Off-wall boundary conditions for turbulent flows obtained from buffer-layer minimal flow units

There is strong evidence that the transport processes in the buffer region of wall-bounded turbulence are common across various flow configurations, even in the embryonic turbulence in transition (Park et al., Phys. Fl. 24). We use this premise to develop off-wall boundary conditions for turbulent simulations. Boundary conditions are constructed from DNS databases using periodic minimal flow units and reduced order modeling. The DNS data was taken from a channel at Reτ=400 and a zero-pressure gradient transitional boundary layer (Sayadi et al., submitted to J. Fluid Mech.). Both types of boundary conditions were first tested on a DNS of the core of the channel flow with the aim of extending their application to LES and to spatially evolving flows.

Hydraulics of stepped chutes: experimental-numerical-theoretical study

O estudo de escoamentos turbulentos em descarregadores em degraus tem sido um desafio para os investigadores. A macro-rugosidade do leito, a ondulação da superfície livre, a intermitência da localização da secção inicial de entrada de ar e o escoamento bi-fásico a jusante da secção inicial de entrada de ar fazem com que a caracterização do escoamento deslizante sobre turbilhões em descarregadores em degraus não seja simples. Actualmente, é possível combinar técnicas de medição fiáveis com simulações numéricas e análise teórica. Nesta dissertação, o estudo experimental baseia-se em resultados experimentais obtidos em duas instalações experimentais: a instalação A, do Laboratório Nacional de Engenharia Civil (LNEC), dotada de um descarregador em degraus com declive de 1V:0.75H e a instalação B, do Instituto Superior Técnico (IST), dotada de um descarregador em degraus com declive de 1V:2H. Uma sonda de ar, um tubo de Pitot modificado e vários hidrómetros permitiram o estudo do escoamento deslizante sobre turbilhões mono- e bifásico ao longo do descarregador em degraus da instalação A. Na bacia de dissipação de energia, a observação visual do escoamento foi auxiliada pelas leituras efectuadas em tomadas de pressão localizadas na soleira da bacia e pelas leituras da altura do escoamento efectuadas em réguas graduadas localizadas nas paredes da bacia. Na instalação B foram utilizados um tubo de Pitot e vários hidrómetros para estudar a região não arejada do escoamento deslizante sobre turbilhões no descarregador em degraus. O estudo numérico é baseado em simulações numéricas da região não arejada do escoamento deslizante sobre turbilhões sobre descarregadores em degraus com o código comercial de CFD FLOW-3D® de modo a reproduzir as condições ensaiadas experimentalmente. As simulações beneficiaram da técnica de blocos múltiplos (multi-block) num sistema de coordenadas cartesianas, da determinação da superfície livre pelo método TruVOF e da utilização de dois modelos de turbulência: os modelos k- e RNG k-. Por último, o estudo teórico consistiu em desenvolver um modelo simplificado 1D para determinar as características hidráulicas principais do trecho não arejado do escoamento deslizante sobre turbilhões em descarregadores em degraus. O modelo foi desenvolvido a partir das equações de Navier-Stokes, conjuntamente com resultados experimentais e numéricos. Os resultados apresentados nesta dissertação contribuem para o conhecimento do escoamento deslizante sobre turbilhões em descarregadores em degraus, nomeadamente na região não arejada, na secção inicial de entrada de ar e na região arejada. A hidráulica dos dissipadores de energia a jusante de descarregadores em degraus, em particular das bacias tipo III do USBR, é também objecto de estudo. Em relação à região não arejada do escoamento em descarregadores com declive acentuado, e com base em resultados experimentais e numéricos, são propostas expressões para estimar o desenvolvimento da altura equivalente de água, da espessura da camada limite, da concentração média de ar, do coeficiente de energia cinética, da dissipação de energia, do factor de resistência e do coeficiente n da fórmula de Manning. São ainda propostas expressões adimensionais para a energia cinética turbulenta e sua dissipação. Para declives moderados, são propostas expressões para estimar o desenvolvimento da altura equivalente de água, do coeficiente de energia cinética e da energia específica residual. São ainda apresentados valores do expoente 1/N da expressão adimensional da distribuição de velocidades, quer para descarregadores com declive acentuado quer com declive moderado. Em conformidade com outros estudos centrados em escoamentos de parede e com derivações teóricas, para a região não arejada do escoamento em descarregadores em degraus de acentuado declive, observa-se que o factor de resistência depende da macro-rugosidade criada pelos degraus e da geometria da secção transversal e que o coeficiente n da fórmula de Manning aumenta com a rugosidade. A descrição estatística da turbulência do escoamento é igualmente explorada, contribuindo para o conhecimento da estrutura do escoamento. Observou-se que para números de Reynolds rugoso não superiores a 6.8x104 a energia cinética turbulência e a sua dissipação cumprem leis de semelhança. Estas expressões adimensionais estão de acordo com os resultados obtidos por outros autores para escoamentos completamente desenvolvidos em canais abertos e no escoamento em rios com leito de gravilha. Em acréscimo, a taxa de dissipação de energia, quer para descarregadores de declive acentuado quer de moderado declive, é baixa. Por último, observa-se que os valores da média temporal da concentração de ar entre 0 e 1 medidos na região não arejada do escoamento dizem respeito não só ao ar capturado entre ondas de água, na zona de ondulação da superfície livre, mas também ao ar emulsionado no escoamento, i.e., sob a forma de bolhas de ar, quando perto da secção média inicial de entrada de ar, devido à diferença entre localizações instantânea e média temporal. Foram revistas metodologias e fórmulas para estimar a localização da secção inicial de entrada de ar e apresentadas expressões para estimar a concentração média de ar e a altura equivalente de água nessa secção. Relativamente à região de escoamento arejado em descarregadores em degraus com declive acentuado, os resultados experimentais apresentados nesta dissertação permitiram estimar a influência da definição da superfície livre nos parâmetros hidráulicos da região do escoamento arejado e estimar a máxima elevação do escoamento nesta região do escoamento. Com base nos resultados experimentais obtidos na bacia de dissipação de energia do tipo III do USBR localizada a jusante do descarregador em degraus da instalação A, observou-se que os perfis da altura piezométrica e da altura do escoamento tendem a seguir o perfil recomendado pelo USBR para bacias tipo III. A excepção ocorre à entrada da bacia, onde as alturas piezométricas apresentadas nesta dissertação excedem largamente as apresentadas pelo USBR. É ainda observado que, tal como entre as bacias tipo I e tipo III do USBR, o ressalto hidráulico estabiliza muito mais rapidamente numa bacia tipo III a jusante de um descarregador em degraus do que uma bacia tipo I a jusante do mesmo descarregador em degraus. Finalmente, observa-se que os blocos de amortecimento a colocar no descarregador não têm influência visível nos resultados da altura piezométrica nem da altura do escoamento ao longo da bacia. Relativamente às simulações numéricas do escoamento não arejado, a proximidade entre resultados experimentais e numéricos permite validar o modelo teórico e a integração numérica usados no FLOW-3D®. As simulações desenvolvidas também mostraram que o modelo de turbulência k- permite representar as características do escoamento não arejado em descarregadores em degraus, uma vez que não foram observadas diferenças significativas entre as simulações com este modelo e com o modelo RNG k-. Finalmente, observou-se que o modelo de entrada de ar usado no FLOW-3D® é válido para estimar a localização da secção inicial de entrada de ar. Por último, a proximidade entre os resultados obtidos da aplicação do modelo teórico desenvolvido no âmbito desta dissertação e os resultados experimentais indica que as hipóteses e simplificações consideradas no desenvolvimento do modelo são adequadas.

