Downloads & Free Reading Options - Results

Several hull designs are studied with parametric based volume and area estimates to obtain preliminary hull forms. The volume and area study includes the effects of technologies which manifest themselves in the parametric study through stack length requirements. Subsequently, the hull forms are studied using a Reynolds Averaged Navier Stokes analysis coupled with a vortex lattice propeller design code. Optimization is done through boundary layer control analysis and through studies on the effect of blade loading magnitudes and profiles. Several hull form afterbody shapes are studied to improve the powering characteristics of a full stern submarine. The hydrodynamic analysis includes the total contribution of the rotor, stator, duct, the body hull form and appendages on the submarine drag. Corrections are developed and applied to extrapolate the model scale hydrodynamic results to a full scale submarine. The end result gives a speed of the hull form which is used to optimize the overall submarine. The basic measure of the overall effect of stern taper is the maximum speed of the submarine while keeping the same shaft horse power propulsion plant, the same volume and the same area requirements. The hydrodynamic powering efficiency is discussed and evaluated using a power coefficient. The resulting designs have marked differences in length but similar displacements and similar maximum speeds. The results promise great potential for the full stern submarine

Linear optimal gains are computed for the subcritical two-dimensional separated boundary-layer flow past a bump. Very large optimal gain values are found, making it possible for small-amplitude noise to be strongly amplified and to destabilize the flow. The optimal forcing is located close to the summit of the bump, while the optimal response is the largest in the shear layer. The largest amplification occurs at frequencies corresponding to eigenvalues which first become unstable at higher Reynolds number. Nonlinear direct numerical simulations show that a low level of noise is indeed sufficient to trigger random flow unsteadiness, characterized here by large-scale vortex shedding. Next, a variational technique is used to compute efficiently the sensitivity of optimal gains to steady control (through source of momentum in the flow, or blowing/suction at the wall). A systematic analysis at several frequencies identifies the bump summit as the most sensitive region for control with wall actuation. Based on these results, a simple open-loop control strategy is designed, with steady wall suction at the bump summit. Linear calculations on controlled base flows confirm that optimal gains can be drastically reduced at all frequencies. Nonlinear direct numerical simulations also show that this control allows the flow to withstand a higher level of stochastic noise without becoming nonlinearly unstable, thereby postponing bypass transition. In the supercritical regime, sensitivity analysis of eigenvalues supports the choice of this control design. Full restabilization of the flow is obtained, as evidenced by direct numerical simulations and linear stability analysis.

Stability experiments are conducted in the Arizona State University Unsteady Wind Tunnel on a 45 deg. swept airfoil. The pressure gradient is designed to provide purely crossflow-dominated transition; that is, the boundary layer is subcritical to Tollmien- Schlichting (T-S) disturbances. The airfoil surface is hand polished to a 0.25 micron rms finish. Under these conditions, stationary crossflow disturbances grow to nonuniform amplitude due to submicron surface irregularities near the leading edge. Spectral de-compositions isolate single-mode growth rates for the fundamental and harmonic disturbances. The measurements show early nonlinear growth causing amplitude saturation well before transition. Comparisons with nonlinear PSE calculations show excellent agreement in both the amplitude saturation and the disturbance mode shape.

A wind tunnel investigation of a leading edge boundary layer control system was conducted on a High Speed Civil Transport (HSCT) configuration in the Langley 14- by 22-Foot Subsonic Tunnel. Data were obtained over a Mach number range of 0.08 to 0.27, with corresponding chord Reynolds numbers of 1.79 x 10(exp 6) to 5.76 x 10(exp 6). Variations in the amount of suction, as well as the size and location of the suction area, were tested with outboard leading edge flaps deflected 0 and 30 deg and trailing-edge flaps deflected 0 and 20 deg. The longitudinal and lateral aerodynamic data are presented without analysis. A complete tabulated data listing is also presented herein.

A variable-porosity suction glove has been flown on the F-16XL-2 aircraft to demonstrate the feasibility of this technology for the proposed High-Speed Civil Transport (HSCT). Boundary-layer transition data have been obtained on the titanium glove primarily at Mach 2.0 and altitudes of 53,000-55,000 ft. The objectives of this supersonic laminar flow control flight experiment have been to achieve 50- to 60-percent-chord laminar flow on a highly swept wing at supersonic speeds and to provide data to validate codes and suction design. The most successful laminar flow results have not been obtained at the glove design point (Mach 1.9 at an altitude of 50,000 ft). At Mach 2.0 and an altitude of 53,000 ft, which corresponds to a Reynolds number of 22.7 X 10(exp 6), optimum suction levels have allowed long runs of a minimum of 46-percent-chord laminar flow to be achieved. This paper discusses research variables that directly impact the ability to obtain laminar flow and techniques to correct for these variables.

