Undergraduate teaching of ideal and real fluid flows: The value of real-world experimental projects

This study describes the pedagogical impact of real-world experimental projects undertaken as part of an advanced undergraduate Fluid Mechanics subject at an Australian university. The projects have been organised to complement traditional lectures and introduce students to the challenges of professional design, physical modelling, data collection and analysis. The physical model studies combine experimental, analytical and numerical work in order to develop students’ abilities to tackle real-world problems. A first study illustrates the differences between ideal and real fluid flow force predictions based upon model tests of buildings in a large size wind tunnel used for research and professional testing. A second study introduces the complexity arising from unsteady non-uniform wave loading on a sheltered pile. The teaching initiative is supported by feedback from undergraduate students. The pedagogy of the course and projects is discussed with reference to experiential, project-based and collaborative learning. The practical work complements traditional lectures and tutorials, and provides opportunities which cannot be learnt in the classroom, real or virtual. Student feedback demonstrates a strong interest for the project phases of the course. This was associated with greater motivation for the course, leading in turn to lower failure rates. In terms of learning outcomes, the primary aim is to enable students to deliver a professional report as the final product, where physical model data are compared to ideal-fluid flow calculations and real-fluid flow analyses. Thus the students are exposed to a professional design approach involving a high level of expertise in fluid mechanics, with sufficient academic guidance to achieve carefully defined learning goals, while retaining sufficient flexibility for students to construct there own learning goals. The overall pedagogy is a blend of problem-based and project-based learning, which reflects academic research and professional practice. The assessment is a mix of peer-assessed oral presentations and written reports that aims to maximise student reflection and development. Student feedback indicated a strong motivation for courses that include a well-designed project component.

Radial displacement of a fluid annulus in a rotating Hele¿Shaw cell

The radial displacement of a fluid annulus in a rotating circular Hele-Shaw cell has been investigated experimentally. It has been found that the flow depends sensitively on the wetting conditions at the outer interface. Displacements in a prewet cell are well described by Darcy's law in a wide range of experimental parameters, with little influence of capillary effects. In a dry cell, however, a more careful analysis of the interface motion is required; the interplay between a gradual loss of fluid at the inner interface, and the dependence of capillary forces at the outer interface on interfacial velocity and dynamic contact angle, result in a constant velocity for the interfaces. The experimental results in this case correlate in the form of an empirical scaling relation between the capillary number Ca and a dimensionless group, related to the ratio of centrifugal to capillary forces, which spans about three orders of magnitude in both quantities. Finally, the relative thickness of the coating film left by the inner interface, alpha i, is obtained as a function of Ca.

New experimental apparatus for the study of the Bénard-Rayleigh problem

A new experimental system to measure the equivalent thermal conductivity of a liquid with regard to the Bénard-Rayleigh problem was constructed. The liquid is enclosed within walls of polymethylmethacrylate between two copper plates in which there are thermocouples to measure the difference in temperature between the lower and upper surfaces of the layer of liquid. Heat flux is measured by means of a linear heat fluxmeter consisting of 204 thermocouples in series. The fluxmeter was calibrated and the linear relationship that exists between the heat flux and the emf generated was verified. The thermal conductivity of the polymethylmethacrylate employed was measured and measurements of the equivalent conductivity in cylindrical boundaries of two silicone oils were made. The critical value of the temperature difference and the contribution of the convective process to the transmission of heat were determined.

Time-resolved imaging of the laser forward transfer of liquids

Time-resolved imaging is carried out to study the dynamics of the laser-induced forward transfer of an aqueous solution at different laser fluences. The transfer mechanisms are elucidated, and directly correlated with the material deposited at the analyzed irradiation conditions. It is found that there exists a fluence range in which regular and well-defined droplets are deposited. In this case, laser pulse energy absorption results in the formation of a plasma, which expansion originates a cavitation bubble in the liquid. After the further expansion and collapse of the bubble, a long and uniform jet is developed, which advances at a constant velocity until it reaches the receptor substrate. On the other hand, for lower fluences no material is deposited. In this case, although a jet can be also generated, it recoils before reaching the substrate. For higher fluences, splashing is observed on the receptor substrate due to the bursting of the cavitation bubble. Finally, a discussion of the possible mechanisms which lead to such singular dynamics is also provided.

