Scaling Issues in Hydraulic Modelling

Introduction

The uncertainties involved in many coastal issues and the lack of complete scientific background in some knowledge fields, especially to evaluate extreme coastal-forcing events, the cumulative environmental evolution and impacts on beaches and coastal structures as well as to confirm design procedures, for instance, lead to the need of using physical modelling. There is also little public awareness of the physics behind several coastal processes and physical modelling can help in describing and illustrating them.

In this paper a brief revue on the importance of physical modelling, its advantages in relation to numerical modelling, some basic aspects of physical modelling, related scaling issues and how to control hydraulic modelling and scale effects as well as three case studies and future challenges will be presented.

The Importance of Physical Modelling

Physical models have played a pivotal role in the growth of coastal engineering as a profession ^[1]. They have given us insight into the complex hydrodynamic regime of the nearshore region, and they have provided us with reliable and economic design solutions to support man’s activities in the coastal zone. Many of our present-day engineering design techniques were developed using laboratory measurements, and numerous theoretical developments have relied on laboratory experiments for validation.
However, many of us can still list some of the limitations of those design approaches, being in some case considered as empirical formulations. This means further tests and measurements are needed to increase the reliability of those formulations, specially performed at scales closer to the prototype, avoiding scale effects and testing new forcing situations. Especially due to climate change and the demand for bigger structures located at higher depths, more accurate design formulations are needed and this will be the most important role of large laboratories of maritime hydraulics. However, as these large tests in large facilities are more expensive they need to work in close relation with other small/medium facilities for preliminary/cheaper analyses.

Physical and numerical modelling tools have developed enormously during the last years. However several issues need still further developments, namely the physics and modelling of sediment transport, the wave-structure interaction analysis and loads determination, erosion and scour near coastal structures as well as medium to long term accurate simulation tools.

From the management side, for instance, plans should be based on an adequate understanding of coastal dynamics. It is necessary to pursue research on many aspects of coastal dynamics in order to better assess and understand erosion and sedimentation problems, predictions of shoreline positions for various scenarios and time scales of climate variability and direct human influence, the vulnerability of beaches, dunes and coastal structures to storms and other extreme events, the impact of artificial coastal structures and ecological changes.

Physical Modelling versus Numerical Modelling

Numerical models represent the real problem but with some simplifications. Thus, the modeller is forced to make a compromise between the details of the model and the prototype. Several advantages and disadvantages of physical model testing are usually reported.

An incorrectly designed model always provides wrong predictions, independently of the sophistication of the instrumentation and measuring methods. The cost of physical modelling is often more than that of numerical modelling, and less than that of major field experiments, but this depends on the exact nature of the problem being studied. Physical modelling has gathered new perspectives due to the development of new sophisticated equipment, allowing the measurement of variables in complex flows, which was previously impossible. New experimental techniques, automated data acquisition and analysis systems, rapid processing and increased data storage capabilities also provide useful information for the validation of numerical models, Frostick et al. (2011)

Other advantages of physical models are the study of new phenomena, the lower level of simplification, to confirm through measurements theoretical results, to obtain measurements from complex phenomena inaccessible from theory, to test extreme conditions, to test a wide variety of environmental conditions and the immediate visual feedback. Despite all these advantages there are still some problems of physical modelling to solve such as the scale effects, the incomplete modelling, the laboratory effects and the costs of installation and maintenance.

With relation to numerical models it can be said that despite the huge developments made they still exhibit deficiencies and limitations when applied to complex flows and situations like breaking, overtopping, wave structure interaction, etc. However, recent developments such as SPH and in computing capacity have made these tools more powerful than even before, leading to a better description of the complexity of the hydraulic phenomena (physical environment and borders as well as non-linear aspects of the equations used). From another perspective this tool is in general more attractive to researchers and practitioners.

To obtain theoretical solutions, simplifications of the physical environment (especially the boundaries) are needed as well as of the equations that govern the phenomena. As a result of that mathematical solutions may have lower quantitative value, and therefore could be more useful for qualitative or comparative analyses. The geometry can be reproduced with the desired detail but it is not enough to ensure a correct reproduction of the reality in the model as this can generate a behaviour sometimes different from the prototype. So calibration is needed. Physical modelling reproduces both linear and nonlinear aspects of the phenomena, avoiding the simplifications of the numerical modelling that simplifies not only the geometry but also fundamental equations.
Other advantages of physical modelling are intermediate and controllable cost; they represent reality at a certain scale; the involved variables and boundaries can be controlled; measurements are in general easy to perform and the comprehension of the processes is facilitated.

