Introduction

The research programme of the JMBC has been ordered in research themes and focal points. The reason for this ordering is to present a combination of projects which have coherence, either in terms of physical models or in terms of mathematical methods.
The main themes are:
1. Complex dynamics of fluids
2. Complex structures of fluids
3. Mathematical and computational methods for fluid flow analysis

Description of the research themes

1. Complex dynamics of fluids

Fluid flows in the environment or in industrial applications are almost always characterised by some form of complexity. Frequently it is this complexity that makes the flow an interesting topic of research. Below we will sketch several examples of such flows and flow phenomena which form research topics carried out in the various groups of the J.M. Burgerscentrum. The first form of complex dynamics which comes to mind is turbulence in contrast to a laminar flow. Here complexity appears in the form of strong nonlinearity. Due to its chaotic behaviour turbulence can be considered as the archetype of a complex flow, and - being far from solved - turbulence will remain a strong focal point of research in the coming period. Turbulence research traditionally addresses the following questions:

• what are the physical processes and interactions governing turbulence,
• how can they be quantified and described mathematically,
• how to predict turbulence and turbulent flow for particular configurations, and
• how to control and manipulate turbulence?

Future research in this field in particular will focus on laminar-to-turbulent and reverse transition, effects of thermal buoyancy, unsteadiness, compressibility and rotation, and on the interaction with chemical reactions. The rol of turbulence in energy conversion processes and equipment are regarded as an intriguing field of applications.

Complexity may also appear in the form of a combined flow of various phases. When these phases are immiscible, phenomena such as free surface flows occur. These may appear in the form of various wave phenomena, for instance on an unobstructed water surface, but also in a confined geometry of a pipe.

Another type of such flow of immiscible phases is when one of the phases is distributed in the form of small particles, bubbles or droplets in the other continuous phase. Various combinations of phases may be selected and each has its own particular problems. This class of flows, generally denoted as
dispersed multi-phase flow, at the moment forms a strong focal point of research within the JMBC. The combination of phases that are miscible leads to other interesting problems such as mixing, and - depending on the fluids that take part in the mixing - chemical reactions or combustion.

Finally, complexity of the flow can also appear through its boundary conditions. For instance the flow geometry can strongly influence the flow characteristics by means of straining, shearing and distortion. An example is the wake behind a body in a shearing or straining flow. Furthermore, the exact formulation of boundary conditions can have a consequence for the type of flow characteristics that appear.

An example is the free convection above a flat surface with a variable the conductivity. Geometry  constraints on the flow are also dominant also when one considers a flow in 2D versus3D. Here one should take as an example the quite different characteristics of 2D turbulence versus 3D-turbulence.

An increasingly important JMBC research activity within Theme 1 is aero-acoustics, aimed at the  dentification and quantification of acoustic sound sources in internal and external flows. Such sources can be related to unsteady vortex shedding, turbulence, combustion and flow-structure interaction. In general there is a strongly non-linear mutual interaction between sound source and acoustic field. The applications and technical implications show a great diversity. The JMBC is actively involved in vortex sounds in ducts, musical instruments (like the flute and the organ pipe), human speech, acoustics
in burner stabilized flames, sound generation by turbulent flames, with much attention to analytical and numerical modelling of these flows.

The flow cases mentioned above, which are by no means an exhaustive list of complex fluid flow phenomena, form research topics in the various groups in the J.M. Burgers Centre.

The tools to carry out this research are primarily numerical and experimental. The numerical techniques used to compute flow phenomena are direct and large eddy numerical simulation, turbulence modelling and computational fluid dynamics. The experimental techniques used nowadays are mostly based on various forms of laser diagnostics (e.g. like PIV and PTV for flow measurements and CARS, LIF and Cavity Ring-Down Spectroscopy for temperatures and concentrations). Experiments, simulations and analytical theories in the field of fluid flow analysis complement each other - perhaps more than in other branches of physics. Future research will inevitably make use and take advantage of combined techniques and their complementing roles. Both the research topics themselves and the research techniques to carry out these investigations, form the basis of a strong collaboration within the J.M. Burgerscentrum.