Theory of Wetting-Induced Fluid Entrainment by Advancing Contact Lines on Dry Surfaces

We report on the onset of fluid entrainment when a contact line is forced to advance over a dry solid of arbitrary wettability. We show that entrainment occurs at a critical advancing speed beyond which the balance between capillary, viscous, and contact-line forces sustaining the shape of the interface is no longer satisfied. Wetting couples to the hydrodynamics by setting both the morphology of the interface at small scales and the viscous friction of the front. We find that the critical deformation that the interface can sustain is controlled by the friction at the contact line and the viscosity contrast between the displacing and displaced fluids, leading to a rich variety of wetting-entrainment regimes. We discuss the potential use of our theory to measure contact-line forces using atomic force microscopy and to study entrainment under microfluidic conditions exploiting colloid-polymer fluids of ultralow surface tension.

Kuumalanka-anemometri virtausmittauksissa

Tässä työssä selostetaan kuumalanka-anemometrin käyttö virtausmittauksissa. Kuumalanka-anemometrilla saadaan mitattua virtausnopeuden ja -suunnan lisäksi nopeusheilahteluja. Mittaustaajuus on tyypillisesti useita kymmeniä tuhansia mittauksia sekunnissa ja signaali on jatkuva. Nykytekniikalla pystytään helposti tallentamaan mittauslaitteistolta saatu viesti tietokoneelle ja muuntamaan se nopeudeksi. Hetkellisten nopeuksien avulla voidaan laskea turbulenttisen virtauksen ominaisuuksia, kuten turbulenssin intensiteetti ja spektri. Kuumalanka-anemometrissa lämmitetään sähköisesti ohutta lankaa, joka on mitattavassa virtauksessa. Langan sähköteho on suunnilleen yhtäsuuri kuin langasta konvektiolla siirtyvä lämpöteho. Tällöin on teoreettisesti mahdollista laskea virtausnopeus lämpötehosta lämmönsiirtokorrelaatioilla. Käytännössä laitteisto joudutaan kuitenkin erikseen kalibroimaan, mutta sähkötehon teoreettista riippuvuutta konvektiosta käytetään hyväksi. Kuumalangan lämmitettävä osuus on tyypillisesti halkaisijaltaan 5 µm ja pituudeltaan noin 1 mm. Sitä käytetään pääasiassa kaasuvirtausten mittaamiseen ja valtaosassa mittauksissa virtausaineena on ilma. Kuumalanka voi olla toteutettu kuumakalvotekniikalla, jossa halkaisijaltaan noin 50 - 70 µm paksuinen kuitu on päällystetty ohuella sähköä johtavalla kalvolla. Kuumakalvoanturin ei tarvitse olla muodoltaan sylinterimäinen, se voi olla mm. kartiomainen tai kiilamainen. Erikoispäällystetyllä kuumakalvoanturilla on mahdollista mitata myös nestevirtauksia. Mitattaessa kaasuvirtauksia kuumakalvon etuna on selvästi parempi kestävyys verrattuna kuumalankaan. Nimitystä kuumalanka-anemometri käytetään yleisesti molemmista anturityypeistä Tämän työn alussa käsitellään sylinterin yli tapahtuvaan virtaukseen liittyvää virtausmekaniikkaa ja lämmönsiirtoa. Anemometrin sähköinen osa, laitteisto ja sen kalibrointi käydään läpi. Langan suuntariippuvuuden laskentaan esitetään tarvittavat yhtälöt. Työssä esitellään kolme laitteistolla tehtyä perusmittausta: anturin kohtauskulman muuttaminen, pyörähdyssymmerisen suihkun nopeuskenttä ja tuulitunnelin rajakerros. Lisäksi esitellään yksi käytännöllinen ja vaativampi mittaus, jossa on mitattu nopeusprofiili radiaalikompressorin diffuusorin loppuosassa.

Measurement of a Structured Backflow in an Open Small Channel Induced by Surface-Tension Gradients

We present experiments in which the laterally confined flow of a surfactant film driven by controlled surface tension gradients causes the subtended liquid layer to self-organize into an inner upstream microduct surrounded by the downstream flow. The anomalous interfacial flow profiles and the concomitant backflow are a result of the feedback between two-dimensional and three-dimensional microfluidics realized during flow in open microchannels. Bulk and surface particle image velocimetry data combined with an interfacial hydrodynamics model explain the dependence of the observed phenomena on channel geometry.

