RICERCA ITALIANA     

Study and Optimization of Buoyancy-controlled Thermal Systems

Università degli Studi di Modena e Reggio Emilia

Abstract

The project is centred on the study of free convection flows of single-phase fluids in totally or partially confined environments. The research program is mainly aimed to provide updated criteria and methodologies useful in the design of a variety of thermal control devices.
Fundamental aspects of the thermal-fluid behaviour of confined buoyant systems are covered by this project, as well as the development of enhanced experimental methods and theoretical tools for system analysis.
Also, a pilot test is attempted on use of automatic optimisation procedures in the context of the thermal design of buoyancy-controlled devices.
Activities will focus on systems in the following typologies: confined fluid systems containing thermal sources, natural circulation loops, buoyant flows through open-ended vertical channels.
As for confined systems, much attention will be devoted to supercritical natural convection regimes, with special concern with the effects of geometrical details on flow stability, and the system behaviour under transient conditions. Thermo-gravitational diffusion in binary mixtures, and the related component separation effects, will finally be investigated.
Interest in natural circulation loops is driven by the present trend towards system-size reduction, in view of possible use of this technology in hi-tech applications. Theoretical and experimental characterization of small- and medium-size loops, in terms of either stability or performances, is the main task of this part of the research program. A fundamental achievement will be the design and construction of monitoring and measuring instrumentation for small-scale circuits.
Open-end vertical channels will be investigated both numerically and experimentally. Of specific concern here will be the presence of horizontal ribs on heating surfaces, and the related effects on heat transfer and flow rate device performances. The effects of rib-roughening will be ultimately clarified.
The above system, i.e. a vertical channel made-up with an adiabatic and an isothermal rib-roughened surface, has been chosen as the test case for a coordinated optimisation project on rib geometry and thermal conductivity. The best final solutions, i.e. the optimised geometries, are planned to be validated by experiments.
The program will therefore improve current knowledge on fundamentals of buoyancy-induced flows within bounded domains, but will also provide brand new technical information and tools.
A pilot estimate of the effectiveness of automatic optimisation processes in the design of buoyancy-driven thermal systems will be provided. This latter feature of the project has special practical relevance, since optimisation techniques represent one of the most promising tools for technological development of today. <<<

Principal Investigator

Giovanni Sebastiano BAROZZI Università degli Studi di MODENA e REGGIO EMILIA

Research Objectives

The general objective of this research program is to provide new criteria and reliable predictive tools for the design and optimization of those thermal systems and devices, whose effectiveness totally relies upon buoyancy-induced flow and circulation. Appropriate technical directions, and design methodologies will possibly be derived for a number of technological applications.

The project is centred on the study of free convection flows in totally or partially confined environments. The program collects different previous experiences of the Research Units (R.U.) in the frame of National Research Projects (PRIN). These were devoted to the development of experimental and numerical methods for investigating combined and free convection heat transfer. The competences gained and the facilities acquired by the Research Units are fully exploited in this project, towards new methodological and technological objectives.

Attention is deliberately restricted and focused on the following single-phase buoyant systems: i. Confined cavities containing immersed thermal sources or having thermally active boundary-walls; ii. Open-ended vertical channels with heating surfaces; hermetic natural circulation (or thermosyphon) systems.

With reference to the above systems, the aims of the research program are detailed as follows:

