On hydraulic control in a stratified fluid

1992 ◽  
Vol 237 ◽  
pp. 605-626 ◽  
Author(s):  
Peter D. Killworth
Keyword(s):  
Froude Number ◽  
Wave Speed ◽  
Stratified Fluid ◽  
Hydraulic Control ◽  
Vertical Coordinate ◽  
Isopycnal Surface ◽  
Suitable Definition ◽  
Definition Of ◽  
Weak Shocks ◽  
Bidirectional Flow

The conditions for hydraulic control to occur in a continuously stratified fluid are discussed, using density as a vertical coordinate in place of height. A suitable definition of Froude number, which varies with depth, is given. Three conditions for control emerge. One is that the flow be everywhere well-behaved; another is that control occurs when the local long-wave speed vanishes. These are shown to be equivalent. The location of the control is determined indirectly by the Froude number, which occurs as the coefficient in an ordinary differential equation; the Froude number must be somewhere less than a critical value for control to occur. The third condition requires the coalescence of two different solutions for the same boundary conditions at the point of control. It is shown that this requirement is non-trivial: examples given include a simple control by topography, a virtual control, and a control by a constriction. A direct connection with layered theory is produced. Brief discussions of bidirectional flow (where the isopycnal surface of zero velocity must be flat) and weak shocks are given.

An LQ Approach to Active Control of Vibrations in Helicopters

1996 ◽  
Vol 118 (3) ◽  
pp. 482-488 ◽  
Author(s):  
Sergio Bittanti ◽  
Fabrizio Lorito ◽  
Silvia Strada
Keyword(s):  
Optimal Control ◽  
Active Control ◽  
Linear Quadratic ◽  
Control Effort ◽  
Vibration Effect ◽  
Suitable Definition ◽  
Lq Optimal Control ◽  
The One ◽  
Definition Of ◽  
And Control

In this paper, Linear Quadratic (LQ) optimal control concepts are applied for the active control of vibrations in helicopters. The study is based on an identified dynamic model of the rotor. The vibration effect is captured by suitably augmenting the state vector of the rotor model. Then, Kalman filtering concepts can be used to obtain a real-time estimate of the vibration, which is then fed back to form a suitable compensation signal. This design rationale is derived here starting from a rigorous problem position in an optimal control context. Among other things, this calls for a suitable definition of the performance index, of nonstandard type. The application of these ideas to a test helicopter, by means of computer simulations, shows good performances both in terms of disturbance rejection effectiveness and control effort limitation. The performance of the obtained controller is compared with the one achievable by the so called Higher Harmonic Control (HHC) approach, well known within the helicopter community.

scholarly journals Gravity currents and internal waves in a stratified fluid

2008 ◽  
Vol 616 ◽  
pp. 327-356 ◽  
Author(s):  
BRIAN L. WHITE ◽  
KARL R. HELFRICH
Keyword(s):  
Internal Waves ◽  
Wave Speed ◽  
Numerical Solutions ◽  
Gravity Current ◽  
Gravity Currents ◽  
Stratified Fluid ◽  
Front Speed ◽  
Long Wave ◽  
Conjugate State ◽  
Energy Conserving

A steady theory is presented for gravity currents propagating with constant speed into a stratified fluid with a general density profile. Solution curves for front speed versus height have an energy-conserving upper bound (the conjugate state) and a lower bound marked by the onset of upstream influence. The conjugate state is the largest-amplitude nonlinear internal wave supported by the ambient stratification, and in the limit of weak stratification approaches Benjamin's energy-conserving gravity current solution. When the front speed becomes critical with respect to linear long waves generated above the current, steady solutions cannot be calculated, implying upstream influence. For non-uniform stratification, the critical long-wave speed exceeds the ambient long-wave speed, and the critical-Froude-number condition appropriate for uniform stratification must be generalized. The theoretical results demonstrate a clear connection between internal waves and gravity currents. The steady theory is also compared with non-hydrostatic numerical solutions of the full lock release initial-value problem. Some solutions resemble classic gravity currents with no upstream disturbance, but others show long internal waves propagating ahead of the gravity current. Wave generation generally occurs when the stratification and current speed are such that the steady gravity current theory fails. Thus the steady theory is consistent with the occurrence of either wave-generating or steady gravity solutions to the dam-break problem. When the available potential energy of the dam is large enough, the numerical simulations approach the energy-conserving conjugate state. Existing laboratory experiments for intrusions and gravity currents produced by full-depth lock exchange flows over a range of stratification profiles show excellent agreement with the conjugate state solutions.

