Relative Friction Factor Research Articles

Optimized design of Helical-Finned Double Pipe heat exchangers via numerical simulation and Artificial Intelligence

Heat exchangers are essential in industrial applications, where optimizing their design offers significant environmental and economic benefits. However, traditional methods of enhancing heat transfer, such as adding fins, often lead to increased friction and pressure drop. This study aims to optimize the design of helical-finned double-pipe heat exchangers to improve heat transfer efficiency while minimizing frictional losses. Numerical simulations, combined with Artificial Neural Networks (ANNs), were used to model the impact of design parameters (Reynolds number, number of fins, fin height, and twist pitch) on performance. The k-ω shear-stress transport turbulence model and finite volume method were used for fluid flow and heat transfer simulations, while Genetic Algorithms (GAs) were employed for optimization. ANN models demonstrated high predictive accuracy (R2≈1), and the optimized designs achieved a relative Nusselt number of 2.01, a relative friction factor of 1.01, and a Performance Evaluation Criterion (PEC) of 1.43. Notably, fins did not always improve thermal efficiency, illustrating the complexity of optimizing heat exchanger designs. This study presents an approach by integrating ANN and GA, providing an effective strategy for improving heat exchanger performance.

Double pass solar air heater with aerofoil and bio-inspired fins: A numerical analysis of thermohydraulic performance

In the present study, a numerical flow analysis is performed on a double pass solar air heater (DPSAH) with a bottom plate surface roughened using aerofoil fins to study its thermohydraulic performance. The experimentally validated DPSAH model was studied considering factors like different fin shapes, diurnal variation of solar radiation, absorber plate material, and the flow conditions at different relative height ratios (h/H) between 0.17 and 0.50 and fin length ratio (l/H) of 0.29. Using the RNG k-ε turbulence model, the relative Nusselt number (Nu/Nus), relative friction factor (f/fs), and thermohydraulic performance factor (THPF) were found for Reynolds number between 3000 and 21000 with an increment of 3000. The maximum enhancements of 4.23 and 2.51 times were achieved in the Nu/Nus and THPF values, respectively, for a Re value of 3000 in a 2-row setup with h/H of 0.50. The DPSAH with bio-inspired fins performed better than optimized aerofoil fins for majority of the tested range even with similar increase in effective heat transfer area. The values predicted using correlations developed in this study and numerically obtained values of the Nusselt number and friction factor matched closely with an extreme deviation of 5 % in f values.

Machine learning analysis of thermophysical and thermohydraulic properties in ethylene glycol- and glycerol-based SiO2 nanofluids

The study investigates the heat transfer and friction factor properties of ethylene glycol and glycerol-based silicon dioxide nanofluids flowing in a circular tube under continuous heat flux circumstances. This study tackles the important requirement for effective thermal management in areas such as electronics cooling, the automobile industry, and renewable energy systems. Previous research has encountered difficulties in enhancing thermal performance while handling the increased friction factor associated with nanofluids. This study conducted experiments in the Reynolds number range of 1300 to 21,000 with particle volume concentrations of up to 1.0%. Nanofluids exhibited superior heat transfer coefficients and friction factor values than the base liquid values. The highest enhancement in heat transfer was 5.4% and 8.3% for glycerol and ethylene glycol -based silicon dioxide Nanofluid with a relative friction factor penalty of ∼30% and 75%, respectively. To model and predict the complicated, nonlinear experimental data, five machine learning approaches were used: linear regression, random forest, extreme gradient boosting, adaptive boosting, and decision tree. Among them, the decision tree-based model performed well with few errors, while the random forest and extreme gradient boosting models were also highly accurate. The findings indicate that these advanced machine learning models can accurately anticipate the thermal performance of nanofluids, providing a dependable tool for improving their use in a variety of thermal systems. This study's findings help to design more effective cooling solutions and improve the sustainability of energy systems.

