Use of artificial neural networks for prediction of discharge coefficient of triangular labyrinth side weir in curved channels

Side weirs have been extensively used in hydraulic and environmental engineering applications. The discharge coefficient of the triangular labyrinth side weirs is 1.5-4.5 times higher than that of rectangular side weirs. This study aims to estimate the discharge coefficient (C_d) of triangular labyrinth side weir in curved channel by using artificial neural networks (ANN). In this study, 7963 laboratory test results are used for determining the C_d. The performance of the ANN model is compared with multiple nonlinear and linear regression models. Root mean square errors (RMSE), mean absolute errors (MAE) and correlation coefficient (R) statistics are used as comparing criteria for the evaluation of the models’ performances. Based on the comparisons, it was found that the neural computing technique could be employed successfully in modeling discharge coefficient from the available experimental data. There were good agreements between the measured values and the values obtained using the ANN model. It was found that the ANN model with RMSE of 0.1658 in validation stage is superior in estimation of discharge coefficient than the multiple nonlinear and linear regression models with RMSE of 0.2054 and 0.2926, respectively.     

Sudden expansions in circular microchannels: flow dynamics and pressure drop

Micro particle shadow velocimetry is used to study the flow of water through microcircular sudden expansions of ratios e = 1.51 and e = 1.96 for inlet Reynolds numbers Re _d < 120. Such flows give rise to annular vortices, trapped downstream of the expansions. The dependency of the vortex length on the Reynolds number Re _d and the expansion ratio e is experimentally investigated in this study. Additionally, the shape of the axisymmetric annular vortex is quantified based on the visualization results. These measurements favorably follow the trends reported for larger scales in the literature. Redevelopment of the confined jet to the fully developed Poiseuille flow downstream of the expansion is also studied quantitatively. Furthermore, the experimentally resolved velocities are used to calculate high resolution static pressure gradient distributions along the channel walls. These measurements are then integrated into the axisymmetric momentum and energy balance equations, for the flow downstream of the expansion, to obtain the irreversible pressure drop in this geometry. As expected, the measured pressure drop coefficients for the range of Reynolds numbers studied here do not match the predictions of the available empirical correlations, which are commonly based turbulent flow studies. However, these results are in excellent agreement with previous numerical calculations. The pressure drop coefficient is found to strongly depend on the inlet Reynolds number for Re _d < 50. Although no length-scale effect is observed for the range of channel diameters studied here, for Reynolds numbers Re _d < 50, which are typical in microchannel applications, complex nonlinear trends in the flow dynamics and pressure drop measurements are discovered and discussed in this work.     

Predicting discharge coefficient of triangular labyrinth weir using extreme learning machine,artificial neural network and genetic programming

Weirs are a type of hydraulic structure used to direct and transfer water flows in the canals and overflows in the dams. The important index in computing flow discharge over the weir is discharge coefficient (C _d). The aim of this study is accurate determination of the C _d in triangular labyrinth side weirs by applying three intelligence models [i.e., artificial neural network (ANN), genetic programming (GP) and extreme learning machine (ELM)]. The calculated discharge coefficients were then compared with some experimental results. In order to examine the accuracy of C _d predictions by ANN, GP and ELM methods, five statistical indices including coefficient of determination (R ²), root-mean-square error (RMSE), mean absolute percentage error (MAPE), SI and δ have been used. Results showed that R ² values in the ELM, ANN and GP methods were 0.993, 0.886 and 0.884, respectively, at training stage and 0.971, 0.965 and 0.963, respectively, at test stage. The ELM method, having MAPE, RMSE, SI and δ values of 0.81, 0.0059, 0.0082 and 0.81, respectively, at the training stage and 0.89, 0.0063, 0.0089 and 0.88, respectively, at the test stage, was superior to ANN and GP methods. The ANN model ranked next to the ELM model.

     

Study on microchannel flows with a sudden contraction–expansion at a wide range of Knudsen number using lattice Boltzmann method

Numerical simulations have been performed on the pressure-driven rarefied flow through channels with a sudden contraction–expansion of 2:1:2 using isothermal two and three-dimensional lattice Boltzmann method (LBM). In the LBM, a Bosanquet-type effective viscosity and a modified second-order slip boundary condition are used to account for the rarefaction effect on gas viscosity to cover the slip and transition flow regimes, that is, a wider range of Knudsen number. Firstly, the in-house LBM code is verified by comparing the computed pressure distribution and flow pattern with experimental ones measured by others. The verified code is then used to study the effects of the outlet Knudsen number Kn _o , driving pressure ratio P _i /P _o , and Reynolds number Re, respectively, varied in the ranges of 0.001–1.0, 1.15–5.0, and 0.02–120, on the pressure distributions and flow patterns as well as to document the differences between continuum and rarefied flows. Results are discussed in terms of the distributions of local pressure, Knudsen number, centerline velocity, and Mach number. The variations of flow patterns and vortex length with Kn _o and Re are also documented. Moreover, a critical Knudsen number is identified to be Kn _oc  = 0.1 below and above which the behaviors of nonlinear pressure profile and velocity distribution and the variations of vortex length with Re upstream and downstream of constriction are different from those of continuum flows.     

Weighted mean of a pair of clusterings

In this paper, we introduce the weighted mean of a pair of clusterings. Given two clusterings C ₁ and C ₂, the weighted mean of C ₁ and C ₂ is a clustering C _w that has distances d(C ₁, C _w ) and d(C _w , C ₂) to C ₁ and C ₂, respectively, such that d(C ₁, C _w ) + d(C _w , C ₂) = d(C ₁, C ₂) holds for some clustering distance function d. C _w is defined such that the sum of the distances d(C ₁, C _w ) and d(C _w , C ₂) is equal to the distance between C ₁ and C ₂. An algorithm for its computation will be presented. Experimental results on both synthetic and real data will be shown to illustrate the usefulness of the weighted mean concept. In particular, it gives a tool for the cluster ensemble techniques.     

Tool-path generation of planar NURBS curves

It has been widely used in CAD field for many years and gradually applied in CAM area with the prevalence of NURBS interpolator equipped in CNC controllers. But few of them provide the tool radius compensation function. In order to achieve the goal of generating tool-path, an algorithm was presented to offset NURBS curves by an optimum process for CAD/CAM systems in this paper. NURBS format is ideal for HSM applications, but not all NURBS outputs are equal and standard. Basically, there are two different ways to generate NURBS tool-paths; one is to fit a NURBS curve to the conventional tool-path output, the other one is to generate a NURBS tool-path from the start. The main targets for the tool-path of this paper are: (1) To keep a constant distance d between progenitor curve C(t) and offset curve C_d(t) on the normal direction of C(t); (2) to alternate the order k of the basis function in offset curve C_d(t); (3) to oscillate the number of control points of offset curve C_d(t) and compare it with progenitor curve C(t). In order to meet the tolerance requirements as specified by the design, this study offsets the NURBS curves by a pre-described distance d. The principle procedure consists of the following steps: (1) construct an evaluating bound error function; (2) sample offset point-sequenced curves based on first derivatives; (3) give the order of NURBS curve and number of control points to compute all initial conditions and (4) optimize the control points by a path searching algorithm.     

Analysis and control of the near-wake flow over a square-back geometry

A 3D numerical simulation, based on the Lattice Boltzmann method is carried out on the near-wake flow behind a generic square-back blunt body to analyze and establish a method to control the near-wake flow. The flow topology is described by the velocity and the pressure fields. The influence of the wake vortices on the aerodynamic drag is clarified and quantified. In order to reduce this drag, an active open-loop flow control is applied by continuous blowing devices distributed around the base periphery. The blowing effect on the behind body flow is a reduction of the wake section and of the total pressure loss in the wake and an increase of the static pressure on the base of the square body. This control leads to a significant drag reduction of ΔC_x = −29% with a blowing velocity of 1.5V₀. The efficiency is then studied, and we found that the most efficient control is obtained for a blowing velocity of 0.5V₀ and a jet angle of 45°. In this case, a 20% drag reduction is obtained, and the energy needed to control the system is seven times lower than the energy saved by the control.     