Active and passive methods for tripping hypersonic boundary layers have been examined in NASA Langley Research Center wind tunnels using a Hyper-X model. This investigation assessed several concepts for forcing transition, including passive discrete roughness elements and active mass addition (or blowing), in the 20-Inch Mach 6 Air and the 31-Inch Mach 10 Air Tunnels. Heat transfer distributions obtained via phosphor thermography, shock system details, and surface streamline patterns were measured on a 0.333-scale model of the Hyper-X forebody. The comparisons between the active and passive methods for boundary layer control were conducted at test conditions that nearly match the Hyper-X nominal Mach 7 flight test-point of an angle-of-attack of 2-deg and length Reynolds number of 5.6 million. For passive roughness, the primary parametric variation was a range of trip heights within the calculated boundary layer thickness for several trip concepts. The passive roughness study resulted in a swept ramp configuration, scaled to be roughly 0.6 of the calculated boundary layer thickness, being selected for the Mach 7 flight vehicle. For the active blowing study, the manifold pressure was systematically varied (while monitoring the mass flow) for each configuration to determine the jet penetration height, with schlieren, and transition movement, with the phosphor system, for comparison to the passive results. All the blowing concepts tested, which included various rows of sonic orifices (holes), two- and three-dimensional slots, and random porosity, provided transition onset near the trip location with manifold stagnation pressures on the order of 40 times the model surface static pressure, which is adequate to ensure sonic jets. The present results indicate that the jet penetration height for blowing was roughly half the height required with passive roughness elements for an equivalent amount of transition movement.

We consider a kind of stochastic exit time optimal control problems, in which the cost function is defined through a nonlinear backward stochastic differential equation. We study the regularity of the value function for such a control problem. Then extending Peng's backward semigroup method, we show the dynamic programming principle. Moreover, we prove that the value function is a viscosity solution to the following generalized Hamilton-Jacobi-Bellman equation with Dirichlet boundary: \[ \left\{ \begin{array} [c]{l} \inf\limits_{v\in V}\left\{\mathcal{L}(x,v)u(x)+f(x,u(x),\nabla u(x) \sigma(x,v),v)\right\}=0, \quad x\in D,\medskip\\ u(x)=g(x),\quad x\in \partial D, \end{array} \right. \] where $D$ is a bounded set in $\mathbb{R}^{d}$, $V$ is a compact metric space in $\mathbb{R}^{k}$, and for $u\in C^{2}(D)$ and $(x,v)\in D\times V$, \[\mathcal{L}(x,v)u(x):=\frac{1}{2}\sum_{i,j=1}^{d}(\sigma\sigma^{\ast})_{i,j}(x,v)\frac{\partial^{2}u}{\partial x_{i}\partial x_{j}}(x) +\sum_{i=1}^{d}b_{i}(x,v)\frac{\partial u}{\partial x_{i}}(x). \]

Active and passive methods for control of hypersonic boundary layers have been experimentally examined in NASA Langley Research Center wind tunnels on a Hyper-X model. Several configurations for forcing transition using passive discrete roughness elements and active mass addition, or blowing, methods were compared in two hypersonic facilities, the 20-Inch Mach 6 Air and the 31-Inch Mach 10 Air tunnels. Heat transfer distributions, obtained via phosphor thermography, shock system details, and surface streamline patterns were measured on a 0.333-scale model of the Hyper-X forebody. The comparisons between the active and passive methods for boundary layer control were conducted at test conditions that nearly match the nominal Mach 7 flight trajectory of an angle-of-attack of 2-deg and length Reynolds number of 5.6 million. For the passive roughness examination, the primary parametric variation was a range of trip heights within the calculated boundary layer thickness for several trip concepts. The prior passive roughness study resulted in a swept ramp configuration being selected for the Mach 7 flight vehicle that was scaled to be roughly 0.6 of the calculated boundary layer thickness. For the active jet blowing study, the blowing manifold pressure was systematically varied for each configuration, while monitoring the mass flow, to determine the jet penetration height with schlieren and transition movement with the phosphor system for comparison to the passive results. All the blowing concepts tested were adequate for providing transition onset near the trip location with manifold stagnation pressures on the order of 40 times the model static pressure or higher.

