Open Channel Design Research Articles

Pressure drop in reverse electrodialysis: Experimental and modeling studies for stacks with variable number of cell pairs

Reverse electrodialysis (RED) is a sustainable technology for salinity gradient energy harvesting. In order to make the process economically competitive, it is desirable to operate it at the highest possible net power density, which depends on the RED stack geometry and on the pressure drop along its pathways and, thus, on the energy spent for solutions pumping. The fluid flow in RED stacks generally occurs in rectangular compartment channels, equipped with spacers. The effects of spacers design and properties have been studied extensively in recent years. However, the other possible causes for a RED stack and their relative impact on the process performance have not yet been systematically studied. In this study the partial pressure drops in (1) distribution ducts, (2) branches, (3) beams, (4) due to sudden section expansion between the beam and the compartment channel and (5) in the compartment channel were taken into consideration. A model for the total pressure drop inside a RED stack, with a parallel fluid flow distribution through the compartments, is proposed and experimentally validated for lab-scale RED stacks with sheet flow spacers and compared with an open channel (spacer-free) design. The importance of each partial pressure drop was then evaluated quantitatively through model simulations for industrial-scale stacks with an increasing number of cell pairs. It was found that the net power density decreases when the cell-pair number increases, since the partial pressure drop in the branches becomes dominant. Moreover, the possible reasons for a non-uniform fluid flow distribution are discussed, thus making the proposed model useful for planning and/or optimization of RED stacks design.

Application of Particle Swarm Optimization Algorithm for Computing Critical Depth of Horseshoe Cross Section Tunnel

Critical depth is an important parameter in the design, operation and maintenance of open channels and analysis of gradually varied flow. For horseshoe cross section channels, the governing equations are highly nonlinear in the critical flow depth and thus solution of the implicit equations involves time consuming numerical methods. In current research, through conversion of critical depth equation to an objective function and then its minimization by using Particle Swarm Optimization algorithm, we calculate critical depth in horseshoe channels. The accuracy of the proposed model was also evaluated by comparing with existing equations. Furthermore this method can be used to deal with other optimization problems in hydraulic engineering.

Interchannel Mixing Minimization in Semi-Packed Micro Gas Chromatography Columns

Semi-packed columns containing an array of micropillars embedded within an open rectangular column structure are a new class of micro gas chromatography (μGC) columns introduced to provide higher separation efficiency and higher sample capacity. Three different semi-packed column configurations are evaluated with respect to pillar spacing along the flow direction and number of pillars across channel. The efficiencies of semi-packed columns, in terms of height-equivalent-to-a-theoretical-plate (HETP), are compared with two microfabricated open-rectangular columns. According to simulation results, arranging the pillars in a symmetrical configuration with spacing equal to the post dimension can suppress multi-path flows. Experimental results confirm the simulation prediction as the design with 2 μm post spacing (SP1) demonstrates the highest performance among other designs. SP1 is found to have HETP of 0.010 cm (15 000 plates/m) at an optimal velocity of 18 cm/s. An open channel design with comparable channel width yields an HETP of 0.025 cm (6000 plates/m) at an optimal velocity of 45 cm/s. The pressure drop in semi-packed columns is experimentally measured to be ~ 9 kPa which falls within the practical range of microfabricated pumps.

Discharge assessment in meandering and straight compound channels

Reliable estimates of discharge capacity in open channels are essential for the design, operation and maintenance of open channels, and more importantly the prediction of flood, water level management and flood design. The methods of discharge estimation that are used in the available river modelling software are principally based on historic hand-calculation formulae, with little or no account taken of the more recent advances in knowledge and understanding. The paper describes some of the conclusions of predicting discharge in meandering and straight compound channels with the proposed method by authors, the diversity of current knowledge and the outline of the targeted program of research that is now underway to produce an improved discharge estimation system. Particular issues of concern are the effects of the interaction between river channels and floodplain.

Equations for critical and normal depths of city-gate sections

Critical and normal depths are two important parameters in the design of open channels and the analysis of varied flow. For many practical sections, the governing equations for critical and normal depths are implicit and no analytical solutions exist. Various explicit equations have been developed for common open-channel sections. However, there are very limited studies on calculations of critical and normal depths for the city-gate section (CGS), which is one of the frequently used cross-sections for free-water conveyance tunnels. This paper presents equations for the geometric elements of standard CGSs used in water conveyance systems such as for irrigation, drainage and water supply projects. Based on the principle of gradual optimisation fitting, explicit equations for normal and critical depths of standard CGSs were developed for manual calculations with maximum relative errors of less than 1%. The proposed equations have a high accuracy for use in hydraulic design.

