Drag Modulation Research Articles

Optimal drag-based collision avoidance: Balancing miss distance and orbital decay

The increasing number of objects in Low Earth Orbit makes active collision avoidance imperative for satellites operating in this region. For satellites non equipped with propulsion systems, the collision risk can be mitigated by exploiting the active modulation of aerodynamic forces through the ballistic coefficient. This article proposes a novel and high-fidelity optimal control approach for collision avoidance via aerodynamic drag modulation for an unpropelled SmallSat. Central to this approach is a cost function that jointly maximizes the miss distance while minimizing orbital decay during the maneuver. Moreover, the proposed approach has been rigorously tested through its application to the real-world scenario of the SOURCE satellite, slated for launch in 2025. For the satellite under investigation and a maneuver altitude of 350km, an in-track separation distance of around 22km can be accomplished within a warning time of 24h, which is large enough to conclude that the collision was successfully avoided. As a downside, however, this results in an additional loss in the semi-major axis of 165m and thus a reduced lifetime of the satellite. This balance between separation distance and additional loss in altitude can be flexibly adjusted by the user, which is demonstrated extensively in the article by means of a parameter study. Compared to the widespread use of chemical propulsion systems, this strategy naturally demands longer warning times due to the significantly lower available forces, and also radial offsets to the potential collision object cannot be in this case. Nevertheless, it offers a very promising alternative for active collision avoidance, especially for low-altitude applications.

Drag modulation by inertial particles in a drag-reduced turbulent channel flow with spanwise wall oscillation

Drag modulation by inertial particles in a drag-reduced turbulent channel flow with spanwise wall oscillation

Feather-inspired triboelectric nanogenerator with lift and drag modulation for wind energy harvesting

Feather-inspired triboelectric nanogenerator with lift and drag modulation for wind energy harvesting

Discrete-Event Drag Modulation Aerocapture for Mars and Titan Missions

Aerocapture is a spaceflight maneuver that uses the atmosphere of a planet or moon to slow down a spacecraft after a single atmospheric pass and capture it into an elliptical orbit around the celestial body. This paper presents a discrete-event drag modulation method for Mars and Titan aerocapture missions. A single-stage jettison is used as a control strategy to modulate the aerodynamic drag for an aerocapture scenario. Entry corridor analysis is performed under worst-case trajectory dispersions for determining the entry flight-path angle. The jettison timing of the high-drag skirt is the single free guidance parameter that adjusts the spacecraft’s trajectory during an aerocapture maneuver. A computationally simple jettison-switching guidance scheme is developed to determine when to jettison the high-drag skirt, and the result is an analytical function that represents the ballistic-coefficient switching curve. The proposed discrete-event drag-modulation strategy is extensively tested using four entry vehicles and three target orbits for Mars and Titan aerocapture scenarios. Monte Carlo simulations show that the simple switching-curve guidance provides performance metrics (apoapsis targeting errors and postexit impulsive maneuvers) that are essentially equal to the performance of more computationally burdensome guidance methods such as an onboard numerical predictor–corrector scheme.

Numerical study on the mechanism of drag modulation by dispersed drops in two-phase Taylor–Couette turbulence

The presence of a dispersed phase can significantly modulate the drag in turbulent systems. We derived a conserved quantity that characterizes the radial transport of azimuthal momentum in the fluid–fluid two-phase Taylor–Couette turbulence. This quantity consists of contributions from advection, diffusion and two-phase interface, which are closely related to density, viscosity and interfacial tension, respectively. We found from interface-resolved direct numerical simulations that the presence of the two-phase interface consistently produces a positive contribution to the momentum transport and leads to drag enhancement, while decreasing the density and viscosity ratios of the dispersed phase to the continuous phase reduces the contribution of local advection and diffusion terms to the momentum transport, respectively, resulting in drag reduction. Therefore, we concluded that the decreased density ratio and the decreased viscosity ratio work together to compete with the presence of a two-phase interface for achieving drag modulation in fluid–fluid two-phase turbulence.