The objective of this work is to experimentally investigate active structural acoustic control of turbulent boundary layer (TBL) induced sound radiation from multiple panels on an aircraft sidewall. One possible approach for controlling sound radiation from multiple panels is a multi-input/multi-output scheme which considers dynamic coupling between the panels. Unfortunately, this is difficult for more than a few panels, and is impractical for a typical aircraft which contains several hundred such panels. An alternative is to implement a large number of independent control systems. Results from the current work demonstrate the feasibility of reducing broadband radiation from multiple panels utilizing a single-input/single-output (SISO) controller per bay, and is the first known demonstration of active control of TBL induced sound radiation on more than two bays simultaneously. The paper compares sound reduction for fully coupled control of six panels versus independent control on each panel. An online adaptive control scheme for independent control is also demonstrated. This scheme will adjust for slow time varying dynamic systems such as fuselage response changes due to aircraft pressurization, etc.

This paper (the first in a series) focuses on using active-control methods to maintain laminar flow in a region of the flow in which the natural instabilities, if left unattended, lead to turbulent flow. The authors review previous studies that examine wave cancellation (currently the most prominent method) and solve the unsteady, nonlinear Navier-Stokes equations to evaluate this method of controlling instabilities. It is definitively shown that instabilities are controlled by the linear summation of waves (i.e., wave cancellation). Although a mathematically complete method for controlling arbitrary instabilities has been developed, the review, duplication, and physical explanation of previous studies are important steps for providing an independent verification of those studies, for establishing a framework for the work which will involve automated transition control, and for detailing the phenomena by-which the automated studies can be used to expand knowledge of flow control.

Wind tunnel test of ground effect of 35-deg swept- back wing jet transport equipped with boundary layer control, trailing & leading edge flaps

The present report briefly reviews the work accomplished on the study of three-dimensional shock wave turbulent boundary layer interactions at a Mach 3. The work consisted of two major thrusts; 1) Modeling of the complex interaction and detailed experiments coordinated with extensive computations; and 2) Exploratory studies of control concepts for a 20 deg fin and crossing shock configurations. The completed works have been reported and are briefly reviewed. A brief resume is presented of incompleted results on complex interactions, new heat transfer techniques, initial spanwise boundary layer effects, and studies in a new Low Turbulence Variable Geometry facility.

Active and passive methods for tripping hypersonic boundary layers have been examined in NASA Langley Research Center wind tunnels using a Hyper-X model. This investigation assessed several concepts for forcing transition, including passive discrete roughness elements and active mass addition (or blowing), in the 20-Inch Mach 6 Air and the 31-Inch Mach 10 Air Tunnels. Heat transfer distributions obtained via phosphor thermography, shock system details, and surface streamline patterns were measured on a 0.333-scale model of the Hyper-X forebody. The comparisons between the active and passive methods for boundary layer control were conducted at test conditions that nearly match the Hyper-X nominal Mach 7 flight test-point of an angle-of-attack of 2-deg and length Reynolds number of 5.6 million. For passive roughness, the primary parametric variation was a range of trip heights within the calculated boundary layer thickness for several trip concepts. The passive roughness study resulted in a swept ramp configuration, scaled to be roughly 0.6 of the calculated boundary layer thickness, being selected for the Mach 7 flight vehicle. For the active blowing study, the manifold pressure was systematically varied (while monitoring the mass flow) for each configuration to determine the jet penetration height, with schlieren, and transition movement, with the phosphor system, for comparison to the passive results. All the blowing concepts tested, which included various rows of sonic orifices (holes), two- and three-dimensional slots, and random porosity, provided transition onset near the trip location with manifold stagnation pressures on the order of 40 times the model surface static pressure, which is adequate to ensure sonic jets. The present results indicate that the jet penetration height for blowing was roughly half the height required with passive roughness elements for an equivalent amount of transition movement.

