Reentry Guidance for Generic RLV Using Optimal Perturbations and Error Weights

The paper considers the application of artificial neural networks to solve the direct and inverse aerodynamic modeling problems using the example of a two-dimensional NACA2415 wing profile. Based on the numerical solution of the steady-state Navier–Stokes equations, a training dataset is formed, which includes aerodynamic lift and drag coefficients for various values of the geometricparameters and angle of attack. A neural network with two hidden layers of 10 neurons and a sigmoid activation function is built and trained on datasets with regular and random distribution of parameters. The feasibility of solving the inverse problem of recovering the geometric parameters of an airfoil and angle of attack from given aerodynamic coefficients with an error of no more than 5% is demonstrated. The results confirm the effectiveness of neural networks for modeling and inverse design of aerodynamic profiles.

A robust suboptimal reentry guidance scheme is presented for a reusable launch vehicle using the recently developed, computationally efficient model predictive static programming. The formulation uses the nonlinear vehicle dynamics with a spherical and rotating Earth, hard constraints for desired terminal conditions, and an innovative cost function having several components with associated weighting factors that can account for path and control constraints in a soft constraint manner, thereby leading to smooth solutions of the guidance parameters. The proposed guidance essentially shapes the trajectory of the vehicle by computing the necessary angle of attack and bank angle that the vehicle should execute. The path constraints are the structural load constraint, thermal load constraint, bounds on the angle of attack, and bounds on the bank angle. In addition, the terminal constraints include the three-dimensional position and velocity vector components at the end of the reentry. Whereas the angle-of-attack command is generated directly, the bank angle command is generated by first generating the required heading angle history and then using it in a dynamic inversion loop considering the heading angle dynamics. Such a two-loop synthesis of bank angle leads to better management of the vehicle trajectory and avoids mathematical complexity as well. Moreover, all bank angle maneuvers have been confined to the middle of the trajectory and the vehicle ends the reentry segment with near-zero bank angle, which is quite desirable. It has also been demonstrated that the proposed guidance has sufficient robustness for state perturbations as well as parametric uncertainties in the model.

Aerodynamics of two capsules of different conception both equipped with aerodynamic control surfaces has been compared at high-altitude Earth reentry path. The capsules are comparable in size but completely different in shape and, hence, in the aerodynamic behavior. The capsules are: 1) a circular cylinder provided with four flapped fins (finned cylinder), 2) a capsule, here tagged as Reentry Space Vehicle (RSV), very similar in shape and dimensions to the Intermediate eXperimental Vehicle. The study was carried out computationally in hypersonic, rarefied flow in terms of aerodynamic global coefficients (lift, drag, moments, etc.) computed by a three-dimensional direct simulation Monte Carlo code at the altitudes of 100 and 120 km, in the interval of angles of attack 0–50 deg and with flap angles of 0 and 20 deg. Computations verified that while RSV exerts a stronger aerodynamic force for the reduction of the capsule reentry velocity, the finned cylinder is better in terms of the attitude control capability. In fact, equilibrium of the finned cylinder is stable at zero angle of attack at the two altitudes, whereas the angle of attack of stable equilibrium of RSV changes with altitude. Hence, RSV needs to be provided with an active attitude control system.

