Aeroelastic aspects of Axial Compressor Stage with Self-Recirculating Casing Treatment

For successful implementation of casing treatment designs in axial compressors, apart from the stall margin improvement benefits, aeroelasticity also plays a major role. This manuscript addresses the not often discussed aeroelastic aspects of a new discrete type of passive Self-Recirculating Casing Treatment (RCT) designed for a transonic axial compressor stage. Experiments are carefully designed for synchronized measurement of the unsteady fluidic disturbances and vibrations during rotating stall for compressor with baseline solid casing and Self-RCT. The modal characteristics of the axial compressor rotor-disk assembly are studied experimentally and numerically. Experimentally it is observed that the rotating stall cells excite the blades in their fundamental mode in a compressor with baseline solid casing at the stall flow condition. In contrast, there is no excitation of the blades in the compressor with self-recirculating casing treatment at the same solid casing stall flow condition. Also, the self-recirculating casing treatment compared to the solid casing can significantly reduce the overall vibration levels of the blades that are excited at the stall flow condition. The casing treatment is able to alter the flow field near the tip region of the rotor blade, and hence influencing the forcing function of the rotating cantilever blades to have the aeroelastic benefit.

COVID-19 as Industry Forcing Function: Challenges for Entrepreneurship in the Post-Pandemic Future

The COVID-19 crisis has changed how firms and industries do business – at least for now. What is uncertain, however, is the duration of that change. Will the industry change induced by the COVID-19 crisis persist and, if so, for how long? Can a crisis, and particularly the COVID-19 crisis, act as a more permanent change agent and create an environment that mimics the entrepreneurial opportunity that industry forcing functions create? If yes, then there is cause to consider the entrepreneurial opportunity that the COVID-19 crisis provides. In this paper, we review the changes that the pandemic has brought to business practices. Furthermore, we discuss the differences between crisis-based opportunity and entrepreneurial opportunity created by industry forcing functions in order to illuminate the ability of a COVID-19 crisis–induced Low Touch Economy to sustainably create entrepreneurial opportunities. We show examples and list the attributes of industry forcing functions that have already provided sustainable entrepreneurial opportunity. Then, we match these attributes with the factors pertaining to the COVID-19-related Low Touch Economy. We find that the COVID-19 crisis has similarities and differences to the traditional industry forcing functions started by disruptive technologies. However, unlike traditional industry forcing functions, the COVID-19 crisis acts in a pan-industrial manner, making the impact of the pandemic more profound. Furthermore, the timing of the pandemic is important too: the COVID-19 crisis struck during the emergence of a Schumpeterian wave of Industry 4.0 and accelerated the adoption of its most important harbingers. We provide researchers and practitioners a lens through which to review not only the COVID-19 crisis’s possibility of lasting effects, but also how it will affect entrepreneurs.

Escaping Orbits Are also Rare in the Almost Periodic Fermi–Ulam Ping-Pong

We study the one-dimensional Fermi–Ulam ping-pong problem with a Bohr almost periodic forcing function and show that the set of initial condition leading to escaping orbits typically has Lebesgue measure zero.

Exploring healthcare staff narratives to understand the role of quality improvement methods in innovative practices during COVID-19

Background COVID-19 has impacted the context in which healthcare staff and teams operate and this has implications for quality improvement (QI) work. Contrary to the usual ambivalent relationship staff have with QI work, there have been examples of unprecedented staff engagement in implementing rapid changes during the pandemic indicating a change in important underlying factors that impact staff involvement in QI. The purpose of this study is to explore staff perspectives about how experience and skills of QI methods supported them in implementing innovative practices during COVID-19. Methods This is a qualitative narrative study based on narrative interviews to collect healthcare staff stories of implementing rapid change. The stories were identified through social media (Twitter) and a national health magazine issued by the Irish health service. Twenty staff members participated in the interviews. Interviews were audio recorded, transcribed, and anonymised. A four-step thematic analysis was conducted. Results The analysis revealed the transformational journey of healthcare staff from the initial shock and anxiety caused by COVID-19 to making sense of the situation, implementing rapid changes, and acknowledging COVID as a learning experience. Six themes were evident from the analysis: COVID anxiety and fear, emotional supports and coping mechanisms, person-centric changes, COVID as a ‘forcing function’ for change, a collective way of working and looking back and thinking ahead. Conclusions While most rapid changes during COVID-19 did not represent a systematic and explicit QI application, QI principles were evident throughout the stories and actions taken, including making small changes, testing changes, learning, reflecting as a team, and improving. Many staff members were able to retrospectively identify the relevance of QI principles. COVID-19 eliminated some traditional barriers to change leading to efficient solutions, thus highlighting a need to sustain these positive changes into routine practice to develop an adaptive healthcare system receptive to QI.

Existence of solutions for the semilinear abstract Cauchy problem of fractional order

In this paper we establish the existence of solutions for the nonlinear abstract Cauchy problem of order α ∈ (1, 2), where the fractional derivative is considered in the sense of Caputo. The autonomous and nonautonomous cases are studied. We assume the existence of an α-resolvent family for the homogeneous linear problem. By using this α-resolvent family and appropriate conditions on the forcing function, we study the existence of classical solutions of the nonhomogeneus semilinear problem. The non-autonomous problem is discussed as a perturbation of the autonomous case. We establish a variation of the constants formula for the nonautonomous and nonhomogeneous equation.