Direct solutions for normal and critical depths in standard city-gate sections

Critical and normal depths are important parameters for computing gradually varied flow and for the design, operation, and maintenance of open channels. For many channel sections, the governing equations for critical and normal depths are implicit and no analytical solutions exist. Thus various approximate equations with various degrees of error have been developed for these sections. No explicit equations exist for critical and normal depths of the standard city-gate cross-sections for entire practical range of the water depth. City-gate sections are one of the commonly used cross-sections for water conveyance tunnels. Standard city-gate cross-sections are also used for water conveyance in irrigation and drainage systems. This study proposes explicit equations for critical and normal depths of standard city-gate cross-sections. The proposed equations are simple and valid for entire practical range of the water depth and have maximum relative error less than 0.13% and thus should be useful tools for evaluation and design of the standard city-gate cross-sections.

Explicit solutions for critical and normal depths in trapezoidal and parabolic open channels

Normal and critical depths are important parameters in the design of open channels and analysis of gradually varied flow. In trapezoidal and parabolic channels, the governing equations are highly nonlinear in the normal and critical flow depths and thus solution of the implicit equations involves numerical methods (except for critical depth in parabolic channels). In current research explicit solutions have been obtained using the non-dimensional forms of the governing equations. For the trapezoidal cross section, the maximum error of critical flow depth is less than 6×10−6% (near exact solution) and the maximum error of normal depth is less than 0.25% (very accurate solution). The maximum error of normal flow depth for parabolic cross section is also less than 8×10−3% (near exact solution). Proposed explicit equations have definite physical concept, high accuracy, easy calculation, and wide application range compared with the existing direct equations.

Computational simulation modelling of bioreactor configurations for regenerating human bladder

The objective of this study was to investigate a bioreactor suitable for human bladder regeneration. Simulations were performed using the computational fluid dynamic tools. The thickness of the bladder scaffold was 3 mm, similar to the human bladder, and overall hold-up volume within the spherical shape scaffold was 755 ml. All simulations were performed using (i) Brinkman equation on porous regions using the properties of 1% chitosan–1% gelatin structures, (ii) Michaelis–Menten type rate law nutrient consumption for smooth muscle cells (SMCs) and (iii) Mackie–Meares relationship for determining effective diffusivities. Steady state simulations were performed using flow rates from 0.5 to 5 ml/min. Two different inlet shapes: (i) straight entry at the centre (Design 1) and (ii) entry with an expansion (Design 2) were simulated to evaluate shear stress distribution. Also, mimicking bladder shape of two inlets (Design 3) was tested. Design 2 provided the uniform shear stress at the inlet and nutrient distribution, which was further investigated for the effect of scaffold locations within the reactor: (i) attached with a 3-mm open channel (Design 2-A), (ii) flow through with no open channel (Design 2-B) and (iii) porous structure suspended in the middle with 1.5-mm open channel on either side (Design 2-C). In Design 2-A and 2-C, fluid flow occurred by diffusion dominant mechanisms. Furthermore, the designed bioreactor is suitable for increased cell density of SMCs. These results showed that increasing the flow rate is necessary due to the decreased permeability at cell densities similar to the human bladder.

Modeling parametric uncertainty in optimal open channel design using FORM-PGSL coupled approach

Optimal design of artificial open channels is essential for the planning and management of irrigation projects. In this paper a modified formulation is presented for the comprehensive design of open channels considering the seepage loss, evaporation loss and land acquisition cost along with the lining and excavation cost. The resulting formulation is solved using a recent meta-heuristic optimization technique namely probabilistic global search Lausanne (PGSL). The uncertainty associated with channel design parameter may lead to the failure of canals (channels). The parametric uncertainty in open channel design is modeled using first order reliability method (FORM). A bi-objective optimization model is presented in the study which minimizes the cost and minimizes the probability of overtopping considering a probabilistic cost function as the objective function. A new approach is proposed to solve the model in a meta-heuristic environment following PGSL as the solution method. Also a chance constrained optimization model which considers overtopping probability constraint and channel capacity constraint simultaneously along with the objective of minimization of cost is propounded and solved using PGSL. The solutions obtained using coupled FORM-PGSL approach is encouraging and the method can be used for optimal and reliable design of artificial open channels.

Division of critical flow at three-branch open-channel intersection

An experimental study of the characteristics of dividing critical flows in a 90° open-channel junction formed by three horizontal equal-width branches is presented, conducted for various inflow discharges and downstream boundary conditions. Outflow discharges and flow depths were also measured. Four main flow patterns are identified considering the location and length of the hydraulic jumps that develop across the main and lateral channels. A relationship between the discharge division ratio and the tailwater Froude number is found, reproducing well the experimental data. Practical applications of this relationship include the design of open channel and pipe networks and one-dimensional numerical modelling of flood propagation in urban areas. The study shows also that a two-dimensional depth-averaged numerical model hardly gives better predictions of the discharge ratios because of the presence of three-dimensional features at the junction.