The Kistler K-l is designed to be a fullyreusable, two stage launch vehicle for economical delivery of small satellite ,payloads to low earth orbit. Greatest efficiency and, hence, lowest cost are achieved by flyback of both vehicle stages to the near vicinity of the launch site. The second stage Orbital Vehicle (OV), after deploying the payload and performing necessary phasing maneuvers, performs a deorbit burn to achieve the desired trajectory conditions at atmospheric entry. After entering the atmosphere, the OV is steered aerodynamically until reaching the deployment point . for a stabilization parachute. Subsequently, drogue and main parachutes complete deceleration of the vehicle for landing orrairbags. This paper presents the design of an atmospheric guidance algorithm for bank-to-turn steering of the OV prior to deployment of the stabilization parachute. Reentry guidance targets a desired geographic position for deployment of the drogue parachute. The algorithm employs a numerical predictor/corrector technique to compute the bank angle and the start time of a single bank reversal required to null the predicted target position miss. Aerodynamic loads and heating are limited implicitly by selection of deorbit target conditions for reentry trajectory shaping. Results obtained using the Draper Laboratory K-l Integrated Vehicle Simulation illustrate guidance performance under nominal and dispersed conditions. * Senior Member of the Technical Staff, Member AIAA. Introduction The K-l Orbital Vehicle (OV) is cylindrical in shape, with a blunt nose and a flared skirt on the aft end (Figure 1). The vehicle trims at an angle of attack of approximately 11 to 12 degrees over the Mach range experienced during reentry. This results in a lift-todrag ratio ranging from 0.1 to 0.15. The only control effecters available are 12 small attitude control system (ACS) jets that are used to provide three-axis attitude stabilization and control. Due .to jet size limitations, alteration of the vehicle angle of attack from the trim condition for purposes of trajectory control is not feasible. Thus, active control of the vehicle trajectory is possible via bank maneuvers only. Given the vehicle mass characteristics and ACS jet properties, the bank acceleration is limited to approximately 2.5 deg/sec/sec. A maximum sustainable bank rate of approximately 15 deg/sec is possible; however, 10 deg/sec is used as a practical limit to avoid excessive Euler coupling (and, hence, fuel usage). Figure 1. Kistler K-l Orbital Vehicle (OV) Copyright 01999 by The Charles Stark Draper Laboratory, Inc. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission: 1275 (c)l999 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization. When the Mach number decreases to 2.5, a stabilization parachute is --deployed to stabilize the vehicle about the pitch and yaw axes in the low supersonic and transonic regimes. When a specified altitude is reached a drogue parachute and main parachutes are deployed to decelerate the vehicle for subsequent landing. on airbags. The landing site may be located either at the Nevada Test Site (NTS) or in Woomera, Australia. The key requirement levied on the reentry guidance is to steer the vehicle to the proper conditions for parachute deployment to achieve the landing target position with a given accuracy. This must be accomplished without exceeding specified aerodynamic loading and heating rate limits (8 g longitudinal, 4 g lateral, and 58 BTU/sq ft/sec, respectively). ACS fuel usage must be limited in the process. These requirements must be satisfied in the presence of potentially significant known and unknown dispersions in vehicle mass and aerodynamics properties, deorbit trajectory, and atmospheric conditions. An adaptive atmospheric reentry guidance algorithm has been designed which, as part of an overall guidance, navigation, and control subsystem, addresses the above vehicle characteristics and mission design requirements. The algorithm uses a numerical predictor/corrector technique to solve for a bank angle magnitude and the start time of a single bank reversal that will null the predicted target position miss. Numerical predictor/corrector guidance has been suggested previously for application to aerobraking and aerocapture.“2’3 -While computationally intensive, this technique allows the use of relatively high-fidelity models of vehicle and environmental characteristics, with ,correspondingly increased accuracy over analytic techniques. This paper presents a discussion of the decision’ process leading to the guidance design in addition to a detailed description of the key elements of ‘. the guidance algorithm. Details of the flight software implementation of the guidance algorithms are included where beneficial. Finally, simulation results are supplied to illustrate guidance performance. under nominal and dispersed-conditions. Reentry Dynamics Figure 2 is a free-body diagram of the OV during atmospheric reentry. The lift and drag accelerations experienced by the vehicle are expressed as where. . p f atmospheric density Vd = velocity relative to air mass C, , C, = vehicle drag and lift coefficients

This paper addresses the aerodynamics ofmembrane flappingwings. In a series ofwind-tunnel experiments on the 25 and 74-cm-wingspan models, the stroke-averaged lift and horizontal force were measured at an angle of attack that varied from 0 deg (horizontal) to 90 deg (hovering position). The flapping frequency was held constant, and freestream velocity was varied with the advance ratio range 0–1.2. For high angles of attack, flapping wings do not exhibit a typical abrupt stall seen with fixed wings. This feature in flapping wings allows a smooth transition from a level flight to hovering and back. The angle of attack, corresponding to a balance of forces in the horizontal direction, decreases exponentially with advance ratio. Aerodynamic coefficients are defined using a reference velocity as a vector sum of a freestream velocity and a stroke-averaged wing-tip flapping velocity. The lift and drag coefficients obtained using this procedure collapse well for the studied advance ratios, especially at lower angles of attack. Polynomial approximations for aerodynamic coefficients are proposed that can be used in flight-performance analysis.