Modern low-pressure turbines, in general, utilize highly loaded airfoils in an effort to improve efficiency and to lower the number of airfoils needed. Typically, the airfoil boundary layers are turbulent and fully attached at takeoff conditions, whereas a substantial fraction of the boundary layers on the airfoils may be transitional at cruise conditions due to the change of density with altitude. The strong adverse pressure gradients on the suction side of these airfoils can lead to boundary-layer separation at the latter low Reynolds number conditions. Large separation bubbles, particularly those which fail to reattach, cause a significant degradation of engine efficiency. A component efficiency drop of the order 2 may occur between takeoff and cruise conditions for large commercial transport engines and could be as large as 7 for smaller engines at higher altitude. An efficient means of of separation elimination/reduction is, therefore, crucial to improved turbine design. Because the large change in the Reynolds number from takeoff to cruise leads to a distinct change in the airfoil flow physics, a separation control strategy intended for cruise conditions will need to be carefully constructed so as to incur minimum impact/penalty at takeoff. The focus in the present paper is an experimental study of active separation control using glow discharge plasma actuators. Separation is induced on a flat plate installed in a closed-circuit wind tunnel by a shaped insert on the opposite wall. The flow conditions represent flow over the suction surface of a modern low-pressure-turbine airfoil ('Pak-B'). The Reynolds number, based on wetted plate length and nominal exit velocity, is varied from 50,000 to 300,000, covering cruise to takeoff conditions. Low (0.2) and high (2.5) free-stream turbulence intensities are set using passive grids. A spanwise-oriented phased-plasma-array actuator, fabricated on a printed circuit board, is surface-flush-mounted upstream of the separation point and can provide forcing in a wide frequency range. Static surface pressure measurements and hot-wire anemometry of the base and controlled flows are performed and indicate that the glow-discharge plasma actuator is an effective device for separation control.

We present the results on numerical testing of the Boundary Control Method in the sound speed determination for the acoustic equation on semiplane. This method for solving multidimensional inverse problems requires no a priory information about the parameters under reconstruction. The application to the realistic Marmousi model demonstrates that the boundary control method is workable in the case of complicated and irregular field of acoustic rays. By the use of the chosen boundary controls, an `averaged' profile of the sound speed is recovered (the relative error is about $10-15\%$). Such a profile can be further utilized as a starting approximation for high resolution iterative reconstruction methods.

Effective delay of turbulent boundary layer separation could be achieved via closed-loop control. Constructing such a system requires that sensor data be processed, real-time, and fed into the controller to determine the output. Current methods for detection of turbulent boundary layer separation are lacking the capability of localized, fast and reliable identification of the boundary layer state. A method is proposed for short-time FFT processing of time series, measured by hot-film sensors, with the purpose of identifying the alternation of the balance between small and large scales as the boundary layer separates, favoring the large scales. The method has been validated by comparison to other criteria of separation detection and over a range of baseline and controlled flow conditions on a simplified high-lift system, incorporating active flow control.

Effective delay of turbulent boundary layer separation could be achieved via closed-loop control. Constructing such a system requires that sensor data be processed, real-time, and fed into the controller to determine the output. Current methods for detection of turbulent boundary layer separation are lacking the capability of localized, fast and reliable identification of the boundary layer state. A method is proposed for short-time FFT processing of time series, measured by hot-film sensors, with the purpose of identifying the alternation of the balance between small and large scales as the boundary layer separates, favoring the large scales. The method has been validated by comparison to other criteria of separation detection and over a range of baseline and controlled flow conditions on a simplified high-lift system, incorporating active flow control.

High maneuverability is one of the major goals in rotorcraft design. In practice, this goal is limited by unsteady (dynamic) stall near blade leading edges. Studies of three-dimensional boundary layer separation on a rotating blade are made. For hovering flight, the blade twist and downwash are included in the effective angle of attack. For forward flight, high angles of attack are used to simulate the most severe situation at the retreating blade. Because of the disparate scales of the leading edge radius and the blade span, separation is found to be quasi two-dimensional, and local singular behaviors at separation are very similar to the two-dimensional cases. Most of the results are obtained using an Eulerian approach, but a Lagrangian formulation is used to study the behavior near the separation singularity. Control mechanisms based on suction and blade oscillations are examined. It is found that oscillations, with a tuned frequency and amplitude, can delay separation. Leading edge suction/injection is also effective in delaying separation for particular (optimized) slot locations.

A review of the work completed during the first year of research on the subject contract is presented. Papers and publications generated, staff, and students involved in research are noted, along with a brief description of the on-going program. Significant results have been obtained in defining the structure of the three-dimensional shock wave turbulent boundary layer interaction by combining detailed experiments with coordinated major computational programs. Keywords: Shock wave, Boundary layer, Supersonic.

