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.     

Analytical pressure drop correlation for adiabatic vertical two-phase flow

A new correlation for two-phase wall friction is proposed derived from analytical considerations and based upon an annular flow model. In spite of this basis in annular flow the correlation is consistent for all flow patterns in vertical two-phase flow.The correlation yields a smooth transition from two-phase flow to single-phase liquid flow, mainly because it incorporates the friction factor of the Moody diagram [1] for single-phase flow.The correlation is checked against 236 measurements from various sources and has turned out to be most favourable in comparison with the correlations of Dukler (case 2) [2] and Lockhart-Martinelli [3]. The standard deviation of these 236 measurements is 27.8%, with 68% having a relative error of less than 28.2%.     

Heat transfer and pressure drop for purely viscous non-Newtonian fluids in turbulent flow through rectangular passages

Experimental measurements of friction factor and heat transfer for the turbulent flow of purely viscous non-Newtonian fluids in a 21 rectangular channel are compared with results previously reported for the circular tube geometry. Comparisons are also made with available analytical and empirical predictions.It is found that the rectangular duct fully established friction factor measurements are within ± 5% of the Dodge-Metzner prediction if the Kozicki generalized Reynolds number is used. A modified form of the simpler explicit equation proposed by Yoo, [i.e.f=0.079n ^0.675(Re ^*)^–0.25], is found to yield predictions for both the rectangular duct and the circular tube geometries with approximately the same accuracy as the Dodge-Metzner equation.Fully developed Stanton numbers for the rectangular duct are in good agreement with the circular tube data over a range ofn from 0.37 to 0.88 for a given Prandtl number,Pr _a , when compared at a fixed value of the Reynolds number based on the apparent viscosity evaluated at the wall shear stress. In general, the experimental data are within ± 20% of Yoo's equation,St=0.0152Re _a ^–0.155 Pr _a ^–2/3 . A new equation is proposed to bring the prediction for circular pipes as well as rectangular channels into better agreement with generally accepted Newtonian heat transfer results.

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Wärmeübergang und Druckverlust für viskose nicht-Newtonsche Fluide in turbulenter Strömung durch rechteckige Kanäle

Zusammenfassung Es werden Messungen des Reibungsfaktors und des Wärmeübergangs bei turbulenter Strömung viskoser nicht-Newtonscher Fluide in einem rechteckigen Kanal mit dem Seitenverhältnis 21 verglichen mit früheren Ergebnissen, die an runden Rohren gewonnen wurden. Weiterhin werden Vergleiche mit aus der Literatur verfügbaren analytischen und empirischen Beziehungen gemacht.Es zeigte sich, daß die Messungen des Reibungsfaktors im rechteckigen Kanal bei vollausgebildeter Strömung auf ± 5% mit der Vorhersage von Dodge-Metzner übereinstimmen, wenn die von Kozicki verallgemeinerte Reynolds-Zahl verwendet wird. Eine modifizierte Form der einfachen von Yoo vorgeschlagenen einfachen Gleichung in explizierter Form (f=0,079n ^0,675(Re ^*)^–0,25) bewies, daß sie sowohl für den rechteckigen Kanal als auch das runde Rohr die Werte mit fast der gleichen Genauigkeit wie die Methode von Dodge-Metzner vorhersagen kann.Die Stanton-Zahlen für den rechteckigen Kanal bei vollausgebildeter Strömung sind in guter Übereinstimmung mit den Werten für das runde Rohr in einem Bereich vonn= 0,37 – 0,88 für eine gegebene Prandtl-Zahl, wenn man den Vergleich bei einem vorgegebenen Wert der Reynolds-Zahl anstellt, die auf die scheinbare Viskosität — abgeleitet aus der Wandschubspannungbezogen ist. Generell läßt sich sagen, daß die Werte auf ± 20% mit der Gleichung von Yoo (St=0,0152Re _a ^–0,155 )Pr _a ^–2/3 ) übereinstimmen. Es wird eine neue Gleichung vorgeschlagen, welche sowohl die Werte für runde Rohre als auch die für rechteckige Kanäle in bessere Übereinstimmung bringt mit den in der Literatur üblichen Ergebnissen für den Wärmeübergang an Newtonsche Fluide.

