Airfoil Chord Length Research Articles

Effect of Airfoil thickness on low-frequency gust-airfoil interaction noise

Interaction between turbulence and an airfoil is a significant aerodynamic noise source for many engineering applications when turbulence in the wake of upstream blades interacts with the leading edge of downstream blades. Modeling the oncoming turbulence as harmonic gusts is a common approach to studying the noise generated by turbulence-airfoil interaction. The airfoil can be considered a compact noise source, resulting in a dipole-like sound directivity pattern when the acoustic wavelength of gust-airfoil interaction is much larger than the airfoil chord length. However, the interaction becomes more complex when the acoustic wavelength is comparable to or smaller than the airfoil chord, as the airfoil cannot be treated as a compact source anymore and multiple lobes appear in the radiated sound directivity. This paper studies airfoil thickness effects using a computational aeroacoustics approach based on the spectral/hp element method for low-reduced frequency gusts. It is found that the sound pressure decreases with the increase of thickness for low reduced frequency gusts. To reveal its mechanism, a semi-analytical method and the convective FW-H equation are used for low reduced frequency to analyze the radiated noise. The interaction between sound sources on the airfoil surface is crucial for the thickness effect.

Optimizing a vertical axis wind turbine with helical blades: Application of 3D CFD and Taguchi method

Vertical axis wind turbines (VAWT) with helical blades are being interested in urban areas due to the low dependency on the wind direction and also due to low noise production. In spite of good self-starting and smooth operation as the advantages of this type of turbine, its optimizing has not been reported in literature yet and is the subject of this research. A primary investigation by 3D computational fluid dynamics (CFD) to simulate the air flow about the above type of VAWT in the first step showed the importance of three design variables of tip speed ratio, helical angle, and airfoil chord length. However, in the second step, CFD runs were very time consuming and costly. For considering five values for each design variable, 53=125 cases had to be simulated by 3D CFD. Thus, by the use of Taguchi method and with definition of an orthogonal array named L-25, the number of required 3D CFD simulations reduced from 125 to 25. Then, the optimum values of variables were obtained as 1.33 for the tip speed ratio, 30 degrees for the helical angle, and 0.4 m for the airfoil chord length. At the optimum point, the average power coefficient increased to 0.17542. The presented research is novel for optimizing VAWT with helical blades.

Effects of Leading-Edge Blowing Control and Reduced Frequency on Airfoil Aerodynamic Performances

Abstract Airfoil leading-edge fluid-blowing control is computationally studied to improve aerodynamic efficiency. The fluid injection momentum coefficient Cμ (the ratio of injection to incoming square velocities times the slot's width to airfoil's half chord length) varies from 0.5% to 5.4%. Both static and dynamic conditions are investigated for a NACA0018 airfoil at low speed and Reynolds number of 250 k based on the airfoil's chord length. The airfoil is dynamically pitched at a reduced frequency (the pitching tangential speed to the freestream speed ratio), varying between 0.0078 and 0.2. Reynolds-averaged Navier–Stokes (RANS) and unsteady RANS (URANS) is used in the simulations as based on the Transition SST and Spalart–Allmaras models, generally achieving good agreement with experimental results in lift and drag coefficients and in the pressure coefficient distributions along the airfoil. It is found that oscillating the airfoil can delay stall, as expected, in dynamic stall (DS). Leading-edge blowing control can also significantly delay stall both in static and dynamic conditions as long as sufficient momentum is applied to the control. On the other hand, for a small Cμ such as 0.5%, the leading-edge control worsens the performance and hastens the appearance of stall in both static and dynamic conditions. The airfoil's oscillation reduces the differences between pitch-up and pitch-down aerodynamic performances. Detailed analysis of vorticity, pressure, velocity, and streamline contours is given to provide plausible explanations and insight to the flow.

Multi-objective optimization study on the performance of double Darrieus hybrid vertical axis wind turbine based on DOE-RSM and MOPSO-MODM

The Double Darrieus Vertical Axis Wind Turbine (DD-VAWT) effectively enhances wind energy efficiency at low tip speed ratios. In this study, the multi-objective optimization method is constructed for DD-VAWT. The optimization objective is to enhance the power coefficient as well as reduce the maximum instantaneous torque coefficient, while decision variables include the inner ring wind turbine diameter, inner ring wind turbine height, inner ring wind turbine blade airfoil chord length and inner and outer ring wind turbine phase angle. Firstly, the computational fluid hydrodynamics model of DD-VAWT is established and validated by experimental data from the literature. Then, the regression model between critical structural parameters and power coefficients, maximum instantaneous torque coefficients is constructed using response surface analysis. Finally, the multi-objective particle swarm optimization algorithm is used to optimize the objective and the optimal solution is selected from the Pareto frontier solution. This work provides a direction to improve the operating performance of DD-VAWT at low tip speed ratios as well as contributes to energy saving and emission reduction.

