150
P. Liu
simplification and assumption. It expresses the left side of the equation
as the classical acoustic wave equation and moves all the terms deviating
from the wave equation to the right side of the equation as the source
term. So people can first use the experimental or computational methods
(DNS, Les, or even turbulence model theory) to obtain the expression of
these source terms, and then regard the sound field as the sound generated by the sound source propagating in the static medium, and then use
the mature classical acoustic methods to calculate the sound field. This
method of treating the flow field and sound field separately is the famous
aeroacoustics analogy. Theoretically, it is possible to solve the sound field
parameters directly from the N-S equation by numerical method, but
the pressure disturbance of sound wave is a very small quantity. Even at
the current level of numerical calculation, it is still a challenging work
to obtain the convergence solution from the equation and ensure that
the results have appropriate accuracy, which was even more impossible
50 years ago. Lighthill proposed a famous 8-power law using the equation,
that is, the radiated sound power of the turbulent jet aerodynamic noise is
directly proportional to the 8-power of the flow characteristic velocity. His
theory of acoustic simulation has been widely used in practical problems,
which ushered in a new era of aeroacoustics.
The theory of Lighthill acoustic simulation is established for the aerodynamic noise of airflow in unbounded space. It is applicable to the case
that the solid boundary does not play a major role, such as jet aerodynamic noise. However, for many practical situations, such as the noise
of stationary objects and moving objects in turbulence, the influence of
solid boundary cannot be ignored. In 1955, Curle first used Kirchhoff ’s
method to generalize Lighthill’s theory to consider the influence of the
static solid boundary and obtained that the effect of the solid boundary
is equivalent to the distribution of the dipole sound source on the whole
solid boundary, and the intensity of the dipole sound source at each point
is equal to the force of the solid surface acting on the fluid at that point.
Therefore, the sound field at this time is composed of a dipole on the
solid surface and a quadrupole (Lighthill stress tensor) source outside the
solid wall. The problem of Aeolian sound and aerodynamic noise induced
by cylinder vortex separation in turbulent flow is solved successfully by
Curle’s theory. In 1969, Ffowcs Williams and Hawkings extended Curle’s
achievement to consider the influence of moving solid wall on sound, that
is, the sound generation of moving objects in fluid, using the generalized
function method. The equation named after them, FW-H equation, was
P. Liu
simplification and assumption. It expresses the left side of the equation
as the classical acoustic wave equation and moves all the terms deviating
from the wave equation to the right side of the equation as the source
term. So people can first use the experimental or computational methods
(DNS, Les, or even turbulence model theory) to obtain the expression of
these source terms, and then regard the sound field as the sound generated by the sound source propagating in the static medium, and then use
the mature classical acoustic methods to calculate the sound field. This
method of treating the flow field and sound field separately is the famous
aeroacoustics analogy. Theoretically, it is possible to solve the sound field
parameters directly from the N-S equation by numerical method, but
the pressure disturbance of sound wave is a very small quantity. Even at
the current level of numerical calculation, it is still a challenging work
to obtain the convergence solution from the equation and ensure that
the results have appropriate accuracy, which was even more impossible
50 years ago. Lighthill proposed a famous 8-power law using the equation,
that is, the radiated sound power of the turbulent jet aerodynamic noise is
directly proportional to the 8-power of the flow characteristic velocity. His
theory of acoustic simulation has been widely used in practical problems,
which ushered in a new era of aeroacoustics.
The theory of Lighthill acoustic simulation is established for the aerodynamic noise of airflow in unbounded space. It is applicable to the case
that the solid boundary does not play a major role, such as jet aerodynamic noise. However, for many practical situations, such as the noise
of stationary objects and moving objects in turbulence, the influence of
solid boundary cannot be ignored. In 1955, Curle first used Kirchhoff ’s
method to generalize Lighthill’s theory to consider the influence of the
static solid boundary and obtained that the effect of the solid boundary
is equivalent to the distribution of the dipole sound source on the whole
solid boundary, and the intensity of the dipole sound source at each point
is equal to the force of the solid surface acting on the fluid at that point.
Therefore, the sound field at this time is composed of a dipole on the
solid surface and a quadrupole (Lighthill stress tensor) source outside the
solid wall. The problem of Aeolian sound and aerodynamic noise induced
by cylinder vortex separation in turbulent flow is solved successfully by
Curle’s theory. In 1969, Ffowcs Williams and Hawkings extended Curle’s
achievement to consider the influence of moving solid wall on sound, that
is, the sound generation of moving objects in fluid, using the generalized
function method. The equation named after them, FW-H equation, was