Fourth-order method for solving the Navier-Stokes equations in a constricting channel

A fourth-order numerical method for solving the Navier-Stokes equations in streamfunction/vorticity formulation on a two-dimensional non-uniform orthogonal grid has been tested on the fluid flow in a constricted symmetric channel. The family of grids is generated algebraically using a conformal transformation followed by a non-uniform stretching of the mesh cells in which the shape of the channel boundary can vary from a smooth constriction to one which one possesses a very sharp but smooth corner. The generality of the grids allows the use of long channels upstream and downstream as well as having a refined grid near the sharp corner. Derivatives in the governing equations are replaced by fourth-order central differences and the vorticity is eliminated, either before or after the discretization, to form a wide difference molecule for the streamfunction. Extra boundary conditions, necessary for wide-molecule methods, are supplied by a procedure proposed by Henshaw et al. The ensuing set of non-linear equations is solved using Newton iteration. Results have been obtained for Reynolds numbers up to 250 for three constrictions, the first being smooth, the second having a moderately sharp corner and the third with a very sharp corner. Estimates of the error incurred show that the results are very accurate and substantially better than those of the corresponding second-order method. The observed order of the method has been shown to be close to four, demonstrating that the method is genuinely fourth-order. © 1977 John Wiley & Sons, Ltd.