Drag-based analytical optimal de-orbiting guidance from low earth orbit via Deep Neural Networks

Controlled de-orbiting is crucial for a low earth orbiting (LEO) satellite or capsule intending to land in a desired location and to prevent damage to people and property on the ground caused by debris. Drag modulation is one possible mechanism to control de-orbiting, exploiting atmospheric drag variation to reduce the necessary orbital energy from the initial conditions to the re-entry interface. In this context, this paper proposes a novel targeted de-orbiting Artificial Neural Network (ANN) and drag-based guidance algorithm for a LEO artificial satellite. It relies on the combination of empirical and analytical relations with Deep Neural Networks (DNNs) to estimate the main parameters of the optimal control law in real time. The training set is composed of several optimal control solutions generated with a previously developed optimal control algorithm, exploiting the formulation in equinoctial modified orbital parameters to manage the large time scale of the problem and the computational cost. An innovative procedure for the training set generation led to the achievement of general results with a limited number of samples. The successful outcome of the guidance algorithm on over 1000 cases demonstrates its robustness and generalization of results. To conclude, a Linear Quadratic Regulator (LQR) feedback control is applied to one case to deal with a more realistic and uncertain density model.

Incremental model predictive control for satellite de-orbiting based on drag modulation

This paper deals with the problem of controlled atmospheric re-entry, which has recently gained growing interest from the aerospace scientific and industrial communities for the economic and environmental benefits related to the development of reusable space vehicles. In this context, an original technique based on the incremental formulation of the Model Predictive Control methodology is proposed to tackle the trajectory tracking problem of a small satellite equipped with a deployable heat shield in the de-orbiting phase, focusing on a range of altitude from 300 km to 130 km, i.e., before the atmosphere is dense enough to begin a terminal re-entry phase. The proposed control logic allows following a given pre-determined guidance law, limiting position offsets due to unmodelled disturbances or uncertainties in the knowledge of spacecraft parameters (e.g., drag coefficient). An extensive numerical simulation campaign to assess the control performances in different perturbing conditions has demonstrated its ability to reach a km-error level in the position error at the final altitude of 130 km.

Energy reference guidance for drag-modulated aerocapture

Aerocapture is a method of achieving orbit insertion via a single pass through the atmosphere of the central body. Single-event jettison drag modulation is a simple way of achieving control during atmospheric flight by effecting a discrete change in the aerodynamics of the vehicle. A novel guidance algorithm, energy reference guidance, is developed and implemented for a reference scenario of a small satellite aerocapture demonstration at Earth, and is compared to the baseline numerical predictor–corrector solution. The new approach is shown to achieve equivalent apoapsis targeting performance as the baseline algorithm with significantly lower CPU demand during atmospheric flight, although more onboard memory is required in exchange. The relationship between targeting performance and required memory is quantitatively explored for the new algorithm; the selected configuration generates approximately 3.3 MB of data, which is expected to be well within the capability of relevant avionics systems.

Time Optimal Drag-Based Targeted De-Orbiting for Low Earth Orbit

Controlled de-orbiting plays a crucial role in any space mission to ensure landing of a satellite or capsule in the desired location and preventing damage to people and property on the ground caused by debris. The necessary orbital energy reduction from the initial conditions to the re-entry interface can be achieved using a de-orbit burn or exploiting drag modulation as a control mechanism. The current work perfectly fits in this scenario, proposing a novel algorithm to generate minimum-time optimal trajectories for a satellite ballistic de-orbiting from a Low Earth Orbit (LEO) to the atmospheric re-entry interface. The formulation is written in terms of modified equinoctial orbital parameters, particularly suitable for trajectory analysis and optimization, even in cases of oscillatory problems with large time scales as in the de-orbiting problem. The optimization problem is solved with the MATLAB software GPOPS-II using a hp adaptive Gaussian quadrature orthogonal collocation method. It is formulated as a single-stage optimization problem considering the exposed surface as a control variable. The cost function to be minimized is the final time, while the imposition of an event constraint on the altitude at the de-orbit point ensures its value is in an acceptable range. A novel class of solutions is defined for the algorithm implementation to guarantee the desired values of latitude and longitude. It has been used to generate high-precision optimal trajectories and corresponding control variable laws in different conditions. The identification of a common trend of solutions along an infinite-shaped pattern allowed the possibility to model a wide range of missions, involving different initial conditions and satellites. A subsequent Monte Carlo analysis showed the algorithm validity and robustness with a successful outcome on 500 cases and an error less of 0.5% for most of them.