Titaanisen valkaisutornin korjaussuunnitelma

Tämän työn tarkoituksena on poistaa toistuvasti esiintyneet vauriot titaanisessa valkaisutornissa Kuusankosken paperitehtailla. Vauriot esiintyivät melko pian käyttöönoton jälkeen ja niitä esiintyi toistuvasti jokaisen korjauksen jälkeen. Jatkuvatoimisen prosessin vuoksi käyttökatkokset eivät olleet suotavia. Aikataulu suunnittelulle ja korjaukselle oli erittäin tiukka, jolloin kenttämittauksia ei ollut mahdollista tehdä laskelmien tueksi. Tämän vuoksi tähän työtön parhaiten soveltuvaksi menetelmäksi valittiin FEA. Alkuperäisessä rakenteessa pääsäiliöön oli hitsattu pintatasku, jota käytettiin välisäiliönä varastoimaan suuri määrä vaarallista nestettä. Tämä aiheutti valkaisutornin vaipalle murtumia ja vuotoja sekä suuronnettomuuden riskin koko valkaisutornille. Kuormitustietojen puutteesta johtuen kuormitukset mallinnettiin virtuaalisesti FE-menetelmällä ja analyyttisin keinoin. Kuormitusten suuruudet arvioitiin konservatiivisesti. Tämän työn tärkein oivallus oli määritellä uudelleen pintataskun toiminto siten, että sitä ei enää käytetty nesteen välivarastona, vaan ohjaimena nesteelle. Tämä innovatiivinen ongelmankorjauskonsepti on havaittu onnistuneeksi, koska vaurioita ei ole enää esiintynyt viimeisimmän korjauksen jälkeen.

Viscous coupling of shear-free turbulence across nearly flat fluid interfaces

The interactions between shear-free turbulence in two regions (denoted as + and − on either side of a nearly flat horizontal interface are shown here to be controlled by several mechanisms, which depend on the magnitudes of the ratios of the densities, ρ+/ρ−, and kinematic viscosities of the fluids, μ+/μ−, and the root mean square (r.m.s.) velocities of the turbulence, u0+/u0−, above and below the interface. This study focuses on gas–liquid interfaces so that ρ+/ρ− ≪ 1 and also on where turbulence is generated either above or below the interface so that u0+/u0− is either very large or very small. It is assumed that vertical buoyancy forces across the interface are much larger than internal forces so that the interface is nearly flat, and coupling between turbulence on either side of the interface is determined by viscous stresses. A formal linearized rapid-distortion analysis with viscous effects is developed by extending the previous study by Hunt & Graham (J. Fluid Mech., vol. 84, 1978, pp. 209–235) of shear-free turbulence near rigid plane boundaries. The physical processes accounted for in our model include both the blocking effect of the interface on normal components of the turbulence and the viscous coupling of the horizontal field across thin interfacial viscous boundary layers. The horizontal divergence in the perturbation velocity field in the viscous layer drives weak inviscid irrotational velocity fluctuations outside the viscous boundary layers in a mechanism analogous to Ekman pumping. The analysis shows the following. (i) The blocking effects are similar to those near rigid boundaries on each side of the interface, but through the action of the thin viscous layers above and below the interface, the horizontal and vertical velocity components differ from those near a rigid surface and are correlated or anti-correlated respectively. (ii) Because of the growth of the viscous layers on either side of the interface, the ratio uI/u0, where uI is the r.m.s. of the interfacial velocity fluctuations and u0 the r.m.s. of the homogeneous turbulence far from the interface, does not vary with time. If the turbulence is driven in the lower layer with ρ+/ρ− ≪ 1 and u0+/u0− ≪ 1, then uI/u0− ~ 1 when Re (=u0−L−/ν−) ≫ 1 and R = (ρ−/ρ+)(v−/v+)1/2 ≫ 1. If the turbulence is driven in the upper layer with ρ+/ρ− ≪ 1 and u0+/u0− ≫ 1, then uI/u0+ ~ 1/(1 + R). (iii) Nonlinear effects become significant over periods greater than Lagrangian time scales. When turbulence is generated in the lower layer, and the Reynolds number is high enough, motions in the upper viscous layer are turbulent. The horizontal vorticity tends to decrease, and the vertical vorticity of the eddies dominates their asymptotic structure. When turbulence is generated in the upper layer, and the Reynolds number is less than about 106–107, the fluctuations in the viscous layer do not become turbulent. Nonlinear processes at the interface increase the ratio uI/u0+ for sheared or shear-free turbulence in the gas above its linear value of uI/u0+ ~ 1/(1 + R) to (ρ+/ρ−)1/2 ~ 1/30 for air–water interfaces. This estimate agrees with the direct numerical simulation results from Lombardi, De Angelis & Bannerjee (Phys. Fluids, vol. 8, no. 6, 1996, pp. 1643–1665). Because the linear viscous–inertial coupling mechanism is still significant, the eddy motions on either side of the interface have a similar horizontal structure, although their vertical structure differs.

