AMESim(CFD一维气体动力学库)(3)

Figure 6: relationship between s and aA on a-s diagram

When the flow is homentropic (uniform and constant entropy), λin, λout are constant on the characterictics defined as

and

dx

=u+a dx

=u a respectively. In that case, λin, λout are called Riemann invariants. The characteristic for λin is shown in Figure 7 in the space-time plane at pipe end, node N.

n-1

Figure 7: characteristics for λin in case of homentropic flow

Since λin is constant along its characteristic,

n+1in,N

λ

n=λin,L.

In the case of non-homentropic flow, the computation of λin includes pipe wall friction, heat transfer, change in the cross-section and change in entropy level. The entropy level at pipe end and the computation of λout depend on the boundary conditions that are applied there.

A description of the different boundary conditions that are used in the CFD 1D Gas Dynamics library (connection with a volume, sudden geometry change between two pipes, multi pipe junction…) can be found in [1].

4. CFD 1D Gas Dynamics library components

4.1. Pipes

The user has access to 4 different components to describe the flow in straight and bent pipes.

The pipes are characterized by their geometry (diameters, length, curvature radius and angle) and the surface roughness which is used to calculate the friction.

The pipe components without a thermal port use a constant wall temperature which is used to simulate the gas/wall convection heat exchanges. A specific gain can be applied to the calculated heat flux. With a gain equal to zero, one has access to adiabatic conditions.

The components with a thermal port can be used to model wall capacity and the heat exchanges between the wall and the surrounding with a dedicated model (thermal library).

The user has two possibilities to get access to variables calculated in the pipe:

The sensor

In every component, a sensor is integrated that makes it possible to observe the flow variables (static and total pressure, temperature, velocity, density, mass flow rate, Mach number) in the pipe at a particular location defined by the user. When a signal port is available, then these variables can be used for post-processing or control purposes. Variables at sensor are computed by the linear interpolation of variables at the cell-centers except for pipe ends where the values at end cell center are given.

The 1D variables (post-processing)

The user can observe the flow field in the pipe using the 1D plot feature. Independently of the calculation mesh for the 1D solver, an integer parameter for number of cells for 1D plot must be set by the user to define the format of the plots. Parameter number of cells for 1D plot is the number of cell centers to be used for the visualization of the flow with 1D plot. Those points are uniformly distributed over the interval defined by the first and the last centers of calculation cells. At the visualization points, variables are determined by linear interpolation. A high number of points will give detailed results but large results files. In the example, 20 points are generated:

We can display the temporal plot by doing a drag and drop of the vector static pressure [1..20] which produces the following graph:

But we can also use the 1D plot from the contextual view, doing a right click on the same variable and selecting plot 1D. Using the slider in the tool bar allows us to follow the evolution of the pressure field: