Open-channel Transitions Research Articles

“Turbulence effect on total mechanical energy budget and energy loss of turbulent flows with different hydraulic regimes in open-channel transitions”

ABSTRACT Transitions are needed in hydraulic structures which are flumed. In expanding transitions, flow separates from the boundary if the angle of divergence exceeds about 5 degrees. The present paper gives an insight into the turbulence effect and energy loss in expanding transition with small angle of divergence. In wide angle expansion, flow separates from the boundary resulting in highly non-uniform velocity distribution at the exit of expansion resulting in erosion of down stream channel. Author performed experiments to control separation of flow in wide angle expansion. The paper discusses about the devices used by the author to control separation in wide angle expanding transition.

Analytical Determination of Irrotational Flow Profiles in Open-Channel Transitions

Transitional free surface flow profiles with a critical point occur with weak vorticity and viscosity effects and thus can be modeled with an irrotational flow approach. Important examples in hydraulic engineering include flow over low obstacles, transition structures in canals, and flow over high spillways. While solving Laplace’s equation is relatively simple, the determination of the unknown free surface and energy head of the flow is challenging. Both hydraulic quantities need to be iterated before solving the Laplace equation. Former models iterated the energy head on a trial-and-error basis, assuming that the linked free surface profile is smooth, i.e., free of waves. The iteration of the free surface for a given head is frequently accomplished using the Newton–Rapshon method, which is difficult for the challenging case of spillway flow, giving no solution in some cases. An alternative method of computing irrotational flow profiles in transitional flows involving a critical point is proposed in this work. The model contains three elements: mapping of Laplace’s equation to directly track the streamlines, determination of the critical point and unknown energy head using a critical flow condition for irrotational flows, and determination of the water surface position using an exact analytical solution. The proposed model is favorably compared with experimental data from different sources and CFD results, indicating a reasonable agreement.

Turbulence effect on total mechanical energy budget and energy loss of turbulent flows with different hydraulic regimes in open-channel transitions

ABSTRACT In this study, a modified form of the total mechanical energy budget equation is developed for 3-D turbulent flows with different hydraulic regimes in open-channel transitions, from which the effect of all turbulence parameters can be evaluated by applying some equalizations and RANS numerical simulations. The total energy equation is also used to extract an explicit relationship for energy loss based on turbulence parameters. The findings are presented in the form of the application of the relationship to calculate the energy loss based on simulation results for subcritical turbulent flow and hydraulic jump in open-channel transitions, which leads to identifying the effect of non-homogeneity and anisotropy of turbulence on flow energy balance. The results show that the work done by viscous shear stresses, the viscous diffusion of turbulence, and the turbulent diffusion have little to no effect on the total mechanical energy budget of open-channel turbulent flows; instead, the effect of the variations of turbulent kinetic energy and the work done by turbulence stresses is more significant. The benefit of using the modified energy equation is demonstrated by the potential for evaluating the details that were not previously considered.

Total mechanical energy budget in open-channel transitions with turbulent flows

Abstract The issue of mechanical energy budget has received a lot of attention in open-channel flows which are frequently turbulent. Turbulent motions play a major role in the total mechanical energy of the flow field. It is difficult to evaluate total mechanical energy balance and energy loss for 3-D turbulent flows in irregular open channels due to the formation of vortices and the presence of secondary currents. In 3-D turbulent flows, the effect of these phenomena has often been considered as the empirical coefficient of energy loss. In this study, these details in the total mechanical energy budget are investigated through theoretical analysis and numerical simulation, a new form of the total mechanical energy equation and a relationship for the energy loss in 3-D turbulent flows are derived, and their applications are examined in open-channel transitions. For this purpose, the Navier-Stokes equations are solved numerically, and the results are used to obtain the various terms in the total mechanical energy balance equation and analyze the details. The relationships derived in this study generally support the concept of the total mechanical energy budget to comprehend the turbulence parameters affecting the mechanical energy balance in various open-channel flows.

Experimental and numerical investigation of the flow field in the gradual transition of rectangular to trapezoidal open channels

ABSTRACTTransitions are structures that can change geometry and flow velocity through varying the cross-sections of their channels. Under subcritical flow and steady flow conditions, it is necessary to reduce the flow velocity gradually due to increasing water pressure and adverse pressure gradients. Due to the separation of flow and subsequent eddy formation, a significant energy loss is incurred along the transition. This study presents the results of experimental investigations of the subcritical flow along the expansive transition of rectangular to trapezoidal channels. A numerical simulation was developed using a finite volume of fluid (VOF) method with a Reynolds stress turbulence model. Water surface profiles and velocity distributions of flow through the transition were measured experimentally and compared with the numerical results. A good agreement between the experimental and numerical model results showed that the Reynolds model and VOF method are capable of simulating the hydraulic flow in open channel transitions. Also, the efficiency of the transition and coefficient of energy head loss were calculated. The results show that with an increasing upstream Froude number, the efficiency of the transition and coefficient of energy head loss decrease and increase, respectively. The results also show the ability of numerical simulation to simulate the flow separation zones and secondary current along the transition for different inlet discharges.

