Search Results (8)

Brush seals using compliant bristle packs can reduce turbomachinery leakage more effectively than conventional labyrinth seals, but their coupled structural and flow behavior makes design difficult. Under large pressure loading, bristles can deflect, lose contact with the rotor, and generate clearance, causing the sharp leakage increase known as blow-out. This study develops a model linking nonlinear bristle deflection, rotor–bristle contact loss, and leakage response. The bristle is treated as an inextensible nonlinear elastic member subjected to distributed pressure loading, backing-plate support, and frictional rotor contact. Contact and separated states are solved iteratively using boundary-value and initial-value solvers. Leakage through the bristle pack is calculated using a random bristle-bed formulation, and leakage through generated clearance is evaluated with an orifice-flow model. The model agrees well with published bristle-deflection predictions. Increasing pressure load reduces normal contact force until lift-off occurs, producing clearance and a sharp rise in leakage. Increasing front-plate free height shifted lift-off from pressure ratio ≈4 to ≈2, while clearance flow contributed up to 36.5% after lift-off. Brush-seal blowout is therefore governed by the transition from rotor–bristle contact to separation. Lower back-plate height can delay blow-out, but hysteresis and durability tradeoffs must be considered. Full article

In the framework of lightweight aircraft preliminary design and optimisation, different computational approaches are formulated and assessed for the large-amplitude static aeroelastic response of very-flexible slender thin wings in subsonic incompressible flow at low speed. Starting from either a continuous or a discrete model, either numerical or semi-analytical solutions are derived and compared for several combinations of flow speed and angle of attack. Exploiting the Euler–Bernoulli beam idealisation for the wing structure and its local deformation, non-linear and quasi-linear models are presented where the elastic axis is inextensible and its global displacement is geometrically nonlinear; to this purpose, Hencky’s model is also adopted. Employing modified strip theory for the airload, reduced-order conceptual assessments and parametric evaluations are possible, and the results are shown for the Pazy wing which exhibit excellent agreement with nonlinear higher-fidelity simulations in the literature. Both closed-loop and open-loop solutions are then provided, with the latter being readily resumed from the former in the low-speed limit far away from static aeroelastic divergence. In conclusion, the novel approaches hereby explored demonstrate overall consistency while offering both theoretical insights and practical recommendations for their trust region, especially in terms of the impact and importance of the linear and nonlinear features as well as their effects. Full article

In this paper, we present the evolutions of ruled surfaces generated by the principal normal, the principal normal’s derivative, and the Darboux vector fields along a space curve that are the elements of an alternative frame. The comprehension of an object’s rotational behavior is crucial knowledge relevant to various realms, and this can be accomplished by analyzing the Darboux vector along the path of a point on the object as it moves through space. In that regard, examining the evolutions of the ruled surfaces based on the changes in their directrices, including the Darboux vector in the alternative frame along a space curve, is significant. As the first step of this study, we express the evolution of the alternative frame elements of a space curve. Subsequently, the conditions for the ruled surfaces generated by them to be minimal, developable, and inextensible are investigated. These findings can allow some physical phenomena to be well understood through surface evolutions satisfying these conditions. In the final step, we provide graphical representations of some examples of inextensible ruled surfaces and curve evolutions. Full article

In this article, we present a finite element method for studying the dynamic behavior of deformable vesicles, which mimic red blood cells, in a non-Newtonian Casson fluid. The fluid membrane, represented by an implicit level-set function, adheres to the Canham–Helfrich model and maintains surface inextensibility constraint through penalty. We propose a two-step time integration scheme that incorporates higher-order accuracy by using an asymmetric composition of discrete flow based on the second-order backward difference formula, followed by a projection onto the real axis. Our framework incorporates variable time steps generated by an appropriate adaptation criterion. We validate our model through numerical simulations against existing experimental and numerical results in the case of purely Newtonian flow. Furthermore, we provide preliminary results demonstrating the influence of the non-Newtonian fluid model on membrane regimes. Full article

The study of the flows of curves is one of the most fascinating research areas in differential geometry. In this paper, we investigate the geometry of the flows of timelike curves according to the quasi-frame in Minkowski space ${\mathbb{R}}^{2,1}$ (In this paper, we refer to these curves as “quasi-timelike curves”). We investigate the evolution of quasi-timelike curves using the velocity functions and obtain the necessary and sufficient conditions for inextensibility. Additionally, we obtain the explicit forms of the time evolution equations for the quasi-orthonormal frames (tangent, quasi-normal, and quasi-binormal vectors) of the quasi-timelike curve as well as the time evolution equations of their quasi-curvatures. We present a new application for motion with velocities equal to the quasi-curvatures of the quasi-timelike curve. In this application, the time evolution equations of the quasi-curvatures arise as a system of partial differential equations with the form of the heat equation, and by solving this system, we visualize the evolution of quasi-curvatures and the evolution of the quasi-timelike curve. In addition, the acceleration functions are used to investigate the flows of inextensible quasi-timelike curves, and an application for accelerations equal to the quasi-curvatures is given. Through this application, the position vector of the quasi-timelike curve satisfies the one-dimensional wave equation, and the time evolution equations of the quasi-curvatures arise as a system of transport equations. We obtain the solutions and graph them using Wolfram Mathematica 12. Full article

This research focused on studying the flows of a null Cartan curve specified by the velocity and acceleration fields. We have proven that the tangential and normal velocities are influenced by the binormal velocity along the motion. The velocity fields are used to drive the time evolution equations for the Cartan frame and the torsion of the null curve. The objective of this work is to construct a family of inextensible null Cartan curves from the flows of the initial null Cartan curve. The surface formed by this family of inextensible flows of the null Cartan curve is obtained numerically and visualized. In this paper, we refer to the surface traced out by the family of the null Cartan curve as the generated or constructed surface. We present a novel model for the inextensible null Cartan curve, which moves with a constant binormal velocity to describe the process of constructing a family of null Cartan curves. Through this model, the time evolution equation for the torsion of the inextensible null Cartan curve arises as the Korteweg-de Vries (K-dV) equation, and we obtain and visualize the soliton solutions. The soliton solutions represent the torsion of the family of null Cartan curves at various time values. We construct the family of inextensible null Cartan curves and visualize the generated surface. In addition, we investigate the flows of inextensible null Cartan curves specified by acceleration fields, and we obtain the explicit relationships between the acceleration and velocity functions. Finally, we provide an application for the inextensible flows of the null Cartan curve with constant normal acceleration. Full article

In this paper, we study inextensible flows of a curve on a lightlike surface in Minkowski three-space and give a necessary and sufficient condition for inextensible flows of the curve as a partial differential equation involving the curvatures of the curve on a lightlike surface. Finally, we classify lightlike ruled surfaces in Minkowski three-space and characterize an inextensible evolution of a lightlike curve on a lightlike tangent developable surface. Full article