Aerocapture Optimization Method with Lift–Drag Joint Modulation Suitable for Variable Structure Spacecraft

Aerocapture, the action of delivering a vehicle from a hyperbolic orbit to a planetary orbit by using the aerodynamic force, could potentially lower fuel consumption. By controlling the direction and size of the aerodynamic force, the vehicle can accurately enter the target orbit. This paper focuses on a preliminary study of the optimal trajectory for aerocapture on the basis of a novel flight control option, which considers lift and drag joint modulation so as to suit variable structure spacecraft. In the preliminary evaluation of such a flight control option, the aerocapture corridors under lift modulation and drag modulation and the influence of the ballistic coefficient on aerocapture were analyzed, demonstrating that joint modulation can achieve complementary advantages compared with pure lift modulation and drag modulation. Based on this flight control option, optimal aerocapture trajectories with different path constraints, target orbital constraints and control variable constraints were found. It bears noting that both the bank angle and the reference area were taken as control variables for lift modulation and drag modulation, respectively, during the atmospheric flight in the process of designing the optimal trajectories. The optimal results indicate that the flight control option with lift and drag joint modulation can greatly broaden the necessary conditions for aerocapture and extend the target orbital range.

Turbulence drag modulation by dispersed droplets in Taylor–Couette flow: the effects of the dispersed phase viscosity

The dispersed phase in turbulence can vary from almost inviscid fluid to highly viscous fluid. By changing the viscosity of the dispersed droplet phase, we experimentally investigate how the deformability of dispersed droplets affects the global transport quantity of the turbulent emulsion. Different kinds of silicone oil are employed to result in the viscosity ratio, $\zeta$ , ranging from $0.53$ to $8.02$ . The droplet volume fraction, $\phi$ , is varied from 0 % to 10 % with a spacing of 2 %. The global transport quantity, quantified by the normalized friction coefficient $c_{f,\phi }/c_{f,\phi =0}$ , shows a weak dependence on the turbulent intensity due to the vanishing finite-size effect of the droplets. The interesting fact is that, with increasing $\zeta$ , $c_{f,\phi }/c_{f,\phi =0}$ first increases and then saturates to a plateau value which is similar to that of the rigid particle suspension. By performing image analysis, this drag modification is interpreted from the point of view of droplet deformability, which is responsible for the breakup and coalescence effect of the droplets. The statistics of the droplet size distribution show that, with increasing $\zeta$ , the stabilizing effect induced by interfacial tension becomes substantial and the pure inertial breakup process becomes dominant. The measurement of the droplet distribution along the radial direction of the system shows a bulk-clustering effect, which can be attributed to the non-negligible coalescence effect of the droplet. It is found that the droplet coalescence effect could be suppressed as $\zeta$ increases, thereby affecting the contribution of interfacial tension to the total stress, and accounting for the observed emulsion rheology.

Correction to: Analytical Guidance for Mars Aerocapture via Drag Modulation

Correction to: Analytical Guidance for Mars Aerocapture via Drag Modulation

Quantitative Assessment of Aerocapture and Applications to Future Solar System Exploration

A quantitative and comparative assessment of the feasibility and mass benefit of using aerocapture at all atmosphere-bearing solar system destinations is presented, considering both lift and drag modulation control techniques. Aerocapture is shown to be feasible at Mars, Titan, and Venus with existing entry vehicles and flight-proven thermal protection system (TPS) materials, and requires no significant technology developments before use on a science mission. Aerocapture at Uranus and Neptune is viable with blunt-body aeroshells ( of 0.30–0.40) and Heatshield for Extreme Entry Environment Technology TPS for certain high arrival interplanetary trajectories. The mass benefit offered by aerocapture is compared to alternative orbit insertion techniques such as purely propulsive insertion and aerobraking. Aerobraking outperforms aerocapture for missions to Mars and Venus with arrival less than . For outer planet missions, aerocapture offers substantial mass benefit depending on the arrival , Titan (300–1700% more mass), Uranus (100–600%), and Neptune (80–400%), in addition to significant reduction in flight time. The study recommends a low-cost drag modulation aerocapture demonstration mission at Earth to establish flight heritage for aerocapture and lower the risk for future science missions.