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Nomenclature a constant in Eq. (8) - A area of cross-section of channel [m²] - b constant in Eq. (8) - c _p specific heat of test fluid [J kg^–1 K^–1] - d capillary tube diameter [m] - D _h hydraulic diameter, 4A/P[m] - f Fanning friction factor, _w/(g9 V²/2) - h axially local (spanwise averaged) heat transfer coefficient,q _w /(T_wi-T_b) [Wm^–2 K^–1] - k _f thermal conductivity of test fluid [Wm^–1K^–1] - K consistency index of power law fluid - n power law index - Nu fully established, local (spanwise averaged) Nusselt numberh D _h /k _f - P perimeter of channel [m] - Pr _a Prandtl number based on apparent viscosjity, c _p /k _f - Pr ^* defined as (Re _a Pr _a )/Re ^* - q _w wall heat flux [Wm^–2] - Re _a Reynolds number based on apparent viscosity, VD _h/ - Re Metzner's generalized Reynolds number in Eq. (2) - Re ^* Reynolds number defined in Eq. (8) - St Stanton number,h/( V c_p) - T _b local bulk temperature of the fluid [K] - T _wi local inside wall temperature [K] - T _wo local outside wall temperature [K] - V bulk flow velocity [m s^–1] - x distance from the inlet of channel along flow direction [m] Greek symbols shear rate [s^–1] - apparent viscosity [Pa s] - density of test fluid [kg m^–3] - shear stress [Pa] - _w shear stress at the wall [Pa] Dedicated to Prof. Dr.-Ing. U. Grigull's 75th birthday     

Correlations for heat transfer coefficient and pressure drop in the annulus of concentric helical coils

Heat transfer and pressure drop characteristics in the annulus of concentric helical coils heat exchangers were experimentally investigated. The effects of coil curvature ratio, flow configuration, number of turns and addition of surfactant were investigated. Five test coils were designed and manufactured to study the effect of different parameters on heat transfer and pressure drop. The liquids used in the present study were water and oleyl-dihydroxy-etheyl-amine-oxide (ODEAO, C₂₂H₄₅NO₃ = 371) non-ionic aqua surfactant solution flowing through the annulus side. The inner side Reynolds number range 11,000–27,000 and the annulus side range 5,000–19,000. The results showed that the annulus Nusselt number decreases as annulus curvature ratio increases and increases when number of turns decrease. Moreover, the friction factor increases with the curvature ratio and also increases as number of turns decreases. Both Nusselt number and friction factor decrease when ODEAO concentration increases.     

Correlations predicting frictional pressure drop and liquid holdup during horizontal gas-liquid pipe flow with a small liquid holdup

Experimental data and correlations available in the literature for the liquid holdup ε_L and the pressure gradient ΔP_TP/L for gas-liquid pipe flow, generally, do not cover the domain 0 < ε_L < 0.06. Reliable pressure-drop correlations for this holdup range are important for calculating flow rates of natural gas, containing traces of condensate. In the present paper attention is focused on reliable measurements of ε_L and ΔP_TPIL values and on the development of a phenomenological model for the liquid-holdup range 0 < ε_L < 0.06. This model is called the “apparent rough surface” model and is referred to as the ARS model. The experimental results presented in this paper refer to air-water and air-water + ethyleneglycol systems with varying transport properties in horizontal straight smooth glass tubes under steady-state conditions. The holdup and pressure gradient values predicted with the ARS model agree satisfactorily with both our experimental results and data obtained from the literature referring to small liquid-holdup values 0 < ε_L < 0.06. Further, it has been shown that in the domain 38 < < 72 mPa m the interfacial tension of the gas-liquid system has no significant effect on the liquid holdup. The pressure gradient, however, increases slightly with decreasing surface tension values.     