The prediction of aerodynamic coefficients on airfoils using machine learning is increasingly popular due to its efficiency in time and cost. Research typically focuses on a single image type without comparing various types and output quantities (single or multi-output). Although convolutional neural networks (CNN) are widely used, their final layer is often suboptimal as a linear operator, and feature extraction results contain many parameters that can still be trained. Support vector regression (SVR) with kernel functions effectively reduces common errors in feature vectors. We propose a hybrid method, AeroCNNSVR, combining CNN as a feature extractor and SVR as a regressor to predict aerodynamic coefficients on airfoils. This study focuses on the shape and position of airfoils according to the angle of attack (AoA) without considering flow conditions. Using 14533 aerodynamic coefficients from 563 airfoil types, we created a dataset of grayscale and RGB airfoil images. Results show the proposed method with grayscale images performs better because combining SVR strengthens the predictive model, while grayscale images accurately represent the airfoil's shape and position. AeroCNNSVR achieves lower RMSE values for Cl (0.101522), Cd (0.016450), and Cm (0.129661) compared to the CNN model’s Cl (0.112493), Cd (0.019060), and Cm (0.130041). Additionally, AeroCNNSVR's R² values for Cl (0.976071), Cd (0.928700), and Cm (0.860574) surpass those of the CNN model (Cl 0.970620, Cd 0.904282, Cm 0.816355). This research contributes by 1) proposing an alternative besides CFD for predicting and identifying trends in aerodynamic coefficients of airfoils in a much shorter time during the design stage; 2) offering wind tunnel practitioners for early detection of configuration errors; 3) providing an overview of the aerodynamic characteristics of the airfoil under test, including the angle at which stall conditions occur.

A new semiempirical dynamic stall model is presented to predict the aerodynamic coefficients of an airfoil in unsteady conditions. The model is mainly based on two modifications on the airfoil angle of attack which introduce an equivalent angle of attack to implement in the proposed aerodynamic coefficients. The first modification includes unsteady wake effects of the airfoil in the proposed model which are not considered in most of the semiempirical models. Hence, an effective angle of attack is introduced based on an unsteady aerodynamic theory using the Wagner function for pitching and plunging oscillations of the airfoil. The second modification takes into account time delay effects and dynamic effects due to the flow separation on the airfoil. These effects are included in the model by developing a semiempirical relationship between static and dynamic angle of attack published in the literature. Finally, the modifications form the equivalent angle of attack to implement in a set of equations based on Kirchhoff flow theory. The proposed approach dynamically approximates trailing edge separation point on the airfoil by a completely new way and contributes its effects in the aerodynamic coefficients. Moreover, apparent mass effects and the airfoil leading edge vortex contributions are sufficiently included in the model. The presented method effectively predicts unsteady lift and pitching moment coefficients of the airfoil undergoing stall conditions. Consequently, the proposed model is verified against experimental data under various test cases where obtained numerical results are in good agreement with the test data. Furthermore, the performance of the proposed model is compared with various dynamic stall models including Leishman–Beddoes model, ONERA model and Boeing–Vertol model. The comparison shows that the proposed model minimizes the number of the semiempirical parameters determined from an experiment in dynamic stall modeling compared with Leishman–Beddoes model and ONERA model. It also demonstrates that the presented model performs as well as other well-known models using the various approaches.

