Evidence for transient disturbance growth in a 1961 pipe-flow experiment

Mayer, Ernst W.; Reshotko, Eli

doi:10.1063/1.869167

Cited by 18 publications

(10 citation statements)

References 14 publications

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“…In pipe Poiseuille flow, Bergström (1995) found experimental evidence for a transient disturbance development. By re-exploring data from Kaskel's (1961) pipe-flow experiment, Mayer & Reshotko (1997) also found evidence of a transient disturbance amplification in pipe Poiseuille flow.…”

Section: Introductionmentioning

confidence: 91%

The initial-value problem for three-dimensional disturbances in plane Poiseuille flow of helium II

Bergström

2008

J. Fluid Mech.

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The time development of small three-dimensional disturbances in plane Poiseuille flow of helium II is considered. The study is conducted by considering the interaction of a normal fluid field and a superfluid field. The interaction is caused by a mutual friction forcing between the two flow fields. Specifically, the stability of the normal fluid affected by the mutual forcing is considered. Compared to the ordinary fluid case where the mutual forcing is not present, the presence of the mutual forcing implies a substantial increase of the transient growth of the disturbances. The increase of the transient growth occurs because the mutual forcing reduces the damping of the disturbances. The phase of transient growth becomes thereby more prolonged and higher levels of amplification are reached. There is also a minor effect on the transient growth caused by the modification of the mean flow owing to the mutual forcing. The strongest transient growth occurs for streamwise elongated disturbances, i.e. disturbances with streamwise wavenumber α = 0. When α increases beyond zero, the transient amplification quickly becomes reduced. Striking differences compared to the ordinary fluid case are that the largest transient amplification does not occur when the spanwise wavenumber (β) is close to two and that the peak level of the disturbance energy density amplification does not depend on the square of the Reynolds number.

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Section: Introductionmentioning

confidence: 91%

The initial-value problem for three-dimensional disturbances in plane Poiseuille flow of helium II

Bergström

2008

J. Fluid Mech.

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“…Substantially fewer studies have been experimental. The earliest experimental results have been reported by Mayer & Reshotko [19], who observed transient growth of disturbance amplitudes in a pipe flow experiment. The formation of streaky structures (i.e., streamwise elongated regions of high and low velocities) in boundary layers, which can be attributed to the non-normal nature of the linearized system, is another example of experimental evidence for transient growth [20].…”

Section: Introductionmentioning

confidence: 99%

Experimental Investigation of Non-Normality of Thermoacoustic Interaction in an Electrically Heated Rijke Tube

Mariappan

Sujith

Schmid

2015

International Journal of Spray and Combustion Dynamics

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An experimental investigation of the non-normal nature of thermoacoustic interactions in an electrically heated horizontal Rijke tube is performed. Since non-normality and the associated transient growth are linear phenomena, the experiments have to be confined to the linear regime. The bifurcation diagram for the subcritical Hopf bifurcation into a limit cycle behavior has been determined, after which the amplitude levels, for which the system acts linearly, have been identified for different power inputs to the heater. There are two main objectives for this experimental investigation. The first one deals with the extraction of the linear eigenmodes associated with the acoustic pressure from experimental data. This is accomplished by the Dynamic Mode Decomposition (DMD) technique applied in the linear regime. The nonorthogonality between the eigenmodes is determined for various values of heater power. The second objective is to identify evidence of transient perturbation growth in the system. The total acoustic energy in the duct has been monitored as the thermoacoustic system evolves from its initial condition. Transient growth, on the order of previous theoretical studies, has been found, and its parameteric dependence on amplitude ratio and phase angle of the initial eigenmode components has been determined. This study represents the first experimental confirmation of non-normality in thermoacoustic systems.

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“…An overview of recent work can be found in review articles (Trefethen et al 1993;Henningson 1995). Experiments and numerical simulations indicate that transient growth mechanisms play a fundamental role in the initial stages of transition in channel and pipe flows (Klingmann 1992;Schmid & Henningson 1992;Henningson, Lundbladh & Johansson 1993;Mayer & Reshotko 1997).…”

Section: Introductionmentioning

confidence: 99%

On stability of streamwise streaks and transition thresholds in plane channel flows

et al. 1998

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Streak breakdown caused by a spanwise inflectional instability is one phase of the following transition scenarios, which occur in plane Poiseuille and Couette flow. The streamwise vortex scenario is described by (SV) streamwise vortices =⇒ streamwise streaks =⇒ streak breakdown =⇒ transition.The oblique wave scenario is described by (OW) oblique waves =⇒ streamwise vortices =⇒ streamwise streaks =⇒ streak breakdown =⇒ transition.The purpose of this paper is to investigate the streak breakdown phase of the above scenarios by a linear stability analysis and compare threshold energies for transition for the above scenarios with those for transition initiated by Tollmien-Schlichting waves (TS), two-dimensional optimals (2DOPT), and random noise (N) at subcritical Reynolds numbers. We find that if instability occurs, it is confined to disturbances with streamwise wavenumbers α 0 satisfying 0 < α min < |α 0 | < α max . In these unstable cases, the least stable mode is located near the centre of the channel with a phase velocity approximately equal to the centreline velocity of the mean flow. Growth rates for instability increase with streak amplitude. For Couette flow streak breakdown is inhibited by mean shear. Using the linear stability analysis, we determine lower bounds on threshold amplitude for transition for scenario (SV) that are consistent with thresholds determined by direct numerical simulations.In the final part of the paper we show that the threshold energies for transition in Poiseuille flow at subcritical Reynolds numbers for scenarios (SV) and (OW) are two orders of magnitude lower than the threshold for transition initiated by Tollmien-Schlichting waves (TS) and an order of magnitude lower than that for (2DOPT). Scenarios (SV) and (OW) occur on a viscous time scale. However, even when transition times are taken into account, the threshold energy required for transition at a given time for (SV) and (OW) is lower than that for the (TS) and (2DOPT) scenarios at Reynolds number 1500.

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Evidence for transient disturbance growth in a 1961 pipe-flow experiment

Cited by 18 publications

References 14 publications

The initial-value problem for three-dimensional disturbances in plane Poiseuille flow of helium II

The initial-value problem for three-dimensional disturbances in plane Poiseuille flow of helium II

Experimental Investigation of Non-Normality of Thermoacoustic Interaction in an Electrically Heated Rijke Tube

On stability of streamwise streaks and transition thresholds in plane channel flows

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