ADVANCED FLOW CALCULATIONS
The art of flow calculations is advancing at a rapid rate. The revolution
in digital computers has inspired an accompanying revolution in the art of
numerical analysis. Even a lengthy treatise at this point would do an
injustice to this subject. Just enough information will be given to describe
what lies behind some of the ongoing activities.
Most of the new procedures embody some form of the Navier-Stokes
equations that include the Reynolds turbulence stresses. Some models for
estimating the distribution of turbulence are also required. The available
models are approximate and subject to opinions and improvements. Nevertheless,
some very useful advances have been made with the crude turbulence
models now existing. Several methods of calculating a flowfield can be
developed from this base. Some procedures use the concept of boundary
layer.
Another technique that was recently introduced borrows an idea from
electromagnetic theory. The flow vector is divided into two components--
one with no curl and the other with no divergence. The latter vector
describes all the vorticity in the flow. In some respects, it is really a
generalization of the boundary-layer concept. Compatibility conditions
between the two vector fields are required. The first field is mixed elliptichyperbolic
and can be solved by known "relaxation" procedures. The
second field is essentially parabolic and is solved by "marching methods."
(An upstream vector does not know what a downstream vector is doing.)
Two classes of computational techniques are being pursued. One class
begins by assuming the flow to be at rest and imposes the boundary
conditions. The time-unsteady equations of motion then estimate the
acceleration of the flow until it reaches equilibrium. The other class uses
finite-difference or finite-element methods. Transformation of coordinates
as a function of the local Mach number and the location of the point of
interest in the flowfield may be used. Methods of taking the finite differences
or of describing the finite elements also vary with both the local Mach
number and the point in the field.
All the programs are very involved and their preparation presently
requires an outstanding ability in computer programming, numerical analysis,
and fluid mechanics. Because of the enormity of the problem, existing
programs must be considered to be only partially developed. Even in this
crude state, their use has, for example, indicated ways of designing turbine
vanes so that the secondary-flow losses are reduced. The experimental test
of the resulting turbine was more than gratifying.
This field is moving forward. Useful new concepts are continually being
disclosed. As a result, the ability to accurately analyze complex flows in
detail is noticeably improving from year to year. Close attention must be
paid to this activity.
The pursuit of advanced three-dimensional analysis will bring about step
improvements in turbomachinery performance. Side benefits will be the
reduction of expensive testing and the delineation of forcing functions that
affect blade vibration
The art of flow calculations is advancing at a rapid rate. The revolution
in digital computers has inspired an accompanying revolution in the art of
numerical analysis. Even a lengthy treatise at this point would do an
injustice to this subject. Just enough information will be given to describe
what lies behind some of the ongoing activities.
Most of the new procedures embody some form of the Navier-Stokes
equations that include the Reynolds turbulence stresses. Some models for
estimating the distribution of turbulence are also required. The available
models are approximate and subject to opinions and improvements. Nevertheless,
some very useful advances have been made with the crude turbulence
models now existing. Several methods of calculating a flowfield can be
developed from this base. Some procedures use the concept of boundary
layer.
Another technique that was recently introduced borrows an idea from
electromagnetic theory. The flow vector is divided into two components--
one with no curl and the other with no divergence. The latter vector
describes all the vorticity in the flow. In some respects, it is really a
generalization of the boundary-layer concept. Compatibility conditions
between the two vector fields are required. The first field is mixed elliptichyperbolic
and can be solved by known "relaxation" procedures. The
second field is essentially parabolic and is solved by "marching methods."
(An upstream vector does not know what a downstream vector is doing.)
Two classes of computational techniques are being pursued. One class
begins by assuming the flow to be at rest and imposes the boundary
conditions. The time-unsteady equations of motion then estimate the
acceleration of the flow until it reaches equilibrium. The other class uses
finite-difference or finite-element methods. Transformation of coordinates
as a function of the local Mach number and the location of the point of
interest in the flowfield may be used. Methods of taking the finite differences
or of describing the finite elements also vary with both the local Mach
number and the point in the field.
All the programs are very involved and their preparation presently
requires an outstanding ability in computer programming, numerical analysis,
and fluid mechanics. Because of the enormity of the problem, existing
programs must be considered to be only partially developed. Even in this
crude state, their use has, for example, indicated ways of designing turbine
vanes so that the secondary-flow losses are reduced. The experimental test
of the resulting turbine was more than gratifying.
This field is moving forward. Useful new concepts are continually being
disclosed. As a result, the ability to accurately analyze complex flows in
detail is noticeably improving from year to year. Close attention must be
paid to this activity.
The pursuit of advanced three-dimensional analysis will bring about step
improvements in turbomachinery performance. Side benefits will be the
reduction of expensive testing and the delineation of forcing functions that
affect blade vibration
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