Slope‐stability‐constrained design of irrigation canals using particle swarm optimization

AbstractThis paper presents a practical methodology for optimal design of open channels considering the slope‐stability aspects and other requirements and propounds the solution of particle swarm optimization (PSO) for solving nonlinear optimization problems. The proposed methodology handles site‐specific conditions such as restrictions on allowable top width and water depths. To ensure the stability of canals under field conditions a slope‐stability constraint is incorporated into the channel design. This constraint is handled through an optimization sub‐routine for computing stability of the canals using PSO. The results of the model show that for all the cases considered in the study the PSO‐based solutions are found to perform well and in some cases better than the traditional solutions. The PSO method provides lot of flexibility in its usage for solving complex channel design problems and it can be used to handle various system requirements in a better way. Copyright © 2011 John Wiley & Sons Ltd.

Explicit solutions for critical and normal depths in channels with different shapes

Critical and normal depths are important for computing gradually varied flow profiles and for the design, operation, and maintenance of open channels. A closed-form analytical equation for the normal depth computation can only be derived for triangular channels. For exponential channels, it is also possible to obtain such equations for the critical depth. This is not possible, however, for other geometries, such as trapezoidal, circular, and horseshoe channels. In these channels, the governing equations are implicit and thus the use of trial procedures, numerical methods, and graphical tools is common. Some channels have explicit solutions for the critical and normal depths, while others do not. This paper presents new and improved explicit regression-based equations for the critical and normal depths of open channels with different shapes. A comparison of the proposed and existing equations is also presented. The proposed equations are simple, have a maximum error of less than 1%, and are well-suited for manual calculations and computer programming.

Capillary Based Patterning of Cellular Communities in Laterally Open Channels

In order to offer an easier way to study interactions between multiple cellular populations, we have developed a novel method to precisely place cells in a variety of nonoverlapping patterns using surface tension in laterally open microchannels. Our design is fundamentally different from previous strategies such as compartmentalization, stamping, stenciling, or mechanical approaches. It relies on capillary action or the propensity for liquid to move more readily through narrow spaces as a result of surface tension. Until now, capillary based patterning has been limited to coating chemically isolated areas. Here, we demonstrate, through use of surface tension and controlled flooding, that it is possible to pattern multiple cells and proteins using laterally open channels in a variety of designs. We demonstrate the relevance of the concept by coculturing different mammalian cell types and evaluating the behavior of engineered quorum sensing circuits in E. coli. In the future, we believe the laterally open channel designs shown here can be useful for rapidly creating and studying cellular ecologies using simple pipetting.

Thermal field-flow fractionation and multiangle light scattering of polyvinyl acetate with broad polydispersity and ultrahigh molecular weight microgel components

The challenging task of characterizing polydisperse polymer mixtures possessing ultrahigh molecular weight (MW) polymers and microgels in organic solvents is addressed with thermal field-flow fractionation (ThFFF) and multiangle light scattering-differential refractive index (MALS- dRI) detection. In initial experiments, a 350,000 g/mol poly(methyl methacrylate) (PMMA) standard is used to evaluate the effects of temperature gradient and temperature gradient programming on the measurements. dRI baseline fluctuations caused by temperature programming were minimized by using a mobile phase heater to thermostat connecting tubing. ThFFF–MALS- dRI is then used to separate and characterize a complex polyvinyl acetate (PVAc) sample containing ultrahigh MW polymers and microgels. The open channel design employed by ThFFF allowed the PVAc sample to be analyzed with minimal sample preparation. Unfiltered PVAc sample showed components with MWs close to 10 9 g/mol and root mean square radius r rms values approaching 400 nm. The same sample, filtered through a 0.5 μm pore-size membrane, yielded a MW that was at least one order of magnitude lower. These results demonstrated that the common practice of prefiltering polymer samples prior to analysis can lead to erroneously low average MWs and polydispersities. The accuracy of MW and r rms calculated using standard light scattering equations developed for small scattering molecules and relatively high wavelengths is also examined.

Application of ant colony optimization to optimal design of open channels

Artificial open channels are expensive infrastructure in terms of material, construction and maintenance and application of optimization models has a great role in minimizing their cost. Two optimization approaches for the cross-sectional design are compared. In the first stage, an equivalent roughness coefficient is considered without any sectional division according to the Manning equation. Then, in the second stage, the horizontal velocity variation over the cross-section is taken into account by dividing the channel into three segments. Both, ant colony optimization, as a new heuristic approach, and the genetic algorithm method have been used to solve the non-linear optimization problem. Considering the obtained results for different design variables, the optimal and appropriate cross-section is proposed for composite trapezoidal open channels by the second model by considering horizontal velocity variation. Furthermore, the efficiency and capability of the ant colony optimization are examined to solve and analyze the optimal design models.