2. Complex structures of fluids

Research in this Theme deals with complex structures of flow, formed in the presence of particles, drops, or bubbles, i.e., two- or even multi-phase flow. Two-phase flow is of paramount importance in contemporary science and technology.

One can readily cite a multitude of examples: the production and transport of oil (where bubbles are purposely injected to help lift thick heavy oil to the surface, or arise due to the release of dissolved gases), energy generation (where boiling is the key process in producing the steam to drive turbines), the chemical industry (where gas-liquid reactors rely on bubbles to increase the contact area between the phases), the oceans (where breaking-wave generated bubbles are important sinks for atmospheric CO2), sedimentation (where sinking sand particles determine the structure oF our coasts), food-industry, and many others.

The challenge in single-phase flow is to understand the complicated dynamics which is generated by the Navier-Stokes equation. In two-phase flow, even the underlying dynamical equations are often not known. E.g., it is not understood why bubbles repel each other when they are close to each other.

But even when the microscopic interactions are known, it is often not clear how the macroscopic structure evolves from this microscopic interaction and the response to external forces.

In many cases instabilities are involved in the macroscopic structure formation process. Very complex self-organising patterns can evolve out of these instabilities. An important example is cluster formation in sedimentating particles and coherent structures in bubble columns and fluidised beds. Related topics are flow-controlled nucleation and droplet growth processes in high-pressure natural gas, which have important technical applications in the natural gas industry. Different JMBC groups are involved in the design of new types of condensate separators and in the numerical description of swirling supersonic two-phase flows, while a dedicated facility has been developed in order to investigate these condensation processes in a well-defined way experimentally.

How to theoretically describe such a complex system? Two types of approaches have been described in literature: In the first type of approach, the particles/bubbles/drops are treated essentially as points, while no attempt is made to simulate their detailed response to the liquid dynamics.

The advantage of this approach is that many particles/bubbles/drops can be treated, but the price to be paid is a lot of ad-hoc modelling. Fluid dynamical simulations in which the particles/bubbles/drops are modelled through averaged equations also belong to this first type of approach. In the second type of approach the detailed interactions of the particles/bubbles/drops with the flow is simulated, paying the price that - at present - the surrounding flow can not really be turbulent and that only "a few" objects can be treated, in particular, when the interfaces are allowed to deform, i.e., for free boundary problems (drops and bubbles).

One of the main objectives for the research in two-phase flow must be to bridge the gap between these two types of approaches and to carry out a detailed investigation of the interaction between one or a few particles/bubbles/ drops and a nontrivial flow field. Another objective must be to better understand the macroscopic structure formation process out of the microscopic interactions, and thus the instabilities in two-phase flow. It is evident that these objectives can only be achieved through a joint experimental, theoretical, and numerical approach.

On the experimental side, the challenge has always been to monitor and document as much information on the dynamics of the flow field as possible. Through the huge advances in bothdigital imaging techniques and information technology (see Research Theme 3), the field is now flourishing, and the research on two-phase flow will strongly benefit from this. The same is to be expected from the advances with numerical techniques (see Research Theme 4), as brute force numerics will not be sufficient to address the problem of structure formation in two-phase flow. New algorithms and techniques are required and moving toward parallel computing will be essential.

3. Mathematical and computational methods for fluid flow analysis

Advanced mathematical and computational techniques have become indispensible instruments for the description and understanding of complicated flow phenomena. This approach to fluid mechanics has evolved into a full-fledged counterpart to the experimental approach and provides new insight in complex flow physics, in for instance turbulence, combustion, multi-phase and rheological flows.

The use of computational flow models is supported with analytical techniques, which provide deeper insight in canonical flow problems, and strongly interacts with advanced experimental techniques, which are capable of measuring and visualizing complex three-dimensional unsteady flow fields. These techniques require advanced post-processing of the flow field data to understand the flow dynamics and have developed into a research subject in itself. Here tools from nonlinear dynamical systems theory can be useful, as well as the decomposition of flow data through POD and wavelet analysis.

