Bryce Campbell | Massachusetts Institute of Technology (MIT) (original) (raw)
Papers by Bryce Campbell
This work considers the role of nonlinear sub-harmonic resonant wave interactions in the developm... more This work considers the role of nonlinear sub-harmonic resonant wave interactions in the development of interfacial waves, which may be under the influence of a linear interfacial instability, in an inviscid two-fluid stratified flow through a horizontal channel. We begin by examining the case of resonant interactions between one linearly unstable mode and its sub-harmonic that may be linearly stable or unstable. Using the method of multiple scales, we derive the nonlinear interaction equations governing the time evolution of interacting wave amplitudes. These nonlinear equations account for the combined effects of both the nonlinear resonant interaction and the linear instability. We show that through this nonlinear coupling, the linearly stable sub-harmonic mode can achieve faster than exponential growth. It is found that such a mechanism is capable of generating large-amplitude long waves that are stable by linear stability analysis. The analytical predictions are cross validated by comparisons with direct nonlinear numerical simulations based on a more general perturbation based spectral method. Good agreement between the analytical and numerical solutions is observed. The more complicated case where a single mode is simultaneously involved in multiple (sub-harmonic and triad) resonances is also investigated numerically. The results demonstrate that chains of resonances can permit the energy generated by the linear instability, among high wavenumber components, to be passed across the spectrum to the longest wave components creating an efficient mechanism for the generation of large-amplitude long waves from unstable short waves.
This work considers the role of nonlinear sub-harmonic resonant wave interactions in the developm... more This work considers the role of nonlinear sub-harmonic resonant wave interactions in the development of interfacial waves, which may be under the influence of a linear interfacial instability, in an inviscid two-fluid stratified flow through a horizontal channel. We begin by examining the case of resonant interactions between one linearly unstable mode and its sub-harmonic that may be linearly stable or unstable. Using the method of multiple scales, we derive the nonlinear interaction equations governing the time evolution of interacting wave amplitudes. These nonlinear equations account for the combined effects of both the nonlinear resonant interaction and the linear instability. We show that through this nonlinear coupling, the linearly stable sub-harmonic mode can achieve faster than exponential growth. It is found that such a mechanism is capable of generating large-amplitude long waves that are stable by linear stability analysis. The analytical predictions are cross validated by comparisons with direct nonlinear numerical simulations based on a more general perturbation based spectral method. Good agreement between the analytical and numerical solutions is observed. The more complicated case where a single mode is simultaneously involved in multiple (sub-harmonic and triad) resonances is also investigated numerically. The results demonstrate that chains of resonances can permit the energy generated by the linear instability, among high wavenumber components, to be passed across the spectrum to the longest wave components creating an efficient mechanism for the generation of large-amplitude long waves from unstable short waves. C 2014 AIP Publishing LLC. [http://dx.The prediction of the formation of slugs in pipes is of critical importance in many practical applications such as in the transport of complex multi-component fluids through oil pipelines. The presence of slugs in the pipeline can lead to pipe fatigue, complications in the separation of the flow into its constitutive components, and reduction in pipeline efficiency. This has motivated the development of various flow transition criteria for the prediction of the formation of slug flow. Traditionally these models are based on the Kelvin-Helmholtz instability and are supplemented with additional models to account for more complex physics such as interfacial and wall friction, 5, 6 normal viscous stresses, 7 and heuristic corrections which are presumed to account for the effects of nonlinearity. 8 A survey of several different transition methods and models was presented by Mata et al. By basing the slug transition criteria on linear instability theory, the possibility of modal energy transfer across time/length scales is prohibited and requires the use of nonlinear methods. The idea of resonant interaction theory 10 provides a simple nonlinear framework for accounting for important nonlinear wave-wave interactions in surface/interfacial wave-field development. Through the use of regular perturbation analysis, the initial growth rate and rate of energy transfer between different wave components can be analytically determined. 11 For long-time and/or large-distance interactions, the analysis based on the use of multiple scales is usually applied.
