Adjoint-based aerodynamic shape optimization with hybridized discontinuous Galerkin methods

peer reviewedWe present a discrete adjoint approach to aerodynamic shape optimization (ASO) based on a hybridized discontinuous Galerkin (HDG) discretization. Our implementation is designed to tie in as seamlessly as possible into a solver architecture written for general balance laws, thus adding design capability to a tool with a wide range of applicability. Design variables are introduced on designated surfaces using the knots of a 2D spline-based geometry representation, while gradients are computed from the adjoint solution using a difference approximation of residual perturbations. A suitable optimization algorithm, such as an in-house steepest descent or the Preconditioned Sequential Quadratic Programming (PSQP) approach from the pyOpt framework, is then employed to find an improved geometry. We present verification of the implementation, including drag or heat flux minimization in compressible flows, as well as inverse design

Reconstructing meteoroid trajectories using forward scatter radio observations from the BRAMS network

peer reviewedIn this paper, we aim to reconstruct meteoroid trajectories using a forward scatter radio system transmitting a continuous wave (CW) with no modulation. To do so, we use the meteor echoes recorded at the receivers of the BRAMS (Belgian RAdio Meteor Stations) network. This system consists, at the time of writing, of a dedicated transmitter and 44 receiving stations located in and nearby Belgium, all synchronized using GPS clocks. Our approach processes the meteor echoes at the BRAMS receivers and uses the time delays as inputs to a nonlinear optimization solver. We compare the quality of our reconstructions with and without interferometric data to the trajectories given by the optical CAMS (Cameras for Allsky Meteor Surveillance) network in Benelux. We show that the general CW forward scatter trajectory reconstruction problem can be solved, but we highlight its strong ill-conditioning. With interferometry, this high sensitivity to the inputs is alleviated and the reconstructed trajectories are in good agreement with optical ones, displaying an uncertainty smaller than 10% on the velocity and 2° on the inclination for most cases. To increase accuracy, the trajectory reconstruction with time delays only should be complemented by information about the signal phase. The use of at least one interferometer makes the problem much easier to solve and greatly improves the accuracy of the retrieved velocities and inclinations. Increasing the number of receiving stations also enhances the quality of the reconstructions

Reconstructing meteoroid trajectories using forward scatter radio observations and the interferometer from the BRAMS network