Estudo teórico-experimental em via de determinação de lei de atrito em escoamentos de fluidos hiperconcentrados

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A numerical study of temperature effects on hot wire measurements inside turbulent channel flows

A way to investigate turbulence is through experiments where hot wire measurements are performed. Analysis of the in turbulence of a temperature gradient on hot wire measurements is the aim of this thesis work. Actually - to author's knowledge - this investigation is the first attempt to document, understand and ultimately correct the effect of temperature gradients on turbulence statistics. However a numerical approach is used since instantaneous temperature and streamwise velocity fields are required to evaluate this effect. A channel flow simulation at Re_tau = 180 is analyzed to make a first evaluation of the amount of error introduced by temperature gradient inside the domain. Hot wire data field is obtained processing the numerical flow field through the application of a proper version of the King's law, which connect voltage, velocity and temperature. A drift in mean streamwise velocity profile and rms is observed when temperature correction is performed by means of centerline temperature. A correct mean velocity pro�le is achieved correcting temperature through its mean value at each wall normal position, but a not negligible error is still present into rms. The key point to correct properly the sensed velocity from the hot wire is the knowledge of the instantaneous temperature field. For this purpose three correction methods are proposed. At the end a numerical simulation at Re_tau =590 is also evaluated in order to confirm the results discussed earlier.

Reynolds-stress turbulence model in the KIVA code for engine simulation

A Reynolds-Stress Turbulence Model has been incorporated with success into the KIVA code, a computational fluid dynamics hydrocode for three-dimensional simulation of fluid flow in engines. The newly implemented Reynolds-stress turbulence model greatly improves the robustness of KIVA, which in its original version has only eddy-viscosity turbulence models. Validation of the Reynolds-stress turbulence model is accomplished by conducting pipe-flow and channel-flow simulations, and comparing the computed results with experimental and direct numerical simulation data. Flows in engines of various geometry and operating conditions are calculated using the model, to study the complex flow fields as well as confirm the model’s validity. Results show that the Reynolds-stress turbulence model is able to resolve flow details such as swirl and recirculation bubbles. The model is proven to be an appropriate choice for engine simulations, with consistency and robustness, while requiring relatively low computational effort.

Membrane-bound state of the colicin E1 channel domain as an extended two-dimensional helical array

Atomic level structures have been determined for the soluble forms of several colicins and toxins, but the structural changes that occur after membrane binding have not been well characterized. Changes occurring in the transition from the soluble to membrane-bound state of the C-terminal 190-residue channel polypeptide of colicin E1 (P190) bound to anionic membranes are described. In the membrane-bound state, the α-helical content increases from 60–64% to 80–90%, with a concomitant increase in the average length of the helical segments from 12 to 16 or 17 residues, close to the length required to span the membrane bilayer in the open channel state. The average distance between helical segments is increased and interhelix interactions are weakened, as shown by a major loss of tertiary structure interactions, decreased efficiency of fluorescence resonance energy transfer from an energy donor on helix V of P190 to an acceptor on helix IX, and decreased resonance energy transfer at higher temperatures, not observed in soluble P190, implying freedom of motion of helical segments. Weaker interactions are also shown by a calorimetric thermal transition of low cooperativity, and the extended nature of the helical array is shown by a 3- to 4-fold increase in the average area subtended per molecule to 4,200 Å2 on the membrane surface. The latter, with analysis of the heat capacity changes, implies the absence of a developed hydrophobic core in the membrane-bound P190. The membrane interfacial layer thus serves to promote formation of a highly helical extended two-dimensional flexible net. The properties of the membrane-bound state of the colicin channel domain (i.e., hydrophobic anchor, lengthened and loosely coupled α-helices, and close association with the membrane interfacial layer) are plausible structural features for the state that is a prerequisite for voltage gating, formation of transmembrane helices, and channel opening.

