IMPLEMENTATION OF TRANSONIC AREA RULE AND SWEPT BACK DELTA WING DESIGN ON AN AIRCRAFT.

The transonic area rule was first implemented in the 1950s. It is an important concept related to the drag on an aircraft or other body in transonic and supersonic flight which states that two airplanes with the same longitudinal cross-sectional area distribution have the same wave drag, independent of how the area is distributed laterally. A swept back delta wing increases the critical Mach number of the wing and performs well at low speeds, as a result of unique swirling vortices that form on the upper surface of the wing. BOOM Supersonic plans to bring back Supersonic Commercial aircrafts by implementing these modifications in the famous Concorde. In this paper two aircraft designs inspired by Concorde and BOOM Overture are compared using ANSYS Fluent. These were designed in CATIA with changes in fuselage dimensions, wing configuration and engine configuration. The lift to drag ratio of both the designs are calculated and compared. Pressure contours, velocity vectors, vector pathlines, turbulence pathlines and pressure pathlines are also compared. The results show that the design with the implementation of transonic area rule and swept back delta wing has a better Lift to Drag ratio when compared to the design with a wide fuselage and a delta wing design.

MODIFIED RULE OF EQUAL AREA FOR APPROXIMATION OF CONDUCTING SURFACES BY WIRE GRID IN SOLVING RADIATION PROBLEMS

A modification of the equal area rule is proposed for approximation conductive surfaces by a grid of wires when solving radiation problems. It was tested in the TALGAT system using the example of a dipole on a conductive plate, with verification in the EMPro system. It is shown that the modification of this rule gives more accurate results compared to the original one.

The area rule for circulation in three-dimensional turbulence

An important idea underlying a plausible dynamical theory of circulation in three-dimensional turbulence is the so-called area rule, according to which the probability density function (PDF) of the circulation around closed loops depends only on the minimal area of the loop, not its shape. We assess the robustness of the area rule, for both planar and nonplanar loops, using high-resolution data from direct numerical simulations. For planar loops, the circulation moments for rectangular shapes match those for the square with only small differences, these differences being larger when the aspect ratio is farther from unity and when the moment order increases. The differences do not exceed about 5% for any condition examined here. The aspect ratio dependence observed for the second-order moment is indistinguishable from results for the Gaussian random field (GRF) with the same two-point correlation function (for which the results are order-independent by construction). When normalized by the SD of the PDF, the aspect ratio dependence is even smaller ( < 2%) but does not vanish unlike for the GRF. We obtain circulation statistics around minimal area loops in three dimensions and compare them to those of a planar loop circumscribing equivalent areas, and we find that circulation statistics match in the two cases only when normalized by an internal variable such as the SD. This work highlights the hitherto unknown connection between minimal surfaces and turbulence.

The Maxwell crossover and the van der Waals equation of state

The well-known Maxwell construction1 (the equal-area rule, EAR) was devised for vapor liquid equilibrium (VLE) calculation with the van der Waals (vdW) equation of state (EoS)2. The EAR generates an intermediate volume between the saturated liquid and vapor volumes. The trajectory of the intermediate volume over the coexistence region is defined here as the Maxwell crossover, denoted as the M-line, which is independent of EoS. For the vdW or any cubic3 EoS, the intermediate volume corresponds to the “unphysical” root, while other two corresponding to the saturated volumes of vapor and liquid phases, respectively. Due to it’s “unphysical” nature, the intermediate volume has always been discarded. Here we show that the M-line, which turns out to be strictly related to the diameter4 of the coexistence curve, holds the key to solving several major issues. Traditionally the coexistence curve with two branches is considered as the extension of the Widom line5,6-9. This assertion causes an inconsistency in three planes of temperature, pressure and volume. It is found that the M-line is the natural extension of the Widom line into the vapor-liquid coexistence region. As a result, the united single line coherently divides the entire phase space, including the coexistence and supercritical fluid regions, into gas-like and liquid-like regimes in all the planes. Moreover, along the M-line the vdW EoS finds a new perspective to access the second-order transition in a way better aligning with observations and modern theory10. Lastly, by using the feature of the M-line, we are able to derive a highly accurate and analytical proximate solution to the VLE problem with the vdW EoS.

Q-Curve and Area Rules for Choosing Heuristic Parameter in Tikhonov Regularization

We consider choice of the regularization parameter in Tikhonov method if the noise level of the data is unknown. One of the best rules for the heuristic parameter choice is the quasi-optimality criterion where the parameter is chosen as the global minimizer of the quasi-optimality function. In some problems this rule fails. We prove that one of the local minimizers of the quasi-optimality function is always a good regularization parameter. For the choice of the proper local minimizer we propose to construct the Q-curve which is the analogue of the L-curve, but on the x-axis we use modified discrepancy instead of discrepancy and on the y-axis the quasi-optimality function instead of the norm of the approximate solution. In the area rule we choose for the regularization parameter such local minimizer of the quasi-optimality function for which the area of the polygon, connecting on Q-curve this minimum point with certain maximum points, is maximal. We also provide a posteriori error estimates of the approximate solution, which allows to check the reliability of the parameter chosen heuristically. Numerical experiments on an extensive set of test problems confirm that the proposed rules give much better results than previous heuristic rules. Results of proposed rules are comparable with results of the discrepancy principle and the monotone error rule, if the last two rules use the exact noise level.

Rules Over Rights? Legal Aspects of the European Commission Recommendation for Resumption of Dublin Transfers of Asylum Seekers to Greece

Five years after the Dublin transfers of asylum seekers to Greece were halted—due to recurrent failings in the detention conditions, living conditions, and asylum procedure—the European Commission recommended a resumption of the practice. This Article analyzes the Recommendation in light of the human rights reports preceding and following it. The examination reveals that the renewal of systematic transfers would be premature, posing serious risks to the rights of asylum seekers under European and EU law. The restoration of a flawed system for distribution of asylum claims among the Member States—without fundamental reforms towards greater solidarity—may lead to a repetition of past mistakes. Despite the paramount importance of the Dublin system for the functioning of the Schengen Area, rule enforcement should not supersede human rights protection.