Freestream turbulence effects on low Reynolds number NACA 0012 airfoil laminar separation bubble and lift generation

Laminar separation bubbles (LSB's) over the suction surface of a wing at low Reynolds number (O(104)−O(106) based on the airfoil chord length) can significantly affect the aerodynamic performance of the wing, and pose a unique challenge for the predictive capabilities of simulation tools due to their high sensitivity to flow environments and wing surface conditions. In this work a series of two-dimensional (2D) and three-dimensional (3D) low-order, and high-order accurate unstructured-grid-based numerical methods with varying model fidelity levels were used to study LSB physics over a NACA 0012 airfoil both in a clean freestream and in a turbulent freestream at a chord-based Reynolds number of 12,000. Lift production and time-averaged flow fields were compared with available experimental results. A major discovery is that in clean freestream flow a 3D high-order numerical scheme is necessary to capture LSB physics. This is due to the sensitivity of LSB-induced laminar-turbulent transition to flow conditions and boundary geometry at low Reynolds number. In freestream flows with moderate background turbulence (∼5%), 2D simulations failed to capture subtle 3D flow physics due to their intrinsic limitation, but can reasonably predict time-averaged airfoil performance. Similarity and distinction between freestream vortex-LSB interaction in 2D and eddy-LSB interaction in 3D were explained. The role of the Kelvin-Helmholtz instability and Klebanoff modes in the transition of 3D airfoils were shown to be critical for understanding laminar-turbulent transition and LSB formation on airfoils in clean and turbulent freestreams.

Performance optimization of vertical axis wind turbine based on Taguchi method, improved differential evolution algorithm and Kriging model

ABSTRACT The capability of vertical axis wind turbine (VAWT) is influenced by its input parameters. In this paper, for the three-bladed VAWT with the NACA0018 airfoil, three important input parameters, i.e. tip speed ratio (TSR), airfoil chord length (C), and pitch angle (β), are selected to explore their impact on the capability of the VAWT, and then to find the best combination of them. Firstly, 16 sets of experiments are determined according to the Taguchi method and are evaluated using the 2D computational fluid dynamics (CFD) numerical simulation, and further studied with the Analysis of Variance. The consequence shows that the TSR and pitch angle are more critical to the performance of the VAWT. In order to obtain the optimal configuration of these parameters, an intelligent method is further proposed. Firstly, a certain number of design schemes are extracted in the selected space through Latin hypercube sampling (LHS), and then the torque coefficient (C m ) of each design scheme was obtained by 2D CFD simulation, the Kriging model is used to establish the correlation among the input parameters and their corresponding torque coefficient. Finally, the improved differential evolution algorithm (JADE) is used to tackle the Kriging model to get the optimal input parameter values. The results show that when the rotor diameter (D) is 2.5 m, the optimal parameters are TSR is 2.6, C is 0.227 m and β is −2.47°, the performance of the VAWT is further improved by about 4.5% compared with the optimal values obtained by the Taguchi method.

Control of flow separation over an aerofoil by external acoustic excitation at a high Reynolds number

The effectiveness of acoustic excitation as a means of flow control at high Reynolds number turbulent flows is investigated numerically by using improved delayed detached eddy simulations (IDDES). Previous studies on low Reynolds number laminar flows have shown that acoustic excitation can substantially suppress flow separation for specific effective frequency and amplitude ranges. However, the effect of acoustic excitation on higher Reynolds number turbulent flow separation has not yet been explored due to limitations on appropriate fidelity computational methods or experimental facility constraints. Therefore, this paper addresses this research gap. A NACA0015 airfoil profile at 1 × 106 Reynolds number based on the airfoil chord length is used for the investigations. Acoustic excitation is applied to the baseline flow field in the form of transient boundary conditions at the computational domain inlet. A parametric study revealed that the effective sound frequency range shows a Gaussian distribution around the frequency of the dominant disturbances in the baseline flow. A maximum of ∼43% increase in lift-to-drag ratio is observed for the most effective excitation frequency F+=1.0 at a constant excitation amplitude of Am=1.8%. The effect of excitation amplitude follows an asymptotic trend with a maximum effective excitation amplitude above which the gains are not significant. A fully reattached flow is observed for the highest excitation level considered (Am=10%) that results in ∼120% rise in airfoil lift-to-drag coefficient. Overall, the findings of the current work demonstrate the higher Reynolds number effectiveness of acoustic excitation on separated turbulent flows, thereby paving the way for application in realistic flow scenarios observed in aircraft and gas turbine engine flow fields.

