Computational fluid dynamics (CFD) is a numerical tool for solving equations of fluid mechanics. CFD is a relatively recent development that has become an indis­pensable tool in the last two decades. It was developed originally for aeronautical uses but now pervades all disciplines involving flow phenomena, such as medical, natural sciences, and engineering applications. The built-in codes of the CFD soft­ware are algorithms of numerical solutions for the fluid-mechanics equations. Flow fields that were previously difficult to solve by analytical means – and, in some situ­ations, impossible – are now accessible by means of CFD.

Today, the aircraft industry uses CFD during the conceptual study phase. There are limitations in obtaining accurate results, but research continues in academic and industrial circles to improve prediction. This chapter aims to familiarize newly initi­ated readers with the scope of CFD in configuring aircraft geometry (those already exposed to the subject may skip this chapter). This is not a book about CFD; there­fore, this chapter does not present a rigorous mathematical approach but rather an overview.

CFD is a subject that requires considerable knowledge in fluid mechanics and mathematics. CFD is introduced late in undergraduate studies, when students have mastered the prerequisites. Commercial CFD tools are menu-driven and it is possi­ble to quickly become proficient, but interpreting the results thus obtained requires considerable experience in the subject.

An accurate 3D model of an aircraft in CAD significantly reduces preprocess­ing time. The CAD software format must be compatible with CFD to transfer the drawing models. Together, CAD and CFD provide a CAE approach to paperless, electronic design methods.

Several good commercial CAD and CFD packages are available in the mar­ketplace. Nowadays, all engineering schools have CAD and CFD application software.

14.1.1 What Is to Be Learned?

This chapter covers the following topics:

Introduction to the concept of CFD Introduction to the current status of CFD An approach to and considerations for CFD analysis Case studies

Hierarchy of CFD simulation methods Summary

14.1.2 Coursework Content

There is no coursework on CFD in the first term. However, it is recommended that CFD studies be undertaken in the second term after readers are formally introduced to the subject. Appropriate supervision is required to initiate the task and analyze the results. Any CFD coursework is separated from the scope of this book. The purpose of this chapter is to give newly initiated readers an introduction to aircraft – design work.

14.2 Introduction

Throughout this book, it is shown that the aerodynamic parameters of lift, drag, and moment associated with aircraft moving through the air are of vital importance. An accurate assessment of these parameters is the goal of aircraft designers.

Mathematically, lift, drag, and moment of an aircraft body can be obtained by integrating the pressure field around the aircraft computed from the governing con­servation equations (i. e., differential or integral forms) of mass, momentum, and energy with the equation of state for air. Until the 1970s, wind-tunnel tests were the only way to obtain the best results of these parameters in the various air­craft attitudes representing what can be encountered within the full flight envelope. Semi-empirical formulae generated from vast amounts of test results, backed up by theory, provided a good starting point for any conceptual study.

Numerical methods for solving differential equations prevailed for some time. The Navier-Stokes equations provided an accurate representation of the flow field around the aircraft body under study. However, solving the equation for 3D shapes in compressible flow was difficult, if not sometimes impossible. Mathematicians devised methods to discretize differential equations into algebraic form that are solvable even for the difficult nonlinear, partial-differential equations. During the early 1970s, CFD results of simple 2D bodies in inviscid flow were demonstrated as comparable to wind-tunnel test results and analytical solutions.

The industry recognized the potential and progressed with in-house research; in some cases, complex flow phenomena hitherto unknown were understood. Subse­quently, CFD proliferated in academies and there was rapid advancement in achiev­ing solution techniques. Over time, the methodologies continued to improve. The latest technique discretizes the flow field into finite volumes in various sizes (i. e., smaller when the fluid properties have steeper variations) matching the wetted sur­face of the object, which also needs to be divided into cells/grids. The cells/grids do not overlap the adjoining volumes but rather mesh seamlessly. The mathematical
formulation of the small volumes now can be treated algebraically to compute the flux of conserved properties between neighboring cells. Discrete steps of algebraic equations are not the calculus of limiting values at a point; therefore, errors creep into the numerical solution. Mathematicians are aware of the problem and struggle with better techniques to minimize errors in the algorithms. This numerical method of solving fluid-dynamic problems became computation-intensive, requiring com­puters to tackle numerous cells; the numbers could run into the millions. The solu­tion technique thus became known as computational fluid dynamics, abbreviated as CFD.

Another problem in the 1970s was the inadequacy of the computing power to deal with the domain consisting of the numerous cells and to handle the error functions. As computer power increased along with superior algorithms, the CFD capability gradually became applicable to the industry. Today, CFD is a proven method that is well supported by advanced computing power. CFD started in the industry and has become an indispensable tool for the industry as well as research organizations.

A difficult area of CFD simulation lies in turbulence modeling. Recently, com­putations of 3D Reynolds-average Navier-Stokes (RANS) equations for complete aircraft configurations have gained credence as a solution technique. Reference [13] summarizes the latest trends in turbulence modeling. Numerous credible soft­ware applications have emerged in the market, some catering to special-purpose applications.

CFD still has limitations: Drag is a viscous-dependent phenomenon; inclusion of viscous terms makes the governing equations very complex, requiring intensive computational time. Capturing all of the elements contributing to the drag of a full aircraft is a daunting task – the full representation is yet to achieve credibility in industrial uses. It is not yet possible to obtain an accurate drag prediction using CFD without manipulating input data based on a designer’s experience. However, once it is set up for the solution, the incremental magnitudes of aerodynamic parameters of a perturbed geometry are well represented in CFD. It is a useful tool for obtain­ing accurate incremental values of a perturbed geometry from a baseline aircraft configuration with known aerodynamic parameters. CFD provides a capability for parametric optimization, to a degree (discussed in the next section).

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