Search Results (61)

To meet the stringent reliability requirements of rotor blades in turbomachines, greater effort should be devoted to improving both aerodynamic and structural performance in blade design. This paper introduces an aero-structural multi-disciplinary design optimization (MDO) method for compressor rotor blades using a discrete adjoint method and an equivalent stress model (ESM). The principles of the ESM are firstly introduced, and its accuracy in calculating equivalent stress is validated through comparison with a commercial program. Both the aerodynamic performance and the maximum equivalent stress (MES) are selected as optimization objectives. To modify the blade profile, the steepest descent optimization method is utilized, in which the necessary sensitivities of the cost function to the design parameters are calculated by solving the adjoint equations. Finally, the aero-structural MDO of a transonic compressor rotor, NASA Rotor 67, is conducted, and the Pareto solutions are obtained. The optimization results demonstrate that the adiabatic efficiency and the MES are competitive in improving multi-disciplinary performance. For most of the Pareto solutions, the MES can be considerably reduced with increased adiabatic efficiency. Full article

This work establishes definitive conditions for the inheritance of categorical completeness and cocompleteness by categories of internal group objects. We prove that while the completeness of $\mathbf{Grp}\left(\mathcal{C}\right)$ follows unconditionally from the completeness of the base category $\mathcal{C}$, cocompleteness requires $\mathcal{C}$ to be regular, cocomplete, and admit a free group functor left adjoint to the forgetful functor. Explicit limit and colimit constructions are provided, with colimits realized via coequalizers of relations induced by group axioms over free group objects. Applications demonstrate cocompleteness in topological groups, ordered groups, and group sheaves, while Lie groups serve as counterexamples revealing necessary analytic constraints—particularly the impossibility of equipping free groups on non-discrete manifolds with smooth structures. Further results include the inheritance of regularity when the free group functor preserves finite products, the existence of internal hom-objects in locally Cartesian closed settings, monadicity for locally presentable $\mathcal{C}$, and homotopical extensions where model structures on $\mathbf{Grp}\left(\mathcal{M}\right)$ reflect those of $\mathcal{M}$. This framework unifies classical category theory with geometric obstruction theory, resolving fundamental questions on exactness transfer and enabling new constructions in homotopical algebra and internal representation theory. Full article

This study presents the development of a discrete algorithm for interpreting ground-penetrating radar (GPR) data in vertically inhomogeneous media for the diagnostics of road structures. Experimental data were obtained using an OKO-2 GPR system, followed by primary radargram processing using the CartScan software. This included noise and interference filtering, as well as the initial estimation of the dielectric permittivity of detected layers. The resulting dataset was used to validate numerical algorithms for solving the forward and inverse problems of geolectrics. The proposed approach is based on minimizing a quadratic misfit functional between the calculated and observed values of the horizontal component of the electromagnetic field. The gradient of the functional required for optimization is obtained via the numerical solution of an adjoint problem. A discrete version of this problem was developed, which satisfies the properties of conservativeness and uniformity according to finite difference theory. The inverse problem reconstruction of dielectric permittivity is considered a non-destructive method for radargram interpretation. Assuming a piecewise-continuous medium structure eliminates the need for computing gradients at material interfaces. The proposed methodology enhances the accuracy and reliability of pavement condition assessment and holds practical value for road infrastructure monitoring. Full article

In actual flight, aircraft rarely operate under a single design condition; multiple flight states must be considered to meet performance requirements. With the push for green and low-carbon aviation, there is growing demand for high-performance, fuel-efficient aircraft. This study focuses on the Blended Wing Body (BWB) configuration. To address large-scale design variables and multiple constraints, a discrete adjoint-based aerodynamic optimization method is developed, improving computational efficiency and reducing cost.The optimization results show reduced drag coefficients across various flight conditions and enhanced drag divergence performance. The robustness of the multi-point optimization approach is validated, confirming its ability to improve aircraft performance across different states. The proposed method is practical and provides an effective reference for aerodynamic design of BWB aircraft. Full article

We study a separable Hilbert space of smooth curves taking values in the Segal–Bergmann space of analytic functions in the complex plane, and two of its subspaces that are the domains of unbounded non self-adjoint linear partial differential operators of the first and second order. We show how to build a Hilbert basis for this space. We study these first- and second-order partial derivation non-self-adjoint operators defined on this space, showing that these operators are defined on dense subspaces of the initial space of smooth curves; we determine their respective adjoints, compute their respective commutators, determine their eigenvalues and, under some normalisation conditions on the eigenvectors, we present examples of a discrete set of eigenvalues. Using these derivation operators, we study a Schrödinger-type equation, building particular solutions given by their representation as smooth curves on the Segal–Bergmann space, and we show the existence of general solutions using an Fourier–Hilbert base of the space of smooth curves. We point out the existence of self-adjoint operators in the space of smooth curves that are obtained by the composition of the partial derivation operators with multiplication operators, showing that these operators admit simple sequences of eigenvalues and eigenvectors. We present two applications of the Schrödinger-type equation studied. In the first one, we consider a wave associated with an object having the mass of an electron, showing that two waves, when considered as having only a free real space variable, are entangled, in the sense that the probability densities in the real variable are almost perfectly correlated. In the second application, after postulating that a usual package of information may have a mass of the order of magnitude of the neutron’s mass attributed to it—and so well into the domain of possible quantisation—we explore some consequences of the model. Full article