Investigation of the effect of critical structural parameters on the aerodynamic performance of the double darrieus vertical axis wind turbine

Double Darrieus Vertical Axis Wind Turbine (DD-VAWT) can efficiently capture wind energy at low tip speed ratios. In this work, the laws governing the effects of critical structural parameters, such as diameter of inner ring wind turbine, height of inner ring wind turbine, inner ring wind turbine blade airfoil chord length, and phase angle of inner and outer ring wind turbine, on the power performance and aerodynamic load are investigated. The power coefficient increases from 0.1670 to 0.2403 when the diameter of the inner ring wind turbine decreases from 1600 mm to 400 mm. The power coefficient increases from 0.1755 to 0.2135 when the height of the inner ring wind turbine increases from 600 mm to 1200 mm. The power coefficient increases from 0.1773 to 0.2135 when the chord length of the inner ring wind turbine blade airfoils increases from 0.15 m to 0.3 m. The power coefficient decreases from 0.2135 to 0.1976 when the phase angle of the inner and outer wind turbine is increased from 0° to 135°. Finally, based on Taguchi's experiments and grey correlation analysis, it is known that the most influential weight on the power coefficient and the maximum instantaneous torque coefficient is the airfoil chord length of the inner ring wind turbine blades, and the least is the phase angle of the inner and outer ring wind turbines. This work provides a reference for enhancing the DD-VAWT's performance.

A novel approach to performance improvement of a VAWT using plasma actuators

The numerous advantages of Vertical-Axis Wind Turbines (VAWTs) have made them suitable for urban areas compared to other types of wind turbines; however, the occurrence of phenomena such as vortices and flow separation around the blades which have adverse effects on the turbine performance, indicates the necessity of using control methods to improve the behavior of the flow around the blades. This study numerically examines the effect of different installation positions and activation timing of plasma actuators and presents new strategies for flow control and turbine performance improvement. The model presented by Shyy et al. was used for the numerical modeling of the plasma actuator. The results showed that applying actuators in ten different positions from 10% to 90% of the airfoil chord length on the outer and inner edges of the blades, can lead to an increase in the turbine production power; however, the high-power consumption of the actuator clarifies the necessity of reducing the actuator activity time to smaller azimuthal intervals. The results revealed that applying the actuators under the optimal combined strategy in a 90° interval, increases the turbine power coefficient by 29.2%, while it leads to the lowest power consumption of the actuator.

Towards smart blades for vertical axis wind turbines: different airfoil shapes and tip speed ratios

Abstract. Future wind turbines will benefit from state-of-the-art technologies that allow them to not only operate efficiently in any environmental condition but also maximise the power output and cut the cost of energy production. Smart technology, based on morphing blades, is one of the promising tools that could make this possible. The present study serves as a first step towards designing morphing blades as functions of azimuthal angle and tip speed ratio for vertical axis wind turbines. The focus of this work is on individual and combined quasi-static analysis of three airfoil shape-defining parameters, namely the maximum thickness t/c and its chordwise position xt/c as well as the leading-edge radius index I. A total of 126 airfoils are generated for a single-blade H-type Darrieus turbine with a fixed blade and spoke connection point at c/2. The analysis is based on 630 high-fidelity transient 2D computational fluid dynamics (CFD) simulations previously validated with experiments. The results show that with increasing tip speed ratio the optimal maximum thickness decreases from 24 %c (percent of the airfoil chord length in metres) to 10 %c, its chordwise position shifts from 35 %c to 22.5 %c, while the corresponding leading-edge radius index remains at 4.5. The results show an average relative improvement of 0.46 and an average increase of nearly 0.06 in CP for all the values of tip speed ratio.

