A significant mathematical error is identified and corrected in a recent highly-cited paper on oscillatory flows of second-grade fluids [Fetecau & Fetecau (2005). Int. J. Eng. Sci., 43, 781--789]. The corrected solutions are shown to agree identically with numerical ones generated by a finite-difference scheme, while the original ones of Fetecau & Fetecau do not. A list of other recent papers in the literature that commit the error corrected in this Comment is compiled. Finally, a summary of related erroneous papers in this journal is presented as an Appendix.
The so-called 'direct' approach to separation of variables in linear PDEs is applied to the hydrodynamic stability problem. Calculations are made for the complete linear stability equations in cylindrical coordinates. Several classes of the exact solutions of the Navier-Stokes equations describing spatially developing and unsteady flows, for which the linear stability problems can be rigorously reduced to eigenvalue problems of ordinary differential equations, are defined. Those exactly solvable nonparallel and unsteady flow stability problems can be used for testing approximate approaches and…
The cavitation behaviour of a four-blade rocket engine turbopump inducer is simulated. A 2D numerical model of unsteady cavitation was applied to a blade cascade drawn fromthe inducer geometry. The physical model is based on a homogeneous approach of cavitation, coupled with a barotropic state law for the liquid/vapour mixture. The numericalresolution uses a pressure-correction method derived from the SIMPLE algorithm and a finite volume discretization. Unsteadybehaviour of sheet cavities attached to the blade suction side depends on the flow rate and cavitation number. Two differentunstable c…
Reduced-order modelling of parametrized unsteady Navier-Stokes equations and application to flow around cylinders with periodic changing boundary conditions
The COVID-19 pandemic illuminated the critical need for flexible mechanical engineering laboratories simultaneously deployable in multiple modalities: face-to-face, hybrid, and remote. A key element in the lesson portfolio of a forward-looking engineering instructor is economical, hands-on, accessible, 'turn-key' lab activities; kits that can be deployed both in brick-and-mortar teaching labs and mailed home to remote learners. The Energy Engineering Laboratory Module pedagogy, described elsewhere, provides an underpinning theoretical framework and examples to achieve these features. In additi…
In this paper, neural network (NN)-based models are generated to replace flamelet tables for sub-grid modeling in large-eddy simulations of a single-injector liquid-propellant rocket engine. In the most accurate case, separate NNs for each of the flame variables are designed and tested by comparing the NN output values with the corresponding values in the table. The gas constant, internal flame energy, and flame heat capacity ratio are estimated with 0.0506%, 0.0852%, and 0.0778% error, respectively. Flame temperature, thermal conductivity, and the coefficient of heat capacity ratio are estima…
In many engineering systems operating with a working fluid, the best efficiency is reached close to a condition of flow separation, which makes its prediction very crucial in industry. Providing that wall-based quantities can be measured, we know today how to obtain good predictions for two and three-dimensional steady and periodic flows. In these flows, the separation is defined on a fixed line attached to a material surface. The last case to elucidate is the one where this line is no longer attached to the wall but on the contrary is contained within the flow. This moving separation is proba…
Deep reinforcement learning (DRL) algorithms are rapidly making inroads into fluid mechanics, following the remarkable achievements of these techniques in a wide range of science and engineering applications. In this paper, a deep reinforcement learning (DRL) agent has been employed to train an artificial neural network (ANN) using computational fluid dynamics (CFD) data to perform active flow control (AFC) around a 2-D circular cylinder. Flow control strategies are investigated at a diameter-based Reynolds number Re_D = 100 using advantage actor-critic (A2C) algorithm by means of two symmetri…
Efficient modeling of rarefied flow has drawn widespread interest for practical engineering applications. In the present work, we proposed the Grad's distribution function for 13 moments-based moment gas kinetic solver (G13-MGKS) and the macroscopic governing equations are derived based on the moment integral of discrete Boltzmann equation in the finite volume framework. Numerical fluxes at the cell interface related to the macroscopic variables, stress and heat flux can be reconstructed from the Boltzmann integration equation at surrounding points of the cell interface directly, so the compli…
Fluid transport networks are important in many natural settings and engineering applications, from animal cardiovascular and respiratory systems to plant vasculature to plumbing networks and chemical plants. Understanding how network topology, connectivity, internal boundaries and other geometrical aspects affect the global flow state is a challenging problem that depends on complex fluid properties characterized by different length and time scales. The study of flow in micro-scale networks focuses on low Reynolds numbers where small volumes of fluids move at slow speeds. The flow physics at t…
OGF: An Online Gradient Flow Method for Optimizing the Statistical Steady-State Time Averages of Unsteady Turbulent Flows
Mathematical Institute, University of Oxford, UK.（牛津大学数学研究所）；Department of Aerospace and Mechanical Engineering, University of Notre Dame, USA.（诺丁汉大学航空航天与机械工程系）
Interactions between fluids and elastic solids are ubiquitous in application ranging from aeronautical and civil engineering to physiological flows. Here we study the pulsatile flow through a two-dimensional Starling resistor as a simple model for unsteady flow in elastic vessels. We numerically solve the equations governing the flow and the large-displacement elasticity and show that the system responds as a forced harmonic oscillator with non-conventional damping. We derive an analytical prediction for the amplitude of the oscillatory wall deformation, and thus the conditions under which res…