Counter current gas-liquid vertical flow, model for flow pattern and pressure drop

Counter-current flow pattern transition and pressure drop are modeled. Emphasis is placed on the understanding of the transition mechanisms from a mechanistic point of view.

Unlike the case of co-current flow, in counter-current flow, the situations of “no solution” as well as “multiple solutions” for the flow pattern and pressure drop exist. These possibilities are discussed and criteria for the actual flow pattern that will take place are suggested.

Some of the results are supported by data (from the literature), others are somewhat tentative suggesting future experimental verification is needed.     

Experiments on elongational flow of dilute polymer solutions Part I: Jet reaction and excess pressure drop for the flow through small apertures

Experiments have been made with dilute polymer solutions on the reaction of jets issuing from small orifices and the excess pressure drop for orifice and capillary flows.Under the flow conditions with vortices occurring upstream of the aperture, the jet reaction is nearly zero below some mean velocity for PEO solutions and similarly zero below some generalized Reynolds number for Separan solutions. The normalized jet reactions, when they possess positive values, are correlated with the generalized Reynolds number irrespective of the aperture diameters for both kinds of solution.In most cases, the pressure is higher than in the corresponding water flow, but for some flows with no vortex it is lower. For the vortex flow of PEO solutions the normalized excess pressure drop is inversely proportional to the Reynolds number for both orifices and capillaries, while for Separan solutions this quantity is not correlated with the generalized Reynolds number for orifice flow but is correlated with it for capillary flow.     

Experimental investigation of heat transfer and pressure drop characteristics of flow through spirally fluted tubes

Spirally fluted tubes are used extensively in the design of tubular heat exchangers. In previous investigations, results for tubes with flute depths e/D_vi < 0.2 were reported, with most correlations applicable for Re ≥ 5000. This paper presents the results of an experimental investigation of the heat transfer and pressure drop characteristics of spirally fluted tubes with the following tube and flow parameter ranges: flute depth e/D_vi = 0.1−0.4, flute pitch p/D_vi = 0.4−7.3, helix angle θ/90° = 0.3−0.65, Re = 500−80,000, and Pr = 2−7. The heat transfer coefficients inside the fluted tube were obtained from measured values of the overall heat transfer coefficient using a nonlinear regression scheme. The friction factor data obtained consisted of 507 data points. The proposed correlation for the friction factor predicts 96% of the database within ±20%. The heat transfer correlation for the range 500 ≤ Re ≤ 5000 predicts 76% of the database (178 data points) within ±20%, and the correlation for the higher Re range predicts 97% of the 342 data points within ±20%. Comparison of heat transfer and friction data show that these tubes are most effective in the laminar and transition flow regimes. The present results show that the increase of flute depth in the range considered does not improve heat transfer.     

Evaluation analysis of prediction methods for two-phase flow pressure drop in mini-channels

Two-thousand and ninety-two data of two-phase flow pressure drop were collected from 18 published papers of which the working fluids include R123, R134a, R22, R236ea, R245fa, R404a, R407C, R410a, R507, CO₂, water and air. The hydraulic diameter ranges from 0.506 to 12 mm; Re_l from 10 to 37,000, and Re_g from 3 to 4 × 10⁵. Eleven correlations and models for calculating the two-phase frictional pressure drop were evaluated based upon these data. The results show that the accuracy of the Lockhart–Martinelli method, Mishima and Hibiki correlation, Zhang and Mishima correlation and Lee and Mudawar correlation in the laminar region is very close to each other, while the Muller-Steinhagen and Heck correlation is the best among the evaluated correlations in the turbulent region. A modified Chisholm correlation was proposed, which is better than all of the evaluated correlations in the turbulent region and its mean relative error is about 29%. For refrigerants only, the new correlation and Muller-Steinhagen and Heck correlation are very close to each other and give better agreement than the other evaluated correlations.     

A separated flow model for predicting two-phase pressure drop and evaporative heat transfer for vertical annular flow

A separated flow model has been developed that is applicable to vertical annular two-phase flow in the purely convective heat transfer regime. Conservation of mass, momentum, and energy are used to solve for the liquid film thickness, pressure drop, and heat transfer coefficient. Closure relationships are specified for the interfacial friction factor, liquid film eddy-viscosity, turbulent Prandtl number, and entrainment rate. Although separated flow models have been reported previously, their use has been limited, because they were tested over a limited range of flow and thermal conditions. The unique feature of this model is that it has been tested and calibrated against a vast array of two-phase pressure drop and heat transfer data, which include upflow, downflow, and microgravity flow conditions. The agreements between the measured and predicted pressure drops and heat transfer coefficients are, on average, better or comparable to the most reliable empirical correlations. This separated flow model is demonstrated to be a reliable and practical predictive tool for computing two-phase pressure drop and heat transfer rates. All of the datasets have been obtained from the open literature.     

Experimental analysis of the pressure drop and heat transfer through metal foams used as volumetric receivers under concentrated solar radiation

The main objective of this work was to evaluate the behavior of porous materials, when treated as volumetric receivers under concentrated solar radiation. For this reason various porous metallic and ceramic materials have been tested as potential receivers for concentrated solar radiation. The experimental investigation showed that their efficiency was depending on both materials parameters and flow conditions. In this work, a variety of foam materials such as Ni and Ni alloy, inconel, copper, aluminum and SiC with different open cell porosity were tested as potential media to be used as volumetric receivers and heat exchangers. However, since the results were similar, for space economy, only the results of two of them, nickel and inconel were presented in detail and compared with each other.     

Determination of slug permeability factor for pressure drop prediction of slug flow pneumatic conveying

Current models for pressure drop prediction of slug flow pneumatic conveying in a horizontal pipeline system assume some type of steady state conditions for prediction,which limits their capability for increased predictive accuracy relative to experimental data.This is partly because of the nature of slug flow pneumatic conveying system,which,as a dynamic system,never becomes stable.By utilising conservation of mass (airflow),a dynamic pressure analysis model is proposed on the basis of the derivative of the upstream pressure behaviour.The rate of air permeation through slug,one of the important factors in the conservation model,is expressed as a function of a slug permeability factor.Other factors such as slug velocity,slug length and the fraction of stationary layer were also considered.Several test materials were conveyed in single-slug tests to verify the proposed pressure drop model,showing good agreement between the model and experimental results.     

Experimental investigation of ice slurry flow pressure drop in horizontal tubes

Pressure drop behaviour of ice slurry based on ethanol–water mixture in circular horizontal tubes has been experimentally investigated. The secondary fluid was prepared by mixing ethyl alcohol and water to obtain initial alcohol concentration of 10.3% (initial freezing temperature ?4.4 °C). The pressure drop tests were conducted to cover laminar and slightly turbulent flow with ice mass fraction varying from 0% to 30% depending on test conditions. Results from flow tests reveal much higher pressure drop for higher ice concentrations and higher velocities in comparison to the single phase flow. However for ice concentrations of 15% and higher, certain velocity exists at which ice slurry pressure drop is same or even lower than for single phase flow. It seems that higher ice concentration delay flow pattern transition moment (from laminar to turbulent) toward higher velocities. In addition experimental results for pressure drop were compared to the analytical results, based on Poiseulle and Buckingham–Reiner models for laminar flow, Blasius, Darby and Melson, Dodge and Metzner, Steffe and Tomita for turbulent region and general correlation of Kitanovski which is valid for both flow regimes. For laminar flow and low buoyancy numbers Buckingham–Reiner method gives good agreement with experimental results while for turbulent flow best fit is provided with Dodge–Metzner and Tomita methods.Furthermore, for transport purposes it has been shown that ice mass fraction of 20% offers best ratio of ice slurry transport capability and required pumping power.     