Flight control methodologies for Neptune aerocapture trajectories

In this work, a comparison of potential flight control methodologies for Neptune aerocapture trajectories is presented. Lifting trajectories pertaining to bank angle modulation and direct force control as well as ballistic trajectories pertaining to continuously-variable drag modulation are investigated. A parametric study of vehicle configurations is explored to quantitatively compare the flight envelope between lifting and ballistic trajectories. A closed-loop numerical predictor–corrector aerocapture guidance architecture is utilized to unify each flight control technique for trajectory comparisons. A series of Monte Carlo simulations of blunt body Neptune aerocapture trajectories are conducted to assess each flight control’s robustness to uncertainties in vehicle aerodynamics, atmospheric knowledge, and entry state. Direct force control can achieve 100% successful science orbit insertion within a 120 m/s total ΔV budget. Bank angle modulation can achieve 100% successful science orbit insertion within a 300 m/s total ΔV budget. Continuously-variable drag modulation can achieve 99.3% successful science orbit insertion within a 190 m/s total ΔV budget but at 3 times lower peak stagnation point convective heating rate.

Direct numerical simulation of frictional drag modulation in horizontal channel flow subjected to single large-sized bubble injection

Bubble drag reduction (BDR) is desirable for achieving better propulsion performance in underwater applications. Large-sized bubbles have significant potential for application in BDR, as they provide excellent drag reduction. In this study, we analyzed the drag modulation effects of large-sized bubbles, especially high-Weber number bubbles, on the horizontal turbulent channel flow using direct numerical simulation. The Weber number (We) was varied from 130 to 337 based on the equivalent diameter and bubble velocity. The two-phase model based on the volume-of-fluid approach and IsoAdvector method for sharpening the bubble interface was used. To study the drag modulation mechanism of large-sized bubble, the skin friction profile along the centerline of the bubble and local mean ratio of skin friction were analyzed at different Weber numbers. The bubble length was found to have a significant effect on drag reduction toward the rear region of the bubble. Based on this observation, we analyzed the influence of the bubble regions on drag modulation by confining each region. The numerical results indicated that the skin friction was sensitive to the bubble size and bubble regions, the changes in the skin friction profile, contour, and local averaged values with the variation in the Weber number were analyzed. Considering the relationship between the bubble regions and skin friction, most bubbles exhibited an increase in drag on the liquid film until We = 337. Meanwhile, the area of drag reduction in the secondary flow increased and broadened with an increasing Weber number. Owing to this tendency, the effect of drag reduction is expected from sufficiently larger bubbles around We = 337. These results afford new insights into bubble-induced drag modulation in different regions of horizontal flow, and important parameters of large-sized bubbly flow for the investigation of overall drag reduction performance.

Performance Assessment of Discrete-Event Drag Modulation for Mars Entry with Real-Time Guidance

Entry flight performance is assessed for single-stage discrete-event drag-modulation trajectory control on Mars with two different real-time guidance algorithms: a heuristic velocity trigger and numerical predictor–corrector. Three degree-of-freedom simulation and Monte Carlo techniques are used to determine flight performance across a range of mission and vehicle design parameters. Trends are identified in flight performance across different initial conditions, ballistic-coefficient ratios, and target ranges. Results indicate that both guidance algorithms can provide landing accuracy better than 10 km across likely vehicle properties and entry conditions. The heuristic velocity trigger performs nearly as well as the numerical predictor–corrector for low-ballistic-coefficient ratios and entry flight-path angles steeper than approximately . The numerical predictor–corrector provides consistent flight performance across all feasible mission and vehicle parameters with accuracy better than approximately 5 km. Overall, single-stage discrete-event drag-modulation trajectory control is a feasible option for accurate landings for ballistic coefficients below approximately and landed altitudes above 0 km.