Available potential energy density for a multicomponent Boussinesq fluid with arbitrary nonlinear equation of state

In this paper, the concept of available potential energy (APE) density is extended to a multicomponent Boussinesq fluid with a nonlinear equation of state. As shown by previous studies, the APE density is naturally interpreted as the work against buoyancy forces that a parcel needs to perform to move from a notional reference position at which its buoyancy vanishes to its actual position; because buoyancy can be defined relative to an arbitrary reference state, so can APE density. The concept of APE density is therefore best viewed as defining a class of locally defined energy quantities, each tied to a different reference state, rather than as a single energy variable. An important result, for which a new proof is given, is that the volume integrated APE density always exceeds Lorenz’s globally defined APE, except when the reference state coincides with Lorenz’s adiabatically re-arranged reference state of minimum potential energy. A parcel reference position is systematically defined as a level of neutral buoyancy (LNB): depending on the nature of the fluid and on how the reference state is defined, a parcel may have one, none, or multiple LNB within the fluid. Multiple LNB are only possible for a multicomponent fluid whose density depends on pressure. When no LNB exists within the fluid, a parcel reference position is assigned at the minimum or maximum geopotential height. The class of APE densities thus defined admits local and global balance equations, which all exhibit a conversion with kinetic energy, a production term by boundary buoyancy fluxes, and a dissipation term by internal diffusive effects. Different reference states alter the partition between APE production and dissipation, but neither affect the net conversion between kinetic energy and APE, nor the difference between APE production and dissipation. We argue that the possibility of constructing APE-like budgets based on reference states other than Lorenz’s reference state is more important than has been previously assumed, and we illustrate the feasibility of doing so in the context of an idealised and realistic oceanic example, using as reference states one with constant density and another one defined as the horizontal mean density field; in the latter case, the resulting APE density is found to be a reasonable approximation of the APE density constructed from Lorenz’s reference state, while being computationally cheaper.

A computational study of some rheological influences on the ""splashing experiment""

In various attempts to relate the behaviour of highly-elastic liquids in complex flows to their rheometrical behaviour, obvious candidates for study have been the variation of shear viscosity with shear rate, the two normal stress differences N(1) and N(2), especially N(1), the extensional viscosity, and the dynamic moduli G` and G ``. In this paper, we shall confine attention to `constant-viscosity` Boger fluids, and, accordingly, we shall limit attention to N(1), eta(E), G` and G ``. We shall concentrate on the ""splashing"" problem (particularly that which arises when a liquid drop falls onto the free surface of the same liquid). Modern numerical techniques are employed to provide the theoretical predictions. We show that high eta(E) can certainly reduce the height of the so-called Worthington jet, thus confirming earlier suggestions, but other rheometrical influences (steady and transient) can also have a role to play and the overall picture may not be as clear as it was once envisaged. We argue that this is due in the main to the fact that splashing is a manifestly unsteady flow. To confirm this proposition, we obtain numerical simulations for the linear Jeffreys model. (C) 2010 Elsevier B.V. All rights reserved.

Boundary and internal conditions for adjoint fluid-flow problems

The ever-increasing robustness and reliability of flow-simulation methods have consolidated CFD as a major tool in virtually all branches of fluid mechanics. Traditionally, those methods have played a crucial role in the analysis of flow physics. In more recent years, though, the subject has broadened considerably, with the development of optimization and inverse design applications. Since then, the search for efficient ways to evaluate flow-sensitivity gradients has received the attention of numerous researchers. In this scenario, the adjoint method has emerged as, quite possibly, the most powerful tool for the job, which heightens the need for a clear understanding of its conceptual basis. Yet, some of its underlying aspects are still subject to debate in the literature, despite all the research that has been carried out on the method. Such is the case with the adjoint boundary and internal conditions, in particular. The present work aims to shed more light on that topic, with emphasis on the need for an internal shock condition. By following the path of previous authors, the quasi-1D Euler problem is used as a vehicle to explore those concepts. The results clearly indicate that the behavior of the adjoint solution through a shock wave ultimately depends upon the nature of the objective functional.

Fluid dynamics of air in a packed bed: velocity profiles and the continuum model assumption

Air flow through packed beds was analyzed experimentally under conditions ranging from those that reinforce the effect of the wall on the void fraction to those that minimize it. The packing was spherical particles, with a tube-to-particle diameter ratio (D/dp) between 3 and 60. Air flow rates were maintained between 1.3 and 4.44 m3/min, and gas velocity was measured with a Pitot tube positioned above the bed exit. Measurements were made at various radial and angular coordinate values, allowing the distribution of air flow across the bed to be described in detail. Comparison of the experimentally observed radial profiles with those derived from published equations revealed that at high D/dp ratios the measured and calculated velocity profiles behaved similarly. At low ratios, oscillations in the velocity profiles agreed with those in the voidage profiles, signifying that treating the porous medium as a continuum medium is questionable in these cases.