An N-methyl-d-aspartate receptor channel blocker with neuroprotective activity

Excitotoxicity, resulting from sustained activation of glutamate receptors of the N-methyl-d-aspartate (NMDA) subtype, is considered to play a causative role in the etiology of ischemic stroke and several neurodegenerative diseases. The NMDA receptor is therefore a target for the development of neuroprotective agents. Here, we identify an N-benzylated triamine (denoted as NBTA) as a highly selective and potent NMDA-receptor channel blocker selected by screening a reduced dipeptidomimetic synthetic combinatorial library. NBTA blocks recombinant NMDA receptors expressed in Xenopus laevis oocytes with a mean IC50 of 80 nM; in contrast, it does not block GluR1, a glutamate receptor of the non-NMDA subtype. The blocking activity of NBTA on NMDA receptors exhibits the characteristics of an open-channel blocker: (i) no competition with agonists, (ii) voltage dependence, and (iii) use dependence. Significantly, NBTA protects rodent hippocampal neurons from NMDA receptor, but not kainate receptor-mediated excitotoxic cell death, in agreement with its selective action on the corresponding recombinant receptors. Mutagenesis data indicate that the N site, a key asparagine on the M2 transmembrane segment of the NR1 subunit, is the main determinant of the blocker action. The results highlight the potential of this compound as a neuroprotectant.

Mutations within the selectivity filter of the NMDA receptor-channel influence voltage dependent block by 5-hydroxytryptamine

Background and purpose: Voltage-dependent block by Mg2+ is a cardinal feature of NMDA receptors which acts as a coincidence detector to prevent the receptor from over-activation. Inhibition of NMDA receptor currents by 5-hydroxytryptamine (5-HT) indicated that 5-HT, similar to Mg2+, binds within the membrane electric field. In the present study, we assessed whether point mutations of critical asparagine residues located within the selectivity filter of NR1 and NR2A subunits of NMDA receptor-channel affect voltage-dependent block by 5-HT. Experimental approach: The mode of action of 5-HT and Mg2+ on wild-type and mutated NMDA receptor-channels expressed in Xenopus oocytes was investigated using the two-electrode voltage clamp recording technique. Key results: The mutation within the NR1 subunit NR1(N0S or N0Q) strongly reduced the voltage dependent block by 5-HT and increased the IC50. The corresponding mutations within the NR2 subunits NR2A(N0Q or N + 1Q) reduced the block by 5-HT to a lesser extent. This is in contrast to the block produced by external Mg2+ where a substitution at the NR2A(N0) and NR2A(N + 1) sites but not at the NR1(N0) site significantly reduced Mg2+ block. Conclusion and implications: The block of NMDA receptor-channels by 5-HT depends on the NR1-subunit asparagine residue and to a lesser extent on the NR2A-subunit asparagine residues. These data suggest that the interaction of 5-HT with functionally important residues in a narrow constriction of the pore of the NMDA receptor-channel provides a significant barrier to ionic fluxes through the open channel due to energetic factors governed by chemical properties of the binding site and the electric field.

Direct numerical simulation of turbulent flow and mass transfer around a rotating circular cylinder

Turbulent flow around a rotating circular cylinder has numerous applications including wall shear stress and mass-transfer measurement related to the corrosion studies. It is also of interest in the context of flow over convex surfaces where standard turbulence models perform poorly. The main purpose of this paper is to elucidate the basic turbulence mechanism around a rotating cylinder at low Reynolds numbers to provide a better understanding of flow fundamentals. Direct numerical simulation (DNS) has been performed in a reference frame rotating at constant angular velocity with the cylinder. The governing equations are discretized by using a finite-volume method. As for fully developed channel, pipe, and boundary layer flows, a laminar sublayer, buffer layer, and logarithmic outer region were observed. The level of mean velocity is lower in the buffer and outer regions but the logarithmic region still has a slope equal to the inverse of the von Karman constant. Instantaneous flow visualization revealed that the turbulence length scale typically decreases as the Reynolds number increases. Wavelet analysis provided some insight into the dependence of structural characteristics on wave number. The budget of the turbulent kinetic energy was computed and found to be similar to that in plane channel flow as well as in pipe and zero pressure gradient boundary layer flows. Coriolis effects show as an equivalent production for the azimuthal and radial velocity fluctuations leading to their ratio being lowered relative to similar nonrotating boundary layer flows.