Discrete-Event Drag-Modulated Guidance Performance for Venus Aerocapture

Drag modulation provides a straightforward approach to aerocapture trajectory control. In this paper, two guidance algorithms are assessed for Venus aerocapture: a predictive-trigger and a numerical predictor–corrector. A hybrid root finder is developed for both single- and multistage jettison. Architecture performance is assessed using Monte Carlo methods. Two apoapsis altitude targets, 2000 and 10,000 km, are considered alongside two entry flight-path angles, and . The hybrid root finder improved targeting accuracy and robustness compared with a standard bisection technique. Each of the guidance algorithms performed better for shallower entry angles. The benefit of multi-event jettison architectures is analyzed in this study. A second jettison event is shown to significantly improve apoapsis targeting accuracy, whereas a third jettison event further improves this accuracy, but to a lesser degree, demonstrating multistage jettison’s potential to improve aerocapture robustness.

Feasibility and Mass-Benefit Analysis of Aerocapture for Missions to Venus

A numerical assessment of the feasibility of aerocapture at Venus is presented, and the mass benefit of aerocapture is compared with propulsive orbit insertion. This paper considers constraints imposed by entry corridor, deceleration loads, and aerodynamic heating on aerocapture for two vehicle control techniques: lift modulation and drag modulation. Feasibility charts are presented to graphically visualize the aerocapture design space spanning interplanetary trajectory and vehicle performance. Results indicate lift modulation aerocapture is feasible at Venus using existing blunt-body aeroshells. Drag modulation technique is also feasible and an attractive option for small satellites, but merits an additional study due to small corridor width and heating constraints. The peak heat rate is within the capability of existing thermal protection system materials for both control techniques. Delivered mass fraction using aerocapture is compared with propulsive insertion with and without aerobraking. Aerocapture allows 90–250% increase in delivered mass to a 400 km circular orbit compared with propulsive insertion.

Controlled Spacecraft Re-Entry of a Drag De-Orbit Device (D3)

For spacecraft containing components that survive re-entry, it is important to de-orbit the satellite over a non-populated area. Because most CubeSats (cube satellites that conform to the CubeSat form factor) do not have their own propulsion systems and cannot perform a de-orbit burn, aerodynamic drag modulation presents an attractive solution to re-enter the satellite at the desired location. The University of Florida Advanced Autonomous Multiple Spacecraft (ADAMUS) lab has developed a drag de-orbit device (D3) for CubeSats, which are affordable systems for demonstrating attitude and orbit control. The device consists of four retractable tape-spring booms that are designed and manufactured to validate the targeted re-entry of a CubeSat in Low-Earth Orbit (LEO). By modulating the D3 drag area, orbital maneuvering and controlled re-entry can be performed. This paper outlines the functional and vibration testing procedures and results for the completed device. The complete drag device was taken to NASA Ames Research Center and subjected to random vibrations at 9.6 times the force of gravity. The device survived vibration testing with no obvious damage. After vibration testing, it was determined that no major mechanical design changes to the D3 will need to be made. Future work for this project includes assembling a final, flight-ready drag device that will be attached to a CubeSat for launch.

On the maximisation of control power in low-speed flight

ABSTRACTThe maximisation of control power is considered for an aircraft with multiple control surfaces, with the force and moment coefficients specified by polynomials of the control surface deflections of degree two. The optimal deflections, which maximise and minimise any force or moment coefficient, are determined subject to constraints on the range of deflection of each control surface. The results are applied to a flying wing configuration to determine: (i/ii) the pitch trim, at the lowest drag for the fastest climb, and at the highest drag for the steepest descent; (iii) the maximum and minimum pitching moment; (iv) the maximum and minimum yaw control power and the fraction needed to compensate an outboard engine failure for several propulsion configurations; (v) the maximum and minimum rolling moment. The optimal use of all control surfaces has significant advantages over using just one, e.g. the range of drag modulation with pitch trim is much wider and the maximum and minimum available control moments larger.