scholarly journals Optimal Transient Growth in an Incompressible Flow past a Backward-Slanted Step

Fluids ◽  
2019 ◽  
Vol 4 (1) ◽  
pp. 33 ◽  
Author(s):  
Marco Martins Afonso ◽  
Philippe Meliga ◽  
Eric Serre
Keyword(s):  
Optimal Control ◽  
Incompressible Flow ◽  
Variational Formulation ◽  
Aerodynamic Drag ◽  
Turbulent Wake ◽  
Transient Growth ◽  
External Forcing ◽  
Adjoint Methods ◽  
Recirculation Bubble ◽  
Maximal Gain

With the aim of providing a first step in the quest for a reduction of the aerodynamic drag on the rear-end of a car, we study the phenomena of separation and reattachment of an incompressible flow by focusing on a specific aerodynamic geometry, namely a backward-slanted step at 25 ∘ of inclination. The ensuing recirculation bubble provides the basis for an analytical and numerical investigation of streamwise-streak generation, lift-up effect, and turbulent-wake and Kelvin–Helmholtz instabilities. A linear stability analysis is performed, and an optimal control problem with a steady volumic forcing is tackled by means of a variational formulation, adjoint methods, penalization schemes, and an orthogonalization algorithm. Dealing with the transient growth of spanwise-periodic perturbations, and inspired by the need of physically-realizable disturbances, we finally provide a procedure attaining a kinetic-energy maximal gain on the order of 10 6 , with respect to the power introduced by the external forcing.

scholarly journals Experiments on transient growth of turbulent spots

2017 ◽  
Vol 829 ◽  
Author(s):  
L. Klotz ◽  
J. E. Wesfreid
Keyword(s):  
Experimental Investigation ◽  
Reynolds Number ◽  
Theoretical Analysis ◽  
Poiseuille Flow ◽  
High Amplitude ◽  
Transient Growth ◽  
External Forcing ◽  
Turbulent Spots ◽  
Maximal Gain ◽  
Theoretical Results

We present detailed experiments on transient growth of turbulent spots induced by external forcing in plane Couette–Poiseuille flow, which are studied in the framework of linear transient growth. The experimental investigation is supplemented with full theoretical analysis. We compare quantitatively the experimental and theoretical results, including maximal gain and the time at which it occurs. We also present the limits of validity for the application of the linear theory at high amplitude perturbation and Reynolds number, showing experiments with self-sustained states.

Extra Drag Force on a Circular Cylinder Due to the Presence of Solid Particles in Subsonic Compressible Flow

1991 ◽  
Author(s):  
Stanley B. Mellsen
Keyword(s):  
Compressible Flow ◽  
Incompressible Flow ◽  
Aerodynamic Drag ◽  
Collection Efficiency ◽  
Reynolds Numbers ◽  
Solid Particles ◽  
Circular Cylinders ◽  
Critical Mach Number ◽  
Wide Range ◽  
Inertia Parameters

Abstract The effect of particles, such as dust in air on aerodynamic drag of circular cylinders was calculated for compressible flow at critical Mach number and for incompressible flow. The effect of compressibility was found negligible for particles larger than about 10 μm, for which the air can be considered a continuum. Drag coefficient and collection efficiency are provided for a wide range of inertia parameters and Reynolds numbers for both compressible and incompressible flow.

Optimal control of strongly driven quantum systems: Fully variational formulation and nonlinear eigenfields

1995 ◽  
Vol 52 (2) ◽  
pp. R891-R894 ◽  
Author(s):  
K. G. Kim ◽  
M. D. Girardeau
Keyword(s):  
Optimal Control ◽  
Variational Formulation ◽  
Quantum Systems

Aerodynamic Drag on Vehicles in Tunnels

1969 ◽  
Vol 91 (4) ◽  
pp. 694-706 ◽  
Author(s):  
S. William Gouse ◽  
B. S. Noyes ◽  
J. K. Nwude ◽  
M. C. Swarden
Keyword(s):  
Laminar Flow ◽  
Drag Coefficient ◽  
Surface Area ◽  
Incompressible Flow ◽  
High Speed ◽  
Aerodynamic Drag ◽  
Diameter Ratio ◽  
Infinite Body ◽  
Tunnel Wall ◽  
Wetted Surface Area

The purpose of this study was to investigate the aerodynamic drag on vehicles moving in guideways of varying degrees of enclosure. The reason for this study was that several potential high speed ground transport system concepts involve high speed motion of vehicles in enclosed guideways for significant portions of their travel time. Analytical and experimental investigations have been carried out. The analytical studies developed the solution for the aerodynamic drag on a vehicle in an enclosed guideway in laminar flow. The analysis is based on an analogy between the governing equations for the unsteady flow resulting when an infinite body is started impulsively from rest and the steady flow that results from steady motion of a semi-infinite body. The results of this analysis for laminar flow provided a base from which to begin in turbulent flow and were used to justify the basing of a drag coefficient on the wetted surface area of a vehicle rather than the frontal area of a vehicle. Preliminary experiments were executed using spheres as vehicle models. Final experimental studies were carried out using cylindrical models in circular tunnels of various lengths and various degrees of wall porosity. A drop testing apparatus was employed and results were obtained for Reynolds number of the order of 5 · 105. Results to date indicate that for vehicle length-diameter ratios of the order of 15 and above, with tunnel to vehicle diameter ratios of 1.5 and greater, a drag coefficient based on the wetted surface area of the vehicle is independent of the vehicle length-diameter ratio for incompressible flow. Results also indicate that, for incompressible flow, employing a tunnel model with a closed end simulates a tunnel length-diameter ratio of infinity. Tunnel wall porosity, assuming relatively unobstructed motion of fluid outside the porous wall, has a marked effect on decreasing the aerodynamic drag on vehicles moving in enclosed guideways and that for the range of variables investigated (clearance ratio as low as 1.4) tunnel wall porosity of 20 per cent is adequate for all the significant drag reduction that is possible. Qualitative predictions of loss coefficient analytical modeling and literature on transonic flow wind tunnel testing with porous walls are in agreement with the data presented.

Experimental sensitivity analysis of the global properties of a two-dimensional turbulent wake

2012 ◽  
Vol 693 ◽  
pp. 115-149 ◽  
Author(s):  
Vladimir Parezanović ◽  
Olivier Cadot
Keyword(s):  
Turbulent Wake ◽  
Base Pressure ◽  
Recirculation Region ◽  
Two Dimensional ◽  
Reynolds Stresses ◽  
Recirculation Bubble ◽  
Global Properties ◽  
Bubble Length ◽  
The Impact ◽  
Control Cylinder

AbstractThe sensitivity of the global properties of a two-dimensional turbulent wake produced by the separated flow of a ‘D’-shaped cylinder at $\mathit{Re}= 13\hspace{0.167em} 000$ is investigated experimentally using a small circular control cylinder as a local disturbance. The height of the main cylinder is $D= 25~\mathrm{mm} $ and control cylinders are of diameters $d= 0. 04D$ and $d= 0. 12D$, the former being smaller than the shear layer thickness detaching from the main cylinder, while the latter is larger. In both cases, the control cylinder is able to modify the global frequency, base pressure and spanwise velocity correlation. The results are presented as sensitivity maps. Reynolds stresses spatial structure and the recirculation bubble length are examined in detail when the control cylinder is displaced vertically across the wake at a fixed downstream location. It is found that the increase of the recirculation bubble length is accompanied by a damping of Reynolds stresses with a downstream shift of their spatial structures together with the base pressure increase. The global frequency can be either decreased or increased independently of the bubble length modification. The sensitivity of these global properties is interpreted on the basis of the ability of the control cylinder to change the size of the formation region of the Kármán vortex street by interacting with the primary detached shear layers. The corresponding physical mechanisms are discussed. The impact of a two-dimensional control cylinder on the three-dimensional properties of the wake is examined through spanwise correlation. This is found to be improved whenever the control cylinder is placed inside the recirculation region of the main cylinder wake.

scholarly journals Erratum: Optimal control of strongly driven quantum systems: Fully variational formulation and nonlinear eigenfields

1996 ◽  
Vol 53 (1) ◽  
pp. 630-630
Author(s):  
K. G. Kim ◽  
M. D. Girardeau
Keyword(s):  
Optimal Control ◽  
Variational Formulation ◽  
Quantum Systems

scholarly journals Optimal Control and Necessary Optimality Conditions for Nonlinear and Perturbed Dynamic Problems

2018 ◽  
Vol 10 (6) ◽  
pp. 63
Author(s):  
Gossan D. Pascal Gershom ◽  
Bailly Balè ◽  
Yoro Gozo
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Variational Formulation ◽  
Necessary Conditions ◽  
Three Dimensional ◽  
Necessary Optimality Conditions ◽  
Cancer Cell Proliferation ◽  
Dynamic Problems ◽  
First Order ◽  
Tumor Growth Model

The main goal of this paper is to establish the first order necessary optimality conditions for a tumor growth model that evolves due to cancer cell proliferation. The phenomenon is modeled by a system of three-dimensional partial differential equations. We prove the existence and uniqueness of optimal control and necessary conditions of optimality are established by using the variational formulation.

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