Numerical modelling of unsteady mixed flows

This thesis concerns mixed flows (which are characterized by the simultaneous occurrence of free-surface and pressurized flow in sewers, tunnels, culverts or under bridges), and contributes to the improvement of the existing numerical tools for modelling these phenomena. The classic Preissmann slot approach is selected due to its simplicity and capability of predicting results comparable to those of a more recent and complex two-equation model, as shown here with reference to a laboratory test case. In order to enhance the computational efficiency, a local time stepping strategy is implemented in a shock-capturing Godunov-type finite volume numerical scheme for the integration of the de Saint-Venant equations. The results of different numerical tests show that local time stepping reduces run time significantly (between −29% and −85% CPU time for the test cases considered) compared to the conventional global time stepping, especially when only a small region of the flow field is surcharged, while solution accuracy and mass conservation are not impaired. The second part of this thesis is devoted to the modelling of the hydraulic effects of potentially pressurized structures, such as bridges and culverts, inserted in open channel domains. To this aim, a two-dimensional mixed flow model is developed first. The classic conservative formulation of the 2D shallow water equations for free-surface flow is adapted by assuming that two fictitious vertical slots, normally intersecting, are added on the ceiling of each integration element. Numerical results show that this schematization is suitable for the prediction of 2D flooding phenomena in which the pressurization of crossing structures can be expected. Given that the Preissmann model does not allow for the possibility of bridge overtopping, a one-dimensional model is also presented in this thesis to handle this particular condition. The flows below and above the deck are considered as parallel, and linked to the upstream and downstream reaches of the channel by introducing suitable internal boundary conditions. The comparison with experimental data and with the results of HEC-RAS simulations shows that the proposed model can be a useful and effective tool for predicting overtopping and backwater effects induced by the presence of bridges and culverts.

Negotiating social and moral order in internet relay chat

Although internet chat is a significant aspect of many internet users’ lives, the manner in which participants in quasi-synchronous chat situations orient to issues of social and moral order remains to be studied in depth. The research presented here is therefore at the forefront of a continually developing area of study. This work contributes new insights into how members construct and make accountable the social and moral orders of an adult-oriented Internet Relay Chat (IRC) channel by addressing three questions: (1) What conversational resources do participants use in addressing matters of social and moral order? (2) How are these conversational resources deployed within IRC interaction? and (3) What interactional work is locally accomplished through use of these resources? A survey of the literature reveals considerable research in the field of computer-mediated communication, exploring both asynchronous and quasi-synchronous discussion forums. The research discussed represents a range of communication interests including group and collaborative interaction, the linguistic construction of social identity, and the linguistic features of online interaction. It is suggested that the present research differs from previous studies in three ways: (1) it focuses on the interaction itself, rather than the ways in which the medium affects the interaction; (2) it offers turn-by-turn analysis of interaction in situ; and (3) it discusses membership categories only insofar as they are shown to be relevant by participants through their talk. Through consideration of the literature, the present study is firmly situated within the broader computer-mediated communication field. Ethnomethodology, conversation analysis and membership categorization analysis were adopted as appropriate methodological approaches to explore the research focus on interaction in situ, and in particular to investigate the ways in which participants negotiate and co-construct social and moral orders in the course of their interaction. IRC logs collected from one chat room were analysed using a two-pass method, based on a modification of the approaches proposed by Pomerantz and Fehr (1997) and ten Have (1999). From this detailed examination of the data corpus three interaction topics are identified by means of which participants clearly orient to issues of social and moral order: challenges to rule violations, ‘trolling’ for cybersex, and experiences regarding the 9/11 attacks. Instances of these interactional topics are subjected to fine-grained analysis, to demonstrate the ways in which participants draw upon various interactional resources in their negotiation and construction of channel social and moral orders. While these analytical topics stand alone in individual focus, together they illustrate different instances in which participants’ talk serves to negotiate social and moral orders or collaboratively construct new orders. Building on the work of Vallis (2001), Chapter 5 illustrates three ways that rule violation is initiated as a channel discussion topic: (1) through a visible violation in open channel, (2) through an official warning or sanction by a channel operator regarding the violation, and (3) through a complaint or announcement of a rule violation by a non-channel operator participant. Once the topic has been initiated, it is shown to become available as a topic for others, including the perceived violator. The fine-grained analysis of challenges to rule violations ultimately demonstrates that channel participants orient to the rules as a resource in developing categorizations of both the rule violation and violator. These categorizations are contextual in that they are locally based and understood within specific contexts and practices. Thus, it is shown that compliance with rules and an orientation to rule violations as inappropriate within the social and moral orders of the channel serves two purposes: (1) to orient the speaker as a group member, and (2) to reinforce the social and moral orders of the group. Chapter 6 explores a particular type of rule violation, solicitations for ‘cybersex’ known in IRC parlance as ‘trolling’. In responding to trolling violations participants are demonstrated to use affiliative and aggressive humour, in particular irony, sarcasm and insults. These conversational resources perform solidarity building within the group, positioning non-Troll respondents as compliant group members. This solidarity work is shown to have three outcomes: (1) consensus building, (2) collaborative construction of group membership, and (3) the continued construction and negotiation of existing social and moral orders. Chapter 7, the final data analysis chapter, offers insight into how participants, in discussing the events of 9/11 on the actual day, collaboratively constructed new social and moral orders, while orienting to issues of appropriate and reasonable emotional responses. This analysis demonstrates how participants go about ‘doing being ordinary’ (Sacks, 1992b) in formulating their ‘first thoughts’ (Jefferson, 2004). Through sharing their initial impressions of the event, participants perform support work within the interaction, in essence working to normalize both the event and their initial misinterpretation of it. Normalising as a support work mechanism is also shown in relation to participants constructing the ‘quiet’ following the event as unusual. Normalising is accomplished by reference to the indexical ‘it’ and location formulations, which participants use both to negotiate who can claim to experience the ‘unnatural quiet’ and to identify the extent of the quiet. Through their talk participants upgrade the quiet from something legitimately experienced by one person in a particular place to something that could be experienced ‘anywhere’, moving the phenomenon from local to global provenance. With its methodological design and detailed analysis and findings, this research contributes to existing knowledge in four ways. First, it shows how rules are used by participants as a resource in negotiating and constructing social and moral orders. Second, it demonstrates that irony, sarcasm and insults are three devices of humour which can be used to perform solidarity work and reinforce existing social and moral orders. Third, it demonstrates how new social and moral orders are collaboratively constructed in relation to extraordinary events, which serve to frame the event and evoke reasonable responses for participants. And last, the detailed analysis and findings further support the use of conversation analysis and membership categorization as valuable methods for approaching quasi-synchronous computer-mediated communication.

