Full-field measurements of flow through a scaled metal foam replica

Open-celled foam geometries show great promise in heat/mass transfer, chemical treatment, and enhanced mixing applications. Flow measurements on these geometries have consisted primarily of observations of the upstream and downstream effects the foam has on the velocity field. Unfortunately, these observations give little insight into the flow inside the foam. We have performed quantitative flow measurements inside a scaled replica of a metal foam, ϕ = 0.921, D _Cell = 2.5 mm, by Magnetic Resonance Velocimetry to better understand the fluid motion inside the foam and give an alternative method to determine the foam cell and pore sizes. Through these 3-D, spatially resolved measurements of the flow field for a cell Reynolds number of 840, we have shown that the transverse motion of the fluid has velocities 20–30% of the superficial velocity passing through the foam. This strong transverse motion creates and dissipates streamwise jets with peak velocities 2–3 times the superficial velocity and whose coherence length is strongly correlated to the cell size of the foam. This complex fluid motion is described as “mechanical mixing” and is attributed to the geometry of the foam. A mechanical dispersion coefficient, D _M, was formed which demonstrates the transverse dispersion of this geometry to be 14 times the kinematic viscosity and 10 times the thermal diffusivity of air at 20°C and 1 atm.     

Are gas velocities in a motored piston engine representative of the pre-ignition fluid motion in a fired engine?

Conclusions The data we have presented comparing mean velocity and turbulence intensity measurements from scavenged and unscavenged engine cycles were obtained for two engine speeds, two intake flow configurations, and two locations of the spark plug relative to the LDV probe volume. The results show that in some circumstances the gas flow in the hotter unscavenged cycles is significantly different from the cooler scavenged cycles, but that for other cases the differences are within the uncertainty of the measurements. In addition, it is apparent that seemingly small changes in the geometry can strongly influence the local flow field. This sensitivity to detail leads us to conclude that it is not possible to make a comprehensive statement about the similarities of gas velocities in motored and fired engines. However, we do feel that some guidelines can be proposed: (1) It should never be presumed that the pre-ignition gas velocities in motored and fired engines are similar. Very large differences can occur. (2) Swirl that persists up to the time of ignition adds order and energy to the flow field, which reduces the likelihood for velocity differences between motored and fired engines; if the swirl motion is destroyed prior to ignition, to produce turbulence, this statement is far less likely to be valid. (3) Motored engine studies are sometimes dictated by the need to use the spark plug port for optical access; in this instance it is doubly important not to presume that the velocities measured are representative of the flow in the spark gap of a fired engine. (4) Skip-firing an engine is a valuable research technique for eliminating the complications of residual gases; however, the pre-ignition flow field of the fired cycles cannot be presumed to be applicable to a continuously fired engine.     

An analytical model for shock wave impact on compressible open-cell foam

A simple model is proposed to describe the main features of the complex phenomena that occur when a plane shock wave strikes a open-cell foam block. The complex two-phase interactions can be simplified using the experimental evidence that the foam face may be treated as a contact surface, that the length of the collapsed foam plug grows linearly in time, and that the gas pressure profile in the region between the head of the plug and the undisturbed material may be treated as being pseudo-stationary. These simplifications enable the prominent features of the compression process to be predicted for a variety of foam types. Analytical results for the reflected shock strength, foam front face velocity, transmitted wave velocity and strength, and maximum peak back wall pressures are presented.      

Turbulence production in flow over a wavy wall

Measurements of the spatial and time variation of two components of the velocity have been made over a sinusoidal solid wavy boundary with a height to length ratio of 2a/λ = 0.10 and with a dimensionless wave number of α⁺ = (2π/λ)(v/u ^?) = 0.02. For these conditions, both intermittent and time-mean flow reversals are observed near the troughs of the waves. Statistical quantities that are determined are the mean streamwise and normal velocities, the root-meansquare of the fluctuations of the streamwise and normal velocities, and the Reynolds shear stresses. Turbulence production is calculated from these measurements. The flow is characterized by an outer flow and by an inner flow extending to a distance of about α^?1 from the mean level of the surface. Turbulence production in the inner region is fundamentally different from flow over a flat surface in that it is mainly associated with a shear layer that separates from the back of the wave. Flow close to the surface is best described by an interaction between the shear layer and the wall, which produces a retarded zone and a boundary-layer with large wall shear stresses. Measurements of the outer flow compare favorably with measurements over a flat wall if velocities are made dimensionless by a friction velocity defined with a shear stress obtained by extrapolating measurements of the Reynolds stress to the mean levels of the surface (rather than from the drag on the wall).     