Effect of trapezoidal louvered winglets on increased heat transfer and exergy in tubular heat exchanger

The effect of inserting a trapezoidal louvered winglet tape (TLWT) into a uniformly heat-fluxed tube on its thermal effectiveness was studied experimentally. The exergy and entropy analyses for turbulent flows, as well as frictional loss and thermal features, were highlighted as key aspects of the experimental finding for the Reynolds number which measured between about 4700 and 30,000. Because fixing baffles to the curved shape of tube wall presented a challenge, the baffles were consequently positioned on double surfaces of a flat tape. Six values of the louver angle (θ1 = 0°, 25°, 30°, 45°, 60°, and 90°) and three values of the relative pitch of winglet (PR = 1.0, 1.5, and 2.0) were employed in the arrangement of TLWTs, with the V-apex oriented upstream (V-up). Each of these had only a fixed height (BR = 0.25) and angle of attack (α = 30°). The winglets were utilized to induce streamwise vortices which can hinder the boundary layer formation, while the louvered openings were adopted to lessen pressure drop without significantly impacting the primary vortices. The experiment results disclosed that the smallest θ1 and PR produced the largest relative friction factor (fR) and NuR, which were about 13.57 and 4.04 times higher, while PR = 1 and θ1 = 45° provide the greatest TEF of about 2.27. The greatest exergy efficiency (ηEx) resulting from the TLWT was reached at θ1 = 0°, but the generation of entropy (S˙g′) dropped with lowering θ1 and Re. A further examination, however, showed that the best scenario with α = 60° and staggered arrays is more desirable since it yields the largest TEF of 2.45 at θ1 = 45° and PR = 1. For the range of parameters under consideration, the Nu and f correlations were additionally established.

Discharge estimation in a compound channel with converging and diverging floodplains using ANN–PSO and MARS

Abstract The discharge estimation in rivers is crucial in implementing flood management techniques and essential flood defence and drainage systems. During the normal flood season, water flows solely in the main channel. During a flood, rivers comprise a main channel and floodplains, collectively called a compound channel. Computing the discharge is challenging in non-prismatic compound channels where the floodplains converge or diverge in a longitudinal direction. Various soft computing techniques have nowadays become popular in the field of water resource engineering to solve these complex problems. This paper uses a hybrid soft computing technique – artificial neural network and particle swarm optimization (ANN–PSO) and multivariate adaptive regression splines (MARS) to model the discharge in non-prismatic compound open channels. The analysis considers nine non-dimensional parameters – bed slope, relative flow depth, relative longitudinal distance, hydraulic radius ratio, angle of convergence or divergence, flow aspect ratio, relative friction factor, and area ratio – as influencing factors. A gamma test is carried out to determine the optimal combination of input variables. The developed MARS model has produced satisfactory results, with a mean absolute percentage error (MAPE) of less than 7% and an R2 value of more than 0.90.

Effect of diameter, twist angle, and blade count on the thermal-hydraulic performance of a decaying twisted swirler

Inserting a decaying swirler into a heat exchanger has been shown to improve heat transfer with minimal effect on the friction factor. The study analyses the effect of diameter, twist angle, and blade count on the thermal-hydraulic performance of a Decaying Twisted Swirler (DTS) in a horizontally heated tube. The diameter, twist angle, and DTS's blade count are examined for 13.5 mm–15.5 mm with a 0.5 mm interval, 0°–360° with a 60° gap, and 2 to 6 blades, respectively. The Nusselt number, friction factor, and thermal-hydraulic performance are examined for Reynolds numbers between 4583 and 35000. The relative Nusselt number and friction factor increase as DTS diameter and twist angle increase, reaching a maximum value at Re = 4583. Despite this, the relative Nusselt number dispersed as the blade count increased. The relative friction factor increases as the blade count increases. Maximum relative Nusselt number and friction factor reached 1.64 and 3.25, respectively with DTS's 15.5 mm diameter, 360° angle, and 4 blades. Nonetheless, the thermal-hydraulic performance is greatest when the DTS has a diameter of 15.5 mm, a twist angle of 180°, and 2 blades with 1.17.