Depth-Averaged Specific Energy in Open-Channel Flow and Analytical Solution for Critical Irrotational Flow over Weirs

AbstractFree surface flow in open-channel transitions is characterized by distributions of velocity and pressure that deviate from uniform and hydrostatic conditions, respectively. Under such circumstances the widely used expressions in textbooks [e.g., E=h+U2/(2g) and hc=(q2/g)1/3] are not valid to investigate the changes in velocity and depth. A depth-averaged form of the Bernoulli equation for ideal fluid flows introduces correction coefficients to account for the real velocity and pressure distributions into the specific energy equation. The behavior of these coefficients in curvilinear motion at and in the neighbourhood of control sections was not documented in the literature. Herein detailed two-dimensional ideal fluid flow computations are used to characterize the entire velocity and pressure fields in typical channel controls involving transcritical flow, namely the round-crested weir, the transition from mild to steep slope and the free overfall. The detailed two-dimensional ideal fluid flow solu...

Singular integral equations in potential flows of open-channel transitions

The free-surface profile of potential flows is calculated in open-channel transitions by using singular integral equation methods. Thus in such free-surface hydraulics applications the analysis of fluid motion is very complicated, as both the subcritical and supercritical flows are presented simultaneously. For the numerical solution of the singular integral equations are used both constant and linear elements. An application is finally given to the determination of the free-surface profile in an open-channel contraction and comparing the numerical results with corresponding results by finite differences.

Discussion of “Direct Solution to Problems of Open-Channel Transitions: Rectangular Channels” by Abdulrahman Abdulrahman

Discussion of “Direct Solution to Problems of Open-Channel Transitions: Rectangular Channels” by Abdulrahman Abdulrahman

Discussion of “Direct Solution to Problems of Open-Channel Transitions: Rectangular Channels” by Abdulrahman Abdulrahman

Discussion of “Direct Solution to Problems of Open-Channel Transitions: Rectangular Channels” by Abdulrahman Abdulrahman

Closure to “Direct Solution to Problems of Open-Channel Transitions: Rectangular Channels” by Abdulrahman Abdulrahman

Closure to “Direct Solution to Problems of Open-Channel Transitions: Rectangular Channels” by Abdulrahman Abdulrahman

Direct Solution to Problems of Open-Channel Transitions: Rectangular Channels

The specific energy equation has many applications in rectangular open-channel flow problems. The existing methods of solving this equation are as follows: trial-and-error solution, graphical solution, and design tables prepared from the specific energy equation expressed in dimensionless form. No direct solutions are available in the technical literature for this equation to date because it was presumed that finding roots of this equation requires a series of substitutions. In this technical note, the writer develops an analytical solution for transitions located in rectangular open channels: (1) to avoid the inconvenience in available solutions; (2) to derive a less time consuming method; and (3) to achieve more accurate results than those as a result of using existing methods.

Single channel studies of inward rectifier potassium channel regulation by muscarinic acetylcholine receptors.

Negative regulation of the heartbeat rate involves the activation of an inwardly rectifying potassium current (I(KACh)) by G protein-coupled receptors such as the m2 muscarinic acetylcholine receptor. Recent studies have shown that this process involves the direct binding of G(betagamma) subunits to the NH(2)- and COOH-terminal cytoplasmic domains of the proteins termed GIRK1 and GIRK4 (Kir3.1 and Kir3.4/CIR), which mediate I(KACh). Because of the very low basal activity of native I(KACh), it has been difficult to determine the single channel effect of G(betagamma) subunit binding on I(KACh) activity. Through analysis of a novel G protein-activated chimeric inward rectifier channel that displays increased basal activity relative to I(KACh), we find that single channel activation can be explained by a G protein-dependent shift in the equilibrium of open channel transitions in favor of a bursting state of channel activity over a long-lived closed state.

Bastadin 10 Stabilizes the Open Conformation of the Ryanodine-sensitive Ca2+ Channel in an FKBP12-dependent Manner

The marine sponge Ianthella basta synthesizes at least 25 tetrameric bromotyrosine structures that possess a stringent structural requirement for modifying the gating behavior of ryanodine-sensitive Ca(2+) channels (ryanodine receptors) (RyR)). Bastadin 5 (B5) was shown to stabilize open and closed channel states with little influence on the sensitivity of the channel to activation by Ca(2+) (Mack, M. M., Molinski, T. F., Buck, E. D., and Pessah, I. N. (1994) J. Biol. Chem. 269, 23236-23249). In the present paper, we utilize single channel analysis and measurements of Ca(2+) flux across the sarcoplasmic reticulum to identify bastadin 10 (B10) as the structural congener responsible for dramatically stabilizing the open conformation of the RyR channel, possibly by reducing the free energy associated with closed to open channel transitions (DeltaG*c --> o). The stability of the channel open state induced by B10 sensitized the channel to activation by Ca(2+) to such an extent that it essentially obviated regulation by physiological concentrations of Ca(2+) and relieved inhibition by physiological Mg(2+). These actions of B10 were produced only on the cytoplasmic face of the channel, were selectively eliminated by pretreatment of channels with FK506 or rapamycin, and were reconstituted by human recombinant FKBP12. The actions of B10 were found to be reversible. A structure-activity model is proposed by which substitutions on the Eastern and Western hemispheres of the bastarane macrocycle may confer specificity toward the RyR1-FKBP12 complex to stabilize either the closed or open channel conformation. These results indicate that RyR1-FKBP12 complexes possesses a novel binding domain for phenoxycatechols and raise the possibility of molecular recognition of an endogenous ligand.

Computation of flow in open-channel transitions

The supercritical flow in open-channel transitions often produces discontinuities in the flow variables. Depending on the size, shape and kind of channels, the flow can generate normal/oblique shock waves, expansion waves, hydraulic jumps and sometimes complex wave patterns due to multiple reflection of the waves at the boundary and their subsequent interactions with one another. In the numerical simulation of these flows, uniform grid distribution may introduce detrimental effects in the prediction and resolution of the How details. The use of the presently available numerical schemes to solve these problems on a uniformly spaced grid systems fail to resolve the characteristic flow features and hence do a poor job in simulating the flows. In this paper, MacCormack second-order accurate explicit predictor-corrector scheme is used to solve the two-dimensional depth averaged shallow water equations to numerically simulate the supercritical free-surface flows in open-channel transitions. However, instead of a fixed grid, an adaptive grid system which adjusts itself as the solution evolves is used for a better resolution of the flow properties. In the present approach, Rai and Anderson's method based on grid speed is used for grid adaptation. In a flow with shock, best solutions are obtained when the coordinate axes are aligned along the shock. Rai and Anderson's method to cluster the grids are found to fulfill this criteria and thus produces better quality solutions, as compared to those obtained with uniformly distributed grid with a specified number of grid points.

Comprehensive Open‐Channel Expansion Transition Design

Open-channel transitions involving an expansion of width are a common feature of canals and flumes. Subcritical flow through an expansion transition can result in significant head loss due to separation of flow and subsequent eddy formation. In addition to more power generation in the case of power channels and increased service area for irrigation canals, the reduction of head loss is desirable from the viewpoint of increasing the life of the transition structure. This paper discusses a methodology based on optimal control theory for designing expansion transitions for gradually varied subcritical flow. Based on a large number of expansion transition designs, usable equations have been obtained for bed-width, side-slope, and bed profiles.

Computation of flows in open-channel transitions

To analyze flows in channel expansions and contractions, two-dimensional, depth-averaged, unsteady flow equations in a transformed coordinate system are solved numerically by using the MacCormack s...

Open Channel Transitions: Rational Method of Design

Existing methods for the design of an open channel transition between a rectangular flume and a trapezoidal channel for subcritical flow have been critically examined. Arising out of some fundamental considerations, a suggestion has been offered to make Hinds transition design a direct method. The problem of flow through open channel transitions has been viewed basically from the fluid mechanics point of view and suitable functions for the boundaries of transition (namely bed width, bed elevation, and side slope) have been identified partly analytically and partly experimentally. Based on these results, a new and rational method of design is suggested.

Direct Solution to Problems of Open Channel Transitions

Existing methods of solving problems of open channel transitions involve trials-and-error solution of higher degree equations and no direct solutions are available in technical literature. This paper presents unique dimensionless discharge-depth relationships for exponential, trapezoidal, and circular channels that facilitate direct solutions to various problems on horizontal, vertical, and combined horizontal-vertical transitions even with change in cross-sectional shape. Use of the proposed relationships is demonstrated with practical examples of culvert and aqueduct transitions.