Numerical Simulation of a Hypersonic Flow over an Aircraft in a High-Altitude Active Movement Area

A hypersonic flow over an axisymmetric aircraft is numerically simulated in the case of a highly underexpanded exhaust plume (jet) of the main engine. The characteristics of the boundary layer separation occurring on the aircraft’s side surface are investigated for several successive points of its takeoff path. The Mach number at the nozzle exit is 6.5. The Mach number of the incoming flow varies from 4 to 7. In this case, the Reynolds number ranges from 2.5 × 10⁵ to 3 × 10³ and the ratio of the nozzle’s exit pressure to the ambient pressure, from 350 to 5 × 10⁴. In the case of the Mach number of the incoming flow M_∞ = 4, the variation range of the pressure ratio extends to 106. Replacement of the exhaust plume with a rigid simulator is considered. Data are obtained on the pressure ratios for which a separation flow begins to form on the side surface, the recirculation zone length, and the level of pressure in it in comparison with the available empirical dependences. A significant increase of the recirculation zone in front of the exhaust plume is shown when it is replaced by a rigid simulator of the same dimensions.     

Bifurcations and buffet of transonic flow past flattened surfaces

Turbulent transonic flow past flattened aerodynamic surfaces is investigated numerically using the RANS equations. The study is focused on: (★) a buffet onset caused by instability of the shock wave/boundary layer interaction, (★★) instability of the entire flow structure and related flow bifurcations.For a symmetric airfoil at zero angle of attack, computations reveal both bifurcations and buffet in a range of the freestream Mach number M_∞. At nonzero angles of attack, α=±1°, there are two ranges of M_∞ in which the buffet onset takes place. For a Whitcomb type airfoil, computations demonstrate instability of the flow structure only at negative α. Axisymmetric flow past axisymmetric bodies is also considered, and instability of the flow structure at certain freestream Mach numbers is shown.     

Numerical investigation of fully developed channel flow using shock-capturing schemes

The ability to simulate wall-bounded channel flows with second- and third-order shock-capturing schemes is tested on both subsonic and supersonic flow regimes, respectively at Mach 0.5 and 1.5. Direct numerical simulations (DNSs) and large-eddy simulations (LESs) are performed at Reynolds number 3000.In both flow regimes, results are compared with well-documented DNS, LES or experimental data.At Ma₀=0.5, a simple second-order centred scheme provides results in excellent agreement with incompressible DNS databases, while the addition of artificial or subgrid-scale (SGS) dissipation decreases the resolution accuracy giving just satisfactory results. At Ma₀=1.5, the second-order space accuracy is just sufficient to well resolve small turbulence scales on the chosen grid: without any dissipation models, such accuracy provides results in good agreement with reference data, while the addition of dissipation models considerably reduces the turbulence level and the flow appears almost laminar. Moreover, the use of explicit dissipative SGS models reduces the results accuracy.In both flow regimes, the numerical dissipation due to the discretization of the convective terms is also interpreted in terms of SGS dissipation in an LES context, yielding a generalised dynamic coefficient, equivalent to the dynamic coefficient of the Germano et al. [Phys. Fluids A 3(7) (1991) 1760] SGS model. This new generalised coefficient is thus developed to compare the order of magnitude of the intrinsic numerical dissipation of a shock-capturing scheme with respect to the SGS dissipation.     

Computing monodromy via continuation methods on random Riemann surfaces

We consider a Riemann surface X defined by a polynomial f(x,y) of degree d, whose coefficients are chosen randomly. Hence, we can suppose that X is smooth, that the discriminant δ(x) of f has d(d−1) simple roots, Δ, and that δ(0)≠0, i.e. the corresponding fiber has d distinct points {y₁,…,y_d}. When we lift a loop 0∈γ⊂C−Δ by a continuation method, we get d paths in X connecting {y₁,…,y_d}, hence defining a permutation of that set. This is called monodromy.Here we present experimentations in Maple to get statistics on the distribution of transpositions corresponding to loops around each point of Δ. Multiplying families of “neighbor” transpositions, we construct permutations and the subgroups of the symmetric group they generate. This allows us to establish and study experimentally two conjectures on the distribution of these transpositions and on transitivity of the generated subgroups.Assuming that these two conjectures are true, we develop tools allowing fast probabilistic algorithms for absolute multivariate polynomial factorization, under the hypothesis that the factors behave like random polynomials whose coefficients follow uniform distributions.     

Neuro-fuzzy approach in estimating Hazen–Williams friction coefficient for small-diameter polyethylene pipes

Low-pressurized multiple outlet pipelines are extensively used to uniformly distribute irrigation water under different types of low-volume micro-irrigation systems. Polyethylene (PE) is the main pipe material for smooth pipes in sub-main unit of a micro-irrigation system due to its flexibility and resistibility to the sun. For computing friction loss in PE pipes, many practicing engineers hesitate to use the generalized Darcy–Weisbach equation since the friction coefficient varies at each section of the lateral. Although its non-dimensional homogeneity and limitations in applicability, the empirical Hazen–Williams equation is still commonly preferred, because of its simplicity in practice. In the current hydraulic computations for friction loss, some typical fixed values for the Hazen–Williams coefficient (C_HW) in PE pipes are still recommended regardless of pipe diameter. Experimental works have confirmed that there is a strong dependence of the C_HW on pipe diameter (D), therefore a single value of the C_HW cannot be used for all ranges of pipe diameters. The primary focus of this research is to investigate the accuracy of a fuzzy rule system approach to estimate the proper value of the C_HW coefficient for different pipe diameters because of the imprecise, insufficient, ambiguous and uncertain data available. A neuro-fuzzy approach was developed to relate the input (flow rate and pipe diameter) and output (C_HW and friction loss) variables. The application of the proposed approach was performed using the measured data for friction losses available from the recent experimental analysis, hence its performance was tested using some statistic parameters for error estimation. The examination results indicated that through fuzzy rules and membership functions the proposed model can be successfully used to identify the proper values of C_HW coefficient hence accurately estimate friction losses through smooth PE pipes.     

Stability bounds in networks with dynamic link capacities

We address the problem of stability in networks where the link capacities can change dynamically. We show that every network running a greedy scheduling policy is universally stable at any injection rate r<1/(Cd), where d is the largest number of links crossed by any packet and C is the maximum link capacity. We also show that system-wide time priority scheduling policies are universally stable at any injection rate r<1/(C(d−1)).     

On weak isometries of Preparata codes

Two codes C ₁ and C ₂ are said to be weakly isometric if there exists a mapping J: C ₁ → C ₂ such that for all x, y in C ₁ the equality d(x, y) = d holds if and only if d(J(x), J(y)) = d, where d is the code distance of C ₁. We prove that Preparata codes of length n ≥ 2¹² are weakly isometric if and only if the codes are equivalent. A similar result is proved for punctured Preparata codes of length at least 2¹⁰ ? 1.     

A silicon rectangular micro-orifice for gas flow measurement at moderate Reynolds numbers: design,fabrication and flow analyses

This work describes a micro-flowmeter for moderate flow rates of gases based on a differential pressure measurement. The micro-flowmeters consist of a microfabricated silicon–glass rectangular micro-orifice plate, with external pressure measurement. We experimentally evaluate the effects of geometrics parameters, Reynolds number and compressibility on the discharge coefficient. The paper examines a series of 13 rectangular micro-orifice sizes, with orifice hydraulic diameters ranging from 115 to 362 µm. The behavior of the discharge coefficient is presented for orifice Reynolds numbers ranging from 200 to 18000. Agreement is shown between the experimental and numerical results of the discharge coefficient. The micro-flowmeters measure moderate flow of air ranging from 1 to 106 mg/s. This demonstration implements a design method of micro-flowmeters that can be used in a broad range of microfluidic applications, such as microreactors and power MEMS.     