HEAT TRANSFER ENHANCEMENT IN A CHANNEL WITH INCLINED BAFFLES UNDER PULSATING FLOW: A CFD STUDY

This study numerically investigated hydraulic and thermal performance in a channel with inclined baffles under pulsating flow conditions. The baffles were placed in a staggered arrangement. The governing equations were discretized with the finite volume method (FVM), and the pressure-velocity coupling was handled by the SIMPLE algorithm. The Strouhal number (St: 0.5,1, 2, 3, and 4), pulsation amplitude (A: 0.2, 0.5, and 0.8), and Reynolds number (200 ≤ Re ≤ 1000) were changed. The top and bottom surfaces of the channel were kept at <i>T</i><sub>ω</sub> = 350 K, and thermal improvement and friction factor were calculated for a pulsating cycle. The results were given in terms of thermal enhancement (η), relative friction factor (<i>f</i><sub>rel</sub>), and performance evaluation criteria (PEC). The flow and temperature contours were presented to determine the impacts of the pulsation frequency, the pulsation amplitude, and the Reynolds number. The results showed that the pulsation amplitude and the pulsation frequency contributed remarkably to thermal enhancement with increasing Reynolds numbers, while the heat transfer improved significantly depending on pulsation parameters together with a slight rise in friction factor. The highest thermal enhancement achieved was about 1.47 at <i>Re</i> = 1000, <i>A</i> = 0.8, and <i>St</i> = 4. The highest PEC obtained was approximately 1.12 at <i>Re</i> = 1000, <i>A</i> = 0.2, and <i>St</i> = 4.

NUMERICAL STUDY OF TURBULENT HEAT TRANSFER PROCESS IN DIFFERENT WAVY CHANNELS WITH SOLID AND PERFORATED BAFFLES

This study numerically investigated the effects of different baffle arrangements on heat transfer enhancement and flow in channels with different wave profiles. Four different wave profiles - rectangular, trapezoidal, triangular, and circular - were considered for the wavy channels. Analyses were made on the solid and perforated baffles that were installed vertically in the channel's central area to determine their hydrodynamic performance and convective heat transfer. Pressure-velocity coupling in discretized equations was handled with the SIMPLE algorithm, and analyses were carried out using the ANSYS Fluent solver. The standard <i>k-ε</i> turbulence model was used to solve the simulations. In this study, the channel geometry, the baffle arrangement, and the Reynolds number (4000 ≤ Re ≤ 12,000) were changed. The wavy surfaces were preserved at <i>T<sub>ω</sub></i> = 360 K. The results were presented with different dimensionless parameters such as Nusselt number (Nu), friction factor (<i>f</i>), and thermal performance factor (TPF). Analyses indicated that the Nu number increased with increasing Re in all channel flows. In all wave profiles, the highest heat transfer was obtained in the solid baffle arrangement. The heat transfer increased by 2.12 times in the rectangular channel with solid baffle at Re = 4000 compared to the channel without a baffle. The highest average Nusselt number and relative friction factor were obtained about 143.34 and 1.24, respectively, in rectangular profile with solid baffle at Re = 12,000. The variation of the friction factor differed according to the wave profile and the baffle arrangement. The triangular profile with two-perforation baffles had the lowest TPF value, 1.09, and the rectangle profile with a solid baffle had the highest TPF value, 2.02. The results of the present study showed that the flow and heat transfer behaviors were similar in trapezoidal and circular channels.

Effect of baffle angles on flow and heat transfer in a circular duct with nanofluids

This work numerically analyzes the hydraulic and thermal performance of CuO-water nanofluid in a circular duct with different baffle angles. In the numerical work, governing equations are discretized with the finite volume method, and the simulations are solved with SIMPLE algorithm. The surfaces of the duct containing baffles are kept at 340 K. In the analysis, the effects of different Reynolds numbers (200 ≤ Re ≤ 1000), nanoparticle volume fractions (1% ≤ ϕ ≤ 3%), and baffle angles (30º ≤ α ≤ 150º) on the thermal enhancement factor (η) and the friction factor are investigated. In addition, the flow and temperature contours are presented for different parameters within the duct. From those contours, it is observed that the baffles cause flow oscillation and recirculation zones are formed. The numerical results show that baffles and nanofluid flow contribute significantly to the thermal enhancement. The Nusselt number (Nu) and relative friction factor (r) increase as the Reynolds number and nanoparticle volume fraction increase. While the highest thermal enhancement factor and relative friction factor are obtained at α = 90º baffle angle, the best performance evaluation criterion (PEC) value is found at α = 150º baffle angle.