The rapid increase in computational power has significantly stimulated the use of computational techniques in flow analysis, but the development of better algorithms has been the most important source for improved numerical techniques for flow analysis.

Many flows are, however, simply too complex for computational techniques and flow modelling remains an essential issue. Compromises have to be found between the inaccuracies in flow modelling and computational constraints. In areas such as turbulent flow simulation much progress has been made through refined modelling via Large-Eddy Simulation (LES) and Direct Numerical Simulation (DNS). There is also an interest for stochastic methods, such as the use of the Langevin equation for the velocity. In the other areas the same trends have become feasible, e.g. PDF modelling in combustion and Brownian Dynamics in rheology.

It can be foreseen that the improvements in numerical algorithms and the growing computational power will open up new applications of flow analysis in other disciplines, such as chemistry, biomedicine and structural mechanics, and will continue to grow in importance. This will be stimulated by the development of new numerical techniques which can efficiently capture flow structures with large differences in length and time scales, the continuous increase in computing power, and by exploiting computational fluid dynamics in multi-physics applications.

Focal points in the research programme

Four “focal points” have been selected from the three research themes, which receive special attention. Abrief description of these “focal points” is given below.

1. Bio fluid mechanics

Most biological organisms live in a flowing medium (air or water). Nature has found solutions for fluid mechanical problems which enable fish to swim fast or cellular organisms to propel. These solutions are intriguing to understand and may lead to new solutions for technical problems. Similarly, fluid flow is essential inside the human body, where the blood is pumped around and the air is inhaled.

Deposition of aerosols in the lung, sound production by speaking, atherosclerotic plaque formation at well determined positions, gene activation at cellular levels are all more or less determined by fluid mechanic processes. Finally, diagnostic and therapeutic techniques make use of fluid mechanic and heat transfer insights. The development of heart valves and the monitoring of temperatures inside the body during operations are examples for that.

Although most of the above mentioned problems can be solved with known physical principles, the complicated geometrical structures and the combination of phenomena (for example the transitional flow of non-Newtonian media in elastic bifurcating channels like blood vessels and airways) form an exciting new area for the development of advanced numerical and experimental techniques. Due to the geometry, three-dimensional unstructured meshes are to be used and the most efficient solvers are required to solve the flow at the relevant dimensionless parameters. Micro-PIV systems are needed to analyse the flow field in micro-vessels and fast optical techniques will enlighten the perfusion in permeable tissues.

New physical insights are needed for several areas, especially in multidisciplinary science. Some examples are given: The combination of fluid mechanics and solid mechanics is apparent in the phenomena at the focal folds where the unsteady flow separation is strongly influenced by the complex movement of the structure. Many modern uses of microbubble ultrasound contrast agents rely on the highly nonlinear response of the bubbles to a driving ultrasonic field and a quantitative model is lacking. The heat transfer processes in the anaestesized body are strongly determined by control mechanisms that are only globally known. Drag reduction occurs at the skin of several fish and reverse transition from
turbulent to laminar flow is present in the nasal cavity and stenotic blood vessels; the relation with the wall structure is unclear.

Fluid mechanical parameters stimulate the activation of genes in cells, with striking downstream effects - unexplained. The interaction between the non Newtonian mucus layer in the airways and the oscillating airflow during cough is undescribed. The settlement and growth of settlements in aquatic ecosystems require the combination of advanced flow and mass transport models. As we have noted, research on this topic is extremely diverse and complex, because it involves a large number of different areas of expertise and advanced techniques. Therefore, this theme is an excellent area for collaboration between research groups inside and outside the fluid-mechanics community.

2. Granular matter

Granular matter exhibits many fascinating phenomena and is attractive both from a fundamental and an applied point of view. Its economic potential is enormous: it has been estimated that no less than 40 percent of the capacity of the industries that process granular matter is wasted due to problems connected to the handling of these materials.