Journal of Fluid Mechanics, 2013
We consider the problem of nonlinear resonant interactions of interfacial waves with the presence... more We consider the problem of nonlinear resonant interactions of interfacial waves with the presence of a linear interfacial instability in an inviscid two-fluid stratified flow through a horizontal channel. The resonant triad consists of a (linearly) unstable wave and two stable waves, one of which has a wavelength that can be much longer than that of the unstable component. Of special interest is the development of the long wave by energy transfer from the base flow due to the coupled effect of nonlinear resonance and interfacial instability. By use of the method of multiple scales, we derive the interaction equations which govern the time evolution of the amplitudes of the interacting waves including the effect of interfacial instability. The solution of the evolution equations shows that depending on the flow conditions, the (stable) long wave can achieve a bi-exponential growth rate through the resonant interaction with the unstable wave. Moreover, the unstable wave can grow unboundedly even when the nonlinear self-interaction effect is included, as do the stable waves in the associated resonant triad. For the verification of the theoretical analysis and the practical application involving a broadbanded spectrum of waves, we develop an effective direct simulation method, based on a high-order pseudo-spectral approach, which accounts for nonlinear interactions of interfacial waves up to an arbitrary high order. The direct numerical simulations compare well with the theoretical analysis for all of the characteristic flows considered, and agree qualitatively with the experimental observation of slug development near the entrance of two-phase flow into a pipe.
Volume 5: Polar and Arctic Sciences and Technology; CFD and VIV, 2009
The objective of this study is to understand the effects of nonlinearity on the interfacial stabi... more The objective of this study is to understand the effects of nonlinearity on the interfacial stability of a two fluid stratified flow through a horizontal channel. An efficient perturbation expansion based high-order spectral method is developed, for the simulation of the generation and nonlinear evolution of interfacial waves. The method is capable of accounting for the nonlinear interactions of a large number of wave components in a broadband spectrum, and obtains an exponential convergence of the solution with grid refinement and interaction order. The method is applied to investigate the role that nonlinear effects have on the initial development of Kelvin-Helmholtz (KH) instabilities and nonlinear wave-wave interactions with the purpose of gaining insight into the physical mechanisms which cause slug flow. It will also be demonstrated that nonlinearity can introduce unstable interfacial wave growth in regions predicted to be stable by linear analysis. In addition, it is shown that energy transfer from short (KH unstable) waves to long (KH stable) waves due to nonlinear resonant wave-wave interactions is an effective mechanism for the development of slug flow.
Offshore Technology Conference, 2013
Two-phase flows in channels and pipelines involve complex multiscale dynamical processes such as ... more Two-phase flows in channels and pipelines involve complex multiscale dynamical processes such as interfacial wave growth due to flow instabilities, wave breaking and mixing, violent slugging, etc. This work describes a collection of three efficient, and physics-based, complementary numerical techniques that are developed to effectively address these nonlinear processes at different scales. In particular, these algorithms are used to study nonlinear interfacial wave interaction effects on flow transition and to develop physics-based turbulence closure models for simulating mixing and slug flows.
This work considers the role of nonlinear sub-harmonic resonant wave interactions in the developm... more This work considers the role of nonlinear sub-harmonic resonant wave interactions in the development of interfacial waves, which may be under the influence of a linear interfacial instability, in an inviscid two-fluid stratified flow through a horizontal channel. We begin by examining the case of resonant interactions between one linearly unstable mode and its sub-harmonic that may be linearly stable or unstable. Using the method of multiple scales, we derive the nonlinear interaction equations governing the time evolution of interacting wave amplitudes. These nonlinear equations account for the combined effects of both the nonlinear resonant interaction and the linear instability. We show that through this nonlinear coupling, the linearly stable sub-harmonic mode can achieve faster than exponential growth. It is found that such a mechanism is capable of generating large-amplitude long waves that are stable by linear stability analysis. The analytical predictions are cross validated by comparisons with direct nonlinear numerical simulations based on a more general perturbation based spectral method. Good agreement between the analytical and numerical solutions is observed. The more complicated case where a single mode is simultaneously involved in multiple (sub-harmonic and triad) resonances is also investigated numerically. The results demonstrate that chains of resonances can permit the energy generated by the linear instability, among high wavenumber components, to be passed across the spectrum to the longest wave components creating an efficient mechanism for the generation of large-amplitude long waves from unstable short waves.
