Mathematica Notebooks for multifluid and multiphase flows
This notebook gives an introduction to multifluid flows by showing how the pressure drop changes significantly if the geometric configuration of the phases (the flow regime) is changed. Exact solutions for laminar flow in stratified, dispersed and alternating (slug) are used as a basis for the comparisons.
Effect of flow regime on pressure drop (PDF)
Effect of flow regime on pressure drop (Notebook format)
This one solves laminar channel flow over a wavy surface and calculates the pressure and shear stress fluctuations. The wavelength of the waves is long compared to the channel height and the amplitude of the wave is small compared to the wavelength and channel height so that the problem can be linearized and solved with a perturbation approach. The laminar flow solution is compared to a polynomial (turbulent) profile and results from a one-dimensional integral momentum equation approach for both turbulent and laminar flow. The overall motivation is for prediction and understanding of the growth of waves and flow regime transitions in gas-liquid flows
Shear and pressure fluctuations for channel flow over a wavy surface (PDF)
Shear and pressure fluctuations for channel flow over a wavy surface (Notebook format)
This one is a basic introduction to hydrodynamic stability and gives example calculations for a simple wave equation and the two-layer inviscid flow problem, the Kelvin-Helmholtz instability. A derivation of the Orr-Sommerfeld equation is also given.
Introduction to hydrodynamic stability (PDF, not the most recent version.)
Introduction to hydrodynamic stability (HTML Version; viewable, but a lot is lost in translation to HTML)
Introduction to hydrodynamic stability (Notebook format)
This one shows how to use a regular perturbation technique to solve an eigenvalue stability problem. The long wave, linear stability of pressure driven channel flow is solved.
Long wave linear stability (PDF)
Long wave linear stability (Notebook format)
This one is a basic introduction to using the Chebyshev-Tau Spectral numerical technique to solve ODE boundary-value problems and differential eigenvalue problems.
Numerical solution of ODE's and differential eigenvalue problems (PDF)
Numerical solution of ODE's and differential eigenvalue problems (Notebook format)
This one shows how to solve the linear stability of a channel flow using a Chebyshev-Tau Spectral technique.
Linear stability of pressure driven channel flow (PDF)
Linear stability of pressure driven channel flow (Notebook format)
This one solves the steady laminar flow of fluids of two different viscosities in the core-annular flow configuration. It is intended for beginning students as it shows the boundary conditions for a two-layer flow and how to find the flow rates. The mechanism of the lubrication and the scaling of the enhancement for a lubricating fluid are shown and the way that pressure drop decreases as the lubricating fluid flow rate is increased is also demonstrated.
Lubricated flow of a viscous liquid in a pipe (Mathematica 4 notebook)
Lubricated flow of a viscous liquid in a pipe (HTML)
This notebook looks at chemical reactions in a stirred tank reactor for single phase, liquid-solid and gas-liquid solid systems. For gas-liquid packed bed (a. k. a. "trickle - bed") reactors, flow disturbances cause fluctuations in the mass transfer rate. This notebook shows how these fluctuations can influence the reaction selectivity. The fluctuation (pulsing) frequency is seen to be a key variable. It uses the notation of and is based on R., M. J. McCready and A. Varma "Influence of mass transfer coefficient fluctuation frequency on performance of three-phase packed bed reactors, Chemical Engineering Science.,
Importance of mass transfer fluctuations on reaction outcome in multiphase reactors (Notebook Format)
Importance of mass transfer fluctuations on reaction outcome in multiphase reactors (html format -- it works but looses a lot.)