Flow Laws in Metal Foams: Compressibility and Pore Size Effects

The aim of our experimental work was to establish a simple relation between the flow parameters and the morphological parameters of metallic foam. We used foam samples made from different metals or alloys (Cu, Ni, Ni-Cr, etc) and of various thicknesses. Pore size ranged between 500 and 5000 μm. We measured the pressure profiles in foam samples using a specific experimental set-up of 12 pressure sensors distributed 1 cm apart along the main flow axis. The experimental loop made it possible to use indifferently water or air as working fluid. For the study of the gas (air) flow, velocities ranged roughly from 0 up to 20 m/s and for the liquid (water) flow, velocities ranged between 0 and 0.1 m/s. The measurements of the pressure gradients were performed systematically. We validated the Forchheimer flow model. The influence of the compressibility effects on permeability and inertia coefficient was emphasized. We demonstrated that the pore size Dp in itself is sufficient to describe flow laws in such high porosity material: K and β are respectively proportional to Dp² and Dp⁻¹.     

Simulation of Entry-Region Flow in Open-Cell Metal Foam and Experimental Validation

Open-cell metal foam is distinguished from traditional porous media by its very high porosities (often greater than 90 %), and its web-like open structure and good permeability. As such, the foam is a very attractive core for many engineered systems, e.g., heat exchangers, filtration devices, catalysts, and reactors. The flow field inside the foam is rather complex due to flow reversal and vigorous mixing. This complexity is increased by the possible presence of an entry region. The entrance region in metal foam is usually underestimated and ignored, just like its counterpart in traditional porous media. In this paper, the actual entry length is determined by simulation and direct experiment on commercial open-cell aluminum foam. It is shown to be dependent on flow velocity and to reach a constant value for higher velocities. The complex and intrinsically random architecture of the foam is idealized using a unit geometrical model, in order to numerically investigate the flow field and pressure drop inside the foam. The Navier–Stokes equations are solved directly, and velocity and pressure fields are obtained for various approach velocities using a commercial numerical package. The entry length is ascertained from the behavior of the velocity field close to the entrance. Comparisons to experimental data were also carried out. The commercial foam that was used in the experiment had 10 ppi and porosity of 91.2 %. Air was forced to flow inside the foam using an open-loop wind tunnel. Good qualitative agreement between the modeling and experimental results are obtained. The agreement lends confidence to the modeling approach and the determined entry length.     

Rheo-PIV analysis of the slip flow of a metallocene linear low-density polyethylene melt

The continuous extrusion of a metallocene linear low-density polyethylene through a transparent capillary die with and without slip was analyzed in this work by rheometrical measurements and particle image velocimetry (PIV). For this reason, a comparison was made between the rheological behaviors of the pure polymer and blended with a small amount of fluoropolymer polymer processing additive. Very good agreement was found between rheometrical and PIV measurements. The pure polymer exhibited stick-slip instabilities with nonhomogeneous slip at the die wall, whereas the blend showed stable flow. The slip velocity was measured directly from the velocity profiles and was negligible for the pure polymer before the stick-slip but increased monotonously as a function of the shear stress for the blend. The flow curves and the slip velocity as a function of the shear stress deviated from a power law and were well fitted by continuous “kink” functions. Comparison of PIV data with rheometrical ones permitted a direct proof of the basic assumption of the Mooney theory. Finally, the analysis of the velocity profiles showed that there is a maximum in the contribution of slip to the average fluid velocity, which is interpreted as the impossibility for the velocity profile to become plug like in the presence of shear thinning.     

Can Moderately Rarefied Gas Transport Through Round and Flat Tight Channels of Fractured Porous Media be Described Accurately?

