Showing papers by "Vaughn College of Aeronautics and Technology published in 2007"

3D particle image velocimetry of the flow field around a sphere sedimenting near a wall: Part 1. Effects of Weissenberg number

Abstract: The flow fields surrounding a sphere sedimenting through a liquid near a vertical wall are characterized using 3D stereoscopic particle-image velocimetry (PIV) experiments. Three different fluids, a Newtonian reference fluid, a constant (shear) viscosity Boger fluid, and a shear-thinning elastic fluid, are used to determine the effects of both elasticity and shear-thinning on the flow field. All three fluids have similar zero shear viscosities. The Weissenberg number is manipulated by varying the diameter and the composition of the ball. Significant differences are found for the different types of fluid, demonstrating both the influence of elasticity and shear-thinning on the velocity fields. In addition, the impact of the wall on the flow field is qualitatively different for each fluid. We find that the flow behind the sphere is strongly dependent on the fluid properties as well as the elasticity. Also, the presence of a negative wake is found for the shear-thinning fluid at high Weissenberg number (Wi > 1).

Systems of Axes and Notation

Abstract: This chapter explores various systems of axes and notation. By making the appropriate choice of axis, systems order and consistency may be introduced to the process of model building. The order and consistency play an important role in the definition of the mathematical framework. Only the most basic commonly used axes systems appropriate to aircraft are discussed in the chapter. It gives a description of the earth axes and various kinds of aircraft body fixed axes. It is not important which axis system is chosen provided it models the flight condition to be investigated, the end-result does not depend on the choice of axis system. However, when compiling data for use in the equations of motion of an aircraft it is quite common for some data to be referred. Further, euler angles and aircraft attitude is explained. The angles defined by the right handed rotation about the three axes of a right handed system of axes are called Euler angles. The chapter also defines controls notion, wherein aerodynamic controls and engine controls are explained. The last section mentions the aerodynamic reference centers.

Lateral—Directional Dynamics

Abstract: This chapter explores the lateral-directional dynamics. It discusses some major aspects of lateral-directional dynamics, and their interpretation, differ significantly from the longitudinal dynamics. It also explores the procedures for interpreting the differences. As in the longitudinal solution, implicit in the response are the dynamic properties determined by the lateral-directional stability characteristics of the aeroplane. The most obvious difference between the solution of the longitudinal equations of motion and the lateral-directional equations of motion is that there is more algebra to deal with. These are the roll subsidence mode, the spiral mode, and the Dutch roll model. The chapter incorporates various examples throughout the text for better illustration of the subject being discussed. It also briefly explains the role of lateral-directional dynamics in flying and handling qualities of an aeroplane. As with longitudinal stability the lateral-directional stability characteristics of the aeroplane are critically important in the determination of its flying and handling qualities and there is no doubt that they must be correct.

The Solution of the Equations of Motion

Abstract: This chapter explains the solutions of the equations of motion. The primary reason for solving the equations of motion is to obtain a mathematical, and hence graphical, description of the time histories of all the motion variables in response to a control input, or atmospheric disturbance. It also enables an assessment of stability to be made. It is also important that the chosen method of solution should provide good insight into the way in which the physical properties of the airframe influence the nature of the responses. The process of solution requires that the equations of motion are assembled in the appropriate format, numerical values for the derivatives and other parameters are substituted, and then the whole model is input to a suitable computer program. The chapter is concerned with a discussion of the use of the Laplace transform for solving the small perturbation equations of motion to obtain the response transfer functions. This is followed by a description of the computational process involving matrix methods that is normally undertaken with the aid of a suitable computer software package. The chapter explores the state space model augmentation. It is a straightforward matter to augment the state description to include the additional dynamics of components such as engines and control surface actuators.

Deterministic Thermal Fracture Life Analysis of a Visco-elastic Cylinder

Abstract: Hollow Cylindrical structures such as a nuclear reactor containments, storage tanks, and solid rocket motor are often subjected to environmental temperature variations, which adversely influence mechanical properties such as strength, relaxation modulus, and fracture toughness. Environmental temperature changes produce cyclic thermal stresses in cylindrical structures. The thermal stress fluctuations may result in growth of a nascent crack in the body. Due to the random nature of thermal stresses, mechanical properties are time and temperature dependent. As a result crack growth will also be random. Here, a visco-elastic cylinder, modeled as a two-layer consisting of a visco-elastic inner layer in a thin elastic case, will be investigated. A finite element analysis will be carried out to determine temperature and thermal stress distribution through the cylindrical wall. Green's integral will be used to determine the crack tip stress intensity factor. The Forman crack growth rate relation, that provides crack extension in cyclically loaded structures, will be used to determine the crack propagation as the crack travels through the varying stress field. Since the stress distribution through the cylindrical wall is not uniform, a step-by-step finite element analysis will be carried out to determine stress intensity and crack growth as the crack travels through the varying stress field. Because of asymmetry in the cross section due to the existence of an initial crack, a two-dimensional finite element formulation is used for thermal analysis. The 2D analysis will take into account the stress distribution at the growing crack tip.

Flying and Handling Qualities

Abstract: This chapter explores the flying and handling qualities of an aeroplane. These qualities are those properties that govern the ease and precision with which the aeroplane responds to pilot commands in the execution of the flight task. Although these rather intangible properties are described qualitatively and are formulated in terms of pilot opinion, it becomes necessary to find alternative quantitative descriptions for more formal analytical purposes. The flying and handling qualities of an aeroplane are, in part, intimately dependent on its stability and control characteristics. This includes the effects of a flight control system when one is installed. The stability and control parameters of an aeroplane are commonly used as indicators and measures of the flying and handling qualities. So, the object of the chapter is to introduce, at an introductory level, the way in which stability and control parameters are used to quantify the flying and handling qualities of an aeroplane. Various examples have been explained throughout the text for better illustration of the subject. The chapter classifies the aeroplane and defines its flight phase. It emphasizes on the importance of the design of an aeroplane and thus a designer designs to achieve the highest level of flying qualities whereas, an evaluator confirms that this gets accomplished.

Static Equilibrium and Trim

Abstract: This chapter explores static equilibrium and trim equilibrium. There is a detailed description of the trim equilibrium. The preliminary considerations and the conditions, degree, and variation of stability are explained. The chapter discusses the longitudinal static stability, wherein two types of stabilities are explained. These are controls fixed stability and controls free stability. Lateral static stability is concerned with the ability of the aircraft to maintain wings level equilibrium in the roll sense. On the other hand, directional static stability is concerned with the ability of the aircraft to yaw or weathercock into wind in order to maintain directional equilibrium. The condition for an aircraft to remain in steady trimmed flight requires that the forces and moments acting on the aircraft sum to zero and that it is stable. Thus, to calculate the trim condition of an aircraft it is convenient to assume straight or symmetric flight.