Fluid Mechanics Research Articles

Clebsch parameterization: Basic properties and remarks on its applications

The Clebsch parameterization (u=∇φ+α∇β) has advantages in elucidating structural properties of vector fields; for example, it helps formulating the Hamiltonian form of ideal fluid mechanics, representing topological constraints (Casimir invariants), integrating the Cauchy characteristics of vortex fields, etc. Because of its “nonlinear” formulation, however, there are some difficulties which must be carefully overcome. (1) It is not complete, i.e., for an arbitrary vector field u, we may fail to find three scalar fields (Clebsch parameters) φ, α, and β that satisfy u=∇φ+α∇β globally in space. (2) It is not uniquely determined, i.e., the map (u1,u2,u3)↦(φ,α,β) is not injective. A generalized form such that u=∇φ+∑j=1ναj∇βj is complete if ν=n−1 (n is the space dimension). However, when we need to control the boundary values of φ, αj, and βj (for example, to determine them uniquely), we have to set ν=n.

Space experimental studies of microgravity fluid science in China

Microgravity fluid physics is an important part of microgravity sciences, which consists of simple fluids of many new systems, gas-liquid two-phase flow and heat transfer, and complex fluid mechanics. In addition to the importance of itself in sciences and applications, microgravity fluid physics closely relates to microgravity combustion, space biotechnology and space materials science, and promotes the developments of interdisciplinary fields. Many space microgravity experiments have been performed on board the recoverable satellites and space ships of China and pushed the rapid development of microgravity sciences in China. In the present paper, space experimental studies and the main results of the microgravity fluid science in China in the last 10 years or so are introduced briefly.

Fluid mechanics demystified

Preface Chapter 1. The Essentials Chapter 2. Fluid Statics Chapter 3. Fluids in Motion Chapter 4. The Integral Equations Chapter 5. The Differential Equations Chapter 6. Dimensional Analysis and Similitude Chapter 7. Internal Flows Chapter 8. External Flows Chapter 9. Compressible Flows Appendix A. Units and Conversions Appendix B. Vector Relationships Appendix C. Fluid Properties Appendix D. Compressible Flow Tables for Air Final Exams Solutions to Quizzes and Final Exams Index

Biomechanical aspects of bone microstructure in vertebrates: potential approach to palaeontological investigations

Biomechanical or biophysical principles can be applied to study biological structures in their modern or fossil form. Bone is an important tissue in paleontological studies as it is a commonly preserved element in most fossil vertebrates, and can often allow its microstructures such as lacuna and canaliculi to be studied in detail. In this context, the principles of Fluid Mechanics and Scaling Laws have been previously applied to enhance the understanding of bone microarchitecture and their implications for the evolution of hydraulic structures to transport fluid. It has been shown that the microstructure of bone has evolved to maintain efficient transport between the nutrient supply and cells, the living components of the tissue. Application of the principle of minimal expenditure of energy to this analysis shows that the path distance comprising five or six lamellar regions represents an effective limit for fluid and solute transport between the nutrient supply and cells; beyond this threshold, hydraulic resistance in the network increases and additional energy expenditure is necessary for further transportation. This suggests an optimization of the size of the bone's building blocks (such as osteon or trabecular thickness) to meet the metabolic demand concomitant to minimal expenditure of energy. This biomechanical aspect of bone microstructure is corroborated from the ratio of osteon to Haversian canal diameters and scaling constants of several mammals considered in this study. This aspect of vertebrate bone microstructure and physiology may provide a basis of understanding of the form and function relationship in both extinct and extant taxa.

Bayesian inverse problems for functions and applications to fluid mechanics

In this paper we establish a mathematical framework for a range of inverse problems for functions, given a finite set of noisy observations. The problems are hence underdetermined and are often ill-posed. We study these problems from the viewpoint of Bayesian statistics, with the resulting posterior probability measure being defined on a space of functions. We develop an abstract framework for such problems which facilitates application of an infinite-dimensional version of Bayes theorem, leads to a well-posedness result for the posterior measure (continuity in a suitable probability metric with respect to changes in data), and also leads to a theory for the existence of maximizing the posterior probability (MAP) estimators for such Bayesian inverse problems on function space. A central idea underlying these results is that continuity properties and bounds on the forward model guide the choice of the prior measure for the inverse problem, leading to the desired results on well-posedness and MAP estimators; the PDE analysis and probability theory required are thus clearly dileneated, allowing a straightforward derivation of results. We show that the abstract theory applies to some concrete applications of interest by studying problems arising from data assimilation in fluid mechanics. The objective is to make inference about the underlying velocity field, on the basis of either Eulerian or Lagrangian observations. We study problems without model error, in which case the inference is on the initial condition, and problems with model error in which case the inference is on the initial condition and on the driving noise process or, equivalently, on the entire time-dependent velocity field. In order to undertake a relatively uncluttered mathematical analysis we consider the two-dimensional Navier–Stokes equation on a torus. The case of Eulerian observations—direct observations of the velocity field itself—is then a model for weather forecasting. The case of Lagrangian observations—observations of passive tracers advected by the flow—is then a model for data arising in oceanography. The methodology which we describe herein may be applied to many other inverse problems in which it is of interest to find, given observations, an infinite-dimensional object, such as the initial condition for a PDE. A similar approach might be adopted, for example, to determine an appropriate mathematical setting for the inverse problem of determining an unknown tensor arising in a constitutive law for a PDE, given observations of the solution. The paper is structured so that the abstract theory can be read independently of the particular problems in fluid mechanics which are subsequently studied by application of the theory.

Von Neumann’s comments about existence and uniqueness for the initial-boundary value problem in gas dynamics

The context is that of a conference, Problems of Cosmical Aerodynamics, held in Paris, France, on August 16–19, 1949. It was organized at the initiative of the newly founded IUTAM and of the IAU. It gathered fifty-two scientists, among which there were thirty-four astronomers and eighteen physicists or fluid mechanicists. The chairs were J. M. Burgers for IUTAM and H. C. van de Hulst for IAU. Among the participants were W. Heisenberg, J. H. Oort, E. Schatzman, T. von Karman, C. F. von Weizsacker and, of course, J. von Neumann. G. I. Taylor could not attend the conference because of sickness. The conference was managed in a rather informal style, the program being decided during the first day, a little bit like our Oberwolfach workshops. Discussion sessions happened every day in the afternoon. I wish to comment here on the session chaired by von Neumann, devoted to the Existence and uniqueness or multiplicity of solutions of the aerodynamical equations. The records of the discussion are reprinted in this issue after these comments. They are taken from pp. 75–85 of the conference proceedings, published by the Central Air Documents Office, Dayton (Ohio), 1951. Instead of a discussion, the session was actually a long monologue by von Neumann, after which he apologize(s) for having taken up so much of the limited time. He then answers the questions of a handful of scientists. The session ends with a comment by Burgers about the consequences of this discussion for astronomical problems. In order to make the context as clear as possible, it is necessary to recall that during WWII, von Neumann had been involved in the Manhattan Project, dedicated to the construction of the American nuclear bomb, while Heisenberg led the German nuclear weapon program, to which Weizsacker collaborated. This was the origin of their common, though independent, interest in fluid mechanics and shock waves. However, the 1949 conference had a peaceful target, and the conversations remained courteous. In addition, Germany was no longer a threat, thus it became meaningful to involve German scientists in such a conference. The

Equation for Calculating Change in Moisture Content Caused by Water Vapor Transfer in Unsaturated Soil

Based on the existing theory such as soil mechanics and fluid mechanics, the transfer mechanism of water vapor inside unsaturated soil is investigated in this paper. A formula that depends on matric suction and temperature is obtained for calculating the saturated water vapor pressure inside the voids of soil. The equation by which the water content changing with time in unsaturated soil resulting from water vapor transfer was also derived. The equation reveals that water vapor transfer is attributed to temperature gradient and water content gradient. The nonuniform distribution of temperature and water content may separately or jointly result in water vapor transfer, which confirms the results demonstrated in experiments. A case history is analyzed using the equation in this paper. The reliability of the equation is verified by analyzing the measured and calculated data. It has to be pointed out that water transfer in unsaturated soil normally occurs simultaneously in both liquid and vapor phases. As a r...

Friction factor correlations for laminar, transition and turbulent flow in smooth pipes

In this paper we derive an accurate composite friction factor vs. Reynolds number correlation formula for laminar, transition and turbulent flow in smooth pipes. The correlation is given as a rational fraction of rational fractions of power laws which is systematically generated by smoothly connecting linear splines in log–log coordinates with a logistic dose curve algorithm. This kind of correlation seeks the most accurate representation of the data independent of any input from theories arising from the researchers’ ideas about the underlying fluid mechanics. As such, these correlations provide an objective metric against which observations and other theoretical correlations may be applied. Our correlation is as accurate, or more accurate, than other correlations in the range of Reynolds numbers in which the correlations overlap. However, our formula is not restricted to certain ranges of Reynolds numbers but instead applies uniformly to all smooth pipe flow data for which data is available. The properties of the classical logistic dose response curve are reviewed and extended to problems described by multiple branches of power laws. This extended method of fitting which leads to rational fractions of power laws is applied to data of Marusic and Perry (1995) [1] for the velocity profile in a boundary layer on a flat plate with an adverse pressure gradient, to data of Nikuradse (1932) [2] and McKeon et al. (2004) [3] on friction factors for flow in smooth pipes and to the data of Nikuradse [4] for effectively smooth pipes.

Solution of linear systems in arterial fluid mechanics computations with boundary layer mesh refinement

Computation of incompressible flows in arterial fluid mechanics, especially because it involves fluid–structure interaction, poses significant numerical challenges. Iterative solution of the fluid mechanics part of the equation systems involved is one of those challenges, and we address that in this paper, with the added complication of having boundary layer mesh refinement with thin layers of elements near the arterial wall. As test case, we use matrix data from stabilized finite element computation of a bifurcating middle cerebral artery segment with aneurysm. It is well known that solving linear systems that arise in incompressible flow computations consume most of the time required by such simulations. For solving these large sparse nonsymmetric systems, we present effective preconditioning techniques appropriate for different stages of the computation over a cardiac cycle.

Gas flow driven by thermal creep in dusty plasma

Thermal creep flow (TCF) is a flow of gas driven by a temperature gradient along a solid boundary. Here, TCF is demonstrated experimentally in a dusty plasma. Stripes on a glass box are heated by laser beam absorption, leading to both TCF and a thermophoretic force. The design of the experiment allows isolating the effect of TCF. A stirring motion of the dust particle suspension is observed. By eliminating all other explanations for this motion, we conclude that TCF at the boundary couples by drag to the bulk gas, causing the bulk gas to flow, thereby stirring the suspension of dust particles. This result provides an experimental verification, for the field of fluid mechanics, that TCF in the slip-flow regime causes steady-state gas flow in a confined volume.

Multiscale sequentially-coupled arterial FSI technique

Multiscale versions of the Sequentially-Coupled Arterial Fluid–Structure Interaction (SCAFSI) technique are presented. The SCAFSI technique was introduced as an approximate FSI approach in arterial fluid mechanics. It is based on the assumption that the arterial deformation during a cardiac cycle is driven mostly by the blood pressure. First we compute a “reference” arterial deformation as a function of time, driven only by the blood pressure profile of the cardiac cycle. Then we compute a sequence of updates involving mesh motion, fluid dynamics calculations, and recomputing the arterial deformation. The SCAFSI technique was developed and tested in conjunction with the stabilized space–time FSI (SSTFSI) technique. Beyond providing a computationally more economical alternative to the fully coupled arterial FSI approach, the SCAFSI technique brings additional flexibility, such as being able to carry out the computations in a spatially or temporally multiscale fashion. In the test computations reported here for the spatially multiscale versions of the SCAFSI technique, we focus on a patient-specific middle cerebral artery segment with aneurysm, where the arterial geometry is based on computed tomography images. The arterial structure is modeled with the continuum element made of hyperelastic (Fung) material.

Wall shear stress calculations in space–time finite element computation of arterial fluid–structure interactions

The stabilized space–time fluid–structure interaction (SSTFSI) technique was applied to arterial FSI problems soon after its development by the Team for Advanced Flow Simulation and Modeling. The SSTFSI technique is based on the Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) formulation and is supplemented with a number of special techniques developed for arterial FSI. The special techniques developed in the recent past include a recipe for pre-FSI computations that improve the convergence of the FSI computations, using an estimated zero-pressure arterial geometry, Sequentially Coupled Arterial FSI technique, using layers of refined fluid mechanics mesh near the arterial walls, and a special mapping technique for specifying the velocity profile at inflow boundaries with non-circular shape. In this paper we introduce some additional special techniques, related to the projection of fluid–structure interface stresses, calculation of the wall shear stress (WSS), and calculation of the oscillatory shear index. In the test computations reported here, we focus on WSS calculations in FSI modeling of a patient-specific middle cerebral artery segment with aneurysm. Two different structural mechanics meshes and three different fluid mechanics meshes are tested to investigate the influence of mesh refinement on the WSS calculations.

