Similitude applied to centrifugal scaling of unsaturated flow

Abstract

Abstract. Centrifuge experiments modeling single-phase flow in prototype porous media typically use the same porous medium and permeant. Then, well-known scaling laws are used to transfer the results to the prototype. More general scaling laws that relax these restrictions are presented. For permeants that are immiscible with an accompanying gas phase, model-prototype (i.e., centrifuge model experiment-target system) scaling is demonstrated. Scaling is shown to be feasible for Miller-similar (or geometrically similar) media. Scalings are presented for a more general class, Lisle-similar media, based on the equivalence mapping of Richards' equation onto itself. Whereas model-prototype scaling of Miller-similar media can be realized easily for arbitrary boundary conditions, Lislesimilarity in a finite length medium generally, but not always, involves a mapping to a moving boundary problem. An exception occurs for redistribution in Lisle-similar porous media, which is shown to map to spatially fixed boundary conditions. Complete modelprototype scalings for this example are derived.

Assessing geotechnical centrifuge modelling in addressing variably saturated flow in soil and fractured rock

“…Such methods are often time consuming, tedious and limited to a small range of measurable hydraulic conductivity (K) values (Šimůnek and Nimmo 2005). However, use of a geotechnical centrifuge allows for simple flow apparatus, decreased experimental time, larger range of measurable K values, and the ability to simulate overburden pressure largely due to the development of the steady state centrifuge method (Barry et al 2001;Basha and Mina 1999;Nimmo 1990;Nimmo et al 1992;Nimmo and Mello 1991;Nimmo et al 1987;Šimůnek and Nimmo 2005;Singh and Gupta 2000;Zornberg and McCartney 2010). In terms of physical modelling of contaminant transport, the geotechnical centrifuge offers an opportunity to bridge laboratory and field experiments by overcoming the limitations of these methods by being able to model complex problems under repeatable conditions using large sample sizes, and better control of experimental boundary conditions, while maintaining the ability to perform in flight monitoring (Mattson et al 2010) In determining the dispersion scaling factor, the mechanical dispersion coefficient cannot be considered a material property because it is a function of both interstitial velocity and pore size (Culligan-Hensley and Savvidou 1995).…”

Lugeon Tests at Partial Saturation: Experimental and Empirical Contributions

“…Geotechnical centrifuges are particularly useful to produce data that can be used to predict behaviour of a process that occurs naturally at a cumbersome spatial scale (Barry et al 2001). This is done by accelerating a model an equivalent N times Earth's gravitational field g (ca.…”

Porous media pressure distribution in centrifugal fields

“…[3] To transfer results from the centrifuge to the prototype, scaling laws are required [Culligan and Barry, 1998;Barry et al, 2001]. Interpretation of data is not easy and requires very careful numerical simulations [Ataie-Ashtiani et al, 2003].…”