This work considers the role of nonlinear sub-harmonic resonant wave interactions in the developm... more This work considers the role of nonlinear sub-harmonic resonant wave interactions in the development of interfacial waves, which may be under the influence of a linear interfacial instability, in an inviscid two-fluid stratified flow through a horizontal channel. We begin by examining the case of resonant interactions between one linearly unstable mode and its sub-harmonic that may be linearly stable or unstable. Using the method of multiple scales, we derive the nonlinear interaction equations governing the time evolution of interacting wave amplitudes. These nonlinear equations account for the combined effects of both the nonlinear resonant interaction and the linear instability. We show that through this nonlinear coupling, the linearly stable sub-harmonic mode can achieve faster than exponential growth. It is found that such a mechanism is capable of generating large-amplitude long waves that are stable by linear stability analysis. The analytical predictions are cross validated by comparisons with direct nonlinear numerical simulations based on a more general perturbation based spectral method. Good agreement between the analytical and numerical solutions is observed. The more complicated case where a single mode is simultaneously involved in multiple (sub-harmonic and triad) resonances is also investigated numerically. The results demonstrate that chains of resonances can permit the energy generated by the linear instability, among high wavenumber components, to be passed across the spectrum to the longest wave components creating an efficient mechanism for the generation of large-amplitude long waves from unstable short waves. C 2014 AIP Publishing LLC. [http://dx.The prediction of the formation of slugs in pipes is of critical importance in many practical applications such as in the transport of complex multi-component fluids through oil pipelines. The presence of slugs in the pipeline can lead to pipe fatigue, complications in the separation of the flow into its constitutive components, and reduction in pipeline efficiency. This has motivated the development of various flow transition criteria for the prediction of the formation of slug flow. Traditionally these models are based on the Kelvin-Helmholtz instability and are supplemented with additional models to account for more complex physics such as interfacial and wall friction, 5, 6 normal viscous stresses, 7 and heuristic corrections which are presumed to account for the effects of nonlinearity. 8 A survey of several different transition methods and models was presented by Mata et al. By basing the slug transition criteria on linear instability theory, the possibility of modal energy transfer across time/length scales is prohibited and requires the use of nonlinear methods. The idea of resonant interaction theory 10 provides a simple nonlinear framework for accounting for important nonlinear wave-wave interactions in surface/interfacial wave-field development. Through the use of regular perturbation analysis, the initial growth rate and rate of energy transfer between different wave components can be analytically determined. 11 For long-time and/or large-distance interactions, the analysis based on the use of multiple scales is usually applied.
Journal of Fluid Mechanics, 2013
We consider the problem of nonlinear resonant interactions of interfacial waves with the presence... more We consider the problem of nonlinear resonant interactions of interfacial waves with the presence of a linear interfacial instability in an inviscid two-fluid stratified flow through a horizontal channel. The resonant triad consists of a (linearly) unstable wave and two stable waves, one of which has a wavelength that can be much longer than that of the unstable component. Of special interest is the development of the long wave by energy transfer from the base flow due to the coupled effect of nonlinear resonance and interfacial instability. By use of the method of multiple scales, we derive the interaction equations which govern the time evolution of the amplitudes of the interacting waves including the effect of interfacial instability. The solution of the evolution equations shows that depending on the flow conditions, the (stable) long wave can achieve a bi-exponential growth rate through the resonant interaction with the unstable wave. Moreover, the unstable wave can grow unboundedly even when the nonlinear self-interaction effect is included, as do the stable waves in the associated resonant triad. For the verification of the theoretical analysis and the practical application involving a broadbanded spectrum of waves, we develop an effective direct simulation method, based on a high-order pseudo-spectral approach, which accounts for nonlinear interactions of interfacial waves up to an arbitrary high order. The direct numerical simulations compare well with the theoretical analysis for all of the characteristic flows considered, and agree qualitatively with the experimental observation of slug development near the entrance of two-phase flow into a pipe.
Volume 5: Polar and Arctic Sciences and Technology; CFD and VIV, 2009
The objective of this study is to understand the effects of nonlinearity on the interfacial stabi... more The objective of this study is to understand the effects of nonlinearity on the interfacial stability of a two fluid stratified flow through a horizontal channel. An efficient perturbation expansion based high-order spectral method is developed, for the simulation of the generation and nonlinear evolution of interfacial waves. The method is capable of accounting for the nonlinear interactions of a large number of wave components in a broadband spectrum, and obtains an exponential convergence of the solution with grid refinement and interaction order. The method is applied to investigate the role that nonlinear effects have on the initial development of Kelvin-Helmholtz (KH) instabilities and nonlinear wave-wave interactions with the purpose of gaining insight into the physical mechanisms which cause slug flow. It will also be demonstrated that nonlinearity can introduce unstable interfacial wave growth in regions predicted to be stable by linear analysis. In addition, it is shown that energy transfer from short (KH unstable) waves to long (KH stable) waves due to nonlinear resonant wave-wave interactions is an effective mechanism for the development of slug flow.
Offshore Technology Conference, 2013
Two-phase flows in channels and pipelines involve complex multiscale dynamical processes such as ... more Two-phase flows in channels and pipelines involve complex multiscale dynamical processes such as interfacial wave growth due to flow instabilities, wave breaking and mixing, violent slugging, etc. This work describes a collection of three efficient, and physics-based, complementary numerical techniques that are developed to effectively address these nonlinear processes at different scales. In particular, these algorithms are used to study nonlinear interfacial wave interaction effects on flow transition and to develop physics-based turbulence closure models for simulating mixing and slug flows.