Using direct numerical simulations of turbulent channel flow, we present new insight into the generation of streamwise vortices near the wall, and an associated drag reduction strategy. Growth of x-dependent spanwise velocity disturbances w(x) is shown to occur via two mechanisms: (1) linear transient growth, which dominates early-time evolution, and (2) linear normal-mode instability, dominant asymptotically at late time (for frozen base flow streaks). Approximately 25% of streaks extracted from near-wall turbulence are shown to be strong enough for linear instability (above a critical vortex line Lift angle!. However, due to viscous annihilation of streak normal vorticity, normal mode growth ceases after a factor of two energy growth. In contrast, the linear transient disturbance produces a 20-fold amplification, due to its rapid, early-time growth before significant viscous streak decay. Thus, linear transient growth of w(x) is revealed as a new, apparently dominant, generation mechanism of x-dependent turbulent energy near the wall.

Using direct numerical simulations of turbulent channel flow, we present new insight into the generation of streamwise vortices near the wall, and an associated drag reduction strategy. Growth of x-dependent spanwise velocity disturbances w(x) is shown to occur via two mechanisms: (i) linear transient growth, which dominates early-time evolution, and (ii) linear normal-mode instability, dominant asymptotically at late time (for frozen base flow streaks). Approximately 25% of streaks extracted from near-wall turbulence are shown to be strong enough for linear instability (above a critical vortex line Lift angle). However, due to viscous annihilation of streak normal vorticity COy, normal mode growth ceases after a factor of two energy growth. In contrast, the linear transient disturbance produces a 20-fold amplification, due to its rapid, early-time growth before significant viscous streak decay. Thus, linear transient growth of w(x) is revealed as a new, apparently dominant, generation mechanism of x-dependent turbulent energy near the wall.

There has been an increased experimental understanding of boundary layer structure and behavior particularly in the turbulent regime as well as significant improvements in our knowledge of the factors affecting the boundary-layer transition in arbitrary flow fields. This symposium was intended to bring together the practitioners of the various applications of boundary layer control with those interested in the underlying fluid mechanics. Contributions covered theoretical and experimental developments in the use of both traditional and non-traditional means of boundary layer control for external flow applications such as lift augmentation, drag reduction and improved effectiveness of controls, and for internal flow applications such as air intakes and exit configurations. Techniques included shaping (geometry) suction and blowing; transverse blowing; vortex generators; heating and cooling; and turbulent boundary layer manipulation. The special emphasis on high-lift systems included consideration of the techniques of boundary layer control on characteristics of wings and wing-body arrangements that involve flaps, slats and jets (blown flaps), and vortex flaps.

There has been an increased experimental understanding of boundary layer structure and behavior particularly in the turbulent regime as well as significant improvements in our knowledge of the factors affecting the boundary-layer transition in arbitrary flow fields. This symposium was intended to bring together the practitioners of the various applications of boundary layer control with those interested in the underlying fluid mechanics. Contributions covered theoretical and experimental developments in the use of both traditional and non-traditional means of boundary layer control for external flow applications such as lift augmentation, drag reduction and improved effectiveness of controls, and for internal flow applications such as air intakes and exit configurations. Techniques included shaping (geometry) suction and blowing; transverse blowing; vortex generators; heating and cooling; and turbulent boundary layer manipulation. The special emphasis on high-lift systems included consideration of the techniques of boundary layer control on characteristics of wings and wing-body arrangements that involve flaps, slats and jets (blown flaps), and vortex flaps.

This article is from Sensors (Basel, Switzerland) , volume 13 . Abstract Physical sensors have a key role in implementation of real-time vector control for an induction motor (IM) drive. This paper presents a novel boundary layer fuzzy controller (NBLFC) based on the boundary layer approach for speed control of an indirect field-oriented control (IFOC) of an induction motor (IM) drive using physical sensors. The boundary layer approach leads to a trade-off between control performances and chattering elimination. For the NBLFC, a fuzzy system is used to adjust the boundary layer thickness to improve the tracking performance and eliminate the chattering problem under small uncertainties. Also, to eliminate the chattering under the possibility of large uncertainties, the integral filter is proposed inside the variable boundary layer. In addition, the stability of the system is analyzed through the Lyapunov stability theorem. The proposed NBLFC based IM drive is implemented in real-time using digital signal processor (DSP) board TI TMS320F28335. The experimental and simulation results show the effectiveness of the proposed NBLFC based IM drive at different operating conditions.

We consider a controlled state equation of parabolic type on the halfline $(0,+\infty)$ with boundary conditions of Dirichlet type in which the unknown is equal to the sum of the control and of a white noise in time. We study finite horizon and infinite horizon optimal control problem related by menas of backward stochastic differential equations.

The focus was on developing means of controlling and reducing unsteady pressure loads in separated shock wave turbulent boundary layer interactions. Section 1 describes how vortex generators can be used to effectively reduce loads in compression ramp interaction, while Section 2 focuses on the effects of 'boundary-layer separators' on the same interaction.

Inflow Control Device (ICD). -- Photographed on: 10/03/97. -- Active noise control by boundary layer modulation fan model test set up with ICD and flow control valves; with far field microphone hoop and without hoop, in building 1218A, Anechoic Noise Facility.

Inflow Control Device (ICD). -- Photographed on: 10/03/97. -- Active noise control by boundary layer modulation fan model test set up with ICD and flow control valves; with far field microphone hoop and without hoop, in building 1218A, Anechoic Noise Facility.

AD-A326 851

In this paper, we develop a reduced basis construction method that allows for separate consideration of baseline and actuated dynamics in the reduced modeling process. A prototype initial boundary value problem, governed by the two-dimensional Burgers equation, is formulated to demonstrate the utility of the method in a boundary control setting. Comparisons are done between reduced and full order solutions under open-loop boundary actuation to illustrate advantages gained by separate consideration of actuated dynamics. A tracking control problem is specified using a linear quadratic regulator formulation. Comparisons of feedback control effectiveness are done to demonstrate benefits in control effectiveness obtained from separate consideration of actuated dynamics during model reduction.

The project objective consists in interdisciplinary investigations aimed at the development of an advanced innovative concept of flow control based on a specially designed microwave discharge generator initiating intrinsic to flow streamwise vortices with a given scale. PART 1 of the Project is the aerodynamic modeling of a boundary layer with an embedded vortical structure of a given scale generated by a system of MW discharges. Efficiency of the flow-control concept and its potential applicability is evaluated from the matched numerical and experimental results aimed to show correlation between the turbulence structure and the aerodynamic performance of the test model. PART 2 of the Project is the research related to generation of localized MW discharges as a versatile tool for the remote flow control. It shows the feasibility of the developed technique that enables to organize microwave (MW) discharges in aerodynamically justified patterns to stimulate and support vortical fluid motion of a given structure.

"Control of Pollution of Streams: The International Joint Commission and the Pollution of Boundary Waters" is an article from Public Health Reports (1896-1970), Volume 32 . View more articles from Public Health Reports (1896-1970) . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-4574426

Inflow Control Device (ICD). -- Photographed on: 10/03/97. -- Active noise control by boundary layer modulation fan model test set up with ICD and flow control valves; with far field microphone hoop and without hoop, in building 1218A, Anechoic Noise Facility.

A boundary control problem for the viscous Cahn-Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first order necessary conditions for optimality are proved. Key words: Cahn-Hilliard equation, dynamic boundary conditions, phase separation, singular potentials, optimal control, optimality conditions, adjoint state system

In this paper, we investigate an optimal boundary control problem for a two dimensional simplified Ericksen--Leslie system modelling the incompressible nematic liquid crystal flows. The hydrodynamic system consists of the Navier--Stokes equations for the fluid velocity coupled with a convective Ginzburg--Landau type equation for the averaged molecular orientation. The fluid velocity is assumed to satisfy a no-slip boundary condition, while the molecular orientation is subject to a time-dependent Dirichlet boundary condition that corresponds to the strong anchoring condition for liquid crystals. We first establish the existence of optimal boundary controls. Then we show that the control-to-state operator is Fr\'echet differentiable between appropriate Banach spaces and derive first-order necessary optimality conditions in terms of a variational inequality involving the adjoint state variables.

We are interested in the determination of the reachable states for the boundary control of the one-dimensional heat equation. We consider either one or two boundary controls. We show that reachable states associated with square integrable controls can be extended to analytic functions onsome square of C, and conversely, that analytic functions defined on a certain disk can be reached by using boundary controlsthat are Gevrey functions of order 2. The method of proof combines the flatness approach with some new Borel interpolation theorem in some Gevrey class witha specified value of the loss in the uniform estimates of the successive derivatives of the interpolating function.