FLOW DISTRIBUTION IN MEANDERING COMPOUND CHANNEL

ABSTRACT When the flows in natural or man made channel sections exceed the main channel depth, the adjoining floodplains become inundated and carry part of the river discharge. Due to different hydraulic conditions prevailing in the river and floodplain of a compound channel, the mean velocity in the main channel and in the floodplain are different. This leads to the transfer of momentum between the main channel water and that of the floodplain making the flow structure more complex. Reliable estimates of discharge capacity and its distribution for a compound channel are essential for the design, operation, and maintenance of open channels, more importantly for the prediction of flood and flood protection measures. Results of some experiments concerning the velocity and flow distribution in meandering and straight compound channels are presented. Discharge distribution in such compound channels is strongly dependant on the interaction between flow in the main channel and that in the floodplain. The influence of the geometry on velocity, flow distribution, and the different functional relationships are obtained. Dimensionless parameters are used to form equations representing the flow distribution between main channel and flood plain subsections. A set of meandering and straight compound sections of rectangular and trapezoidal cross section is studied with width ratio varying between 2 to 16.08. The equations agree well with experimental discharge data. Using the proposed area method, the error between the measured and calculated discharge distribution for the meandering and straight compound sections is found to be the minimum when compared with that using other investigators.

Flooding Probability-Based Optimal Design of Trapezoidal Open Channel Using Freeboard as a Design Variable

A flooding probability based cost effective design of open channel section has been proposed using freeboard as an additional design variable. The freeboard of the channel is calculated based on the flooding probability value. The proposed model is solved using classical optimization techniques as well as a nondominated sorting genetic algorithm. The results of the model are compared with an earlier reported model to demonstrate its superiority and field applicability.

Optimization of membrane processes in white biotechnology

White biotechnology for the production of fine chemicals will substitute some chemistry based on petrol and gas in the near future. A standard process for this technology is fermentation. The downstream treatment with membranes is an essential and cost-intensive part of the processing. For downstream processing plate and frame systems are very common due to their robustness and their open channel design. Another essential part of the process is the optimization of membrane fouling. A process for a protease production was used as a reference. The antifoam agent that was used had a strong fouling tendency. It could be shown that a high priced polyamide-imide/polyethersufone membrane could be substituted with a standard, lower priced polyethersufone membrane by optimizing the temperature and antifoam agents.

Optimal Design of Channel Having Horizontal Bottom and Parabolic Sides

The cost of open channels can be minimized by using (1) the optimal design concept; (2) a new geometric shape to substitute for the trapezoidal channels, and/or (3) a composite channel. The channels in which the roughness along the wetted perimeter become distinctly different from part to part of the perimeter are called composite channels. The feasibility of a new cross-sectional shape that has a horizontal bed and two parabolic sides and lined as a composite channel is investigated to substitute for the trapezoidal cross section. The optimal design concept is used to establish the efficacy of the proposed new cross-sectional shape, because it gives the best and unique design of open channels. In optimal design concept, the geometric dimensions of a channel cross section are determined in a manner to minimize the total construction costs. The constraints are the given channel capacity and other imposed restrictions on geometric dimensions. The Lagrange multiplier technique is used to solve the resulting channel optimization models. The developed optimization models are applied to design the proposed and trapezoidal channels to convey a given design flow considering various design scenarios which include unrestricted, flow depth constrained, side slopes constrained, and top width constrained design. Each of these design scenarios again takes into account fixed freeboard, and depth-dependent freeboard cases of design. An analysis of the optimization results establishes the cost-saving capability of the proposed cross-sectional shape in comparison to a trapezoidal cross section.

Spatially-resolved current and impedance analysis of a stirred tank reactor and serpentine fuel cell flow-field at low relative humidity

A 20 cm(2) segmented anode fuel cell is used to investigate the performance of a hydrogen-air fuel cell at 1 atm. with two different flow-fields using spatially-resolved current and impedance measurements. A self-draining stirred tank reactor (STR) fuel cell and a single-channel serpentine fuel cell are compared with humidified and dry feed conditions. The current density distribution, impedance distribution, heat distribution and water evolution are compared for the two different flow-fields. With inlet feed dew points of 30 degrees C, the STR fuel cell and serpentine system performed comparably with moderate current gradients. With drier feeds, however, the STR fuel cell exhibited superior overall performance in terms of a higher total current and lower current, impedance and temperature distribution gradients. The STIR fuel cell design is superior to a single-channel serpentine design under dry conditions because its open channel design allows the feed gases to mix with the product water and auto-humidify the cell. (c) 2006 Elsevier B.V. All rights reserved.