Date of Award

3-2020

Document Type

Dissertation - Open Access

Degree Name

Doctor of Philosophy in Mechanical Engineering

Department

College of Engineering

Committee Chair

Dr. Yongho Lee

First Committee Member

Dr. Eduardo Diva

Second Committee Member

Dr. William Engblom

Third Committee Member

Dr. Bertrand Rollin

Fourth Committee Member

Dr. Birce Dikici

Abstract

The hydrodynamic instability of purely oscillating pipe flows is investigated in terms of the quasi-steady formulation assuming the temporal changes of the laminar base flow relative to disturbances are slow. A simple model equation is introduced to compare the exact solution of the current approach with those of the major theories dedicated for unsteady flows. The results of the analysis show that the quasi-steady assumption and the multiple scales method are more efficient and accurate than the formal Floquet theory in predicting the transient instabilities within a period in addition to the long-term growth or decay of disturbances. The most significant contribution of the present quasi-steady analysis is the neutral stability curves, from which the critical Reynolds numbers are obtained for a wide range of oscillation frequencies. The stability criterion pertains to the cycle-averaged growth rates obtained from the eigenvalues of the parametric stability problem. Moreover, the approximate accuracy of the quasi-steadiness is assessed by proposing a new mathematical relation, confirming the validity of the method for the stability analysis. The theoretical findings are consistent with some experimental results although some others show quantitative discrepancies, which can be attributed mostly to the deviations in the second spatial derivative of base flow.

In the computational analyses of this research, direct numerical simulations (DNS) based on the spectral element method are performed to verify the theoretical predictions and to accurately examine the transition to turbulence. The onset of transition in smooth pipe, identified as a disturbed laminar flow after imposing small random perturbations as initial conditions, qualitatively agrees with that estimated by the quasi-steady theory. The later transition stage at which the turbulence and relaminarization phenomena first emerge is detected from the high-amplitude velocity fluctuations. The turbulence intensity increases with the Stokes number proportional to oscillation frequency. Furthermore, surface roughness constructed utilizing the overset-grid technique is also considered as the triggering mechanism to induce transition and turbulence with small wavy imperfections distributed along the inner wall of a pipe. The influence of the surface roughness on flow stability is evaluated and the critical Reynolds number is close to that of the smooth pipe unless the roughness height is large. The friction coefficients at a few flow conditions for both smooth and rough pipes are determined according to the maximum values of the wall shear stress and found to be compatible with those shown by experiments in the literature.

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