We are interested in the determination of the reachable states for the boundary control of the one-dimensional heat equation. We consider either one or two boundary controls. We show that reachable states associated with square integrable controls can be extended to analytic functions onsome square of C, and conversely, that analytic functions defined on a certain disk can be reached by using boundary controlsthat are Gevrey functions of order 2. The method of proof combines the flatness approach with some new Borel interpolation theorem in some Gevrey class witha specified value of the loss in the uniform estimates of the successive derivatives of the interpolating function.

A boundary layer control device was designed to change significantly the case-wall boundary layer thickness entering a large-scale, multistage axial compressor. The device was intended to double the boundary layer thickness in order to evaluate the influence of the inlet boundary layer in controlled tip clearance experiments being conducted on the compressor. The boundary layer characteristics expected to be produced by the control device were predicted empirically and experimental verification was required. Kiel, cobra, and impact probes were used in the experiments and pressures were recorded manually using water manometers. The geometry of the boundary layer control device, an annular array of spires, was derived from shapes developed for simulating the atmospheric boundary layer in large rectangular section wind tunnels. A significantly thicker boundary layer was measured in the compressor than was intended. However, the results were interpreted and recommendations were made for geometry changes necessary to achieve the intended control for the tip clearance investigation. Keywords: Axial flow compressor blades; Boundary layer spires; Boundary layer control; Theses. (EDC)

We study the infinite horizon Linear-Quadratic problem and the associated algebraic Riccati equations for systems with unbounded control actions. The operator-theoretic context is motivated by composite systems of Partial Differential Equations (PDE) with boundary or point control. Specific focus is placed on systems of coupled hyperbolic/parabolic PDE with an overall `predominant' hyperbolic character, such as, e.g., some models for thermoelastic or fluid-structure interactions. While unbounded control actions lead to Riccati equations with unbounded (operator) coefficients, unlike the parabolic case solvability of these equations becomes a major issue, owing to the lack of sufficient regularity of the solutions to the composite dynamics. In the present case, even the more general theory appealing to estimates of the singularity displayed by the kernel which occurs in the integral representation of the solution to the control system fails. A novel framework which embodies possible hyperbolic components of the dynamics has been introduced by the authors in 2005, and a full theory of the LQ-problem on a finite time horizon has been developed. The present paper provides the infinite time horizon theory, culminating in well-posedness of the corresponding (algebraic) Riccati equations. New technical challenges are encountered and new tools are needed, especially in order to pinpoint the differentiability of the optimal solution. The theory is illustrated by means of a boundary control problem arising in thermoelasticity.

We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary. We employ optimal control framework, where boundary heat flux and free boundary are components of the control vector, and optimality criteria consists of the minimization of the sum of $L_2$-norm declinations from the available measurement of the temperature flux on the fixed boundary and available information on the phase transition temperature on the free boundary. This approach allows one to tackle situations when the phase transition temperature is not known explicitly, and is available through measurement with possible error. It also allows for the development of iterative numerical methods of least computational cost due to the fact that for every given control vector, the parabolic PDE is solved in a fixed region instead of full free boundary problem. We prove well-posedness in Sobolev spaces framework and convergence of discrete optimal control problems to the original problem both with respect to cost functional and control.

This paper deals with an optimal control problem related to a phase field system of Caginalp type with a dynamic boundary condition for the temperature. The control placed in the dynamic boundary condition acts on a part of the boundary. The analysis carried out in this paper proves the existence of an optimal control for a general class of potentials, possibly singular. The study includes potentials for which the derivatives may not exist, these being replaced by well-defined subdifferentials. Under some stronger assumptions on the structure parameters and on the potentials (namely for the regular and the logarithmic case having single-valued derivatives), the first order necessary optimality conditions are derived and expressed in terms of the boundary trace of the first adjoint variable.

We present a finite element method along with its analysis for the optimal control of a model free boundary problem with surface tension effects, formulated and studied in \cite{HAntil_RHNochetto_PSodre_2014a}. The state system couples the Laplace equation in the bulk with the Young-Laplace equation on the free boundary to account for surface tension. We first prove that the state and adjoint system have the requisite regularity for the error analysis (strong solutions). We discretize the state, adjoint and control variables via piecewise linear finite elements and show optimal $O(h)$ error estimates for all variables, including the control. This entails using the second order sufficient optimality conditions of \cite{HAntil_RHNochetto_PSodre_2014a}, and the first order necessary optimality conditions for both the continuous and discrete systems. We conclude with two numerical examples which examine the various error estimates.

