1 Foundation of Fluid Mechanics
67
1.11 Turbulence Advanced Numerical
Simulation Technology
Turbulence is a complex multi-scale and multi-level flow phenomenon. The
prediction and control of turbulence are closely related to people’s cognitive level and understanding level. For example, when only time-averaged
changes are needed, the Reynolds time-averaged equations (RANS) can be
used to solve them; if large-scale turbulence structure is needed, LEM (Large
Eddy Simulation) is developed; and if all information of turbulent flow field
is needed, the direct numerical simulation technique of full-scale turbulent
motion must be developed from the instantaneous N-S equation. The three
simulation techniques have different resolutions to the flow field and different
turbulence scales. Generally speaking, direct numerical simulation requires
the simulation of turbulence components at all scales, ranging from the
minimum scale to the dissipative scale, which is equivalent to the Re number
of the grid approaching 1.0. In Reynolds time-averaged method, turbulence
fluctuation components are closed by a statistical turbulence model, and
the grid scale of numerical simulation can be determined by the nature of
the time-averaged flow. Large eddy simulation (LES) technology can simulate large-scale turbulence component because the grid scale is above the
inertial sub-region and the dissipative scale component is replaced by the
modeling equation. Direct numerical simulation technology was developed
in the 1970s. Orzag and Patterson (1972) were the first to use direct numerical simulation to calculate isotropic turbulence with only 32 3 meshes and
the corresponding Reynolds number is Re λ = 35. On the contrary, the
experimental measurements can only obtain limited flow field information,
including finite scale turbulence components. For example, the vorticity
distribution in the turbulent flow field is difficult to measure. So far, the
development and evolution of turbulent vorticity structure can only be quantitatively observed by flow visualization or numerical simulation. Direct
numerical simulation is an effective tool for studying the mechanism of
turbulence and controlling turbulence (as shown in Fig. 1.84). The database
of direct numerical simulation can also be used to evaluate the existing
turbulence model, and then study the way to improve the turbulence model.
It has been found that in turbulent motion, besides many small-scale
vortices with strong randomness, there are also some large-scale vortices with
good organization. They have a relatively regular vortices’ structure. Their
shape and scale are of universal significance for the same type of turbulent
motion. They play an important role in the turbulent Reynolds stress and the
turbulent transport process of various physical quantities. For this reason, the
67
1.11 Turbulence Advanced Numerical
Simulation Technology
Turbulence is a complex multi-scale and multi-level flow phenomenon. The
prediction and control of turbulence are closely related to people’s cognitive level and understanding level. For example, when only time-averaged
changes are needed, the Reynolds time-averaged equations (RANS) can be
used to solve them; if large-scale turbulence structure is needed, LEM (Large
Eddy Simulation) is developed; and if all information of turbulent flow field
is needed, the direct numerical simulation technique of full-scale turbulent
motion must be developed from the instantaneous N-S equation. The three
simulation techniques have different resolutions to the flow field and different
turbulence scales. Generally speaking, direct numerical simulation requires
the simulation of turbulence components at all scales, ranging from the
minimum scale to the dissipative scale, which is equivalent to the Re number
of the grid approaching 1.0. In Reynolds time-averaged method, turbulence
fluctuation components are closed by a statistical turbulence model, and
the grid scale of numerical simulation can be determined by the nature of
the time-averaged flow. Large eddy simulation (LES) technology can simulate large-scale turbulence component because the grid scale is above the
inertial sub-region and the dissipative scale component is replaced by the
modeling equation. Direct numerical simulation technology was developed
in the 1970s. Orzag and Patterson (1972) were the first to use direct numerical simulation to calculate isotropic turbulence with only 32 3 meshes and
the corresponding Reynolds number is Re λ = 35. On the contrary, the
experimental measurements can only obtain limited flow field information,
including finite scale turbulence components. For example, the vorticity
distribution in the turbulent flow field is difficult to measure. So far, the
development and evolution of turbulent vorticity structure can only be quantitatively observed by flow visualization or numerical simulation. Direct
numerical simulation is an effective tool for studying the mechanism of
turbulence and controlling turbulence (as shown in Fig. 1.84). The database
of direct numerical simulation can also be used to evaluate the existing
turbulence model, and then study the way to improve the turbulence model.
It has been found that in turbulent motion, besides many small-scale
vortices with strong randomness, there are also some large-scale vortices with
good organization. They have a relatively regular vortices’ structure. Their
shape and scale are of universal significance for the same type of turbulent
motion. They play an important role in the turbulent Reynolds stress and the
turbulent transport process of various physical quantities. For this reason, the