Friction Factor and Heat Transfer of Giesekus-Fluid-Based Nanofluids in a Pipe Flow

The friction factor and heat transfer of Giesekus-fluid-based nanofluids in a pipe flow were studied in the ranges of 0.5 ≤ Reynolds number (Re) ≤ 500, 1 ≤ Weissenberg number (Wi) ≤ 8, 0.5% ≤ particle volume concentration (Φ) ≤ 3.0%, 0 ≤ viscosity ratio (β0) ≤ 1, and 0 ≤ mobility parameter (α) ≤ 0.5. Our numerical method was validated by comparing the results with available ones in the literature. The effects of Wi, Φ, β0, Re, and α on the relative friction factor (Cf/CfNew), Nusselt number (Nu), and ratio (PECnf/PECf) of energy performance evaluation criterion for Giesekus-fluid-based nanofluids to those for Giesekus fluid were discussed. The results showed that the values for the Cf/CfNew and Nu of Giesekus-fluid-based nanofluids were larger than those for Newtonian fluid-based nanofluids and those for pure Giesekus fluid. The values for Cf/CfNew increased with increasing Φ and Re, but they increased with decreasing β0 and α. As Wi increased, the values of Cf/CfNew first increased and then decreased. The values of Nu and PECnf/PECf were enhanced with increasing Wi, Φ, Re, and α, but with decreasing β0. It is more effective to use Giesekus-fluid-based nanofluids to improve heat transfer with the conditions of a larger Wi, Φ, Re, and α and a smaller β0. Finally, the correlation formula for PECnf/PECf as a function of Wi, Φ, β0, Re, and α was derived.

Research for a Non-Standard Kenics Static Mixer with an Eccentricity Factor

The Kenics static mixer is one of the most widely studied static mixers, whose structure–function relationship has been studied by varying its aspect ratio and modifying the surface. However, the effect of the symmetric structure of the Kenics static mixer itself on twisting the fluid has been neglected. In order to study how the symmetrical structure of the Kenics static mixer impacts the fluid flow, we changed the center position of elements at twist angle 90° and introduced the eccentricity factor γ. We applied LHS-PLS to study this non-standard Kenics static mixer and obtained the statistical correlations of the aspect ratio, Reynolds number, and eccentricity factor on relative Nusselt number and relative friction factor. We analyzed the results by comparing the PLS model with the univariate analysis, and it was found that the underlying logic of the Kenics static mixer with an asymmetric structure became different. In addition, a non-standard Kenics static mixer with an asymmetric structure was investigated using vortex generation and dissipation through fluid flow simulation. The results demonstrated that the classical symmetric structure has a minor pressure drop, but the backward eccentric one has a higher thermal-hydraulic performance factor. It was found that the nature of the eccentric structure is that two elements with different aspect ratios are being combined at θ=90°, and this articulation leads to non-standard Kenics static mixers with different underlying logic, which finally result in the differences between the PLS model and the univariate analysis.

Investigation of Pressure Drop Calculation for Twisted Tape Swirl Tubes by Conventional Channel Flow Correlations with Fusion Applications

Twisted tape inserts are commonly used for heat transfer enhancement in fusion applications. Although these devices have been extensively studied, existing correlations relating friction factor to Reynolds number and system geometry are applicable only for tight-fitting inserts and cannot account for system roughness and fouling. In this work, we examine pressure losses in twisted tapes of various twist ratios using both a typical twisted tape correlation and a newer formulation that incorporates conventional channel flow correlations. We study flows down to a Reynolds number of 4000 and find that the channel flow treatment predicts experimental outcomes well for turbulent conditions, like those expected in the ITER divertor. For calculations at low Reynolds numbers (expected during start-up and show-down of the divertor), we propose that channel flow correlations be merged with twisted tape correlations. This new, merged correlation is seen to be applicable across all Reynolds numbers observed, although it predicts small divergences among tape pitches at low Reynolds numbers that are not clearly reflected in our experimental data. Experimental and legacy data show that conventional channel flow friction factor correlations can be used under this formulation for pressure drop predictions at Reynolds number above 15 000. We suggest the use of this twisting channel treatment for loose-fitting inserts and systems in which fouling and roughness may be of concern, allowing existing straight channel models to be used for twisted tape pressure drop calculations.

Flow structure and heat transfer characteristics of microchannel heat sinks with split protrusion