When meteoroids hit Earth's atmosphere molecules, they leave a trail of plasma behind. This region, composed of free electrons and positively charged ions, is capable of reflecting radio signals. The analysis of such signals along the meteoroid path can be used for various scientific purposes: quantification of the electron line density, analysis of the thermosphere properties, characterization of the meteor ablation process, etc. To achieve these objectives, the meteoroid trajectory needs first to be determined. The reflection on the plasma trails is usually assumed to be specular, which means that the radio wave is reflected only at a given point along the meteoroid trajectory. For forward scatter systems, the position of this specular point depends on the trajectory on the one hand, and on the position of both the emitter and the receiver on the other hand. Using non-collocated receivers, one obtains several specular points along the trajectory. The receivers will thus detect the reflected signal at different time instants on a given trajectory. In this work, we propose a method that aims at reconstructing meteoroid trajectories using only the time differences of the meteor echoes measured at the receivers of a forward scatter radio system, such as the BRAMS (Belgian RAdio Meteor Stations) network. The latter uses the forward scatter of radio waves on ionized meteor trails to study meteoroids falling in the Earth's atmosphere. It is made of a dedicated transmitter and 42 receiving stations located in and nearby Belgium. Given that all the BRAMS receivers are synchronized using GPS clocks, we can compute the time differences of the meteor echoes and use them to find the meteoroid trajectory. Assuming a constant speed motion, the position (three degrees of freedom) and the three velocity components have to be determined. This inverse problem is non-linear and requires the definition of a target objective to minimize. Two different formulations are compared: the first one is based on the minimization of the bistatic range while the second one uses a forward model, which defines the trajectory as being tangential to a family of ellipsoids whose loci are the emitter and each receiver. A Monte-Carlo analysis is performed to highlight the sensitivity of the output trajectory parameters to the input time differences. The BRAMS network also includes an interferometer in Humain (south of Belgium). Unlike the other receiving stations, it uses 5 antennas in the so-called Jones configuration (Jones et al., 1998; Lamy et al., 2018) and allows to determine the direction of arrival of the meteor echo to within approximately 1°. In that case, the problem becomes much easier to solve because the interferometer gives information about the direction of a reflection point. The benefits brought by such a system regarding the accuracy of the trajectory reconstruction are highlighted. The post-processing steps allowing to extract meteor echoes from the raw radio signals are described. An approach to properly filter out the direct beacon signal is introduced. Indeed, each receiver detects a more or less strong direct signal coming from the transmitter. This signal does not contain any information about the meteor path since it simply propagates through the atmosphere and is not reflected on the meteor trail. Knowing that the BRAMS transmitter emits a continuous cosine wave, the amplitude, the frequency and the phase are fitted in the frequency domain. The beacon signal is finally reconstructed in the time domain and subtracted. This process in illustrated in the following figure, which shows an example of spectrograms (i.e. time-frequency maps where the power is color-coded) before and after the beacon signal subtraction. The proper removal of the horizontal line at around 1005 Hz (corresponding to the direct signal) is apparent in the bottom spectrogram. Afterwards, a bandpass filter is necessary to fully exploit the echoes of the detected meteors. Indeed, the raw signal at the time of the meteor echo is noisy and can have interfering signals caused by the reflections on aircrafts. If the latter are at slightly different frequencies than the meteor echo, they produce interference beats. A windowed-sinc filter Blackman filter of high order is therefore used to remove the signal components at frequencies where the meteor echo does not appear. The time corresponding to half-peak power in the rising edge of the echo (which marks the passage of the meteoroid at the specular reflection point) is finally retrieved and the time differences are computed. To analyze the accuracy of the trajectory reconstructions, data from the optical CAMS-BeNeLux network are used. Promising results showing the reconstructed position, velocity and inclination of several meteoroid trajectories with and without the interferometer are discussed. In the following figure, an example of CAMS trajectory reconstruction obtained with our post-processing is shown. The blue line corresponds to the trajectory determined with the CAMS network, while the purple line is obtained through our analysis of the radio signals obtained at the BRAMS receivers. The reconstructed trajectory using the time differences only (method 1) is shown on the left. The trajectory obtained thanks to the combination of time differences and interferometric data (method 2) is given on the right

R-adaptive algorithms for supersonic flows with high-order Flux Reconstruction methods

peer reviewedThe present paper addresses the development and implementation of the first r-adaptive mesh refinement (r-AMR) algorithm for a high-order Flux Reconstruction solver. The r-refinement consists on nodal re-positioning while keeping the number of mesh nodes and their connectivity frozen. The developed algorithm is based on physics-driven spring-analogies, where the mesh can be seen as a network of fictitious springs. While AMR increases the local mesh density, the high-order Flux Reconstruction method potentially provides a more accurate detection of complex flow features over relatively coarser mesh, when compared to low-order methods. In this work, a concise overview of the Flux Reconstruction method and spring-based AMR techniques will be given, followed by some promising results of r-AMR applied to benchmark high-order steady-state supersonic flow simulations

Aerodynamic Shape Optimization with Hybridized Discontinuous Galerkin Schemes

editorial reviewedWe present a discrete adjoint approach to aerodynamic shape optimization (ASO) based on a hybridized discontinuous Galerkin (HDG) discretization. Our implementation is designed to tie in as seamlessly as possible into a solver architecture written for general balance laws, thus adding design capability to a tool with a wide range of applicability. Design variables are introduced on designated surfaces using the knots of a spline-based geometry representation, while gradients are computed from the adjoint solution using a difference approximation of residual perturbations. A suitable optimization algorithm, such as an in-house steepest descent or the Preconditioned Sequential Quadratic Programming (PSQP) approach from the pyOpt framework, is then employed to find an improved geometry. The resulting ASO module is currently set up for 2D test cases governed by balance laws, including linear scalar equations or nonlinear systems of equations. We present verification of the implementation, including drag or heat flux minimization in compressible flows, as well as inverse design