An important aspect of pressurized water reactor (PWR) lifetime monitoring is supporting radiation shielding analyses which can quantify various in-core and out-core effects induced in reactor materials by varying neutron–gamma fields. A good understanding of such a radiation environment during normal and accidental operating conditions is required by plant regulators to ensure proper shielding of equipment and working personnel. The complex design of a typical PWR is posing a deep penetration shielding problem for which an elaborate simulation model is needed, not only in geometrical aspects but also in efficient computational algorithms for solving particle transport. This paper presents such a hybrid shielding approach of FW-CADIS for characterization of the reactor pressure vessel (RPV) irradiation using SCALE6.2.4 code package. A fairly detailed Monte Carlo model (MC) of typical reactor internals was developed to capture all important streaming paths of fast neutrons which will backscatter the biological shield and thus enhance RPV irradiation through the cavity region. Several spatial differencing and angular segmentation options of the discrete ordinates S_N flux solution were compared in connection to a S_N mesh size and were inspected by VisIt code. To optimize MC neutron transport toward the upper RPV head, which is a particularly problematic region for particle transport, a deterministic solution of discrete ordinates in forward/adjoint mode was convoluted in a so-called contributon flux, which proved to be useful for subsequent S_N mesh refinement and variance reduction (VR) parameters preparation. The pseudo-particle flux of contributons comes from spatial channel theory which can locate spatial regions important for contributing to a shielding response. Full article

The improved heat dissipation observed in 3D micro-ribbed tubes is primarily influenced by the intricate interplay of multiple structural parameters. Nevertheless, research into the coupling mechanisms of these multi-structural parameters remains constrained by the absence of effective methodology in numerical solutions. In the present work, a new 3D micro-rib structure based on discrete adjoint method is established. Firstly, the research examines the interplay of different parameters (such as arrangement, relative roughness height, angle of attack, and circumferential rows) on the thermo-hydraulic performance. It is noted that the heat transfer efficiency is notably impacted by the relative roughness height. And the arrangement methodology dictates the optimal positioning for heat transfer efficiency. An increase in the number of circumferential rows enhances fluid mixing, while the angle of attack plays a crucial role in the formation of longitudinal vortices. Secondly, the coupling optimization technique is employed to obtain the optimal structure featuring non-uniform relative roughness height by the developed numerical solution. Overall, in comparison to the smooth tube, the optimized ribbed tube exhibits a remarkable 64.9% enhancement in performance evaluation criteria. Finally, a notable enhancement of 10.65–22.78% is observed when comparing with the prevailing micro-rib structures. Full article

This article proposes a novel robust invariance condition for uncertain linear discrete-time systems with state and control constraints, utilizing a method of semidefinite programming duality. The approach involves approximating the robust invariant set for these systems by tackling the dual problem associated with semidefinite programming. Central to this method is the formulation of a dual programming through the application of adjoint mapping. From the standpoint of semidefinite programming dual optimization, the paper presents a novel linear matrix inequality (LMI) conditions pertinent to robust positive invariance. Illustrative examples are incorporated to elucidate the findings. Full article

During this research, aerodynamic shape optimization is conducted on the Ahmed body with the drag coefficient as the objective function and the ramp shape as the design variable, while aero-structural optimization is conducted on NACA 0012 to reduce the drag coefficient for the aerodynamic performance with the shape as the design variable while reducing structural mass with the thickness of the panels as the design variables. This is accomplished through a gradient-based optimization process and coupled finite element and computational fluid dynamics (CFD) solvers under fluid–structure interaction (FSI). In this study, DAFoam (Discrete Adjoint with OpenFOAM for High-fidelity Multidisciplinary Design Optimization) and TACS (Toolkit for the Analysis of Composite Structures) are integrated to optimize the aero-structural design of an airfoil concurrently under the FSI condition, with TACS and DAFoam as coupled structural and CFD solvers integrated with a gradient-based adjoint optimization solver. One-way coupling between the fluid and structural solvers for the aero-structural interaction is adopted by using Mphys, a package that standardizes high-fidelity multiphysics problems in OpenMDAO. At the end of the paper, we compare and discuss our findings in the context of existing research, specifically highlighting previous results on the aerodynamic and aero-structural optimization of wind turbine blades. Full article

This paper introduces a low-boom aircraft optimization design method guided by equivalent area distribution, which effectively improves the intuitiveness and refinement of inverse design. A gradient optimization method based on discrete adjoint equations is proposed to achieve the fast solution of the gradient information of target equivalent area distribution relative to design variables and to drive the aerodynamic shape update to the optimal solution. An optimization experiment is carried out based on a self-developed supersonic civil aircraft configuration with engines. The results show that the equivalent area distribution adjoint equation can accurately solve the gradient information. After optimization, the sonic boom level of the aircraft was reduced by 13.2 PLdB, and the drag coefficient was reduced by 60.75 counts. Moreover, the equivalent area distribution adjoint optimization method has outstanding advantages, such as high sensitivity and fast convergence speed, and can take both the low sonic boom and the low drag force of the aircraft into account, providing a powerful tool for the comprehensive optimization design of supersonic civil aircraft by considering sonic boom and aerodynamic force. Full article

