2.4.3 Hydraulic Scaling Implications for Riprap Studies
Physical hydraulic models are either scaled up or down (normally down) in relation to the real-world prototype. However, for technical and economic optimisation reasons the laboratory model is generally built to be smaller than the prototype. According to Heller (2011), scale effects arise due to force ratios that are inconsistent between the hydraulic model and its pertinent prototype. The consequences of the influence of scale effects result in deviations between the upscaled model and prototype observations (Heller, 2011).
Heller (2011) argues that decreasing a model size may increase scale effects and upscaling the model size may as well result in deviations in the hydraulic parameter observations of the prototype. Thus, choosing a scale is both a technical and economic optimisation problem. As a result, physical models are normally downscaled and are consequently subjected to a degree of scale effects. To minimize the degree of scale effects on the results of a physical model the scale of the model should be made as large as is technically and economically feasible.
The following methods can be applied to achieve model-prototype similarity, to quantify or at least understand the influence of the scale effects on the hydraulic parameters being investigated (the reader is referred to Heller (2011) for an in-depth description of each of the methods):
• Inspectional analysis- similarity is achieved when both model and prototype follow a similar set of equations describing the hydrodynamic force balances.
• Dimensional analysis-similarity is achieved when each of the dimensionless parameters in the model and the prototype are quantitatively similar.
• Calibration- similarity is achieved when the model tests are executed for a prototype with observed data available, the data is generally used to calibrate the model and prototype results. • Scale series- similarity is achieved when at least three kinematically similar models of
different scales are tested in the same manner at the appropriate scale ratios.
According to Wang et. al. (2013) depending on the phenomena and parameters, scale effects related to employing small scale models might be corrected by means of correction parameters. This is achieved by implementing mutually-calibrated physical models and numerical models. However, it is not always possible, especially in the case where the hydraulic model being numerically modelled comprises parameters that are complex to model and quantify. For example, in this thesis, riprap is a porous media. It is physically complex to model the accurate roughness of the bed as well as the porous flow through the riprap.
2-47 Sediment transport and incipient motion studies involve the use of very small sediment particles. Wang et. al. (2013) argues that prototype sediment is not feasible to act as model bed material if the grain size is too fine because cohesive forces begin to emerge. According to Heller (2011), the grain median diameter in sediment transport is critical. As a result, in Heller (2011), Kobus (1980) suggests that the median grain size required to ignore the effects of cohesion in sediment transport hydraulic models should be greater than 0.0005 m (0.5mm), also the limiting median grain size was defined to be between 0.0008 m (0.8mm) by Oliverto and Hager(2005) and 0.001 m (1mm) by Schmoker and Hager(2009).
Heller (2011) and Wang et. al. (2013) suggest that there are common practices to deal with hydraulic model scale effects. One of the main practices of dealing with scale effects includes “avoidance”. The appropriate way to avoid significant scale effects in a Froude model requires the satisfaction of the limiting values of force ratios known as the Froude Number, Reynolds Number, Weber Number, Cauchy Number and the Euler Number.
However, rules of thumb are generally applied without doing an inspectional analysis, dimensional analysis, calibration or scale series modelling to ensure similarity in the model and prototype. Heller (2011) provides descriptive tables that can be used for applying the rule of thumbs in which the scale effects on a Froude model may be avoided. It is important to note that the rules of thumb must be applied not only based on the scale, but the investigator must look at the type of investigation executed, the hydraulic phenomenon, as well as the related prototype features to choose an appropriate scale.
From table one in Heller (2011), the limiting criteria specifically for riprap studies were not available. However, studies based on mountain rivers investigating bed morphology were referenced as generally scaled at 1:10 to 1:20 and the sediment median sizes are specified as between 0.2m to 0.9 m at slopes of up to 13%. The rule of thumb applicable to river expansion investigation were referenced as comprise a limiting criteria scale of up to 1:55 and the bed load transport was generally the investigated hydraulic phenomena.
Based on the above literature, it makes logical sense that, to avoid significant scale effects in a Froude physical hydraulic model, the chosen median riprap size needs to be large enough to ignore cohesive forces between particles as well as the model scale should range between 1:10 to 1:20, or up to 1:55. Without checking the similarity force ratios, the limiting criteria of a large scale models with large riprap median stone size investigated provides confidence that scale effects in the physical hydraulic model may be avoided in a Froude model, even though the scale effects still exist since it is impossible to obtain 100% similarity in any physical hydraulic model (Heller, 2011).
2-48 In the zones of low flow velocities where the particle Reynolds number is too small, the viscous forces become relatively large in comparison with gravitational and inertial forces (Froude scale) – the model then does not fully represent the prototype and we say scale effects influence the model results such that the model is not fully representative of the prototype in that low flow particle Reynolds number zone. In areas of high flow and consequent high turbulence, the turbulence “breaks” the viscous layers around particles/rock in the flow and then inertial and gravitational forces dominate so that the Froude scale law is then satisfied.
Based on the literature study on scale effects in Froude scaled models and specifically the statement by Heller (2011), that studies based on mountain rivers investigating bed morphology were referenced as generally scaled at 1:10 to 1:20 and the prototype sediment median sizes are specified as between 0.2 m to 0.9 m at slopes of up to 13%, it was decided to use a physical Froude scaled model (with scaling laws as per Table 5) of scale 1:15 to minimize scale effects and therefore to ensure that the results from the physical model study are reliable.