Other disadvantages of physical modelling are the time spent and the cost of building alternatives, the particle similarity, the partial control of boundaries and the difficulty in measuring parameters in some model areas. The actual level of research needs common efforts between the various available tools, namely physical and numerical modelling in order to decrease the lack of knowledge in some areas of Maritime Hydraulics. The problems to solve or which are not solved yet are so complex that only this integrated approach is feasible in order to obtain better accurate results not only for researchers but also for designers and practitioners.
There is still a need to design and construct new and more advanced laboratory facilities, develop new reliable measuring instruments and techniques, minimize laboratory effects, and understand the scale effects that arise from incomplete modelling.

Physical and numerical model input conditions can be controlled and systematically varied, whereas field studies have no such control. However, many problems in coastal engineering are not amenable to mathematical analysis because of the nonlinear character of the governing equations of motion, lack of information on wave breaking, turbulence or bottom friction, or numerous connected water channels. In these cases it is often necessary to use physical models for predicting prototype behaviour or observing results not readily examined in nature. The growing use of numerical models in coastal engineering has not stopped the use of physical models and in some cases they made progress in conjunction with each other. Recent trends have included the concept of “hybrid modelling” where results from a physical model of complex region are used as input or boundary conditions for a comprehensive numerical model covering a wider region of interest. Alternatively, numerical model results may be used to provide input conditions at the boundaries of the physical model.

The rationale for continued support of physical modelling in support of project design is that “Theory cannot cover all the complications that are encountered in practice. Consequently, most major hydraulics projects are model tested to optimize design”.
Due to the quantitative deficiencies and limitations of predictive numerical models when applied to complex flows, the need for physical modelling still remains and investments in laboratory facilities, equipment and new techniques are more and more needed, highlighting the need for synergies between the various research tools, physical and numerical modelling included, not only because of the actual complexity of the maritime hydraulics problems, but also to improve some design approaches.

Basic Aspects of Physical Modelling

A physical hydraulic model represents a real prototype and is used to find or confirm solutions for engineering problems. Differences between the model and prototype behaviour and results may be due to scale (similarity laws considered and incomplete reproduction of the forces involved), laboratory (model geometry – 2D or 3D influences, reflections; flow or wave generation techniques – turbulence intensity levels, linear wave theory approach; fluid properties, etc.) or measurement (different equipments used in model and prototype – intrusive or not, probe sizes) effects. The estimation of these effects (qualitatively and quantitatively) affects the results and to know if they can be neglected is a challenge for physical modellers, Heller (2011). They can also justify differences between physical and numerical models (e.g. kinematic viscosity). The examples of the overflow spillway or a wave breaking are classic ones.

Considering the usual geometric scale parameter λ=L_m/L_p or N=L_p/L_m, the required space, time and cost of experiments decrease with λ², λ^1/2 and λ³, but scale effects will increase, and the results cannot be properly extrapolated to the prototype. So a proper selection of λ is an economic and technical issue and if related effects cannot be neglected this must be known and taken into account.

The basic aspects of mechanical similarity (geometric - dimensions, kinematic – time, velocity, acceleration and discharge, and dynamic – forces: inertial, gravitational, viscous, surface tension, elastic, pressure) are well known, leading to the different numbers (similarities or laws) when considering the ratios of all the forces in relation to the inertial one (the most relevant in fluid mechanics) – Froude, Reynolds, Weber, Cauchy, Euler.

It is also known that although a perfect similarity would need the same value of these numbers between the prototype and the model, this is in general not possible as some of these similarities are incompatible (when using the same fluid or considering the same environment – gravity). So the most relevant force(s) present in the prototype must be selected and if compatible the model must be build according to the related similarity.

The relevant forces for most coastal hydrodynamics problems are the gravitational forces, friction, and surface tension (Dalrymple, 1985). Thus, the dimensionless products are combinations of the Froude, Reynolds, and Weber numbers. Neglected are compressibility and elasticity effects. Yet the use of the same fluid on both model and prototype prohibits simultaneously satisfying the Froude, Reynolds and Weber number scaling criteria and thus, most coastal models are run respecting Froude’s similarity only, which implies assuming that gravitational effects are the most significant and that the viscosity and surface tension of water do not play significant roles.

For coastal sediment models, another set of scale relationships governing the initiation of motion, the transport mode, and the transport rate have to be introduced into the model, again with inevitable scale effects. The coastal mobile bed sediment transport and morphology model is perhaps the most difficult of all physical hydraulic models (Kamphuis, 2009); yet despite the shortcomings it is, in many cases, the most important available instrument to bring about improvements with respect to sediment transport, and erosion.