In this paper, we introduce a discretization scheme for the Yang–Mills equations in the two-dimensional case using a framework based on discrete exterior calculus. Within this framework, we define discrete versions of the exterior covariant derivative operator and its adjoint, which capture essential geometric features similar to their continuous counterparts. Our focus is on discrete models defined on a combinatorial torus, where the discrete Yang–Mills equations are presented in the form of both a system of difference equations and a matrix form. Full article

Flow topology optimization (TopOpt) based on Darcy’s source term is widely used in the field of TopOpt. It has a high degree of freedom, making it suitable for conceptual aerodynamic design. Two problems of TopOpt are addressed in this paper to apply the TopOpt method to high-Reynolds-number turbulent flow that is often encountered in aerodynamic design. First, a strategy for setting Darcy’s source term is proposed based on the relationship between the magnitude of the source term and some characteristic variables of the flow (length scale, freestream velocity, and fluid viscosity). Second, we construct two modified turbulence models, a modified Launder–Sharma k − ϵ (LSKE) model and a modified shear stress transport (SST) model, that consider the influence of Darcy’s source term on turbulence and the wall-distance field. The TopOpt of a low-drag profile in turbulent flow is studied using the modified LSKE model. It is demonstrated by comparing velocity profiles that the model can reflect the influence of solids on turbulence at Reynolds numbers as high as one million. The TopOpt of a rotor-like geometry, which is of great importance in aerodynamic design, is conducted using the modified SST model. In all the cases considered, the drag, the total pressure loss, and the energy dissipation are significantly reduced by TopOpt, indicating the proposed model’s ability to handle the TopOpt of turbulent flow. Full article

This paper presents a topology optimization (TopO) method for conjugate heat transfer (CHT), with turbulent flows. Topological changes are controlled by an artificial material distribution field (design variables), defined at the cells of a background grid and used to distinguish a fluid from a solid material. To effectively solve the CHT problem, it is crucial to impose exact boundary conditions at the computed fluid–solid interface (FSI); this is the purpose of introducing the cut-cell method. On the grid, including also cut cells, the incompressible Navier–Stokes equations, coupled with the Spalart–Allmaras turbulence model with wall functions, and the temperature equation are solved. The continuous adjoint method computes the derivatives of the objective function(s) and constraints with respect to the material distribution field, starting from the computation of derivatives with respect to the positions of nodes on the FSI and then applying the chain rule of differentiation. In this work, the continuous adjoint PDEs are discretized using schemes that are consistent with the primal discretization, and this will be referred to as the “Think Discrete–Do Continuous” (TDDC) adjoint. The accuracy of the gradient computed by the TDDC adjoint is verified and the proposed method is assessed in the optimization of two 2D cases, both in turbulent flow conditions. The performance of the TopO designs is investigated in terms of the number of required refinement steps per optimization cycle, the Reynolds number of the flow, and the maximum allowed power dissipation. To illustrate the benefits of the proposed method, the first case is also optimized using a density-based TopO that imposes Brinkman penalization terms in solid areas, and comparisons are made. Full article

This article presents single- and multi-disciplinary shape optimizations of a generic business jet wing at two transonic cruise flow conditions. The studies performed are based on two high-fidelity gradient-based optimization tools, assisted by the adjoint method (following both discrete and continuous approaches). Single discipline and coupled multi-disciplinary sensitivity derivatives computed from the two tools are compared and verified against finite differences. The importance of not making the frozen turbulence assumption in adjoint-based optimization is demonstrated. Then, a number of optimization runs, ranging from a pure aerodynamic with a rigid structure to an aerostructural one exploring the trade-offs between the involved disciplines, are presented and discussed. The middle-ground scenario of optimizing the wing with aerodynamic criteria and, then, performing an aerostructural trimming is also investigated. Full article

In order to merge continuous and discrete analyses, a number of dynamic derivative equations have been put out in the process of developing a time-scale calculus. The investigations that incorporated combined dynamic derivatives have led to the proposal of improved approximation expressions for computational application. One such expression is the diamond alpha (${\diamond }_{\alpha }$) derivative, which is defined as a linear combination of delta and nabla derivatives. Several dynamic equations and inequalities, as well as hybrid dynamic behavior—which does not occur in the real line or on discrete time scales—are analyzed using this combined concept. In this study, we consider a ${\diamond }_{\alpha }$ Dirac system under boundary conditions on a uniform time scale. We examined some basic spectral properties of the problem we are considering, such as the simplicity, the reality of eigenvalues, orthogonality of eigenfunctions, and self adjointness of the operator. Finally, we construct an expression for the eigenfunction of the ${\diamond }_{\alpha }$ Dirac boundary value problem (BVP) on a uniform time scale. Full article