Abstract. In the presence of viscosity the hydraulic jump in one dimension is seen to be a first-order transition. A scaling relation for the position of the jump has been determined by applying an averaging technique on the stationary hydrodynamic equations. This gives a linear height profile before the jump, as well as a clear dependence of the magnitude of the jump on the outer boundary condition. The importance of viscosity in the jump formation has been convincingly established, and its physical basis has been understood by a time-dependent analysis of the flow equations. In doing so, a very close correspondence has been revealed between a perturbation equation for the flow rate and the metric of an acoustic white hole. We finally provide experimental support for our heuristically developed theory.
Low Reynolds number steady and unsteady incompressible flows over two circular cylinders in tandem are numerically simulated for a range of Reynolds numbers with varying gap size. The governing equations are solved on an unstructured collocated mesh using a second-order implicit finite volume method. The effects of the gap and Reynolds number on the vortex structure of the wake and on the fluid dynamic forces acting on the cylinders are reported and discussed. Both the parameters have significant influence on the flow field. An attempt is made to unify their influence on some global parameters.
The two-dimensional incompressible laminar viscous flow of a conducting fluid past a square cylinder placed centrally in a channel subjected to an imposed transverse magnetic field has been simulated to study the effect of a magnetic field on vortex shedding from a bluff body at different Reynolds numbers varying from 50 to 250. The present staggered grid finite difference simulation shows that for a steady flow the separated zone behind the cylinder is reduced as the magnetic field strength is increased. For flows in the periodic vortex shedding and unsteady wake regime an imposed transverse magnetic field is found to have a considerable effect on the flow characteristics with marginal increase in Strouhal number and a marked drop in the unsteady lift amplitude indicating a reduction in the strength of the shed vortices. It has further been observed, that it is possible to completely eliminate the periodic vortex shedding at the higher Reynolds numbers and to establish a steady flow if a sufficiently strong magnetic field is imposed. The necessary strength of the magnetic field, however, depends on the flow Reynolds number and increases with the increase in Reynolds number. This paper describes the algorithm in detail and presents important results that show the effect of the magnetic field on the separated wake and on the periodic vortex shedding process.
a b s t r a c tFlow over open cavities is mainly governed by a feedback mechanism due to the interaction of shear layer instabilities and acoustic forcing propagating upstream in the cavity. This phenomenon is known to lead to resonant tones that can reach 180 dB in the far-field and may cause structural fatigue issues and annoying noise emission. This paper concerns the use of optimal control theory for reducing the noise level emitted by the cavity. Boundary control is introduced at the cavity upstream corner as a normal velocity component. Model-based optimal control of cavity noise involves multiple simulations of the compressible Navier-Stokes equations and its adjoint, which makes it a computationally expensive optimization approach. To reduce the computational costs, we propose to use a reduced-order model (ROM) based on Proper Orthogonal Decomposition (POD) as a surrogate model of the forward simulation. For that, a control input separation method is first used to introduce explicitly the control effect in the model. Then, an accurate and robust POD ROM is derived by using an optimization-based identification procedure and generalized POD modes, respectively. Since the POD modes describe only velocities and speed of sound, we minimize a noise-related cost functional characteristic of the total enthalpy unsteadiness. After optimizing the control function with the reduced-order model, we verify the optimality of the solution using the original, high-fidelity model. A maximum noise reduction of 4.7 dB is reached in the cavity and up to 16 dB at the far-field. .in (K.K. Nagarajan). roof of cars, etc. These flows are largely characterized by the presence of a global instability, that dominates the flow, and belong to the oscillators' category as defined by Huerre and Rossi [21] . Reducing the cavity noise is then of extreme importance for the development of quieter transport means. It is now well-known that the control of instabilities for oscillator flows is feasible with a model-based approach relying on linear control tools [35] . In this paper, the objective is to reduce the level of noise emitted by the cavity with an optimal control approach based on a nonlinear model of the dynamics. High-fidelity numerical simulations, like Direct Numerical Simulation (DNS) of Navier-Stokes equations (NSE), are too expensive for flow control applications. This observation is particularly true when iterative optimization methods are used as in the case of optimal control [19] . It is then necessary to derive surrogate models for reducing the computational costs related to optimal control of high-dimensional nonlinear systems. Starting from an experimental or computational database, the objective is to derive Reduced-Order Models (ROMs) which mine the relevant information content in terms of dynamics.
Purpose -The purpose of this paper is to simulate the flow of a conducting fluid past a circular cylinder placed centrally in a channel subjected to an imposed transverse magnetic field to study the effect of a magnetic field on vortex shedding at different Reynolds numbers varying from 50 to 250. Design/methodology/approach -The two-dimensional incompressible laminar viscous flow equations are solved using a second-order implicit unstructured collocated grid finite volume method. Findings -An imposed transverse magnetic field markedly reduces the unsteady lift amplitude indicating a reduction in the strength of the shed vortices. It is observed that the periodic vortex shedding at the higher Reynolds numbers can be completely suppressed if a sufficiently strong magnetic field is imposed. The required magnetic field strength to suppress shedding increases with Reynolds number. The simulation shows that the separated zone behind the cylinder in a steady flow is reduced as the magnetic field strength is increased. Originality/value -In this paper, due attention is given to resolve and study the unsteady cylinder wake and its interaction with the shear-layer on the channel wall in the presence of a magnetic field. A critical value of the Hartmann number for complete suppression of the shedding at a given Reynolds number is found. IntroductionThe flow over a circular cylindrical body is a common phenomenon in many engineering applications. The flow is essentially unsteady except at very low Reynolds numbers less than about 50. The steady flow at a low Reynolds number is characterized by steady separation and a closed near wake of recirculating flow. At relatively higher Reynolds numbers, the relevant unsteady flows are characterized by the periodic shedding of vortices and unsteady separated vortex wake. The unsteady flow exerts fluctuating forces on the immersed bodies. The fluctuating forces on the bluff body may cause the body to vibrate, which may be severe for a range of natural frequency to the vortex shedding frequency ratio, particularly if the mass ratio and damping are low. The control of such "flow-induced vibration" can be achieved if the vortex shedding and/or the size of the separated zone behind the body are controlled. An imposed transverse magnetic field does the job satisfactorily when the fluid is electrically conducting. The use of magnetic field in the cross-stream direction is a novel method of controlling the separated zone behind the body, which in turn
Incompressible flows at low Reynolds numbers over two identical side-by-side circular cylinders have been investigated numerically using unstructured finite volume method. The gap between the cylinders (g) and Reynolds number (Re) considered in the study lies respectively in the range of 0.2 ≤ g/D ≤ 4.0 (D being the diameter of the cylinder) and 20 ≤ Re ≤ 160. Low Reynolds number steady flows are given considerable importance. Two types of wakes are observed in the steady flow regime; the first type is characterized by attached vortices as in the case of an isolated cylinder and the other type is identified by detached standing vortices in the downstream. Reynolds number at which flow turns unsteady is quantified for each gap width. Five different types of wake patterns are observed in the unsteady flow regime: single bluff body wake, deflected wake, flip-flopping wake, in-phase synchronized, and anti-phase synchronized wakes. Present simulations of the evolution of single bluff-body wake demonstrate presence of vortices in the gap side too. The very long time simulations show that below a limiting Re depending on the gap, there is a transition of fully developed initial anti-phase flow to the in-phase flow at a later time. The limiting Reynolds number for this phase bifurcation phenomenon is evaluated in the (Re, g/D) space. A properly calibrated reduced order model based stability analysis is carried out to investigate the phase transition.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.