Aircraft post-flight reduction is one of the most important research topics, since post-reduction is effective in all parameters of bird performance, such as maximum speed, fast acceleration, shortening the runway required, high maneuverability, and reduced fuel consumption. Therefore, it is important to examine how the force applied to the airfoil changes in different streams from an industrial point of view. In this study, NACA( National Advisory Committee for Aeronautics) Airfoil 0012 has been studied. Numerical solution is used for the study. In the simulations, the air fluid and Mach number 0.5 are considered and the lift, drag and pressure coefficients at different attack angles are investigated. The results show that this airfoil has a lift factor of 0 due to its symmetric geometry at angle of attack 0 but its drag coefficient is about 0.01384 and its pressure coefficient is about -0.483. By varying the angle of attack from -12 to +12, it was observed that for the positive attack angle the lift coefficient increases and for the negative attack angle increases the lift coefficient decreases. Also with increasing angle of attack the drag coefficient always increases and the coefficient of pressure coefficient decreases. Cite this Article Ali Kamranpay, Alireza Mehrabadi. Numerical Analysis of NACA Airfoil 0012 at Different Attack Angles and Obtaining its Aerodynamic Coefficients. Journal of Mechatronics and Automation. 2019; 6(3): 8–16p.

Applying flexible variable shape control surfaces (wing and elevator) structures is a way to increase efficiency and maneuverability of the planes, which is recently under research. In this paper, modeling of the flight of an unmanned ultra light plane is discussed. The modeling is done based on a real ultra light plane presented recently. To increase maneuverability of the plane, flexible variable shape structures are designed for the wing and the elevator. In design procedure, having an ultra light plane is considered. The elevator and the wing are used as control surfaces for longitudinal and lateral maneuvers respectively. Shape memory alloys (SMA) are used for reshaping the flexible structures of the wing and the elevator. Because of its high power and low weight and nearly unlimited resolution, SMA is best suited as the actuator of the reshaping wing and elevator structures. In flight dynamic modeling of an ultra light plane with variable shape wing, aerodynamic coefficients are needed. Coefficients are computed using computational fluid dynamics (CFD). To determine the reshaped structures, finite element models of structures are constructed in ANSYS®. Using finite element analysis (FEA), reshaped structures are produced and transferred to FLUENT® for CFD analysis. Aerodynamic coefficients with respect to reshaped structures are computed and related to actuator forces as functions. Also, aerodynamic coefficients and their derivatives with respect to flight parameters, like the angle of attack and the angular velocities are computed. Finally, the results are combined for the complete simulation in MATLAB/Simulink®.

Experimental study of aerodynamic force coefficients for a bridge deck sitting above water waves

where C~ and C~ are the stationary aerodynamic lift and drag coefficients; the dash stands for the derivative with respect to the angle of attack a. The conclusions of [1] were verified on the experimental data published in [2]. Large vibrations (with amplitudes greater than a meter) of phase wires, mainly in the vertical direction along the O Y axis (Fig. 1), were observed repeatedly in high-voltage power lines. In the special literature such motions are called a dance or galloping of a single wire of a power line. Condition (1) was obtained by Den-Hartog [3] in studies of one-dimensional motion of a mechanical model of a wire as a necessary condition of self-excited vibrations in the vertical plane. Thus, the consideration of one-dimensional self-excited vibrations of an airfoil led to condition (1), which may rightfully be called the Glauert-Den-Hartog condition. It is interesting to note that , in our opinion, Russian researchers are not familiar with the paper of Glauert [1]. Thus, for example, there are no references to [1] in [4], although stability questions are considered, and other papers of Glauert are cited. Fedyaevskii and Blyumina [5] studied the conditions of loss of aerodynamic damping by an angle airfoil rotating about a fixed axis. They obtained a rather complex inequality containing moment aerodynamic coefficients and came to the conclusion (from experimental data) that condition (1), which they call DenHartog's condition, can also be used as a criterion. Therefore, in our opinion, it would be useful for researchers to know that the book-stacks of the Russian State Public Library of Scientific and Technical Literature contain rather complete sets of the Proceedings of the British Advisory Committee for Aeronautics for 1909-1980. Condition (1) was confirmed experimentally [5, 6] and has been applied in civil engineering. In designing skyscrapers, which are subjected to wind loads, the cross section of the building must be oriented so that the angles of attack with respect to the direction of prevailing winds are beyond the interval in which inequality (1) holds [71. In simulating the behavior of a power-line wire under the action of wind, Van'ko [8] considered motion of an airfoil with three degrees of freedom: motion along the O X and O Y axes and rotation about the center of mass (Fig. 1). The conditions of existence of static solutions of the system of equations of motion were established: if the airfoil is lifting and the lift Y ~ 0, equilibrium positions exist for any wind (air flow) velocity V > 0. In studies of the Lyapunov stability of possible equilibrium positions, the following results were obtained:

This study examines the aerodynamic performance of a NACA 4412 airfoil that is covered with denticles, comparing it to a smooth NACA 4412 airfoil. The aim was to assess the lift-to-drag ratio of the airfoil utilizing biomimetic surfaces inspired by the dermal denticles of Isurus oxyrinchus. To achieve this, the airfoils were subjected to testing in a wind tunnel. Both the denticles-covered and smooth airfoils, measuring 355 by 184 mm, were equipped with 27 pressure taps distributed across three spanwise sections: the leading edge, upper surface, and lower surface. Nine flexible tubes were connected to pressure sensors for each row of static taps. Wind tunnel tests were conducted at various angles of attack (AOAs), ranging from −10.8° to 16.2° with an increment of 1.8°. Testing was carried out at wind speeds of 3, 6, and 9 m/s. Computational fluid dynamics (CFD) simulations were conducted on the smooth airfoil under identical conditions to validate the wind tunnel testing setup. The lift and drag coefficients were derived from the recorded static pressures. A comparison between the aerodynamic coefficients obtained from experiments and CFD simulations indicated that higher wind speeds are preferable for wind tunnel testing as they yield more consistent results. When examining the aerodynamic coefficients of the smooth airfoil compared to the denticle-covered airfoil, it was found that the latter generally produced higher lift and drag, resulting in a lower lift-to-drag ratio across different angles of attack and wind speeds. Specifically, at 3 m/s, the denticle-covered airfoil exhibited better lift at most AOAs, higher drag at certain AOAs, and improved lift-to-drag ratios. At wind speeds of 6 and 9 m/s, the denticle-covered airfoil demonstrated higher lift for all tested AOAs and increased drag for several AOAs, yet it consistently had lower lift-to-drag ratios. These findings point to the potential benefits of utilizing the denticle-covered NACA 4412 airfoil due to its enhanced lift characteristics at lower wind speeds. Further research is warranted to quantify the differences between the airfoil types.

To understand the working principle of ornithopters, various surveys were made on the natural flyers with flapping wings and their ability to produce lift and thrust. The crank mechanism is chosen to make the micro air vehicle (MAV) for spy work without being identified. This mechanism is one of the most complex ones, as its flow condition changes along with its wing motion. The flapping wing mechanism is analysed at two different speeds: 3 and 6 m/s. To analyse the aerodynamic characteristics, the lift and drag coefficient is measured at a different angle of attack using ANSYS software. The results are compared at various times with different working conditions to get the most suitable and reliable conditions. The designed flapping wings exhibit more efficiency with speed 6 m/s and the angle of attack at 15°.

Effect of bleeding on aerodynamics of non-slender delta wing in ground effect

When the vehicle makes large maneuvers with a wide range of Angle of attack, the relationship between the aerodynamic force or aerodynamic moment and angle of attack will become complex and nonlinear. The aerodynamic coefficient are also not constant. At this point, a single linear model cannot fit the relationship between explanatory variables and dependent variables. In this paper, we divide a large range of explanatory variables into several sub-regions with a small range using data segmentation. Breaking up the whole into parts, a complex nonlinear modeling problem is transformed into several local modeling problems. Firstly, it is considered that the nonlinearity of the aerodynamic model only depends on the nominal angle of attack, and the angle of attack coverage is partitioned. Then, an accurate local model is obtained using frequency domain least square method for parameter estimation in each subinterval. Finally, the weighted function is used to combine the local models to make the transition between subspaces smooth and ensure the continuity of the whole model.KeywordsLinear approximationLocal modelingFrequency domainAerodynamic parametersLarge scale maneuver