14.2 Introduction

14.1.1 What Is to Be Learned?

This chapter covers the following topics:

Section 14.2: Introduction to the concept of CFD

Section 14.3: Introduction to the current status of CFD

Section 14.4: An approach to and considerations for CFD analysis

Section 14.5: Case studies

Section 14.6: Hierarchy of CFD simulation methods

Section 14.7: 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 aircraftdesign 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).

14.3 Current Status

In his classic review, Chapman [1] (1979) advocated the indispensability of CFD, as computers began showing the promise of overtaking experiments as a principal source of detailed design information. His view is now regarded as an overly optimistic estimate. CFD capabilities complement experiments. Chapman listed the following three reasons for his conclusion:

Experiments cannot represent the real flight envelope (e.g., Re and temperature) and are limited by flow nonuniformity, wall effects, and transientdependent separation.

There are very high energy costs associated with large wind tunnels.

CFD is faster and less costly than experiments for obtaining valuable insight at an initial stage.

Figure 14.1. CFD simulation of wingbody drag polar [7]

Chapman showed the chronology of progress as four stages, starting in the late 1960s by solving linear potential flow equations and then reaching a stage where the nonlinear Navier–Stokes equations could be solved.

In a later paper, Chapman [2] reviewed the rapid progress achieved in the 1990s. With a better understanding of turbulence and advances in computer technology in both hardware and software development, researchers successfully generated aerodynamic results that had been impossible to obtain until then.

A more recent review by Roache [3] demonstrated that considerable progress has been achieved in CFD, but the promise is still far from being fulfilled in estimating complete aircraft drag. The AGARD AR256 report [4] is a technical status review of drag prediction and analysis from the CFD perspective. In the report, Schmidt [5] categorically stated that “consistent and accurate prediction of absolute drag for aircraft configuration is currently beyond CFD reach. . . . ” Ashill [6] was of the same opinion, stating that the CFD flow modeling was found to be lacking in “certain respects.” Both agreed that the current state of the art in CFD is a useful tool at the conceptual design stages for comparison of shapes and diagnostic purposes.

An essential route to establish the robustness of CFD is through the success of the conceptual model code verification and validation. Roache [3] used the semantics of “verification” as solving the equations correctly and “validation” as solving the correct equations. The process of benchmarking (i.e., code-to-code comparison) results in the selection of software with the best economic value, although not necessarily the best software on the market.

Experimental results are used to validate and calibrate CFD codes. Various degrees of success have been achieved in the case studies. Melnik [5] showed that the CFD status in aircraft drag prediction of a subsonic-jet, transport-type aircraft wing on a simple circular cross-section fuselage had mixed success, as shown in Figure 14.1. Some correlation was achieved after considerable “tweaking” of the results. The results using these methods are not certifiable because of considerable “gray” areas.

Currently, the industry uses CFD as a tool for flow-field analysis wherever it is possible to estimate drag in inviscid flow (e.g., induced drag and wave drag), but it is not used for complete aircraft drag estimation. In the industry, CFD is a generalpurpose tool to simulate flow around objects for qualitative studies and diagnostic purposes.