Lie groups of variable cross-section channel flow
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
This paper considers Lie groups of scaling transformations for the system of equations governing inviscid, compressible, quasi-one dimensional (quasi-1D) fluid flow in channels with variable cross-section. We determine the coupling between the admissibility of the group transformations and the equation of state (EOS) model used to close the system as well as the spatial and temporal dependence of the channel cross-section. The results presented extend prior group analysis performed in Ovsiannikov and Boyd et al. on the equations of gas dynamics for 1D flow. In the context of channel flow, the analysis in Ovsiannikov and Boyd et al. is only applicable for a very limited scope of channels, namely for channels possessing planar, cylindrical and spherical symmetry where the flow is truly 1D. To illustrate the extension achieved using the quasi-1D model, we consider the classical Noh problem set up in a channel with a variable area cross-section. First, a new set of canonical variables are derived using the admissible scaling transformations. Then, by re-expressing the governing equations of motion in terms of the new variables, a solvable system of ordinary differential equations (ODEs) is acquired. The resulting explicit solutions of the problem extend the previous results of Ramsey et al. to solutions of the Noh problem for quasi-1D flow.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- DOE Contract Number:
- 89233218CNA000001
- OSTI ID:
- 1523203
- Report Number(s):
- LA-UR-19-24724
- Country of Publication:
- United States
- Language:
- English
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