We study the generation and flow of foam through rough-walled, fractured marble rocks that mimic natural fracture systems in carbonate reservoirs. Flow was isolated to the fracture network because of the very low rock permeability of the marble samples and foam generated in situ during co-injection of surfactant solution and gas. The foam apparent viscosities were calculated at steady pressure gradients for a range of gas fractions, and similar to foam flow in porous media, we identified two flow regimes for foam flow in fractures: a high-quality flow regime only dependent on liquid velocity and a low-quality flow regime determined by the gas and liquid velocities. Variations in local fluid saturation during co-injection were visualized and quantified using positron emission tomography combined with computed tomography.

     

Foam Generation Hysteresis in Porous Media: Experiments and New Insights

Foam application in subsurface processes including environmental remediation, geological carbon-sequestration, and gas-injection enhanced oil recovery (EOR) has the potential to enhance contamination remediation, secure \(\hbox {CO}_{2}\) storage, and improve oil recovery, respectively. Nanoparticles are a promising alternative to surfactants in creating foam in harsh environments. We conducted \(\hbox {CO}_{2}\)-in-brine foam generation experiments in Boise sandstones with surface-treated silica nanoparticle in high-salinity conditions. All the experiments were conducted at the fixed \(\hbox {CO}_{2}\) volume fraction and fixed flow rate which changed in steps. The steady-state foam apparent viscosity was measured as a function of injection velocity. The foam flowing through the cores showed higher apparent viscosity as the flow rate increased from low to medium and high velocities. At very high velocities, once foam bubbles were finely textured, the foam apparent viscosity was governed by foam rheology rather than foam creation. A noticeable hysteresis occurred when the flow velocity was initially increased and then decreased, implying multiple (coarse and strong) foam states at the same superficial velocity. A normalized generation function was combined with CMG-STARS foam model to cover full spectrum of foam behavior in the experiments. The new model successfully captures foam generation and hysteresis trends in presented experiments in this study and data from the literature. The results indicate once foam is generated in porous media, it is possible to maintain strong foam at low injection rates. This makes foam more feasible in field applications where foam generation is limited by high injection rates that may only exist near the injection well.     

In vivo blood flow and wall shear stress measurements in the vitelline network

The wall shear stress plays a key role in the interaction between blood flow and the surrounding tissue. To obtain quantitative information about this parameter, velocity measurements are required with sufficient spatial (and temporal) resolution. We present a methodology for the determination of the wall shear stress in vivo in the vitelline network of a chick embryo. Velocity data is obtained by microscopic particle image velocimetry using correlation ensemble averaging; the latter is used to increase the signal-to-noise ratio of the measurements. The temporal evolution of the pulsatile flow is reconstructed by sorting the image pairs based on a phase estimate. From these flow measurements, the wall shear stress can be derived either directly from the magnitude of the gradients or from fits to velocity profiles. Both methods give results that are in good agreement with each other, while the former method is significantly easier to implement. For more accurate studies, the full three-dimensional velocity field may be required. It is demonstrated how this velocity field can be obtained by scanning the measurement volume.

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Modification of equation of motion of fluid-conveying pipe for laminar and turbulent flow profiles

Considering the non-uniformity of the flow velocity distribution in fluid-conveying pipes caused by the viscosity of real fluids, the centrifugal force term in the equation of motion of the pipe is modified for laminar and turbulent flow profiles. The flow-profile-modification factors are found to be 1.333, 1.015–1.040 and 1.035–1.055 for laminar flow in circular pipes, turbulent flow in smooth-wall circular pipes and turbulent flow in rough-wall circular pipes, respectively. The critical flow velocities for divergence in the above-mentioned three cases are found to be 13.4%, 0.74–1.9% and 1.7–2.6%, respectively, lower than that with plug flow, while those for flutter are even lower, which could reach 36% for the laminar flow profile. By introducing two new concepts of equivalent flow velocity and equivalent mass, fluid-conveying pipe problems with different flow profiles can be solved with the equation of motion for plug flow.     