Reconstructing meteoroid trajectories using BRAMS data

editorial reviewedThis paper summarizes our recent efforts in retrieving meteoroid trajectories using data from the forward scatter radio system BRAMS. Two methods are presented, one based only on the knowledge of time delays measured between meteor echoes observed at various receiving stations, and one including information from a radio interferometer in addition to the time delays measurements. For comparison about the quality of trajectory reconstruction, data from the optical CAMS-BeNeLux network are used. A third method is briefly presented assuming the total range traveled by the radio wave is known at all receiving stations. This work contains only preliminary results available at the end of summer 2021. Discussions about improvements are provided at the end of the paper

Reconstructing Meteoroid Trajectories Using Forward Scatter Radio Observations from the BRAMS Network

When meteoroids hit Earth’s atmosphere molecules, a trail of plasma located downstream of the meteoroid is created. This region, composed of free electrons and positively charged ions, is capable of reflecting radio signals. The reflection on the plasma trails is usually assumed to be specular, which means that the radio wave is reflected only at a given point along the meteoroid trajectory. For forward scatter systems, the position of this specular point depends on the trajectory on the one hand, and on the position of both the emitter and the receiver on the other hand. Using non-collocated receivers, one obtains several specular points along the trajectory. The receivers will thus detect the reflected signal at different time instants on a given trajectory. In this work, we introduce a method that aims at reconstructing meteoroid trajectories using only the time differences of the meteor echoes measured at the receivers of a forward scatter radio system. Assuming a constant speed motion, the position (three degrees of freedom) and the three velocity components have to be determined. Two alternative formulations to solve this complex problem through non-linear optimization are compared. The first one is based on the minimization of the bistatic range, while the second looks for the tangent line to several ellipsoids. A Monte-Carlo analysis is performed to highlight the sensitivity of the output trajectory parameters to the input time differences. The application of this method to actual radio observations from the BRAMS (Belgian RAdio Meteor Stations) network is also presented. The post-processing steps allowing to extract meteor echoes from the raw radio signals are described. For comparison about the quality of trajectory reconstruction, data from the optical CAMS-BeNeLux network are used. Promising results showing the reconstructed position, velocity and inclination of several meteoroid trajectories are discussed

Phase-enhanced trajectory and speed reconstruction of meteoroids using BRAMS data

In this project, we aim to reconstruct meteoroid trajectories thanks to a forward scatter radio system using a pure continuous wave (CW) transmitted signal with no modulation. To do so, we use the meteor echoes recorded at the receivers of the BRAMS (Belgian RAdio Meteor Stations) network. The latter is made of a dedicated transmitter and currently 48 receiving stations located in and nearby Belgium, all synchronized using GPS clocks. Our approach processes the signals recorded at the BRAMS receivers and uses the time delays between the meteor echoes as inputs to a nonlinear optimization solver. We compare the quality of our reconstructions data to the trajectories given by the optical CAMS (Cameras for Allsky Meteor Surveillance) network in Benelux. To do so, we solve the general CW forward scatter trajectory reconstruction problem, but we highlight its strong ill-conditioning if the only inputs are the time delays of the echoes at the receivers. To obtain a better accuracy for a large number of meteoroids, the time delays are complemented by information about the signal phase. The approach used for this work is based on the pre-t0 phase technique introduced for backscatter radars. In this project, we extend and adapt the method to forward scatter systems and we illustrate the improved accuracy that it brings on the meteoroid trajectory and speed reconstruction