced a geometry with up to 16% improvements in energy absorption. The parametric study is used to define the “true” Pareto front, which is the set of non-dominated designs and the solution to the optimization problem. The response surface methodology (RSM) is used to perform the multi-objective optimization analysis. The traditional RSM approach is compared to an adaptive surrogate-assisted response surface method (ASA-RSM) in their speed and ability to identify the true Pareto front correctly. Using the traditional metamodel constraint, the traditional RSM approach could only identify 18% of the true Pareto front using up to 8% of the design domain. After relaxing the constraint, the traditional RSM approach still required approximately 63% of the entire domain to identify 67% of the true Pareto front accurately. In comparison, the ASA-RSM approach was able to identify 84.5% of the true Pareto front using 42% of the entire domain. In some instances, the ASA-RSM approach correctly identified 100% of the true Pareto front by using as little as 18% of the domain. However, the ASA-RSM approach’s peak performance is dependent on the initial sampling and resulting metamodel. This study provides a comprehensive understanding of the performance gains of multi-objective optimization in the application of structural crashworthiness considering various loading conditions.

Axial force coefficient of APFSDS projectile


 
 
 
 Armor-piercing ammunition is primarily used to combat against heavy armored targets (tanks), but targets can be light armored vehicles, aircraft, warehouse, structures, etc. It has been shown that the most effective type of anti-tank ammunition in the world is the APFSDS ammunition (Armor Piercing Fin Stabilized Discarding Sabot). The APFSDS projectile flies to the target and with his kinetic energy acts on the target, that is, penetrates through armor and disables the tank and his crew. Since the projectile destroys target with his kinetic energy, then it is necessary for the projectile to have the high impact velocity.
 The decrease in the velocity of a projectile, during flight, is mainly influenced by aerodynamic forces. The most dominant is the axial force due to the laid trajectory of the projectile. By knowing the axial force (axial force coefficient), it is possible to predict the impact velocity of the projectile, by external ballistic calculation, in function of the distance of the target, and to define the maximum effective range from the aspect of terminal ballistics.
 In this paper two models will be presented for predicting axial force (the axial force coefficient) of an APFSDS projectile after discarding sabot. The first model is defined in STANAG 4655 Ed.1. This model is used to predict the axial force coefficient for all types of conventional projectiles. The second model for predicting the axial force coefficient of an APFSDS projectile, which is presented in the paper, is the CFD-model (Computed Fluid Dynamics).
 
 
 

Analysis aerodynamics diffuser-augmented wind turbines

A complete and consistent, one-dimensional momentum theory is derived for the aero-dynamics of slotted diffuser-augmented wind turbine (sDAWT). This theory does not require empirical relations. It results in a set of three-parameter relations for aerodynamic characteristics such as power coefficient Cp , rotor resistance k, rotor axial force coefficient CT , axial induction factor α, wake-expansion factor β, duct axial force coefficient CT,duct and slot mass flux . The theory predicts that the maximum achievable power coefficient Cp of (s)DAWT’s increases monotonically with increasing β, surpassing the Betz limit of open-rotor wind turbines (ORWT’s), already for modest (>2) β’s. The slot of an sDAWT feeds outside air into the diffuser, which for given β decreases the flow through the rotor and therewith Cp . However, the flow through the slot delays the onset of flow separation in the diffuser, increasing the maximum achievable β and therewith the power coefficient of sDAWT’s beyond that of DAWT’s.Based on a vortex model of the (s)DAWT, an expression is derived for the velocity induced at the rotor plane by the diffuser and for the corresponding circulation of the diffuser.The derived three-parameter relations for sDAWT’s reduce to two-parameter relations for DAWT’s and the familiar one-parameter relations for ORWT’s.

Effects of flap on the reentry aerodynamics of a blunt cone in the supersonic flow

Flap over blunt asymmetric reentry vehicles improves the aerodynamic stability and control. The present study has focused on the reentry aerodynamics of blunt-nosed conical body with flap configurations. Three dimensional, steady, viscous and compressible flow over the reentry body configurations were numerically analyzed by solving Reynolds averaged Navier-Stokes equations and SST K-ω turbulence model. The fundamental governing equations were discretized from the partial differential form to numerical analogue using the finite volume approach. Numerical simulations were carried out to investigate the flow characteristics of the three different reentry body configurations at different pitch angles, flap angles, the Mach numbers, and altitudes. For increment in the pitch angle from 0∘ to 6∘, the axial force coefficient is invariant, while the normal force coefficient linearly increases. It is found that the axial force coefficient is directly proportional to the flap angle and inversely proportional to the Mach number. Presence of flap introduces streamwise vortices and increases the flow complexity after the base to a large extent.