Local characteristics of upward gas-liquid flows

The results of two-phase flow structure measurements in an upward gas-liquid flow in a 86.4 mm i.d. tube by the electrochemical and conductivity techniques are presented. Measurements were made in bubble and slug flow regimes at liquid flow rates ranging from 0.2 to 2 m/s.The flow instability and ambiguity in a bubble regime at low velocities is shown to exist. Great discrepancy between measured wall shear stress values and those predicted by the Lockhart-Martinelli model are due to the nonuniform distribution of gas over the tube cross section. Measurements of intensity of wall shear stress and liquid velocity fluctuations in a two-phase flow are presented.     

Stick-slip flow of high density polyethylene in a transparent slit die investigated by laser Doppler velocimetry

The oscillating flow instability of a molten linear high-density polyethylene is carefully studied using a single screw extruder equipped with a transparent slit die. Experiments are performed using laser Doppler velocimetry in order to obtain the local velocities field across the entire die width. At low flow rate, the extrusion is stable and steady state velocity profiles are obtained. During the instability, the velocity oscillates between two steady state limits, suggesting a periodic stick-slip transition mechanism. At high flow rate, the flow is mainly characterized by a pronounced wall slip. We show that wall slip occurs all along the die land. An investigation of the slip flow conditions shows that wall slip is not homogeneous in a cross section of the slit die, and that pure plug flow occurs only for very high flow rates. A numerical computation of the profile assuming wall slip boundary conditions is done to obtain the true local wall slip velocity. It confirms that slip velocities are of the same order of magnitude as those measured with a capillary rheometer.     

Measuring the velocity of a gas wake in a shock tube from the induced electromotive force

It is shown that the velocity of the gas wake in a shock tube can be measured from the induced electromotive force for argon and xenon at initial pressures greater than 1 mm Hg and conductivities above 1 mho/cm. In a strongly ionized gas ( > 0. 01) the flow velocities measured directly behind the shock front are close to the flow velocities corresponding to steady-state ionization equilibrium. It is noted that the expenditure of energy to dissociate an admixture of air causes a noticeable increase in the velocity of the flow along the entire plug of hot gas. A 3–6% acceleration of the flow along the plug. in the equilibrium ionization zone is observed; this is probably caused by the action of the boundary layer formed on the walls of the shock tube on the free flow.     

PIV measurements of turbulent flow in planar mixing layer

A turbulent mixing layer consists of two different flow types, i.e. shear layer (shear-flow turbulence) and free stream regions (nearly homogeneous turbulence). The inherent non-uniform seeding tracer distributions observed around the interfaces between the shear layer and two free stream regions usually lead to a difficulty in particle image velocimetry (PIV) measurements. A parametric study on the application of PIV to the measurement of velocity field in a planar mixing layer is made by means of six factors, including interrogation window size, aspect ratio of interrogation window, interrogation window offset, threshold of data validation, sharpening spatial filters (Prewitt and Sobel masks), and smoothing spatial filter (median mask). The objective of this study is to obtain accurate turbulent measurements in both mean and fluctuating velocities using PIV under an appropriate parametric setting. The optimal levels, which are trade-off in between the accuracy and fine spatial resolution of velocity field measurements, are determined with the aid of the Taguchi method. It is shown that the PIV measurements made with this optimal set of parameters are in good agreement with the measurements made by a two-component hot-wire anemometer. Case independency of the proposed optimal set of parameters on the flow condition of the mixing layer is validated through the applications to two additional tests under the different experimental conditions in changing solely either velocity ratio of high-speed to low-speed free stream velocities or Reynolds number.     

Experimental study of gas-liquid slug flow in a small-diameter vertical pipe

Experimental investigation of upward gas-liquid slug flow in a vertical pipe in 15 mm ID has been carried out. The electrochemical method which permits the determination of the value and direction of instantaneous wall shear stress as well as the mean and fluctuating components of the liquid velocity is used for measurements. It is shown that the change of the sign of the velocity near the wall usually occurs at the moment of slug passage; the time-averaged wall shear stress at low liquid velocities is significantly lower than the value obtained by means of common prediction methods. The results of measuring of the local void fraction. liquid velocity and components of liquid velocity fluctuations are presented. The time-dependent behavior of the instantaneous hydrodynamic characteristics is described.     