Depending on the situation, granular matter can behave similar to a solid, a liquid, or a gas. E.g., when dry sand is poured, it acts as a fluid. The pile on which it is poured is solid-like, stabilised by forces in between the sand beeds. These forces organise themselves in tree-like networks. Finally, when dry sand is strongly shaken or fluidized through a gas stream, it behaves gas-like.

The transition from one to the other regime can be very sudden and the dynamics of such a transition is very rich. When in a gas-like or fluid-like state, the granular particles can all the locally sudden cluster. In many applications this can lead to serious problems, as whole production lines get stuck or the free available surface of some heterogenous catalysator all the sudden gets to small. So it is crucial to better understand the transition to the clustered state in order to avoid it.

The origin of the potential to cluster lies in the inelasticity of the particle-particle collision: If two particles collide, they loose kinetic energy and will thus stay closer to each other, trapping even further particles in the developing cluster.

Even without the phase transitions granular dynamics is difficult to understand. For the fluidised phase the brute-force approach is molecular dynamical simulations, based on some interaction potential between the particles. If this potential is chosen realistically (i.e., rather hard), the time step of advancing the numerical simulation can only be extremely slow, making this approach inpracticable. Better results have been obtained with either (unrealistically) soft potentials or with event driven codes. The ultimate goal must be to achieve at some continuum description, similar to the Navier-Stokes equation for fluid dynamics. Though considerable success in this direction has meanwhile been achieved, the problem is far from being solved. One of the main questions is how to pick the boundary conditions for such a continuum field.

One of the current physical questions one wants to answer is: How do average velocity profiles and velocity fluctuations look like in granular flow? On the experimental side, tomographical methods have turned out to be very successful to reveal these questions. Another intriguing problem of granular dynamics is size segregation. The most famous example presumably is the so called "Brazil nut" effect: In vibro-fluidised granular material big particles tend to "swim" to the top. Two explanations compete. The original interpretation was that the smaller particles can easier fall into gaps which the big ones are leaving when jumping up. In this way the big particles would be pushed towards the top. The second
explanation is based on convection roles and channels which would form, which are too small for the big particles to dive down again, so that they must stay on the top.

Both of these interpretations are challenged by the recent discovery of an inverse Brazil nut effect which pushes big particles to the bottom. Finally, we would like to mention the interaction of granular matter ("sand") with water, which often leads to pattern formation, e.g., the famous sand ripples on the beach. On a larger scale, this interaction is crucial (in particular for the Netherlands) for the protection of the coastline.

3. Measurement techniques

Optical diagnostics become more important for the investigation of flows. The principal differences with conventional methods, such as hot-wire anemometry, is that these optical methods can be considered as non-intrusive and that they provide data on the instantaneous spatial structure of the flow field. These optical methods can be divided into two categories: one in which the flow information is extracted from tracer particles added to the fluid (seeded flows), and one in which the fluid information is extracted from the fluid itself (spectroscopic methods).

Seeded flows
The motion of the flow can be detected by adding to the fluid very small tracer particles that are small enough to consider the method as non-intrusive. Essentially the motion is recorded by measuring the displacement of the tracers between to recordings taken with a small time delay. These methods are collectively known as particle image velocimetry, or PIV. In its most basic implementation, the fluid motion is recorded in a planar cross section of the flow, yielding between 103 and 105 velocity vectors per image, with a precision better than 1%. By using stereoscopic recording, it is possible to measure all three velocity components in a plane. This can now be considered as a standard configuration that can be applied for a broad range of applications, ranging from creeping flows to transonic flows.
The challenge in the near future is to further extend the capabilities of these methods:

• Combination of PIV methods with other (optical) diagnostics makes it possible to determine more complex flow properties. For example, the combination of PIV with measurements of the concentration field or temperature field makes it possible to directly measure scalar flux and heat flux;
• Currently under development is a PIV method that can be used for the investigation of two-phase flow, in which one fluid (viz., liquid) is seeded with tracer particles, and the second fluid (viz., bubbles, droplets, or solid particles) is observed simultaneously. Here the challenge is to obtain measurements in a flow system with very strong optical aberrations due to the second phase;
• One major challenge is to be able to measure the full three-dimensional flow field. Within the JMBC a photogrammetric technique is developed and applied to various flow problems, and a 3D holographic recording method for PIV is under development.