Heat transfer capacity of compact heat exchanger is critical for applications with confined space and with large heat duty, in order to maintain the safety and efficiency of equipment. As a high-efficient and energy-saving compact heat exchanger, microchannel heat sinks have attracted extensive attention from both academics and industries. However, the development of thermal boundary layer in microchannel reduces the efficiency of heat transfer. Therefore, extensive efforts have been paid to improve the heat transfer performance in microchannel, for example, through incorporation of periodic rough elements of pin-fin, groove, rib and protrusion, which could disrupt the development of thermal boundary layer and induce secondary flow for thorough mixing between near-wall hot fluid and main fluid. Despite of superiority in the microchannel heat sink with protrusion, further structural optimizations are necessary to reduce resistance and enhance the heat transfer efficiency. Investigations on the flow resistance of shark, as well as the geometry of sharkskin, show that the discrete gap and hump of sharkskin reduce the flow resistance. Therefore, the split protrusion was proposed in this work, which was based on the common protrusion and shark skin bionic concept. And, the detailed flow structure and heat transfer mechanisms of microchannel heat sinks with split protrusion were studied. Transitional periodic boundary conditions were applied at the inlet and outlet with water as the working fluid, and the Reynolds number (Re) at the inlet were varied from 50 to 350. Moreover, a uniform constant heat flux of q′′ =5×105 W m−2 and no-slip boundary condition were specified at other surfaces of the microchannel. Furthermore, to avoid local hot spot of microchannel surfaces due to the existence of non-uniform temperature distribution, the temperature uniformity was discussed as well. The results show that thermal performance ( TP ) increases with the increase of Re and the superior heat transfer capacity is reached when the split width is 10 μm. In this study, the largest TP is 185.3% at the case of Plan A with Re=350 and 10 μm split width, where the relative friction factor ( f / f 0) is much large. As the width of split increases to 15 μm in Plan A, its f / f 0 significantly decreases but the thermal performance is relative large. Moreover, f / f 0 is also smaller than others at the case of PlanB with 15 μm width split. For Plan B with large split width, the value of TP increases with the split width at large Re (>250), while there is an opposite trend with the split width at small Re ( w / D ). Keeping other conditions at the same, the TP for Plan A is larger than that for Plan B when w / D is larger, while the f / f 0 is relatively smaller in PlanB at the case of smaller w / D , especially for the cases with wide split passage . However, the f / f 0 in PlanC with the smaller w / D is much larger than that of others, especially at large Re, since the sideward-inclined split in PlanC guides the part of main flow to side walls, enhancing the secondary passage flow of whole channel. Therefore, the temperature of side wall corners has been decreased effectively and the temperature uniformity of all walls in Plan C increases.

An experimental, computational and flow visualization study on the air-side thermal and hydraulic performance of louvered fin and round tube heat exchangers

The aim of this study is to determine heat transfer and pressure drop characteristics in different louvered fin geometries for manufacturing of commercial louvered fin and round tube heat exchangers. Numerical simulations were carried out for various louver angles, louver lengths (pitches), fin pitches and frontal air velocities. The heat transfer and pressure drop characteristics of the louvered fin and round tube heat exchangers, Colburn and friction factors, were respectively normalized with Colburn and friction factors of the flat plate fin and round tube heat exchangers operating under the same conditions and they were presented as the relative Colburn factor j∗ and the relative friction factor f∗. Thermal & hydraulic performance was presented as JF∗. Temperature and local Nusselt number contours, and streamline patterns were provided to reveal the mechanisms behind the heat transfer enhancement. Among different heat exchangers for which heat transfer and pressure drop characteristics were obtained, one was chosen to manufacture a real size heat exchanger. Flow visualization studies were also conducted with a PIV system in an open water channel to determine whether the flow structure is louvered directed or not. The louvered fin heat exchanger tested in the PIV system was a five times scaled up model of the real size louvered fin heat exchanger and made from a transparent plexiglas material. PIV results were presented and evaluated based on streamlines and velocity vectors. Furthermore, a numerical analysis was performed using exactly the same dimensions and conditions of the model tested in the PIV system. The comparison between numerical and experimental results was done to validate the numerical model. Consequently, the performance of the fabricated real size heat exchanger was tested at different air velocities in a wind tunnel in a conditioned room. The experimental results were compared with numerical analyses and found to be compatible with each other. Finally, thermal and hydraulic performance of the louvered fin and round tube heat exchanger was compared with a wavy fin and round tube heat exchanger with identical size and specifications. It was found that the thermal and hydraulic performance of the louvered fin and round tube heat exchanger is higher than that of the wavy fin and round tube heat exchanger. The Colburn factor j, friction factor f and JF of the louvered fin and round tube heat exchanger are higher about 16.8–7%, 19.9–8.2% and 10–4.3% than that of the wavy fin and round tube heat exchanger depending on the Reynolds number, respectively.