Determination of slug permeability factor for pressure drop prediction of slug flow pneumatic conveying

Current models for pressure drop prediction of slug flow pneumatic conveying in a horizontal pipeline system assume some type of steady state conditions for prediction, which limits their capability for increased predictive accuracy relative to experimental data. This is partly because of the nature of slug flow pneumatic conveying system, which, as a dynamic system, never becomes stable. By utilising conservation of mass （airflow）, a dynamic pressure analysis model is proposed on the basis of the derivative of the upstream pressure behaviour. The rate of air permeation through slug, one of the important factors in the conservation model, is expressed as a function of a slug permeability factor. Other factors such as slug velocity, slug length and the fraction of stationary layer were also considered. Several test materials were conveyed in single-slug tests to verify the proposed pressure drop model, showing good agreement between the model and experimental results.     

Characterization of wettability effects on pressure drop of two-phase flow in microchannel

The Characterization of the effects of surface wettability and geometry on pressure drop of slug flow in isothermal horizontal microchannels is investigated for circular and square channels with hydraulic diameter (D _h ) of 700 μm. Flow visualization is employed to characterize the bubble in slug flow established in microchannels of various surface wettabilities. Pressure drop increases with decrease in surface wettability, while the channel geometry influences slug frequency. It is observed that the gas–liquid contact line in advancing and receding interfaces of bubble change with surface wettability in slug flows. Flow resistance, where capillary force is important, is estimated using Laplace–Young equation considering the change of dynamic contact angles of bubble. The experimental study also demonstrates that the liquid film presence elucidates the pressure drop variation of slug flows at various surface wettabilities due to diminishing capillary effect.     

Flow pattern,void fraction and pressure drop of refrigerant two-phase flow in a horizontal pipe—II: Analysis of frictional pressure drop

Two-phase flow in horizontal pipe was analyzed with simplified models for annular and stratified flow. The velocity profiles for the liquid and gas phase were described with the Prandtl mixing length. From this analysis, the frictional pressure drop was calculated with the modified Baker map for flow pattern transition. The intermediate region, i.e. wavy flow, was interpolated between annular and stratified flow. Comparison of this analysis with existing experimental data of refrigerants showed good agreement.     

A mathematical model for pressure drop of two-phase dry-plug flow in circular mini/micro channels

Dry-plug flow is a variation of two-phase plug flow that occurs in small scale channels and refers to the dry wall conditions at gas portions of the flow regime. Previous experimental studies found a significant increase in pressure drop in this flow regime from the two-phase wet-plug flow regime. In this work an analytical model for the pressure drop of this flow regime is developed and phenomena that influence pressure drop are examined. Unlike previous models, the proposed model seems to be applicable to a wide range of capillary numbers and give good estimations for all static contact angles. Contact angle hysteresis turned out to play a major role in inducing pressure drop in this flow regime. Model’s predictions were in good agreement with previous experimental data. Finally the model is applied to very low capillary number region and pressure drop predictions for this region are presented.     

Burn-out,circumferential film flow distribution and pressure drop for an eccentric annulus with heated rod

Measurements of (1) burn-out, (2) circumferential film flow distribution, and (3) pressure drop in a $\text{17 × 27.2 × 3500}\text{mm}$ concentric and eccentric annulus geometry are presented. The eccentric displacement was varied between 0 and 3 mm. The working fluid was water. Burn-out curves at 70 bar are presented for mass velocities between 500 and 1500 kg/m²s and for inlet subcoolings of 10°C and 100°C. The film flow measurements correspond to the steam qualities $\text{χ = 19 \%}$ and 24 % for the mass velocity $\text{G = 602}$ kg/m²s and $\text{χ = 20 \%}$ and 23 % for $\text{G = 1200}$ kg/m²s. The influence of the circumferential rod film flow variation on burn-out is discussed.     

Simulation of viscous fluid flow with consideration of boundary outflow and pressure drop

The problem of modeling a viscous fluid flow over the surface of a plate is considered when the pressure changes along the longitudinal coordinate according to a linear law. The corresponding boundary conditions are formulated for this problem. The Navier-Stokes equations are solved exactly in the problem of flow past the plate for the case of fluid outflow and a longitudinal pressure drop. Several formulas to determine the velocity profile are derived. The limiting cases are analyzed to study the consistency of various models. The corresponding pressure conditions are proposed for the case when the Navier-Stokes system has a known exact solution.