A tool for simulating fluid flows and processes
With the help of Computational Fluid Dynamics (CFD), ITT Water & Wastewater is able to offer a high level of accuracy in predicting hydraulic, and in some cases mass transfer, results.
Flow visualisation is used to translate vast quantities of data into an intelligible form. In most cases, time averages are considered, rather than snap-shots of an unsteady flow. To help evaluate and develop mixing solutions, visualisation is combined with analysis of critical parameters that relate to overall performance. Sometimes, however, it might be necessary to analyse the flow structure in more detail.
The CFD softwares used by ITT Water & Wastewater are being utilised in a wide range of industries such as automotive, aircraft, shipbuilding and space. Great care has been taken to ensure that the numerical simulations are consistent with the measurable, physical reality of mixing applications typical of our applications. Laboratory and full scale validation have proven the computational tools to be highly reliable.
Accuracy and interpretation of simulation
Turbulent flow simulation by CFD is associated with uncertainties based on the statistical nature of turbulence. Although the basic equations for fluid motion - commonly mass and momentum conservation equations - appear deterministic in nature, the extreme sensitivity to small scale phenomena makes it impossible to set up any specific simulation problem unless statistical data is used for surface roughnesses, inaccuracy in boundary and initial conditions, etc. It is a part of sound validation work to establish such data, and a part of sound skepticism to examine the sensitivity of results to variations in such parameters. The use of such data for new simulation projects will then be associated with confidence intervals, that can only be determined by a thorough characterization of the new tank walls etc., or by another complete experimental validation. However, experience will often allow an estimation of the uncertainty involved. This requires that no unknown extreme conditions prevail in the physical environment.
Furthermore, present-day computer capacity presupposes additional statistical simplification of the description of the turbulent part of the motion. At present, our industrial simulations adopt the method of Reynolds averaging and usually a special version of the so-called k-ε turbulence model, which has proven apt for these applications. It is recognized, that to resolve some specific turbulence fine-structure (anisotropy) in the most turbulent part of a mixer jet, another turbulence model or approach is needed. For the purpose of resolving the hydrodynamics relevant to the type of applications often dealt with by ITT Water & Wastewater, it is unnecessary to attempt such detailed analysis.
Although it is somewhat easier to consider just one or a few numbers for the assessment of system performance, it should be recognized that e.g. the spatial distribution of local mixing, in combination with bulk flow, needs to be taken into account for a correct analysis. Hence distribution diagrams are sometimes presented next to the usual graphical representations. However, average data expressed as numbers may also be used, as it may be used for case-by-case copmparison, or because of its relation to measurable quantities.
The quantity that is often the easiest to measure is the flow velocity u, in a specified set of measurement points. In the simple case of a channel flow, such as in oxidation ditches, measurement points in a cross section can be defined to best represent the whole cross section, and an average of the velocity across this section can be obtained to a high accuracy according to a standard technique. The same averaging can then be performed for velocity values obtained from small volume elements surrounding the points in the simulation. The exact cross-section average may of course also be obtained in the simulation, to assess the deviation between the measured and the true flow rate.
If a measurement cross section is hard to define, or is impracticably large to traverse, there is a procedure for defining a "cloud" (limited volume) in which velocity measurements may be made for comparison with simulation data relating to this "cloud".
The average velocity uAV is defined as the root-mean-square (RMS) velocity, where the total velocity squared in the entire body of liquid is included. For local mixing, the square of the velocity is a more relevant entity than the actual velocity itself. This is evident, for example, in the relation between velocity and shear stress, which in turn correlates to local bottom scour, local solids suspension performance, local liquid blending, etc. To the extent that a single average value could adequately describe the mixing performance in the whole tank - and this needs considerable qualification - the value of uAV or of puAV² would be a likely candidate. (The mixed liquid density is denoted by p.)
The average bottom shear stress tB,AV is in that sense an interesting number, although the fraction of the bottom area, which will be subject to at least a threshold value judged necessary for sediment resuspension, is probably a more useful number.