Start-up Flow of a Bingham Fluid in a Pipe

We present an analytical solution of axisymmetric motion for a Bingham fluid initially at rest subjected to a constant pressure gradient applied suddenly. Using the Laplace transform, we obtain expressions which allow the calculation of the instantaneous velocity, plug radius and rate of flow as a function of time. We also give a relation for the shear stress in the plug and in the region where the behaviour of the fluid is Newtonian.     

Near-wall flow in a three-dimensional boundary layer on the endwall of a 30° bend

 Turbulence measurements are reported on the three-dimensional turbulent boundary layer along the centerline of the flat endwall in a 30° bend. Profiles of mean velocities and Reynolds stresses were obtained down to y ⁺≈2 for the mean flow and y ⁺≈8 for the turbulent stresses. Mean velocity data collapsed well on a simple law-of-the-wall based on the magnitude of the resultant velocity. The turbulence intensity and turbulent shear stress magnitude both increased with increased three-dimensionality. The ratio of these two quantities, the a ₁ structure parameter, decreased in the central regions of the boundary layer and showed profile similarity for y ⁺<50. The shear stress vector angle lagged behind the velocity gradient vector angle in the outer region of the boundary layer, however there was an indication that the shear stress vector tends to lead the velocity gradient vector close to the wall. Received: 16 July 1996/Accepted: 14 July 1997     

Effect of surfactants on liquid loading in vertical wells

Most gas wells produce some amount of liquid. The liquid is either condensate or water. At high rates, the gas is able to entrain liquid to the surface; however, as gas well depletes, the liquid drops back in a gas well (called liquid loading) creating a back pressure on the reservoir formation. Addition of surfactants to the well to remove liquid is one of the common methods used in gas wells. Liquid loading in vertical gas wells with and without surfactant application was investigated in this study. Anionic, two types of amphoteric (amphoteric I and amphoteric II), sulphonate and cationic surfactants were tested in 2-inch and 4-inch 40-feet vertical pipes. Pressure gradient and liquid holdup are measured. Visual observation with a high speed camera was used to gain insight into the direction of foam flow in intermittent flow and foam film flow under annular flow conditions.Liquid loading is initiated when the liquid film attached to the wall in annular flow starts flowing downwards. Introduction of foam causes the gas velocity at which film reversal occurs to decrease; this shift increases with increasing surfactant concentration and it is more pronounced in 2-inch pipe than in 4-inch pipe. That is, the benefit of surfactants is much more pronounced in 2-inch pipe than in 4-inch pipe. The reason for postponement of liquid loading is reduction in the liquid holdup at low gas velocities which reduces the liquid holdup in foam flow compared to air-water flow. However, at higher gas velocities, the pressure drop in 2-inch compared to 4-inch pipe increases rapidly as the surfactant concentration increases. The selection of optimum concentration of the surfactant is a balance between the reductions in the gas velocity at which liquid loading occurs compared to increase in the frictional loss as the concentration increases. We provide guidelines about the selection of the surfactant concentration.Visual observations using high speed camera show differences in the behavior under foam flow conditions. Unlike air-water flow, the liquid film attached to the wall is replaced by thick foam capturing the gas bubbles. The type of roll waves which carry the liquid in 2-inch pipe is different than what was observed in 4-inch pipe. Compared to 4-inch pipe, the roll waves in 2-inch pipe are much thicker. This partly explains the differences in 2-inch versus 4-inch pipe behavior.     

Structure of turbulent bubbly jets—II. Phase property profiles

This is the second part of a two-part study reporting structure measurements in bubbly turbulent round jets in a still environment. Measurements are compared with three theoretical approaches: (1) locally homogeneous flow analysis, where velocity differences between the phases were neglected; (2) deterministic separated flow analysis, where relative velocity was considered but bubble/turbulence interactions were ignored; and (3) stochastic separated flow analysis, where both relative velocity and bubble/turbulence interactions were considered using random-walk methods. This part of the study considers measurements and predictions of mean and fluctuating phase velocities and mean bubble number intensities at several axial stations. Locally homogeneous flow analysis was not very satisfactory since effects of relative velocity were important for present test conditions. Deterministic separated flow analysis was also ineffective, since neglecting turbulent dispersion caused the width of the bubble-containing region to be underestimated. In contrast, the stochastic separated flow analysis yielded reasonably good predictions.