Assessment of Turbulence Models for Unsteady Separated Flows Past an Oscillating NACA 0015 Airfoil in Deep Stall

This paper provides 2D Computational Fluid Dynamics (CFD) investigations, using OpenFOAM package, of the unsteady separated fully turbulent flows past a NACA 0015 airfoil undergoing sinusoidal pitching motion about its quarter-chord axis in deep stall regime at a reduced frequency of 0.1, a free stream Mach number of 0.278, and at a Reynolds number, based on the airfoil chord length, , of . First, eighteen 2D steady-state computations coupled with the SST model were carried out at various angles of attack to investigate the static stall. Then, the 2D Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations of the flow around the oscillating airfoil about its quarter-chord axis were carried out. Three eddy viscosity turbulence models, namely the Spalart-Allmaras, Launder-Sharma , and SST were considered for turbulence closure. The results are compared with the experimental data where the boundary layer has been tripped at the airfoil’s leading-edge. The findings suggest that the SST performs best among the other two models to predict the unsteady aerodynamic forces and the main flow features characteristic of the deep stall regime. The influence of moving the pitching axis downstream at mid chord was also investigated using URANS simulations coupled with the SST model. It was found that this induces higher peaks in the nose-down pitching moment and delays the stall onset. However, the qualitative behavior of the unsteady flow in post-stall remains unchanged. The details of the flow development associated with dynamic stall were discussed

Variations with Mach number for gust–airfoil interaction noise

The interaction of turbulence with airfoil is an important noise source in many engineering fields, including helicopters, turbofans, and contra-rotating open rotor engines, where turbulence generated in the wake of upstream blades interacts with the leading edge of downstream blades and produces aerodynamic noise. One approach to study turbulence–airfoil interaction noise is to model the oncoming turbulence as harmonic gusts. A compact noise source produces a dipole-like sound directivity pattern. However, when the acoustic wavelength is much smaller than the airfoil chord length, the airfoil needs to be treated as a non-compact source, and the gust–airfoil interaction becomes more complicated and results in multiple lobes generated in the radiated sound directivity. Capturing the short acoustic wavelength is a challenge for numerical simulations. In this work, simulations are performed for gust–airfoil interaction at different Mach numbers using a high-fidelity direct computational aeroacoustic (CAA) approach based on a spectral/hp element method verified by a CAA benchmark case. It is found that the squared sound pressure varies approximately as the fifth power of Mach number, which changes slightly with the observer location. This scaling law can give a better sound prediction than the flat-plate theory for thicker airfoils. Furthermore, another prediction method, based on the flat-plate theory and CAA simulation, has been proposed to give better predictions than the scaling law for thicker airfoils.

Proper Orthogonal Decomposition Analysis of an Airfoil Performances under a Small Vortical Gust

This paper investigates the performance of a non-symmetric airfoil in a perturbed flow for a low Reynolds number by creating small vortical structures. A newly designed two-dimensional numerical tool is used to examine the interaction between the NACA 23015 airfoil and the vortex shedding from a square cylinder. Different airfoil position ratios are numerically simulated concerning the square cylinder G/D (D: square cylinder diameter), the channel centerline T/d (d=D/2), and the vortices scale size D/c (c: airfoil chord length). Results show that the maximum values of the lift and drag aerodynamic coefficients are influenced by the airfoil’s lateral and longitudinal positions. The Proper Orthogonal Decomposition (POD) method is used to identify the most energetic flow structures. For all simulated scenarios, it was found that the first two modes reflect the dominating coherent structures in the flow field. The results also show that a leading-edge vortex is formed over the airfoil. The observed phenomena of symmetric and antisymmetric shedding vortex mechanisms essentially depend on the lateral distance of the airfoil T/d and the vortex scale size D/c. However, the spectral analysis demonstrates that the shedding frequency mainly depends on the gap distance G/D.