scholarly journals Modern vision for critical flow in an egg-shaped section

2021 ◽  
Author(s):  
Hachemi Rachedi Lamia ◽  
Lakehal Moussa ◽  
Achour Bachir
Keyword(s):  
Froude Number ◽  
Critical Regime ◽  
Critical Flow ◽  
New Approach ◽  
Smooth Channel ◽  
Critical Flow Regime ◽  
Modern Vision ◽  
The One ◽  
Definition Of ◽  
Steep Slopes

Abstract The critical regime plays a primordial role in the study of gradually varying flows by classifying flow regimes and slopes. Through this work, a new approach is proposed to analyze critical flow regime in an egg-shaped channel. Based on both the definition of Froude number and Achour and Bedjaoui general discharge relationship, a relation between critical and normal depths is derived and then graphically represented for the particular case of a smooth channel characterized by a generating diameter equal to one meter. The results show the influence of the slope on the frequency of occurrence of the critical regime. At the same time and independently of the flow rate, a very advantageous approach for the calculation of the Froude number has been proposed. The study shows that there are six zones to differentiate the various flow states, namely: on the one hand for steep slopes two subcritical zones interspersed by a supercritical zone and on the other hand for mild slopes a zone corresponding to uniform flow, an area where the flow is probably gradually varied and finally an area where the flow is abruptly varied. Based on the specific energy equation, a validation process concluded that the proposed relationships were reliable.

scholarly journals On the Inversion of the Gauss Transformation

1957 ◽  
Vol 9 ◽  
pp. 459-464 ◽  
Author(s):  
P. G. Rooney
Keyword(s):  
Differential Operator ◽  
Recent Work ◽  
Suitable Definition ◽  
Inversion Theory ◽  
The Subject ◽  
Definition Of ◽  
Image Position ◽  
Gauss Transformation ◽  
Operational Methods

The inversion theory of the Gauss transformation has been the subject of recent work by several authors. If the transformation is defined by1.1,then operational methods indicate that,under a suitable definition of the differential operator.

scholarly journals One Dimensional Shock Refraction at a Plasma-cold Gas Interface

1973 ◽  
Vol 28 (10) ◽  
pp. 1668-1675
Author(s):  
J. Gerofi ◽  
H. K. Messerle
Keyword(s):  
Plasma Temperature ◽  
Region Of Interest ◽  
Initial Pressure ◽  
Step Function ◽  
Initial Plasma ◽  
Function Discontinuity ◽  
Definition Of ◽  
Shock Refraction ◽  
Weak Shocks ◽  
Cold Gas

Refraction and reflection of a shockwave at a plasma/cold gas interface has been studied using an R.F. preheated section in an electrothermal shock tube. The gas used in the experiment was Argon at initial pressures from 10 to 30 Torr, with initial temperature of 9000 K.A detailed numerical analysis of the refraction event has been undertaken using a method that does not require definition of an effective γ. Methods that do use such a γ are not accurate, except for very weak shocks. Because of short ionization times it has been possible to assume equilibrium behind the various shock waves. Calculations suggest that in the region of interest, reflected and refracted shock velocities depend primarily on initial shock velocity, slightly on initial plasma temperature and very weakly on initial pressure. The analysis covers initial temperatures of 6000 to 12 000 K and initial pressures of 10 to 50 Torr.Calculations and experimental results are presented. These show that a step function discontinuity is a good approximation to the nature of the plasma cold gas interface in this situation.