The fluid mechanics of scleral buckling surgery for the repair of retinal detachment

Scleral buckling is a common surgical technique used to treat retinal detachments that involves suturing a radial or circumferential silicone element on the sclera. Although this procedure has been performed since the 1960s, and there is a reasonable experimental model of retinal detachment, there is still debate as to how this surgery facilitates the re-attachment of the retina. Finite element calculations using the COMSOL Multiphysics system are utilized to explain the influence of the scleral buckle on the flow of sub-retinal fluid in a physical model of retinal detachment. We found that, by coupling fluid mechanics with structural mechanics, laminar fluid flow and the Bernoulli effect are necessary for a physically consistent explanation of retinal reattachment. Improved fluid outflow and retinal reattachment are found with low fluid viscosity and rapid eye movements. A simulation of saccadic eye movements was more effective in removing sub-retinal fluid than slower, reading speed, eye movements in removing subretinal fluid. The results of our simulations allow us to explain the physical principles behind scleral buckling surgery and provide insight that can be utilized clinically. In particular, we find that rapid eye movements facilitate more rapid retinal reattachment. This is contradictory to the conventional wisdom of attempting to minimize eye movements.

Editorial: Lisbon 2008 special issue

Experiments in Fluids is pleased to present, for the fourth time, a special issue arising from the International Symposia on Applications of Laser Techniques to Fluid Mechanics, held biennially in Lisbon since 1982. The 14th Symposium was held from July 7th to 10th, 2008. This special issue comprises 24 articles presented at the Symposium, preselected by the organizing committee of the meeting, and subsequently submitted to the normal review process of Experiments in Fluids. The editors are very grateful to the organizing committee for this assistance, and we feel that these articles, together with the proceedings of the conference, represent an excellent overview of the state-of-the-art of laser techniques and applications in fluid mechanics. Our thanks go to the authors and referees for keeping to a strict time schedule and, of course, to the Springer-Verlag staff, in particular Mr. Kalithasan Natarajan, who coordinated the final production of the issue. At this opportunity, we would like to draw our readers’ attention to a number of changes at Experiments in Fluids. The first concerns our editorial staff. Prof. Don Rockwell, Editor-in-Chief since 1994, has stepped down in Feb. 2009 and Prof. Noel Clemens from the University of Texas at Austin has taken over this position as Co-Editor-in-Chief with Prof. Cam Tropea from the Technische Universitat Darmstadt. Experiments in Fluids has benefitted greatly from the leadership and judgement of Prof. Rockwell, an appropriate tribute to his service at Experiments in Fluids is forthcoming. Furthermore, Experiments in Fluids has maintained its vigorous program of special issues, both those arising from selected conferences, and topical issues coordinated by guest editors. Our readers are invited to examine our last special issue on the topic of Animal Locomotion: The Physics of Flying (Vol. 46, No. 5, May 2009). The editorial staff is committed to continuing this program of issues, and we look forward to an increased authorship and readership as we explore specific areas of fluid mechanics in more detail. Finally, we would like to note that our efforts over the past years to accelerate the review process at Experiments in Fluids have been very successful, thanks to the efforts of our referees. We now have a submission-to-first-decision time median of under 60 days. Our impact factor has risen continually over this same period as has the number of pages per volume, now *2,400 per year. The editors would like to thank our readers for their sustained support of Experiments in Fluids, and we hope you enjoy this special issue from the Lisbon Symposium.