Large Eddy Simulation of Transitional Separated Flow Over a Low Reynolds Number Cambered Airfoil

Abstract The accurate simulation of the aerodynamic behavior of low Reynolds number (Re) cambered airfoils requires the ability to capture the transitional separated boundary layer (BL) that occurs naturally on the surface of the airfoil. In this study, simulations are performed using a modern cambered airfoil designed for use in low Re applications, which are an advancement from previous studies using flat plate geometries or symmetric NACA airfoils. The cambered SD 7037 airfoil is simulated using wall-resolved large eddy simulation (LES) at a modest Re of 4.1×104 and at 1 deg, 5 deg, and 7 deg angles of attack (AOAs), with results validated against experimental data. Simulated predictions of pressure and skin friction coefficients clearly capture the correct location of the laminar separated bubble (LSB) which forms during the natural BL transition process. Sensitivity to elevated inflow turbulence is found to cause early BL reattachment at higher AOAs without impacting the location of BL separation. An integral BL analysis verifies the accuracy of the simulated velocity profiles against experimental values. The scale of horseshoe structures visualized in the transitional BL is larger in comparison to airfoil chord length than what is seen in previous simulations at Re of the order of 105, which highlights the importance of investigating cambered airfoils at a modest Re.

Effects of blade airfoil chord length and rotor diameter on aerodynamic performance of straight-bladed vertical axis wind turbines by numerical simulation

Straight-bladed Vertical Axis Wind Turbines (SB-VAWTs) have recently attracted much attention as they are considered to be an option for wind energy utilization, whether in offshore or urban environments. In this study, the effects of airfoil chord length and rotor diameter (circumference) on the aerodynamic characteristics of SB-VAWTs were explored by numerical simulation. The research object is a three-bladed SB-VAWT fitted with a NACA0018 symmetric airfoil. A dimensionless parameter RCC is proposed, that is, the ratio of the airfoil chord length to the circumference of the rotor. There are 43 different combinations of chord length and rotor diameter designed for the present study, making the RCC ranges between 1.4% and 57.3%. When the length of airfoil chord is constant and the diameter of rotor changes, the recommended RCC is supposed to be approximately 8% for the SB-VAWT. Differently, when the diameter of the rotor is constant and the length of airfoil chord changes, the recommended RCC is supposed to range between 9.5% and 13.4%. Based on the results, it is confirmed that the RCC is a significant parameter for the design of the SB-VAWT. This study is expected to provide a practical reference for the parametric structural design of SB-VAWTs.

Direct numerical simulation of transitional flow past an airfoil with partially covered wavy roughness elements

We perform direct numerical simulation of flow past the NACA (National Advisory Committee for Aeronautics) 0012 airfoil with partially covered wavy roughness elements near the leading edge. The Reynolds number Rec based on the freestream velocity (U0) and airfoil chord length (C), and the angle of attack (AoA) is fixed, i.e., Rec=5×104, AoA=10°. The leading edge roughness elements are characterized by streamwise sinusoidal-wave geometry that is uniform in the spanwise direction with fixed height, whereas varying wave numbers (k) from 0 to 12. Based on the validation of the smooth baseline case (k = 0), the roughness effects on the aerodynamic performance are evaluated in terms of the lift and drag coefficients. The drag coefficient decreases monotonically with k, while the variation of the lift coefficient with k is similar to the “drag crisis” phenomenon observed in cylinder flows. The sharp variations of lift and drag coefficients from k = 6 to 8 indicate that k = 8 is a critical case, beyond which massive separation occurs and almost covers the airfoil's suction side and dominates the airfoil aerodynamic performance. To further reveal the underlying mechanism, the flow structures, pressure, skin friction coefficients, shear layer transition onset, and boundary layer separation are quantified to investigate the roughness effects. The roughness elements strongly modify the separation behavior, whereas they have little effect on the transition onset. The unsteady interactions and convections of separation bubbles downward the trailing edge also change the wake evolution. Based on the scaling of the asymmetric wake profiles, we find that the wake defect is gently decreasing with k, but the increase in the wake width is much stronger. This scaling analysis gains a better insight into the roughness effects on the momentum deficit flow rate, which confirms the drag mechanism with different roughness wave numbers.

Effects of blowing and suction jets on the aerodynamic performance of wind turbine airfoil

This work experimentally investigates the effects of blowing and suction jets on the aerodynamic performance of a NACA0012 airfoil at a moderate Reynolds number Re = 1.0 × 105. The performance of a single blowing jet is only examined first, and then combinations of blowing and suction are implemented. The loadcell and surface oil flow visualization techniques are respectively used to measure the aerodynamic forces and flow structures on the uncontrolled and controlled airfoil. Effects of momentum coefficient and location of blowing and suction jets on the lift, drag, stall angle, cut-in speed, flow separation, and flow reattachment are studied to find an optimum control case. The results prove that the single blowing jet located at 0.2c from the leading edge has the best performance in the lift enhancement, where c is the airfoil chord length. The maximum enhancements of peak lift force coefficient CL and lift-to-drag ratio CL/CD are achieved as 18.4% and 804%, respectively. The underlying physics of aerodynamic performance enhancement relies on suppression of the flow separation and formation of separation bubbles.