1) to probe into a few fundamental aspects of thermal control by pure free convection, not completely resolved in the literature, and more specifically:
a) for confined fluid systems, the relation between heat transfer performances and buoyant-flow regimes is still largely unexplored. The effects of the cavity shape, the size and position of internal heat sources, the thermal boundary conditions, and the thermal fluid properties, are of practical concern here. The case of a horizontal cylindrical source will be considered for two basic enclosure geometries (parallelepiped and cylinder). The sequence of buoyant-flow regimes progressively occurring for increasing the Rayleigh number will be investigated. The range encompassing steady laminar, periodic up to chaotic regimes will be investigated. New quantitative heat transfer data will be provided for steady and time-dependent flow-regimes. Attention will also be dedicated to transient conditions. A part of the research effort will finally be directed to investigate the additional effects of thermo gravitational diffusion in binary mixtures.
The final objective of the above activities is the derivation of general criteria for predicting, at least qualitatively, the behaviour of more complex real-world systems. It is pointed out that, for the time being, no indication of this type can be found in the literature.
b) Open-ended vertical channels are frequently encountered in a number of practical applications like, i.e., cooling of electronics, and passive solar heating. Buoyant effects promoted by heated vertical channels have been thoroughly investigated, and reliable heat transfer correlations are now available in the literature for the basic conditions of symmetric, and non-symmetric wall-heating channels with smooth walls. With the aim of improving system performance in terms of flow rate and heat exchange, the use of rib-roughened surfaces has recently been proposed. Effects of horizontal ribs are however controversial.
This program is aimed to provide definite information on rib efficiency over a full range of Rayleigh number values, together with some tools and criteria for best-design practice.
c) Single-phase natural circulation loops have definite advantages in terms of reliability, economy, and noiseless. They therefore provide an interesting alternative to other thermal control systems even for high technology applications. Before the system can be used for electronics and avionics cooling, technical and technological problems must however be faced. These are mainly connected with reliability problems due to the possible onset of unstable time-dependent regimes, and the risk of fluid subcooled boiling inside the circuit. The latter aspect becomes increasingly crucial when reducing the circuit size.
The tasks of the program are i. to characterize natural circulation systems in terms of stability, by both experiments and theoretical work, and ii. to design a specific sensor to check the formation of vapour bubbles in the experimental rig.
2) an extensive employment of non intrusive experimental techniques for temperature and velocity field determination. The project will benefit of the recognized competence in optical techniques gained by two of the Research Units. Comparative experiments are planned with holographic interferometry and a "shlieren" technique, so as to obtain a massive and concurrent data set on the case of concern. At the same time, advantages and shortcomings of the two methods will be comparatively elucidated.
Ultrasound Pulsed Doppler Velcimetry (UPDV) is a potential alternative to laser-employing techniques, since it does not demand optical windows. However, its accuracy and repeatability limits over the range of free-convection velocities remain to be defined.
To set up and validate non-intrusive measuring techniques for thermal flows is within the objectives of the program. The training of highly qualified personnel, the development of measuring procedures, the production of software for automatic data processing and for uncertainty analysis are not secondary fall-out of the above activity.
3) The testing of automatic geometrical and functional optimization procedures for free-convection systems. Optimization techniques are rapidly improving, and find increasing application in the industrial environment. In fact, they can be extremely effective in reducing the prototyping processes, with benefits in terms of quality of the solutions and time-to-market reductions, in comparison with the standard approach, in particular when the number of design variables is large . The effectiveness of any optimization technique is however dependent on the correct and complete recognition of design variables and of their variability constrains. This operation is delicate in the case of buoyant systems, and is probably reason of the absence of application examples. A coordinated experiment of geometrical and functional optimization is planned in the context of this research program. The reference case is a vertical parallel-plate channel with heateing on one side. The heated wall is provided with horizontal ribs, whose profile, size, thermal conductivity and placement are the object of the optimization process. Experimental validation of the most effective geometries will possibly be performed.
The activity is directed to qualify optimization tools in terms of practicability, efficiency, and effectiveness, for applications involving free convection heat transfer. The final aim is to supply the thermal designer with an economic and efficient procedure, as an alternative to experimental optimization. At the same time, possible operative limits of the available technical tools will be pointed out.