Bed Slope Effect on Non-uniform Flow through Porous Media

The tilting angle or bed slope (φ) effect on piezometric head was studied in a tilting angle converging permeameter for different rate of flows and for different bed slopes or tilting angles (φ) and the equipotential lines of piezometric head are depicted pictorially to establish the suitability of the convergent flow assumption and have a proper insight into the subject of seepage flow. The porosity effect is considered while computing seepage velocity (V), linear parameter, non-linear parameter, increases with decrease of porosity (N) and increases with decrease of angle of inclination. In order to meet the objective of this study, a crushed rock of size 7.30 mm was used as media and water as fluid, to develop curves relating friction factor (FR) and Reynolds number (RR) for different ratios of width using hydraulic radius (R) as characteristic length for different bed slopes or tilting angles (φ). The effect of varying tilting angles (φ) on head loss of fluid flow through porous media when packed between convergent boundaries for different ratios of width (B1/B2) was studied and inferred that tilting angles (φ) have a significant effect on the non uniform flow.

Effect of Convergent and Divergent Boundaries on Flow Resistance through Porous Media

An experimental investigation on the effect of convergent and divergent streamlines on the total energy loss in the porous medium and the effect on linear parameter, a, and non-linear parameter, b, for different ratios of radii of the test section was studied in a convergent and divergent permeameter. This paper presents the results of applying dimensional analysis to obtain a relationship between friction factor (fd) and Reynolds number (Rd) for flow in porous media with convergent and divergent boundaries, using pore size of the media (d) as characteristic length. Using friction factor (fd) and Reynolds number (Rd) relationship, theoretical curves, are developed and verified with the help of existing experimental data. In the present case, Mc Corquodale data of size 1.66 cm was used as media and water as fluid, to develop curves relating friction factor (fd) and Reynolds number (Rd) for different ratios of radii of the test section of convergent permeameter and divergent permeameter with the same convergent and divergent angle of 0.328 rad.

EFFICIENCY OF STEADY NON-UNIFORM FLOW THROUGH HOMOGENEOUS POROUS MEDIA

ABSTRACT An experimental investigation on the effect of convergent flow on the linear and non-linear parameters for different ratios of radii of the test section in a converging permeameter was studied. The relationship relating friction factor and Reynolds number using the square root of intrinsic permeability as the characteristic length is examined for flow in porous media with converging boundaries. Using the friction factor (fk) and Reynolds number (Rk) relationship, theoretical curves, which are similar to a Moody diagram used for pipe flow are developed and verified with the help of existing experimental data. In the present case, crushed rock of size 4.73 mm was used as media and water as fluid, to develop curves relating friction factor and Reynolds number with efficiency for different rate of flows of the test section of permeameter.

Effect of Convergence on Nonlinear Flow in Porous Media

The behavior of flow through porous media has been the subject of study for a long time. The relationship relating friction factor and Reynolds number using the square root of intrinsic permeability as the characteristic length is examined for flow in porous media with converging boundaries. An experimental investigation of the effect of convergence of streamlines on the linear and nonlinear parameters for different radial flow lines in a converging permeameter for different ratios of radii of the test section is also studied. In the present case, crushed rocks of sizes 11.64 and 4.73 mm were used as media and water as fluid, to develop curves relating friction factor and Reynolds number for different radial flow lines with different ratios of radii of the test section of the permeameter.

AN EXPERIMENTAL STUDY ON THE EFFECT OF CONVERGING BOUNDARY ON FLOW THROUGH POROUS MEDIA

ABSTRACT Flow behaviour through porous media with converging boundaries is analysed theoretically and the modifications in the Forchheimer equation needed to incorporate the effect of convergence are brought out. An experimental investigation on the effect of convergence factors on the resistance law relating friction factor (fR) and Reynolds number (RR) using the hydraulic radius as the characteristic length was carried out in a Convergent flow permeameter. In the present case, crushed rock of size 4.93 mm were used as media and water as fluid, to study the variation of friction factor (fR) and Reynolds number (RR) with different ratios of the width and with convergence factors.

Validation of Forchheimer's Law for Flow through Porous Media with Converging Boundaries

Modifications to the Forchheimer equation, which describes the flow behavior through coarse porous media, to account for the convergence of streamlines are made and experimentally verified. The applicability of a resistance law relating friction factor and Reynolds number using the square root of intrinsic permeability as the characteristic length is examined for flow with converging boundaries, and theoretical curves similar to Moody diagram for pipe flow are developed. The effect of convergence of streamlines on the linear and nonlinear parameters is demonstrated.