Solute Transport Process Modelling Flashcards
What is advection?
Advection is the bodily movement of a parcel of fluid resulting from an imposed current. Differential advection is when parcels of material in a flow experience different velocities, whether at different spatial positions or at the same location at different times. This differential advection produces a spreading that is commonly termed shear dispersion
What is diffusion?
Diffusion at a molecular scale is due to small scale localised fluctuations, the effect of Brownian motion. Often in environmental hydraulics problems, the effects of the fluctuations in flow velocity caused by turbulence are considered to produce a similar effect. However, the turbulence fluctuations are much greater than those of molecular Brownian motion and typically produce effects one million times greater. Molecular diffusion coefficients are a property of the fluid and of the order 10-10 to 10-9 m2/s.
Fick’s first law
The rate of transfer of tracer should be proportional to the concentration gradient between the two regions.
Turbulent flow
Characterised by random short term fluctuations. The most common flow type in environmental hydraulics. Re = 2000. Magnitude of mixing is 10-3 to 10-1 m2/s
Plot ±2sigmax on your concentration versus distance plot, and your cumulative area versus distance plot, what do you notice about the enclosed range?
Standard deviation (square root of variance), sigmax is used as a measure of the spread of a distribution. 4 times the standard deviation covers 95% of a Gaussian distribution.
Initial work predicting the effects of longitudinal dispersion on solutes was undertaken by G.I. Taylor (1953 & 1954) and this still forms the basis of many techniques used today to describe longitudinal dispersion. Briefly describe the major processes that are included in this analysis and the limitations when applying it to natural channels.
Initially Taylor looked at the effects of differential longitudinal advection, i.e. cross-sectional spatial variations in longitudinal velocity in laminar flow. This acted to spread material in the flow direction, i.e. longitudinally due to the advection or transport at different velocities. The only process opposing this in laminar flow is molecular diffusion, which acts to damp any cross-sectional concentration gradients. So in laminar flow conditions, transverse mixing is very small, being mainly due to molecular diffusion. As a result there is very little exchange between parcels of flow travelling at different longitudinal velocities, causing very large values of the longitudinal dispersion coefficient. Within turbulent flow the differential longitudinal velocities within the flow cross-section is the major process creating longitudinal dispersion. This acts to stretch or spread a tracer cloud and this is counter-acted by any transverse spreading. In turbulent flows this transverse spreading is caused by the turbulent fluctuations within the flow, is greater than in laminar flow and acts to redistribute material around the cross-section, reducing the impact of the longitudinal differential velocities. There is therefore an inverse relationship between the magnitude of the transverse mixing and the magnitude of the longitudinal dispersion coefficient. In turbulent flows the transverse mixing is orders of magnitude greater than for laminar flow and as a result the longitudinal dispersion is proportionally smaller.
More recent approaches have considered the effects of transient storage. What is “transient storage”? How does it influence spatial concentration distributions and how can the conventional advection-dispersion model be modified? Describe one practical example of where such processes might occur and explain how these may be included within a simulation technique.
Transient storage is the temporary detainment of solutes within the body of flowing water e.g. eddied and stagnant pockets of water, flow moving through the porous area of the streambd and banks. This is often described algebraically by introducing further parameters to the conventional 2 parameter ADE model. The additional parameters describe the transfer into and out of storage and may be exchange coefficients and or storage volume, depending on how the equations have been formulated. Two specific cases have been described in the seminars, either would answer the question: 1 surcharged manhole structure 2 river bed, boundary storage, hyporheic exchange