Overall, the research activities will improve the current knowledge on fundamental heat transfer and fluid flow for confined free convection. This will be accompanied by the development of competences and procedures in either thermal-flow measurements or CFD.
Operative criteria will be derived for predicting confined buoyant flow regimes and natural circulation systems; updated heat transfer correlations will be provided for confined systems.
The effectiveness of alternative automatic optimization procedures will be tested for free convection systems. The results will have primary practical importance, since optimization techniques are one of the most advanced and promising design tools available today, which can deliver a further advantage for product innovation. <<<

Timescale

24 months

National and international background

Natural (or free) convection flows are induced by buoyancy forces in fluids under the action of the gravity field. In homogeneous fluids these forces are generated by density gradients, due to temperature differences deriving by heat transfer processes. Natural convection flows are also designated as "thermogravitational flows". In the case of mixtures, buoyancy forces can also be promoted by concentration gradients.
Free convection effects are directly exploited in a variety of technological applications. A non exhaustive list of examples would include thermal control of electronic devices, natural ventilation and exhaust systems, air distribution in halls, thermal storages, thermosyphon loops, and thin-film-deposition technologies.
Free-convection-based systems are very attractive due to their reliability and low cost. They are free from moving parts, and are automatically activated by the thermal system itself. Their range of application is however limited by low heat transfer coefficients, and difficulties in controlling the transport processes. In fact, buoyancy effects are difficult to improve when heat transfer needs to be increased and impossible to suppress when heat loss reduction is of concern. The efficiency of these processes is also very unpredictable, particularly in confined systems, where the thermal-fluid behaviour of buoyant flows is significantly dependent on geometrical details.
The non dimensional groups relevant to free convection are the Grashof (Gr) and the Prandtl (Pr) numbers, the former being often substituted by the Rayleigh number (Ra). They are related to the heat transfer coefficient through the Nusselt number (Nu), and heat transfer correlations for basic geometries are found in the literature [1,2].
The Project is focused on convective systems of the following types: i. confined enclosures with internal or boundary-wall heat sources; ii. natural circulation (or thermosyphon) loops; iii. vertical channels with heating wall. These systems are well distinct in terms of applications, but are strictly correlated in terms of the underlying physics and working principles.
The Project exploits previous experiences of the Research Units: their experimental (iv), numerical and optimization (v) tools to be used in the frame of this Project will be described.

i. Buoyancy induced flows in confined enclosures
Buoyant flows in fully confined cavities have been investigated into detail only for few basic geometries. Among them, the rectangular cavity, differentially heated at the vertical walls, has been the subject of intensive study over the whole set of flow regimes - laminar, transitional and turbulent – occurring at different Ra-values [3-5]. It is now well established that convective circulations within a square cavity, initially single-cellular, becomes multi-cellular and, afterwards, undergoes a series of successive flow transitions for increasing Ra. The sequence of steady, periodic, quasi-periodic, chaotic, and turbulent regimes have been recognized [6]. For this geometry an analytical method has been derived to predict the first critical Ra-value [7].
The horizontal annular enclosure between co-axial cylinders at different temperatures, is the second reference case for which a research is currently carried out. The characterization of flow regimes, and the definition of critical Ra-values are of concern, on account of the cavity aspect ratio [8-10].
The Project will provide analytical and numerical predictions, and experimental data for this system.
Rectangular enclosures with internal heat sources have technical importance, but have received minor attention. Numerical approaches were used to investigate buoyant flows within 2D enclosures containing point sources [11,12], cylindrical [13] or rectangular [14] sources, or a parallel-plate channel [15]. Experimental data are limited to the low-Ra range for cylindrical sources [16,17].
All the analyses corroborate the idea that the behaviour of confined systems in the presence of internal sources is similar to the ones observed for the rectangular and the annular cavities: a long-term-steady circulation is attained at low Ra-values, and different time-dependent regimes onset at some critical Ra-value. Critical values however depend on a number of factors, such as the enclosure geometry, the source shape and position, the thermal boundary conditions, and the fluid thermal properties. Heat transfer performances may differ for different flow regimes.
The Project includes an extensive investigation, both numerical and experimental, on transitional flow regimes in a cavity containing a cylindrical heat source.
An important aspect of confined buoyancy-dominated flow systems is their time-response to thermal inputs. It is actually possible that, under practical circumstances, the system transient becomes exceedingly long, and long-term data become useless [15]. The few relevant experiments are for horizontal cylinders in unbounded domains [18]. Results indicate that transients are characterized by a time-leg within which a conductive regime prevails. The time-leg seems to be related to the heat dissipation rate of the source.
The Project is intended to provide transient experimental data and predictions for an enclosed cylinder.
A last item covered by the Project is related to thermodiffusion (or Soret) effect in binary mixtures. The effect connects the concentration gradients of the components to the temperature gradient. It therefore tends to separate the components. The coupling of thermodiffusion with thermogravitational flows gives rise to thermogravitational diffusion. If properly optimized, this accelerates separation towards simple thermodiffusion [19]. This combined effect has great potential in chemical and desalination processes.

