AMESim(CFD一维气体动力学库)(2)

The parameters for the left-hand-side source are shown below:

In the figure that follows, we present the parameters for the pipe:

The parameters of the pipe make it possible to set geometry features, initial conditions, sensor position, numerical parameters and useful information for the visualization tool. The details of these parameters will be presented later in the document.

The gas state in the right-hand-side source is the same as in the pipe:

Now, let’s go to the Simulation mode .

The Run parameters for our example are as follows:

Let us mention here that the AMESim fixed step integrator is a priori not compatible with the use of the CFD1D library. Although it may be useful to consider using it in very specific settings, do not use it unless you know exactly what you are doing.

. Then plot the variables in the system and Run the simulation by clicking on the icon

use the visualization tools. For instance, the static pressure at sensor can be displayed:

By default, the plots are generated using time for the X-axis (temporal evolution). However you can also plot the 1D variables as a function of distance and time. This is useful for getting a comprehensive understanding of the flow characteristics. In the example below, we used the plot 1D feature to observe the velocity in the pipe:

In this case, a slider located in the tool bar makes it possible to follow the evolution of the variable as a function of the time.

There is no interpolation of the flow variables in the pipe between two synchronization times (exchange of data between the standard AMESim solver and the 1D solver). As a consequence, we can observe the discrete state when displaying the variables in the system if the communication interval is smaller than the synchronization time. For instance, if the communication interval (Run

Parameters) is set to 10

6

seconds in our example, the following static pressure

at sensor can be observered on the time interval

[0,0.5 10]s:

3

It is also possible to graphically output variables at all CFD integration times through the ‘discontinuities printout’ option in the Run Parameters window:

3. Modeling the gas flow

3.1. Flow variables

The gas inside the pipe is characterized by its density ρ, its static pressure p and its velocity u. When the gas is composed of different species (like in IFP-Engine and IFP-Exhaust libraries), a vector of mass fraction χ is also considered. Each component i of the vector is defined as

χi=

ρρ

,

where ρi is the density of the considered species.

We have: and

0≤χi≤1

∑χ

i

i

=1, =ρ.

since

∑ρ

i

i

The temperature T of the gas is a function of p, ρ andχ. That function depends on the gas property model that is chosen.

The pipe section S can vary as a function of the curvilinear abscissa x, the associated diameter D is defined as

D=2

π

.

3.2. Governing equations

The retained equations that describe the dynamic of the fluid in the pipe are the following ones:

The continuity equation for each species i in conservative law form

The momentum equation in conservative law form

ρS ρuS

=0 +

The total energy equation in conservative law form

ρuS ρu2+pS S1

+ p+fuρu=0 ρES (ρE+p)uS

+ 2hc(Twall T=0. 1

E=cvT+u2,

2

()

In these equations, Twall is the pipe wall temperature, E is the specific total energy defined as

where cv is the specific heat at constant volume.

The friction coefficient f depends on the roughness cr and on Reynold’s number Re defined as:

Re=

ρDu

, µ

where µ is the dynamic viscosity of the fluid.

The convective heat transfer coefficient hc is defined as

hc=Nu

λ

where λ is the heat transfer coefficient and Nu Nusselt’s number depending on Re ,f, cr and Prandtl’s number Pr which is defined as

,

Pr=

µcp

. λ

cp is the specific heat at constant pressure.

The retained models for f and Nu will be presented further in the document.

3.3. Computation of friction term and Nusselt’s number

The friction coefficient is computed using the following formula based on Moody’s diagram

flif Re≤2000

f= (1 β)fl+βftif Re>2000 and Re≤6000,

ftelse

where

fl=

ft=

164

max 10, ,

1

2

cr/D 0.9 5.7416 log+Re

1 3+α2

+1β= α

+α

,

and

with

α=

Nusselt’s number is computed by using the following formula

Re1

.

40002

1

frRePrif Re≤3500

Nu= 9.2Re0.2if Re>3500 and Re≤7115,

0.07Re3/4else

fr=min(0.25,max(0.005,

16)). with

3.4. Numerical scheme

The governing equations can be written in symbolic vector form as:

with

W F

++C=0, 0 ρ1S ρ1uS

. 0W= ρNS , F= ρNuS and C=

S 2

ρpfuu + ρuS ρuS+pS ρES (ρE+p)Su 2()hTT cwall

The discretization of this system is done by dividing the pipe into N-1 cells of size x giving N

discretization nodes as shown in Figure 4.

Figure 4: pipe mesh

Variables are then estimated at the cell centers of the pipe. For this, the two step Lax-Wendroff scheme, proposed by Richtmyer and Morton [12] and modified by Bassett et al. [10] is use …… 此处隐藏：4914字，全部文档内容请下载后查看。喜欢就下载吧 ……