Experimental Study of Aerodynamic Characteristics of Partially Flexible NACA0012 Airfoil

In this study, aerodynamic characteristics of a NACA0012 airfoil section whose part of the skin of the upper surface was constructed of polydimethylsiloxane membrane (PDMS) were experimentally studied in a wind tunnel at a Reynolds number (based on the airfoil chord length) of . The aim of this concept is to take advantage of passive vibration of an elastic membrane in the air to enhance mixing, which energizes the flow near the blade surface. As a result, flow separation on blades can be delayed or even suppressed, widening the usable range of angles of attack for a general-purpose airfoil having a wide range of applications. During the experiment, the blade model was connected to a rotary table with an attached stepper motor, which allowed the angle of attack to vary. A two-component balance was used to measure the lift and drag forces on models, and a smoke-wire technique was adopted to visualize the flowfield around the tested airfoil. Influences of geometric parameters of the PDMS on the effectiveness of flow separation control over the airfoil were systematically analyzed. The results suggested that with the appropriate thickness and Young’s modulus the airfoil having the leading-edge membrane displayed better aerodynamic characteristics such as a delay in dynamic stall angle and higher lift-to-drag ratio at relatively large angles of attack compared to its conventional counterpart. As PDMS is an inexpensive, durable, and readily available material, the present study therefore provides a potentially feasible approach for passive flow separation control in numerous aeronautical and turbomachine applications.

Lift enhancement based on virtual aerodynamic shape using a dual synthetic jet actuator

The Dual Synthetic Jet Actuator (DSJA) is used to develop a new type of lift enhancement device based on circulation control, and to control the flow over the two-dimensional (2D) NACA0015 airfoil. The lift enhancement device is composed of a DSJA and a rounded trailing edge (Coanda surface). The two outlets of the DSJA eject two jets (Jet 1 and Jet 2). Jet 1 ejects from the upper trailing edge, which increases the circulation of airfoil with the help of the Coanda surface. Jet 2 ejects from the lower trailing edge, which acts as a virtual flap. The Reynolds number based on the airfoil chord length and free flow velocity is 250000. The results indicate that the circulation control method based on Dual Synthetic Jet (DSJ) has good performance in lift enhancement, whose control effect is closely related to momentum coefficient and reduced frequency. With the increase of the reduced frequency, the control effect of the lift enhancement is slightly reduced. As the momentum coefficient increases, the control effect becomes better. When the angle of attack is greater than 4°, the increments of lift coefficients under the control of DSJ are larger than those under the control of the steady blowing at a same momentum coefficient. The maximum lift augmentation efficiency can reach 47 when the momentum coefficient is 0.02, which is higher than the value in the case with steady blowing jet circulation control.

Effect of Stagger on Low-Speed Performance of Busemann Biplane Airfoil

In this study, the low-speed performances of the Busemann biplane were clarified, focusing on the relative contributions of the upper and lower elements to the total aerodynamic characteristics of the biplane. Also, the effects of the staggered biplane, which changes the horizontal distance between two wings in a biplane configuration, were investigated by balance measurements and numerical simulations. The flow velocity was 15 m/s, and the Reynolds number based on the airfoil chord length was 2.1 × 105. In the tests of the integrated biplane wing, the attack angles of the wing elements were varied by a balance system and turntable, which were set in the wind tunnel sidewall. The results show that the lower element generated most of the lift and drag of the Busemann biplane (or the baseline biplane model with no stagger) at high angles of attack. At angles above 20 deg, the contribution of the lower element to total aerodynamic characteristics is almost constant, with 95% of the total lift and 88% of the total drag. The total lift and drag of the baseline model were smaller than the sum of the individual elements that were treated as a single configuration. The increments of lift and drag due to the stagger effects were confirmed, especially at high angles of attack. When the stagger value increases, the high-pressure area near the leading edge of the lower surface of the upper element also increases, which increases the lift and drag of the up-per element. This is the main reason for the increments of total lift and drag of the biplane model. The stagger effects also prevented the leading-edge separation of the lower element in the biplane configuration and increased the lift slopes of the biplane model.