ii. Natural circulation in closed loops
In contrast with forced convection, natural circulation in closed loops has the evident advantage that it does not require the use of active components, since flow is activated by buoyancy forces within the fluid itself. This is an important feature in systems where it is mandatory to guarantee heat transfer even in the absence of an external power supply. However, thermosyphon loops can become unstable and, under certain conditions, sudden flow inversion may occur [20]. This behaviour depends on the non-linearities between buoyancy forces, promoting the flow, and passive viscous resistances. Other parameters can influence the thermohydraulics of the loop, such as the system inclination, the thermal properties of the fluid and the materials, the presence of localized head losses. Those effects have been investigated in the frame of previous projects [21-23]. Analytical and numerical approaches based on neural networks, were also set up, to predict stability of natural circulation loops [24,25].
New possible applications of thermosyphon loops are in biomedical applications or in electronics cooling. These demand the scaling of the loop down to tube sizes of the order of millimetres, while guaranteeing maximum system reliability up to the limit working conditions. The boiling threshold is in fact closely approached, but must not be exceeded, since boiling can compromise the device functionality.
Theoretical and experimental studies on single-phase natural circulation loops, with specific regard to their reduction to small/medium size, are carried out in this Project. The scaling of control and measuring instruments is of concern, with regard to the detection of vapour bubbles.

iii. Convection flows in vertical channels – effects of rib-roughening
Free convection flows within vertical parallel-plate channels are of primary technical importance. This asset is in fact very common in many engineering applications such as finned heat sinks.
Reliable heat transfer correlations for open-end vertical channels with smooth walls, are available in the literature [2]. Even so, they are currently investigated, to improve their heat transfer performances [26,27]. The addition of artificial roughness elements to one or both heated surfaces has recently been suggested as a viable strategy for heat transfer augmentation. It is expected that the presence of ribs of various shapes may increase the heat transfer rate and promote earlier transition to turbulence. Under certain circumstances, however, the roughness elements seem to cause fluid stagnation in their downstream and upstream zones, with consequent heat transfer reductions. Thus, the effects of roughening is still controversial. Recent investigations on horizontal rectangular ribs have shown that the thermal properties of the rib material definitely affect thermal performance. Surprisingly enough, a lower thermal conductivity of the ribs is preferable, since it provides reduction of the stagnation zones [28-30].
The effects of rib-roughening will be dealt within the Pproject, with both experiment and numerical simulation. The rib geometry will also be the focus of a coordinated optimization experiment.