Direct numerical simulation of turbulent spots

A group of high-order finite-difference schemes for incompressible flow was implemented to simulate the evolution of turbulent spots in channel flows. The long-time accuracy of these schemes was tested by comparing the evolution of small disturbances to a plane channel flow against the growth rate predicted by linear theory. When the perturbation is the unstable eigenfunction at a Reynolds number of 7500, the solution grows only if there are a comparatively large number of (equispaced) grid points across the channel. Fifth-order upwind biasing of convection terms is found to be worse than second-order central differencing. But, for a decaying mode at a Reynolds number of 1000, about a fourth of the points suffice to obtain the correct decay rate. We show that this is due to the comparatively high gradients in the unstable eigenfunction near the walls. So, high-wave-number dissipation of the high-order upwind biasing degrades the solution especially. But for a well-resolved calculation, the weak dissipation does not degrade solutions even over the very long times (O(100)) computed in these tests. Some new solutions of spot evolution in Couette flows with pressure gradients are presented. The approach to self-similarity at long times can be seen readily in contour plots.

Chapman-Enskog analysis for finite-volume formulation of lattice Boltzmann equation

The classical Chapman-Enskog expansion is performed for the recently proposed finite-volume formulation of lattice Boltzmann equation (LBE) method D.V. Patil, K.N. Lakshmisha, Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh, J. Comput. Phys. 228 (2009) 5262-5279]. First, a modified partial differential equation is derived from a numerical approximation of the discrete Boltzmann equation. Then, the multi-scale, small parameter expansion is followed to recover the continuity and the Navier-Stokes (NS) equations with additional error terms. The expression for apparent value of the kinematic viscosity is derived for finite-volume formulation under certain assumptions. The attenuation of a shear wave, Taylor-Green vortex flow and driven channel flow are studied to analyze the apparent viscosity relation.

Probe for Measurements of Density/Conductivity in Flows of Conducting Fluids

A probe utilizing the bipolar pulse method to measure the density of a conducting fluid has been developed. The probe is specially designed such that the concentration of a stream tube can be sampled continuously. The density was determined indirectly from the measurement of solution conductivity. The probe was calibrated using standard NaCl solutions of varying molarity and was able to rapidly determine the density of a fluid with continuously varying conductance. Measurements of the conductivity profiles, corresponding density profiles, and their fluctuation levels are demonstrated in a channel flow with an electrolyte injected from a slot in one wall.