Page 7 - Computational Fluid Dynamics for Engineers

VI Preface

understanding and subsequent improvement of the processes in question. The
second is to solve simplified versions of fluid dynamics equations for conservation
of mass, momentum and energy for comparatively simple boundary conditions.
There is great advantage in combining both approaches when addressing com-
plex fluid dynamics problems, but interaction between these two approaches has
been limited until recently by the narrow range of useful solutions that could
be obtained by analytic methods or simple numerical computations. It is evi-
dent, therefore, that any method for increasing the accuracy of computational
methods by solving more complete forms of the conservation equations than has
been possible up to now is to be welcomed. The numerical approaches of CFD
have, in most cases, proven much more powerful than the closed-form analytical
solutions of the past. As an example, the flow through the blade passage of a
gas turbine is three-dimensional, and, even if we ignore the problem of model-
ing the behavior of turbulence, the corresponding equations can only be solved
by numerical methods; even the inviscid flow in an axisymmetnc engine intake
cannot be calculated by purely analytic methods. Thus, without computational
fluid dynamics, we cannot calculate detailed flow characteristics essential to
improving understanding and supporting the design process.
It should be recognized that both experimental and computational fluid
dynamics require resources. The cost of experiments in some cases can be pro-
hibitive as, for example, with extensive flight tests of airplanes, full-scale tests
of a gas turbine, or destructive testing of expensive components. In such cases,
it may be possible to reduce the number of experimental tests by using CFD,
since only a relatively small number of experiments are required to check the
accuracy of the numerical results. Of course, the cost of obtaining accurate
numerical solutions of differential equations may also be large for a complex
flow, but still are usually much less than the cost of the additional experiments
that would otherwise be required. In reality, the most cost-effective approach
to solving a fluid dynamics problem is likely to be a combination of measure-
ments and calculations. Both are subject to uncertainties, but the combination
of these two approaches can result in a more cost-effective and more reliable
design than by using only one approach or the other, and thus may be neces-
sary to meet today's more stringent requirements for improved performance and
reduced environmental impact, along with technical innovation and economy.
This book is an introduction to computational fluid dynamics with emphasis
on the solution of conservation equations for incompressible and compressible
flows with two independent variables. From the range of formulations in CFD,
such as finite-difference, finite volume, finite element, spectral methods and
direct numerical simulation, it concentrates on the first two, which are widely
used to solve engineering problems. The restriction to two-dimensional flow and
the omission of finite element, spectral methods and direct numerical simulation
are imposed to facilitate understanding and to allow the essential material to be