iv. Experimental techniques
Experimental studies on natural convection regimes require the use of specialized non-intrusive field techniques. The presence of sensors within the fluid can, in fact, alter the system dynamics. In addition, the frequency response of the instrumentation must comply with the system time-scale when transient behaviours or time-dependent regimes are considered. Finally, in laboratory experiments with liquids, the convective velocities are often of the order of 1 mm/s, with obvious implications in terms of measure repeatability and accuracy. Experiments with air are planned, making extensive use of optical methods. These present very favourable properties, since they allow a large portion of the thermal field to be visualized, and are characterized by fast responses.The measuring principles of most optical methods are linked to the temperature-dependent refractive index of transparent fluids. A phase object with a non-uniform refractive index distribution has two basic effects on a light beam: (a) a change in phase, and (b) a deflection of the beam from its original direction. The phase change is detected in interferometric techniques, such as holographic interferometry [31], while the beam deflection is involved in shadowgraph and schlieren methods [32].
In the former case the temperature field is directly visualized, and numerical differentiation is needed to obtain the convection heat transfer coefficients. In the latter case, the temperature-gradient field is directly obtained, and numerical integration is used to reconstruct the temperature field.
Each technique involves specific instrumentation and data processing. The experimental uncertainty and the range of application of the methods are case-dependent.
Holographic interferometry is highly sensible, and in its most recent developments, allows real-time investigation of free convection phenomena to be performed. The reconstruction of 3D thermal fields is also made possible by multiple interferogram processing (optical tomography), as well as the simultaneous reconstruction of the thermal field and the convection coefficients [33]. Schlieren method has greatly improved, due to the evolution of laser and image acquisition/handling tools. They are now one of the most reliable techniques to investigate thermal convection effects. After the introduction of colour filters the thermal-flow fields can be visualized with relative ease, and local values of the heat transfer coefficient are derived with good accuracy [34].
Holographic interferometry and schlieren methods will both be used in the frame of the Project. The two techniques will be directly compared on the same experiment, so as to elucidate their relative merits and drawbacks.
Ultrasound Pulsed Doppler Velocimetry (UPDV) constitutes a viable alternative to the more consolidated Particle Image Velocimetry (PIV) and Laser Doppler Velocimetry (LDV) techniques, when the velocity field in a liquid is of concern.
UPDV is particularly useful when the test section walls or the fluid are not optically transparent. The technique is based on the measurement of the Doppler frequency produced by the interaction of an ultrasonic ray, and a particle carried by the flow. Real-time samplings of a velocity component are acquired along the axis of the ultrasound probe [35].
The extension of UPDV to the velocity range typical of confined convection, is among the objectives of this Project.

v. CFD modelling and optimization techniques
Nowadays, Computational Fluid Dynamics (CFD) commercial packages are robust and versatile, and are of potential use even for the analysis of very complex phenomena, such as transitional flows in free convection. Among them, FLUENT, CFX, and FEMLAB are currently used by the Research Units involved in this research program.
However, the numerical prediction of time-dependent free-convection regimes demands the algorithm's accuracy to be at least 2nd order in both space and time [36]. These properties are not necessarily guaranteed by commercial CFD products. A predictive technique has been set up in the frame of previous National Projects, having the prescribed accuracy level. The technique falls in the class of the "projection methods" [37], and is based on a control-volume discretization of the momentum and energy equations over variable-step Cartesian grids. The method was validated for steady-state test-cases, and was employed to investigate transitional and transient regimes in buoyancy-induced cavity flows. Recently it was extended to the treatment of non-Cartesian internal and external boundaries [38]. Alternative direct simulation techniques [39,40] have also been developed, and can find use within the Project.

In the last years, optimization software has been commercialized, for the purposes of industrial design.
Optimization techniques have great potential in thermal and fluid-dynamic design, but, for the time being, applications have been restricted to cases of forced flow, forced convection, and conduction. No example involving free convection has been found in the literature.
In general terms, an optimization process consists in the research of the best design result in a given context. The basic idea is that the desired "benefit", i.e. the design result, can be expressed as a function of certain "decision variables". Optimization can therefore be defined as the process of finding the conditions that give the maximum value of that function. A number of optimization methods have been developed for solving different types of problems [41,42]. Independent on the specific method adopted, an optimization path includes the following procedural steps: i. Parameterization of the problem, i.e. the parameters (design variables) that can be modified during optimization are defined; ii. Determination of the variability range of each design variable; iii. Selection of the numerical or analytical model of the problem (this is often built-up as a system of algebraic equations generated by the discretization of p.d.e.'s); iv. Generation of a population of design solutions within the variability limits of the design variables; v. Evaluation of the best solutions, according to an optimization criterion, also called "objective function".
The various approaches differ as for the way of generating the solution populations. Genetic algorithms, coupled with CFD software, have shown to give very satisfactory results in fluid-dynamic and thermal problems [43-45]. Therefore, they are potential candidates for the treatment of buoyancy-controlled systems.
A comparative optimization experiment is planned in the frame of this Project, in order to test the potential of optimization software in the design of free-convection heat transfer systems. The experimental test of optimized solutions is planned at the end of the optimization task. <<<