Structured input–output analysis of transitional wall-bounded flows

Input–output analysis of transitional channel flows has proven to be a valuable analytical tool for identifying important flow structures and energetic motions. The traditional approach abstracts the nonlinear terms as forcing that is unstructured, in the sense that this forcing is not directly tied to the underlying nonlinearity in the dynamics. This paper instead employs a structured-singular-value-based approach that preserves certain input–output properties of the nonlinear forcing function in an effort to recover the larger range of key flow features identified through nonlinear analysis, experiments and direct numerical simulation (DNS) of transitional channel flows. Application of this method to transitional plane Couette and plane Poiseuille flows leads to not only the identification of the streamwise coherent structures predicted through traditional input–output approaches, but also the characterization of the oblique flow structures as those requiring the least energy to induce transition, in agreement with DNS studies, and nonlinear optimal perturbation analysis. The proposed approach also captures the recently observed oblique turbulent bands that have been linked to transition in experiments and DNS with very large channel size. The ability to identify the larger amplification of the streamwise varying structures predicted from DNS and nonlinear analysis in both flow regimes suggests that the structured approach allows one to maintain the nonlinear effects associated with weakening of the lift-up mechanism, which is known to dominate the linear operator. Capturing this key nonlinear effect enables the prediction of a wider range of known transitional flow structures within the analytical input–output modelling paradigm.

Simulations of nonlinear parabolic PDEs with forcing function without linearization

This paper aims at producing numerical solutions of nonlinear parabolic PDEs with forcing term without any linearization. Since the linearization of nonlinear term leads to lose real features, without doing linearization, this paper focuses on capturing natural behaviour of the mechanism. Therefore we concentrate on analysis of the physical processes without losing their properties. To carry out this study, a backward differentiation formula in time and a spline method in space have been combined in leading to the discretized equation. This method leads to a very reliable alternative in solving the problem by conserving the physical properties of the nature. The efficiency of the present method are proved theoretically and illustrated by various numerical tests.

Computing Radiated Sound Power using Quadratic Power Transfer Vector (QPTV)

Pressure Acoustic Transfer Functions or Vectors (PATVs) relate the surface velocity of a structure to the sound pressure level at a field point in the surrounding fluid. These functions depend only on the structure geometry, properties of the fluid medium (sound speed and characteristic density), the excitation frequency and the location of the field point, but are independent of the surface velocity values themselves. Once the pressure acoustic transfer function is computed between a structure and a specified field point, we can compute pressure at this point for any boundary velocity distribution by simply multiplying the forcing function (surface velocity) with the acoustic transfer function. These PATVs are usually computed by application of the Reciprocity Principle, and their computation is well understood. In this work, we present a novel way to compute the Velocity Acoustic Transfer Vector (VATV) which is a relation between the surface velocity of the structure and fluid particle velocity at a field point. To our knowledge, the computation of the VATV is completely new and has not been published in earlier works. By combining the PATVs and VATVs at a number of field points surrounding the structure, we obtain the Quadratic Power Transfer Vector (QPTV) that allows us to compute the sound power radiated by a structure for ANY surface velocity distribution. This allows rapid computation of the sound power for an arbitrary surface velocity distributions and is useful in designing quiet structures by minimizing the sound power radiated.

Estimating the forcing function in a mechanical system by an inverse calibration method

This article proposes and demonstrates a calibration-based integral formulation for resolving the forcing function in a mass–spring–damper system, given either displacement or acceleration data. The proposed method is novel in the context of vibrations, being thoroughly studied in the field of heat transfer. The approach can be expanded and generalized further to multi-variable systems associated with machine parts, vehicle suspensions, translational and rotational systems, gear systems, etc. when mathematically described by a system of constant property, linear, time-invariant ordinary differential equations. The analytic approach and subsequent numerical reconstruction of the forcing function is based on resolving a parameter-free inverse formulation for the equation(s) of motion. The calibration approach is formulated in the frequency domain and takes advantage of several observations produced by the dimensionality reduction leading to an algebratized system involving an input–output relationship and a transfer function possessing all the system parameters. The transfer function is eliminated in lieu of experimental data, from a calibration effort, thus leading to a reduction of systematic errors. These parameter-free, reduced systematic error aspects are the distinct and novel advantages of the proposed method. A first-kind Volterra integral equation is formed containing only the unknown forcing function and experimental data. As with all ill-posed problems, regularization must be introduced for system stabilization. A future-time technique is instituted for forming a family of predictions based on the chosen regularization parameter. The optimal regularization parameter is estimated using a combination of phase–plane analysis and cross-correlation principles. Finally, a numerical simulation is performed verifying the proposed approach.

Piezo-based flexural vibration suppression for an annular rotor via rotating-frame H2 control optimization

Elastic vibration can arise in annular and thin-walled rotor structures, impacting on operating performance and the risk of failure. Feedback control to reduce flexural vibration can be realized using lightweight actuators and sensors embedded in the rotor structure. To design optimal controllers, rotating-frame models of both the structural dynamics and sources of excitation are required. This paper describes a solution to this problem for the case of an annular rotor equipped with piezo patch actuators and sensors. To account for space-fixed external excitation sources, a forcing function is considered involving specified spatial and frequency domain distributions. A model-based [Formula: see text] synthesis is used to compute optimal control solutions. These are tested experimentally on a thin-walled cylindrical steel rotor for cases with narrowband and broadband excitation sources, applied from the fixed frame. The results show that frequency-splitting within the rotating-frame dynamics plays a key role in predicting and controlling resonance. The effectiveness of the optimal control methodology in reducing circumferential vibration of the annular rotor is also confirmed.