Direct measurements of local bed shear stress in the presence of pressure gradients

This paper describes the development of a shear plate sensor capable of directly measuring the local mean bed shear stress in small-scale and large-scale laboratory flumes. The sensor is capable of measuring bed shear stress in the range \(\pm\) 200 Pa with an accuracy up to \(\pm\) 1 %. Its size, 43 mm in the flow direction, is designed to be small enough to give spatially local measurements, and its bandwidth, 75 Hz, is high enough to resolve time-varying forcing. Typically, shear plate sensors are restricted to use in zero pressure gradient flows because secondary forces on the edge of the shear plate caused by pressure gradients can introduce large errors. However, by analysis of the pressure distribution at the edges of the shear plate in mild pressure gradients, we introduce a new methodology for correcting for the pressure gradient force. The developed sensor includes pressure tappings to measure the pressure gradient in the flow, and the methodology for correction is applied to obtain accurate measurements of bed shear stress under solitary waves in a small-scale wave flume. The sensor is also validated by measurements in a turbulent flat plate boundary layer in open channel flow.     

Diffusion-Thermo and Radiation Effects on Unsteady MHD Flow Through Porous Medium Past an Impulsively Started Infinite Vertical Plate with Variable Temperature and Mass Diffusion

The objective of this study is to investigate diffusion-thermo (Dufour effect) and radiation effects on unsteady MHD free convection flow past an impulsively started infinite vertical plate with variable temperature and uniform mass diffusion in the presence of transverse applied magnetic field through porous medium. At time t > 0, the plate is given an impulsive motion with constant velocity u ₀ in the vertical upward direction against to the gravitational field. At the same time, the plate temperature is raised linearly with time t and the level of concentration near the plate is raised to ${{C}_{\rm w}^{\prime}}$ . A magnetic field of uniform strength B ₀ is applied normal to the direction to the flow. The dimensionless governing equations are solved in closed form by Laplace transform technique. The effect of flow parameters on velocity, temperature, concentration, the rate of heat transfer and the rate of mass transfer are shown through graphs.     

Magnetic and Gravitational Convection of Air in a Porous Cubic Enclosure with a Coil Inclined Around the Y Axis

The natural convection heat transfer of air in a porous media can be controlled by gradient magnetic field. Thermomagnetic convection of air in a porous cubic enclosure with an electric coil inclined around the $Y$ axis was numerically investigated. The Biot–Savart law was used to calculate the magnetic field. The governing equations in primitive variables were discretized by the finite-volume method and solved by the SIMPLE algorithm. The flow and temperature fields for the air natural convection were presented and the mean Nusselt number on the hot wall was calculated and compared. The results show that both the magnetic force and coil inclination have significant effect on the flow field and heat transfer in a porous cubic enclosure, the natural convection heat transfer of air can be enhanced or controlled by applying gradient magnetic field.     

High sensitivity measurements of normal force under large amplitude oscillatory shear

The two aims of this publication are to introduce a new and rheometer-independent rheometric tool for measuring the axial normal force in oscillatory shear rheology and to study the normal forces of polyolefin melts under large amplitude oscillatory shear (LAOS). A new plate geometry with an incorporated highly sensitive piezoelectric normal force sensor was designed for a rotational rheometer. The new geometry was used to investigate normal forces of polyethylene (PE) melts under LAOS. The resulting stress and normal force data was compared with the data from measurements in commercial high performance rotational rheometers. The stress and the normal force response were Fourier-transformed and their resulting spectra were analysed. The non-linear contributions to the FT-magnitude spectra (i.e. the intensities of the higher harmonics) were analysed using the framework of the Q-parameter, \(Q=I_{3/1}/{\gamma ^{2}_{0}}\) for both the stress spectrum and the normal force spectrum, resulting in the strain-dependent \(Q\left (\gamma _{0}\right )\) and \(Q_{NF}\left (\gamma _{0}\right )\), respectively. The newly designed normal force geometry had a sensitivity in the measurement starting from \(5\times 10^{-5}\) N up to 20 N, and respectively a signal-to-noise ratio (SNR) of \(1:\) 16.000, which is about a factor of 1.8 times better than the best performing commercial rheometers. The new geometry was used to determine \(Q\left (\gamma _{0}\right )\) and \(Q_{NF}\left (\gamma _{0}\right )\), to characterize the shear rheological behaviour of the PE melts. Even rather simple rheometers, those without normal force detection, can be extended utilizing the here presented tools for high sensitive FT-rheology analysing the normal forces.     

Development of a feedback model for the high-speed impinging planar jet

This article experimentally investigates the self-excited impinging planar jet flow, specifically the development and propagation of large-scale coherent flow structures convecting between the nozzle lip and the downstream impingement surface. The investigation uses phase-locked particle image velocimetry measurements and a new structure-tracking scheme to measure convection velocity and characterize the impingement mechanism near the plate, in order to develop a new feedback model that can be used to predict the oscillation frequency as a function of flow velocity ( $U_o$ ), impingement distance ( $x_o$ ) and nozzle thickness ( $h$ ). The resulting model prediction shows a good agreement with experimental tone frequency data.     

Dynamics of a two-dimensional flow subject to steady electromagnetic forces

A novel experimental setup is presented to study the dynamics of a two-dimensional (2D) flow formed of an electrolyte subject to steady electromagnetic forcing. A thin layer of potassium hydroxide is poured into a square-base container with a strong magnetic field ( $\vec{B}$ ) achieved by permanent neodymium magnets inserted underneath the base. The set of electrodes of alternating polarity distributed along the perimeter of the container generates currents ( $\vec{j}$ ) in opposite directions. Coherent primary vortices of scales about 2 cm are thus generated by the $\vec{j} \times \vec{B}$ force. We also show, and for the first time, that fluid motion is caused by the magnetic field gradient where the amplitude of $\vec{B}$ is equal to zero. It leads to the generation of jets with size about that of the container, that is, 25 cm. The interaction between these gradB jets and the edge vortices leads to a final flow dominated by large-scale vortices resulting from the inverse cascade process that destroys the small-scale coherent structures on one hand and on the other modifies the initial scale and direction of the gradB jets.     

A self-aligning parallel plate (SAPP) fixture for tribology and high shear rheometry

This paper introduces a novel self-aligning parallel plate fixture for rotational rheometers. The ring-shaped shearing surface of this fixture is held on a low friction single contact point bearing and uses hydrodynamic lubrication forces in order to maintain the parallelism of the freely tilting surfaces over a full rotation. The optimized parallelism of the plates enables to conduct tribological measurements of low frictional stress between the shearing surface materials and a fluid at normal loads down to 1.3 kPa. Limited only by the degree of non-flatness of the surfaces, the new fixture can determine boundary lubrication sliding frictions within 10 % and down to angular velocities of 400 μrad/s. In a controlled gap mode, this setup reaches a gap error of 3.4 μm which enables to reliably conduct rheological measurements down to absolute gaps of the parallel plates of 10 μm and to reach high shear rates up to $10^{5}\;{\rm s}^{-1}$ .     

Measurement and Correlation of Pressure Drop Characteristics for Air Flow Through Sintered Metal Porous Media

Sintered metal porous media are currently used to replace conventional orifices as restrictors in air-bearing systems. The flow properties in porous media are generally approximated by Darcy and Forchheimer regimes in different flow regions. In this study, an ISO expanded expression is proven defective when it is used to represent flow properties through porous media under slight pressure drops ( ${<}10$  kPa). A modified Forchheimer equation is therefore developed to correlate the pressure drop with flow rate, including compressibility and inertial effects. Experimental and theoretical investigations on pressure drop characteristics are conducted with a series of metal-sintered porous media. Permeability is first determined in a strict Darcy region with $Re<0.1$ , followed by the inertial coefficient with $Re>0.1$ , rather than determining these two simultaneously. The theoretical mass flow rate in terms of the modified Forchheimer equation provides close approximations to the experimental data.     

Heat Transfer in Incompressible Magnetic Fluid

In this paper we study the equations describing the dynamics of heat transfer in an incompressible magnetic fluid under the action of an applied magnetic field. The system is a combination of the Navier?CStokes equations, the magnetostatic equations and the temperature equation. We prove global-in-time existence of weak solutions with finite energy to the system posed in a bounded domain of ${\mathbb{R}^3}$ and equipped with initial and boundary conditions. The main difficulty comes from the singularity of the terms representing the Kelvin force due to the magnetization and the thermal power due to the magnetocaloric effect.     

A Model for Spontaneous Imbibition as a Mechanism for Oil Recovery in Fractured Reservoirs

The flow of oil and water in naturally fractured reservoirs (NFR) can be highly complex and a simplified model is presented to illustrate some main features of this flow system. NFRs typically consist of low-permeable matrix rock containing a high-permeable fracture network. The effect of this network is that the advective flow bypasses the main portions of the reservoir where the oil is contained. Instead capillary forces and gravity forces are important for recovering the oil from these sections. We consider a linear fracture which is symmetrically surrounded by porous matrix. Advective flow occurs only along the fracture, while capillary driven flow occurs only along the axis of the matrix normal to the fracture. For a given set of relative permeability and capillary pressure curves, the behavior of the system is completely determined by the choice of two dimensionless parameters: (i) the ratio of time scales for advective flow in fracture to capillary flow in matrix $\alpha =\tau ^f/\tau ^m$ ; (ii) the ratio of pore volumes in matrix and fracture $\beta =V^m/V^f$ . A characteristic property of the flow in the coupled fracture–matrix medium is the linear recovery curve (before water breakthrough) which has been referred to as the “filling fracture” regime Rangel-German and Kovscek (J Pet Sci Eng 36:45–60, 2002), followed by a nonlinear period, referred to as the “instantly filled” regime, where the rate is approximately linear with the square root of time. We derive an analytical solution for the limiting case where the time scale $\tau ^{m}$ of the matrix imbibition becomes small relative to the time scale $\tau ^{f}$ of the fracture flow (i.e., $\alpha \rightarrow \infty $ ), and verify by numerical experiments that the model will converge to this limit as $\alpha $ becomes large. The model provides insight into the role played by parameters like saturation functions, injection rate, volume of fractures versus volume of matrix, different viscosity relations, and strength of capillary forces versus injection rate. Especially, a scaling number $\omega $ is suggested that seems to incorporate variations in these parameters. An interesting observation is that at $\omega =1$ there is little to gain in efficiency by reducing the injection rate. The model can be used as a tool for interpretation of laboratory experiments involving fracture–matrix flow as well as a tool for testing different transfer functions that have been suggested to use in reservoir simulators.     

Onset of Buoyancy-Driven Convection in a Fluid-Saturated Porous Medium Bounded by a Long Cylinder

A theoretical analysis of convective instability driven by buoyancy forces under the transient concentration fields is conducted in an initially quiescent, liquid-saturated, cylindrical porous column. Darcy’s law and Boussinesq approximation are used to explain the characteristics of fluid motion and linear stability theory is employed to predict the onset of buoyancy-driven motion. Under the principle of exchange of stabilities, the stability equations are derived in self-similar boundary-layer coordinate. The present predictions suggest the critical $R_D$ , and the onset time and corresponding wavenumber for a given $R_D$ . The onset time becomes smaller with increasing $R_D$ and follows the asymptotic relation derived in the infinite horizontal porous layer.     

Experimental exploration of underexpanded supersonic jets

Two underexpanded free jets at fully expanded Mach numbers $M_\mathrm{j}$ = 1.15 and 1.50 are studied. Schlieren visualizations as well as measurements of static pressure, Pitot pressure and velocity are performed. All these experimental techniques are associated to obtain an accurate picture of the jet flow development. In particular, expansion, compression and neutral zones have been identified in each shock cell. Particle lag is considered by integrating the equation of motion for particles in a fluid flow and it is found that the laser Doppler velocimetry is suitable for investigating shock-containing jets. Even downstream of the normal shock arising in the $M_\mathrm{j}$ = 1.50 jet, the measured gradual velocity decrease is shown to be relevant.     

Investigation of Self-Similar Interface Evolution in Carbon Dioxide Sequestration in Saline Aquifers

In this work, we investigate numerically the injection of supercritical carbon dioxide into a deep saline reservoir from a single well. We analyze systematically the sharp-interface evolution in different flow regimes. The flow regimes can be parameterized by two dimensionless numbers, the gravity number, \(\Gamma \) and the mobility ratio, \(\lambda \) . Numerical simulations are performed using the volume of fluid method, and the results are compared with the solutions of the self-similarity equation established in previous works, which describes the evolution of the sharp interface. We show that these theoretical solutions are in very good agreement with the results from the numerical simulations presented over the different flow regimes, thereby showing that the theoretical and simulation models predict consistently the spreading and migration of the created \(\hbox {CO}_{2}\) plume under complex flow behavior in porous media. Furthermore, we compare the numerical results with known analytic approximations in order to assess their applicability and accuracy over the investigated parametric space. The present study indicates that the self-similar solutions parameterized by the dimensionless numbers \(\lambda , \Gamma \) are significant for examining effectively injection scenarios, as these numbers control the shape of the interface and migration of the \(\hbox {CO}_{2}\) plume. This finding is essential in assessing the storage capacity of saline aquifers.     

软铁磁薄板磁弹性屈曲的理论模型

铁磁弹性薄板的磁弹性屈曲问题一直作为电磁——弹性力学相互作用的一个基本模型进行研究，而作用在其磁介质上的磁力计算则是定量理论预测准确与否的关键．到目前为止，文献上已有的理论模型对悬臂铁磁梁式悬臂板在横向磁场中磁弹性屈曲的理论预测值始终高于实验值，有的甚至相差１００％左右．本文基于电磁力计算的微观安培电流模型，严格给出了软铁磁薄板等效横向磁力的宏观计算表达式．在此基础上，建立了电磁——力学相互耦合作用的非线性理论模型．该模型能描述铁磁薄板结构在非均匀横向磁场环境中的磁弹性失稳（或屈曲）．其定量分析采用了有限元法和有限差分法相结合．数值结果显示：本模型给出的磁弹性屈曲的临界磁场值与实验值符合良好．与此同时，文中还对文献中认为较成功的Ｍｏｏｎ－Ｐａｏ模型的基本假设进行了分析．定量结果发现：Ｍｏｏｎ－Ｐａｏ理论模型的基本假设仅在梁式板的长厚比Ｌ／ｈ比较大时（约在２００左右），是可以接受的，而当Ｌ／ｈ较小时，该假设将导致理论值与实验值的较大误差．Ｌ／ｈ比值越小，理论值与实验值的误差越大     

Active flow control on a 1:4 car model

Lift and drag of a passenger car are strongly influenced by the flow field around its rear end. The bluff body geometry produces a detached, transient flow which induces fluctuating forces on the body, affecting the rear axle, which may distress dynamic stability and comfort significantly. The investigations presented here deal with a 1:4 scale model of a simplified test car geometry that produces fluctuating lift and drag due to its strongly rounded rear geometry. To examine the influence of active flow control on this behavior, steady air jets were realized to exhaust from thin slots across the rear in three different configurations. Investigations were performed at $Re = 2.1 \times 10^{6}$ and included the capturing of effective integral lift and drag, velocity measurements in the surrounding flow field with Laser Doppler Anemometry, surface pressure measurements and surface oil flow visualization on the rear. The flow field was found to be dominated by two longitudinal vortices, developing from the detachment of the flow at the upper C-pillar positions, and a recirculating, transverse vortex above the rear window. With an air jet emerging from a slot across the surface right below the rear window section, tangentially directed upstream toward the roof section, total lift could be reduced by more than 7 %, with rear axle lift reduction of about 5 % and negligible drag affection ( $<$ 1 %).     

Experimental investigation of the fluid–structure interaction in an elastic 180° curved vessel at laminar oscillating flow

Fluid–structure interaction phenomena are extremely important when laminar flows through elastic vessels such as in biomedical flow problems are considered. In general, such elastic vessels are curved which is why an elastic 180° bend at a curvature ratio \(\delta = D/D_{\rm C} = 0.\bar{2}\) defines the reference geometry in this study. It is the purpose of this study to compare the results with the steady flow through a 180° rigid pipe bend and to quantify the impact of the fluid–structure interaction on the overall flow pattern and the vessel deformation at oscillating fully developed entrance flow. The findings comprise velocity, pressure, and structure deformation measurements. The vessel dilatation amplitude was varied between 3.75 % and 7 % of the vessel diameter at Dean De and Womersley number Wo ranges of \(327\,\le\,De\,\le\,350\) and \(7\,\le\,Wo\,\le\,8.\) The flow is investigated by time-resolved stereoscopic particle-image velocimetry in five radial cross sections located in the elastic 180° bend and in the inlet pipes. The unsteady static vessel pressure is measured synchronously at these cross sections. The comparison of the steady with the unsteady flow field shows a strong change in the axial and secondary velocity distributions at periods of transition between the centrifugal forces and the unsteady inertia forces dominated regimes. These changes are characterized by asymmetric fluctuations of the centers of the counter-rotating vortex pair. The investigation of the impact of the structure deformation amplitude on these fluctuations reveals a significant attenuation at high deformation amplitudes. The spatial motion of the elastic vessel due to the forces applied by the flow exhibits amplitudes up to 15 % of the vessel diameter. Considering the fluid–structure interaction, an amplification of the volume flux amplitude by a factor of 2.1 at the vessel outlet and phase lags up to 30° occur. The static pressure distribution is characterized by a pronounced asymmetry between forward and backward flow with a 40 % higher peak magnitude at backward flow and phase lags of 35°. The results evidence that a strong distortion of the velocity distribution in the bend, which is caused by the oscillating nature of the flow, is reduced as a result of the fluid–structure interaction.     

Identification of flow regimes around two staggered square cylinders by a numerical study

The flow over two square cylinders in staggered arrangement is simulated numerically at a fixed Reynolds number (\(Re =150\)) for different gap spacing between cylinders from 0.1 to 6 times a cylinder side to understand the flow structures. The non-inclined square cylinders are located on a line with a staggered angle of \(45^{\circ }\) to the oncoming velocity vector. All numerical simulations are carried out with a finite-volume code based on a collocated grid arrangement. The effects of vortex shedding on the various features of the flow field are numerically visualized using different flow contours such as \(\lambda _{2}\) criterion, vorticity, pressure and magnitudes of velocity to distinguish the distinctive flow patterns. By changing the gap spacing between cylinders, five different flow regimes are identified and classified as single body, periodic gap flow, aperiodic, modulated periodic and synchronized vortex shedding regimes. This study revealed that the observed multiple frequencies in global forces of the downstream cylinder in the modulated periodic regime are more properly associated with differences in vortex shedding frequencies of individual cylinders than individual shear layers reported in some previous works; particularly, both shear layers from the downstream cylinder often shed vortices at the same multiple frequencies. The maximum Strouhal number for the upstream cylinder is also identified at \({G}^{*}=1\) for aperiodic flow pattern. Furthermore, for most cases studied, the downstream cylinder experiences larger drag force than the upstream cylinder.     

Measurements of an unsteady liquid metal flow during spin-up driven by a rotating magnetic field

A cylindrical cavity with an aspect ratio of unity is filled with liquid metal and suddenly exposed to an azimuthal body force generated by a rotating magnetic field (RMF). This experimental study is concerned with the secondary meridional flow during the time, if the fluid spins up from rest. Vertical profiles of the axial velocity have been measured by means of the ultrasound Doppler velocimetry. The flow measurements confirm the spin-up concept by Ungarish (J Fluid Mech 347:105–118, 1997) and the continuative study by Nikrityuk et al. (Phys Fluids 17:067101, 2005) who suggested the existence of two stages during the RMF-driven spin-up, in particular the so-called initial adjustment phase followed by an inertial phase which is dominated by inertial oscillations of the secondary flow. Evolving instabilities of the double-vortex structure of the secondary flow have been detected at a Taylor number of 1.24 × 10⁵ verifying the predictions of Grants and Gerbeth (J Fluid Mech 463:229–240, 2002). Perturbations in form of Taylor–Görtler vortices have been observed just above the instability threshold.     

Toward a New Method of Porosimetry: Principles and Experiments

Current experimental methods used to determine pore size distributions (PSD) of porous media present several drawbacks such as toxicity of the employed fluids (e.g., mercury porosimetry). The theoretical basis of a new method to obtain the PSD by injecting yield stress fluids through porous media and measuring the flow rate $Q$ at several pressure gradients $\nabla P$ was proposed in the literature. On the basis of these theoretical considerations, an intuitive approach to obtain PSD from $Q(\nabla P)$ is presented in this work. It relies on considering the extra increment of $Q$ when $\nabla P$ is increased, as a consequence of the pores of smaller radius newly incorporated to the flow. This procedure is first tested and validated on numerically generated experiments. Then, it is applied to exploit data coming from laboratory experiments and the obtained PSD show good agreement with the PSD deduced from mercury porosimetry.