### Abstract

Linear stability analysis is a tool used to help identify the sensitivity of a particular domain to perturbations and evaluate the system dynamics as a transition, if any, occurs. The development of a time invariant base flow for future use in a linear stability analysis is the focus of this investigation. A test case, with a Reynolds number of 100, was brought to a steady state using the spectral element code NekSOOO and the method of selective frequency damping. The convergence criteria for this method is the volume averaged value of the forcing function which, after approximately 80,000 time-steps, decreased to 3.6^{∗}10. Analysis shows that the case has yet to have reached the tolerance desired, 1 × 10^{-6}, With the simulation in the process of converging a preliminary perturbation analysis was conducted. Due to the low Reynolds number of this case, 100, it was hypothesized that the flow would be linearly stable. This preliminary stability analysis only focused on the largest fundamental mode and the energy growth ofthat perturbation over time. Upon evaluation of the perturbation energy, which was shown to be monotonicaiiy decreasing in time, it was concluded that, despite not yet being converged, the system is in fact linearly stable. Future work includes evaluating the domain at higher Reynolds numbers, solving the eigenvalue problem created when the linearized Navier-Stokes are written in operator form and calculating the energy evolution of the optimal perturbation.

Original language | English (US) |
---|---|

Pages (from-to) | 1435-1438 |

Number of pages | 4 |

Journal | Transactions of the American Nuclear Society |

Volume | 115 |

State | Published - Jan 1 2016 |

Event | 2016 Transactions of the American Nuclear Society, ANS 2016 - Las Vegas, United States Duration: Nov 6 2016 → Nov 10 2016 |

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### All Science Journal Classification (ASJC) codes

- Nuclear Energy and Engineering
- Safety, Risk, Reliability and Quality

### Cite this

*Transactions of the American Nuclear Society*,

*115*, 1435-1438.

}

*Transactions of the American Nuclear Society*, vol. 115, pp. 1435-1438.

**Toward linear stability analysis of upper plenum flows.** / Mulloy, John; Merzari, Elia; Marin, Oana; Hassan, Yassin.

Research output: Contribution to journal › Conference article

TY - JOUR

T1 - Toward linear stability analysis of upper plenum flows

AU - Mulloy, John

AU - Merzari, Elia

AU - Marin, Oana

AU - Hassan, Yassin

PY - 2016/1/1

Y1 - 2016/1/1

N2 - Linear stability analysis is a tool used to help identify the sensitivity of a particular domain to perturbations and evaluate the system dynamics as a transition, if any, occurs. The development of a time invariant base flow for future use in a linear stability analysis is the focus of this investigation. A test case, with a Reynolds number of 100, was brought to a steady state using the spectral element code NekSOOO and the method of selective frequency damping. The convergence criteria for this method is the volume averaged value of the forcing function which, after approximately 80,000 time-steps, decreased to 3.6∗10. Analysis shows that the case has yet to have reached the tolerance desired, 1 × 10-6, With the simulation in the process of converging a preliminary perturbation analysis was conducted. Due to the low Reynolds number of this case, 100, it was hypothesized that the flow would be linearly stable. This preliminary stability analysis only focused on the largest fundamental mode and the energy growth ofthat perturbation over time. Upon evaluation of the perturbation energy, which was shown to be monotonicaiiy decreasing in time, it was concluded that, despite not yet being converged, the system is in fact linearly stable. Future work includes evaluating the domain at higher Reynolds numbers, solving the eigenvalue problem created when the linearized Navier-Stokes are written in operator form and calculating the energy evolution of the optimal perturbation.

AB - Linear stability analysis is a tool used to help identify the sensitivity of a particular domain to perturbations and evaluate the system dynamics as a transition, if any, occurs. The development of a time invariant base flow for future use in a linear stability analysis is the focus of this investigation. A test case, with a Reynolds number of 100, was brought to a steady state using the spectral element code NekSOOO and the method of selective frequency damping. The convergence criteria for this method is the volume averaged value of the forcing function which, after approximately 80,000 time-steps, decreased to 3.6∗10. Analysis shows that the case has yet to have reached the tolerance desired, 1 × 10-6, With the simulation in the process of converging a preliminary perturbation analysis was conducted. Due to the low Reynolds number of this case, 100, it was hypothesized that the flow would be linearly stable. This preliminary stability analysis only focused on the largest fundamental mode and the energy growth ofthat perturbation over time. Upon evaluation of the perturbation energy, which was shown to be monotonicaiiy decreasing in time, it was concluded that, despite not yet being converged, the system is in fact linearly stable. Future work includes evaluating the domain at higher Reynolds numbers, solving the eigenvalue problem created when the linearized Navier-Stokes are written in operator form and calculating the energy evolution of the optimal perturbation.

UR - http://www.scopus.com/inward/record.url?scp=85033241661&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85033241661&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:85033241661

VL - 115

SP - 1435

EP - 1438

JO - Transactions of the American Nuclear Society

JF - Transactions of the American Nuclear Society

SN - 0003-018X

ER -