Functional Modeling: A Key Point in CAD Systems

2013 ◽  
Author(s):  
Francesco Ferrise ◽  
Monica Bordegoni ◽  
Umberto Cugini
Keyword(s):  
Open Source ◽  
Computer Aided Design ◽  
Design Method ◽  
Methodological Approach ◽  
Product Lifecycle Management ◽  
Product Development Process ◽  
Hydraulic Control ◽  
Functional Modeling ◽  
Cad Tools ◽  
Definition Of

For more than 40 years the development of Computer Aided Design (CAD) tools has been focused on the description of the geometry of products. More recently, CAD tools have evolved in tools to support the Product Lifecycle Management (PLM), which are more oriented to support the management aspects of the product development process than the design process itself. Recently, it has been introduced a new design method that adopts a top-down approach, which starts from the definition of a Functional MockUp (FMU) allowing to simulate the overall behavior and the use of the concept level before the detailed design. This method is closer to the typical logical sequence of design, where the designer has at first an overall view of a system and of its sub-components, and then he takes care of the details. This method is supported by commercial tools, as the LMS-Amesim suite, or by open-source software tools based on the Modelica language. This is an open-source language allowing designers to integrate and describe at functional level several aspects of a system, including mechanical, electrical, thermal, hydraulic, control and others allowing to simulate all together. The paper analyses this methodological approach and presents some applications where some systems are designed using a functional modeling approach.

The Algebra of Dimension-Linking Operators

1965 ◽  
Vol 8 (2) ◽  
pp. 203-222 ◽  
Author(s):  
R. H. Bruck
Keyword(s):  
Group Theory ◽  
Special Reference ◽  
Mathematical Society ◽  
Summer Institute ◽  
Burnside Problem ◽  
The Third ◽  
Australian Mathematical Society ◽  
Suitable Definition ◽  
Definition Of ◽  
Restricted Burnside Problem

In the course of preparing a book on group theory [1] with special reference to the Restricted Burnside Problem and allied problems I stumbled upon the concept of a dimension-linking operator. Later, when I lectured to the Third Summer Institute of the Australian Mathematical Society [2], G. E. Wall raised the question whether the dimension-linking operators could be made into a ring by introduction of a suitable definition of multiplication. The answer was easily found to be affirmative; the result wasthat the theory of dimen sion-linking operators became exceedingly simple.

scholarly journals On Near-Rings of Quotients

1979 ◽  
Vol 22 (2) ◽  
pp. 77-86 ◽  
Author(s):  
A. Oswald
Keyword(s):  
Finite Rank ◽  
Minimum Condition ◽  
Suitable Definition ◽  
Definition Of ◽  
Rings Of Quotients

In (2), Holcombe investigated near-rings of zero-preserving mappings of a group Γ which commute with the elements of a semigroup S of endomorphisms of Γ and examined the question: under what conditions do near-rings of this type have near-rings of right quotients which are 2-primitive with minimum condition on right ideals? In the first part of this paper (§2) we investigate further properties of near-rings of this type. The second part of the paper (§3) deals with those near-rings which have semisimple near-rings of right quotients. Our results here are analogous to those of Goldie (1); in particular, with a suitable definition of finite rank we prove that a near-ring which has a semisimple near-ring of right quotients has finite rank

Inferring earth structure from combined measurements of rotational and translational ground motions

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCD41-WCD47 ◽  
Author(s):  
Moritz Bernauer ◽  
Andreas Fichtner ◽  
Heiner Igel
Keyword(s):  
Seismic Tomography ◽  
Wave Speed ◽  
Ground Motions ◽  
Regional Scale ◽  
S Wave ◽  
Tomographic Images ◽  
Teleseismic Tomography ◽  
Local Structures ◽  
Novel Variant ◽  
Definition Of

We introduce a novel variant of seismic tomography that is based on colocated measurements of rotational and translational ground motions. Our aim is to assess whether rotations may be incorporated successfully into seismic inverse problems to produce better resolved and more realistic tomographic images. Our methodology is based on the definition of apparent S-wave speed as the ratio of rms velocity and rotation amplitudes. The principal advantages of this definition are that (1) no traveltimes measurements are needed and (2) the apparent S-wave speed is independent of source magnitude and source timing. We derive finite-frequency kernels for apparent S-wave speed by using a combination of the adjoint method and ray approximation. The properties of these kernels as a function of frequency bandwidth can be illustrated along with their usefulness for seismic tomography. In multifrequency synthetic inversions, we consider local crosshole tomography and regional-scale earthquake tomography. Our results indicate that S-wave speed variations can be retrieved accurately from colocated rotation and translation measurements, suggesting that our methodology is a promising extension of conventional seismic tomography. Further, apparent S-wave speed can be used to increase vertical resolution in teleseismic tomography for local structures.

Sign in / Sign up

Export Citation Format

Share Document