Eshbach's handbook of engineering fundamentals

Eshbach's handbook of engineering fundamentals

Simulation of Temperature Mitigation by a Stormwater Detention Pond1

Abstract: A numerical model has been developed to simulate the hydraulic and heat transfer properties of a stormwater detention pond, as part of a simulation tool to evaluate thermal pollution of coldwater streams from stormwater runoff. The model is dynamic (unsteady) and based on principles of fluid mechanics and heat transfer. It is driven by hourly weather data, and specified inflow rates and temperatures. To calibrate and validate the pond model field data were collected on a commercial site in Woodbury, Minnesota. The relationship between pond inflow and outflow rates to precipitation was effectively calibrated using continuously recorded pond levels. Algorithms developed for surface heat transfer in lakes were found to be applicable to the pond with some modification, resulting in agreement of simulated and observed pond surface temperature within 1.0°C root mean square error. The use of an unshaded pond for thermal mitigation of runoff from paved surfaces was evaluated using the pond model combined with simulated runoff from an asphalt parking lot for six years of observed rainfall events. On average, pond outflow temperature was 1.2°C higher than inflow temperature, but with significant event‐to‐event variation. On average, the pond added heat energy to runoff from an asphalt parking lot. Although the pond added total heat energy to runoff, it did reduce the rate of heat outflow from the pond by an order of magnitude due to reductions in volumetric outflow rate compared with the inflow rate. By reducing the rate of heat flow, the magnitude of temperature impacts in a receiving stream were also reduced, but the duration of impacts was increased.

Simulation of the Flow Behavior of Thin Polymer Film during Nanoimprint Lithography Based on a Viscoelastic Model

Based on viscoelastic fluid mechanics, this paper presents a simulation model of the flow behaviour of thin polymer film during nanoimprint lithography (NIL). The polymer is imprinted at a constant temperature of 180oC and at a constant imprint speed of 100nm/s by using a tool with a single convex feature of 100 nm in width and 500 nm in height. At the imprint beginning, only a very limited area adjacent to the tool top is affected by the imprint, but subjects to a sudden change of pressure. With the imprint process forward, the wave-like polymer front and the trumpet-shaped profile are predicted to travel out from the imprint patterns. When the tool base intimately contacts the polymer film, another sudden change of the pressure occurs in the area under the interface between the polymer surface and the tool base. These results are of significance to understand the flow behaviour of NIL.

Analysis of the human phonation with different vocal fold geometries by applying a two-dimensional fully coupled fluid-solid-acoustic finite element scheme.

A numerical two-dimensional model is presented simulating the human laryngeal voice production. Air flowing through the larynx interacts with the structural mechanics of the vocal folds forcing them to vibrate and induce sound. In turn, the vibrations of the vocal folds cause the airflow to pulsate which acts as a further sound source inside the larynx. This coupled field problem is modeled by utilizing an enhanced finite element method. The presented approach takes all three involved physical fields consisting of fluid mechanics, solid mechanics, acoustics, and their interactions fully into account. The results of these simulations clearly demonstrate the impact of different vocal fold geometries on the fluid field, e.g., changing the occurrence of the Coanda effect. In addition, influences on the produced sound signal resulting in modified main acoustic frequencies are observed. An additional eigenfrequency analysis on the vocal fold model was performed showing that the first eigenmode and the vibrational frequency in the transient case are identical. The first eigenmode was in the range of about 100 Hz depending on the vocal fold geometry.

A Fluid Mechanics Model of Tissue Fluid Flow in Limb Connective Tissue—A Mechanism of Acupuncture Signal Transmission

This article explores the mechanisms of acupuncture meridians by determining characteristics of the tissue fluid flow in the connective tissue along meridians. Based on deep dissection of acupoints on the upper and lower limbs of the human body and micro and macro observation and measurement, a mathematical model of the flow of tissue fluid in interosseous membranes is constructed. It is shown that the signal transmission along acupuncture meridians may be determined by unique anatomical and physiological factors that govern the flow of tissue fluid in the connective tissue and involve mast cell degranulation. Our results provide a preliminary explanation of the phenomenon of the “de qi” sensation and the mechanism of acupuncture signal transmission along acupuncture meridians.

Simulation of the hydrodynamics of multiphase heterogeneous media in a centrifugal field

A mathematical model has been constructed for the motion of multiphase heterogeneous media over the surface of rotating extension pieces and in hydrocyclones. The model takes into account the separation and thickening of the medium and the existence of a hydrodynamic starting length. Continuum- and trajectory-based approaches to the problem of the motion of multiphase heterogeneous media are suggested. The conservation equations of heterogeneous fluid mechanics have been solved by the flow rate isosurface method. The results of numerical calculations are presented for flows over the inner surface of a conical rotor and in a hydrocyclone.