文档介绍：Conservation Equations
pressible Turbulent
Flows
Introduction
In this chapter we consider the Navier-Stokes equations for pressible fluid
and show how they can be put into a form more convenient for turbulent flows.
We follow the procedure first introduced by Reynolds in pressible flows:
we regard the turbulent motion as consisting of the sum of the mean part
and a fluctuating part, introduce the sum into the Navier-Stokes equations,
and time I average the resulting expressions. The equations thus obtained give
considerable insight into the character of turbulent motions and serve as a basis
for attacking mean-flow problems, as well as for analyzing the turbulence to
find its ponents. However, before these governing conservation
equations pressible turbulent flows are obtained, it is appropriate to
write down the conservation equations for mass, momentum, and energy.
In the following sections we shall discuss the conservation equations and their
reduced forms in terms of rectangular coordinates, and for convenience we shall
use the summation notation. For a discussion of the conservation equations in
terms of another coordinate system, the reader is referred to [1].
The Navier-Stokes Equations
The well-known Navier-Stokes equations of motion for pressible, viscous,
heat-conducting, perfect gas may be written in the following form [2]:
Continuity
0Q 0
+ -5-:-(Ouj) = 0, ()
0--~ uxj
1 See Section for a discussion of various kinds of averaging.
32 2. Conservation Equations pressible Turbulent Flows
Momentum
0 0 OP l OTij , ()
Ot uxj Oxi Oxj
Energy
0 0 Op O
--Ot (QH) + __~x4(Quill) = --~ + ~xj (ujTij - qj) , ()
where the stress tensor Tij, heat-flux vector qj, and total enthalpy H are given
by
OUl Ouj) ()
Tij -- ASij ~x l + # Oxj + ~ '
OT
qj = -k~ ()
Oxj '
H = h + i . ()
In these equations, z~ is the bulk viscosity (= -2/3#), # the