Part I: Inviscid, swirling flows and vortex breakdown. Part II: A numerical investigation of the Lundgren turbulence model

Citation

Buntine, James D. (1994) Part I: Inviscid, swirling flows and vortex breakdown. Part II: A numerical investigation of the Lundgren turbulence model. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/5rah-r125. https://resolver.caltech.edu/CaltechETD:etd-10182005-082716

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. Abstract for part I A study of the behaviour of an inviscid, swirling fluid is performed. This flow can be described by the Squire-Long equation if the constraints of time-independence and axisymmetry are invoked. The particular case of flow through a diverging pipe is selected and a study is conducted to determine over what range of parameters (both pipe inlet conditions and geometry) does a (unique) solution exist. The work is performed with a view to understanding how the phenomenon of vortex breakdown develops. Experiments and previous numerical studies have indicated that the flow is sensitive to boundary conditions particularly at the pipe inlet. A "quasi-cylindrical" simplification of the Squire-Long equation is compared with the more complete model and shown to be able to account for most of its behaviour. An advantage of this latter representation is the relatively undetailed description of the flow geometry it requires in order to calculate a solution. "Criticality" or the ability of small disturbances to propagate upstream is related to results of the quasi-cylindrical and axisymmetric flow models. This leads to an examination of claims made by researchers such as Benjamin and Hall concerning the interrelationship between "failure" of the quasi-cylindrical model and the occurrence of a "critical" flow state. Other criteria for predicting the onset of vortex breakdown are considered in the context of the model employed, particularly those of Brown & Lopez and Spall, Gatski & Grosch. Abstract for part II Lundgren (1982) developed an analytical model for homogeneous turbulence based on a collection of contracting spiral vortices each embedded in an axisymmetric strain field. Using asymptotic approximations he was able to deduce the Kolmogorov [...] behaviour for inertial scales in the turbulence energy spectrum. Pullin & Saffman have enlarged upon his work to make a number of predictions about the behaviour of turbulence described by the model. This work investigates the model numerically. The first part considers how the flow description compares with numerical simulations using the Navier-Stokes equations. Integration of the full expressions proposed by Lundgren for the energy spectrum is also performed to determine how the various parameters available affect the behaviour and validity of the result.

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