Multi-criteria scheduling: an agent-based approach for expert knowledge integration

In this work, we present an agent-based approach to multi-criteria combinatorial optimization. It allows to flexibly combine elementary heuristics that may be optimal for corresponding single-criterion problems. We optimize an instance of the scheduling problem 1|d _j |∑C _j ,L _max and show that the modular building block architecture of our optimization model and the distribution of acting entities enables the easy integration of problem specific expert knowledge. We present a universal mutation operator for combinatorial problem encodings that allows to construct certain solution strategies, such as advantageous sorting or known optimal sequencing procedures. In this way, it becomes possible to derive more complex heuristics from atomic local heuristics that are known to solve fractions of the complete problem. We show that we can approximate both single-criterion problems such as P _m |d _j |∑U _j as well as more challenging multi-criteria scheduling problems, like P _m ||C _max,∑C _j and P _m |d _j |C _max,∑C _j ,∑U _j . The latter problems are evaluated with extensive simulations comparing the standard multi-criteria evolutionary algorithm NSGA-2 and the new agent-based model.     

Sports ball aerodynamics: A numerical study of the erratic motion of soccer balls

The application of the commercial CFD code, FLUENT, to sports ball aerodynamics was assessed and a validated 3D analysis technique was established for balls that have been scanned with a 3D laser scanner or drawn in CAD. The technique was used to examine the effects of surface geometry on the aerodynamic behaviour of soccer balls by comparing the flow around different balls and predicting the aerodynamic force coefficients. The validation process included performing CFD studies on 3D smooth spheres and various soccer balls, and comparing the results to wind tunnel tests and flow visualisation. The CFD technique used a surface wrapping meshing method and the Reynolds Averaged Navier-Stokes approach with the realizable k-ε turbulence model, which was found to be able to predict the drag, lift and side force coefficients (C_D, C_L and C_S) reliably, to compare the wake behaviour, and to give good pressure distributions near the stagnation point. The main limitations of the technique with the available computational resources were its inability to accurately predict boundary layer transition or growth, but despite this, several conclusions could be drawn regarding soccer ball aerodynamics. C_D was not significantly different between balls. C_L and C_S were found to be significantly affected by the orientation of the ball relative to its direction of travel, meaning that balls kicked with low amounts of spin could experience quasi-steady lift and side forces and move erratically from side-to-side or up and down through the air. For different balls, C_D, C_L and C_S were predicted and their variation with orientation entered into a modified trajectory simulation program. The erratic nature of this type of kick was found to vary with details of the surface geometry including seam size, panel symmetry, number, frequency and pattern, as well as the velocity and spin applied to the ball by the player. Exploitation of this phenomenon by players and ball designers could have a significant impact on the game.     

Relationship between the attenuation of downwelling irradiance at 490 nm with the attenuation of PAR (400 nm-700 nm) in the Baltic Sea

The vertical attenuation coefficient of diffuse downwelling irradiance at 490 nm (K_d 490) is a parameter that we routinely derive from SeaWiFS images of the Baltic Sea. Here, through model simulations, we examine the relationship between K_d(490), and the vertical attenuation coefficient of PAR (K_d PAR), as this later coefficient determines the light available for aquatic photosynthesis. A simple semi-analytical model is used to predict K_d(490) and K_d(PAR), as a function of the concentrations of chlorophyll, colored dissolved organic material (CDOM), suspended inorganic, and suspended organic particulate material. A series of model simulations based on variations in these optically significant constituents over a range realistic for the Baltic Sea, are used to define the relationship between the two attenuation coefficients.

Kd(PAR)=0.6677Kd^0.6763(490).     

You can (sometimes) tell an image by its cover

For a digital image D let the cover of D be defined by C(D) = Σ_P.Q?Dd(P,Q) where d is the city block distance. Formulas are obtained for C(D) for various shapes including upright line segments, rectangles, isosceles triangles and diamonds. It is shown that certain images can be recognized from their cover values in the presence of additional geometric symmetry conditions.