In this paper, we consider boundary stabilization for a cascade of ODE-heat system with state delay under actuator saturation. To stabilize the system, we design a state feedback controller via the backstepping method and find a bound on the domain of attraction. The latter bound is based on Lyapunov method, whereas the exponential stability of the delayed cascaded systems is proved by using Halanay's inequality. Numerical examples illustrate the efficiency of the method.

This report presents the results of an investigation to determine the effect of boundary layer control on the lift and drag of an airfoil equipped with a backward opening slot. Various slot locations, widths of opening, and pressures, were used. The tests were conducted in the Five-Foot Atmospheric Wind Tunnel of the Langley Memorial Aeronautical Laboratory. The greatest increase in maximum lift was 96 per cent, the greatest decrease in minimum drag was 27 per cent, and the greatest increase in the ratio, maximum lift coefficient/minimum drag coefficient, was 151 per cent.

No Abstract Available

In recent years, active and passive control of sound and vibration in aeroelastic structures have received a great deal of attention due to many potential applications to aerospace and other industries. There exists a great deal of research work done in this area. Recent advances in the control of sound and vibration can be found in the several conference proceedings. In this report we will summarize our research findings supported by the NASA grant NAG-1-1175. The problems of active and passive control of sound and vibration has been investigated by many researchers for a number of years. However, few of the articles are concerned with the sound and vibration with flow-structure interaction. Experimental and numerical studies on the coupling between panel vibration and acoustic radiation due to flow excitation have been done by Maestrello and his associates at NASA/Langley Research Center. Since the coupled system of nonlinear partial differential equations is formidable, an analytical solution to the full problem seems impossible. For this reason, we have to simplify the problem to that of the nonlinear panel vibration induced by a uniform flow or a boundary-layer flow with a given wall pressure distribution. Based on this simplified model, we have been able to study the control and stabilization of the nonlinear panel vibration, which have not been treated satisfactorily by other authors. The vibration suppression will clearly reduce the sound radiation power from the panel. The major research findings will be presented in the next three sections. In Section II we shall describe our results on the boundary control of nonlinear panel vibration, with or without flow excitation. Section III is concerned with active control of the vibration and sound radiation from a nonlinear elastic panel. A detailed description of our work on the parametric vibrational control of nonlinear elastic panel will be presented in Section IV. This paper will be submitted to the Journal of Acoustic Society of America for publication.

Wind tunnel test of ground effect of 35-deg swept- back wing jet transport equipped with boundary layer control, trailing & leading edge flaps

The paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand, we give an example showing that exact controllability in finite time cannot be achieved, in general.

The objective of this project is improved understanding of the response of boundary layers to surface variations for control. The subsonic studies provide a significant advancement in our understanding of boundary layer stability to small-scale roughness, which has the potential for significant drag and heat transfer reduction across all Mach numbers. The high-speed (M=5) high Reynolds number studies provide improved understanding of the response of turbulence to mechanical non-equilibrium, which led to a flow control strategy, where 25% reductions in turbulence levels were demonstrated. Our modeling suggests this could lead to a 40% reduction in surface heat transfer.

This study addresses the usage and effects of atmospheric plasma discharges on the near wall flow conditions for a Pak-B low-pressure turbine blade. A plasma actuator was built normal to the freestream flow in a low-speed wind tunnel. The test section of the wind tunnel had a contoured upper wall geometry designed to mimic the suction side of a Pak-B turbine blade. A high frequency ac voltage source supplied three voltages in the kilovolt range at four Reynolds numbers in the experiment, between 10,000 and 103,000. The effect of the plasma on the near-wall boundary layer conditions was evaluated at each of the Reynolds numbers and each of the three voltage levels. The corresponding power levels were between 15 and 25 W. Particle image velocimetry (PIV) was used to determine the 2D boundary layer characteristics of the flow. This research showed that the plasma discharges were able to dramatically increase the flow velocity near the wall; however, the plasma was unable to reattach an already detached boundary layer. Boundary layer traces were taken to validate the PIV results. Additionally, multiple manufacturing techniques were evaluated in an effort to make the electrodes more usable in turbine blade applications.