Spectroscopic methods
The development of laser diagnostic techniques is essential for detailed non-intrusive studies of physical and chemical processes in reactive and non-reactive gas flows. At the University of Nijmegen various sensitive detection techniques have been developed and applied to different systems, such as laminar flames, optically accessible diesel engines and nonreactive turbulent flows. Most of these techniques are molecule specific, such as Laser Induced Fluorescence (LIF) detection, Cavity Ring Down Spectroscopy (CRDS) or Raman scattering, which allows for the determination of molecular
concentrations. By the application of optical imaging techniques using CCD camera's two-dimensional density distributions can be determined with high spatial and temporal resolution.

The obtained data are used to validate numerical model calculations, which are being performed by other collaborating JMBC groups. For the study of non-reactive flows both Rayleigh and Raman scattering is applied to characterise the density distribution close to boundaries, whereas filtered Rayleigh scattering and Molecular Tagging Velocimetry (MTV) are used for nonseeding velocity measurements. Recently a new promising MTV technique has been developed at Nijmegen, Air
Photolysis And Recombination Tracking (APART), which can be used also at high pressure (at least up to 40 bar) to measure velocities with very high spatial resolution. This latter technique is applied for the study of turbulence in collaboration with the groups of Nieuwstadt and Van de Water.

In the near future these laser techniques will be further improved and applied to both combustion and non-reactive flow research. At the University of Groningen LIF, CARS, infrared Cavity Ringdown  Spectroscopy and spontaneous Raman scattering are being used for quantitative characterisation of the physics and chemistry of combustion processes, specifically pollutant formation and ignition processes, at atmospheric and reduced pressure.

4. Advanced numerical techniques

An essential tool in studying flow problems is computational fluid dynamics (CFD). CFD is a collective term for a large number of numerical techniques, often each with its own area of application. The last decades have shown a growing knowledge of the fundamental concepts of CFD, and the efficiency of numerical algorithms has progressed at a considerable pace. It is foreseen that this growth will continue for some time.

Although much emphasis is on turbulent flows at high Reynolds number and multi-phase or reacting flows (which are posing the more challenging problems from a physical point of view), insights in simpler problems may be equally useful and often even essential for constructing stable and efficient methods, to be used in more general contexts. Of the latter kind one should mention basic progress in iterative methods and in discretisation approaches. Iterative developments have shown widespread use of multigrid methods and special fast solvers for large linear systems. Combination with implicit timeintegration can deal with the issue of stiffness in e.g. reacting flow.

Discretisation methods are challenged by complex geometries and moving boundaries, and by large ranges of lengthand time scales. Within the JMBC both Cartesian and unstructured (adaptive) grid approaches are being pursued to deal with the geometric and topological challenges. The (structured) Cartesian grid approach is combined with local grid refinement based on defect correction. The scale resolution problem is tackled e.g. by symmetry-preserving finitevolume methods (with a benign behaviour on underresolved flow features) and by space-time discontinuous finite-element methods
(offering flexible spatial and temporal grid adaptation). Also unified algorithms for low-Mach number flow are under development. Further, following a different discretisation philosophy, Lattice-Boltzmann methods are being studied, which possess potential advantages in multi-phase flow simulation. Another important tool in enabling the computations to be performed in a 'reasonably limited' time is parallellisation. Besides a more straightforward use of multiprocessors where the parallelism is taken care of by the compiler, a variety of domain decomposition techniques is in development. In particular
within a context where different flow modelling is used in the individual subdomains, research will open up interesting applications, e.g. in turbulent flow simulation where a mixture of RaNS, LES and/or DNS modelling can be envisaged.