Fourth-order method for solving the Navier-Stokes equations in a constricting channel

A fourth-order numerical method for solving the Navier-Stokes equations in streamfunction/vorticity formulation on a two-dimensional non-uniform orthogonal grid has been tested on the fluid flow in a constricted symmetric channel. The family of grids is generated algebraically using a conformal transformation followed by a non-uniform stretching of the mesh cells in which the shape of the channel boundary can vary from a smooth constriction to one which one possesses a very sharp but smooth corner. The generality of the grids allows the use of long channels upstream and downstream as well as having a refined grid near the sharp corner. Derivatives in the governing equations are replaced by fourth-order central differences and the vorticity is eliminated, either before or after the discretization, to form a wide difference molecule for the streamfunction. Extra boundary conditions, necessary for wide-molecule methods, are supplied by a procedure proposed by Henshaw et al. The ensuing set of non-linear equations is solved using Newton iteration. Results have been obtained for Reynolds numbers up to 250 for three constrictions, the first being smooth, the second having a moderately sharp corner and the third with a very sharp corner. Estimates of the error incurred show that the results are very accurate and substantially better than those of the corresponding second-order method. The observed order of the method has been shown to be close to four, demonstrating that the method is genuinely fourth-order. © 1977 John Wiley & Sons, Ltd.

Experimental setup for measuring roll waves on laminar open channel flows

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Development of a low-Reynolds-number k-ω model for FENE-P fluids

A low-Reynolds-number k-ω model for Newtonian fluids has been developed to predict drag reduction of viscoelastic fluids described by the FENE-P model. The model is an extension to viscoelastic fluids of the model for Newtonian fluids developed by Bredberg et al. (Int J Heat Fluid Flow 23:731-743, 2002). The performance of the model was assessed using results from direct numerical simulations for fully developed turbulent channel flow of FENE-P fluids. It should only be used for drag reductions of up to 50 % (low and intermediate drag reductions), because of the limiting assumption of turbulence isotropy leading to an under-prediction of k, but compares favourably with results from k-ε models in the literature based on turbulence isotropy. © 2012 Springer Science+Business Media Dordrecht.

Numerical solution of the FENE-CR model in complex flows

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Aplicação de modelos hidrológicos para avaliação de reservatórios de retenção e detenção combinados à obra de recuperação do canal de macrodrenagem no controle de cheias em uma bacia hidrográfica urbanizada

The aim of this paper was to evaluate the effect of retention and detention reservoirs along with the regulation in channel flow upgrade on flood for an urban watershed located at Rio Claro, SP. For this purpose, modeling and simulation techniques were applied for runoff determination and its propagation in channel. The Soil Conservation Service – SCS hydrologic model as well as Pulz and non-linear Muskingum-Cunge model were used. The software IPHS1 was applied on simulations. The results pointed out that the combination of retention increasing and detention reservoir implementation (120,000 m3, corresponding to 1.5% of the watershed area) with the streamflow upgrade (n decreasing from 0,04 to 0,02) can minimize the flood on the investigated Servidão watershed. Further, after the proposed intervention, the flood was eliminated for the investigated times of recurrence: 5, 20, 50 and 100 years. The prognostic indicated that the available area occupation had a minor effect on flow increasing due to the observed high urbanization.

A study of a numerical solution of the steady two dimensions Navier-Stokes equations in a constricted channel problem by a compact fourth order method

We present a numerical solution for the steady 2D Navier-Stokes equations using a fourth order compact-type method. The geometry of the problem is a constricted symmetric channel, where the boundary can be varied, via a parameter, from a smooth constriction to one possessing a very sharp but smooth corner allowing us to analyse the behaviour of the errors when the solution is smooth or near singular. The set of non-linear equations is solved by the Newton method. Results have been obtained for Reynolds number up to 500. Estimates of the errors incurred have shown that the results are accurate and better than those of the corresponding second order method. (C) 2002 Elsevier B.V. All rights reserved.

Phosphite determination in fertilizers after online sequential sample preparation in a flow injection system

A flow injection spectrophotometric system is proposed for phosphite determination in fertilizers by the molybdenum blue method after the processing of each sample two times on-line without and with an oxidizing step. The flow system was designed to add sulfuric acid or permanganate solutions alternately into the system by simply displacing the injector-commutator from one resting position to another, allowing the determination of phosphate and total phosphate, respectively. The concentration of phosphite is obtained then by difference between the two measurents. The influence of flow rates, sample volume, and dimension of flow line connecting the injector-commutator to the main analytical channel was evaluated. The proposed method was applied to phosphite determination in commercial liquid fertilizers. Results obtained with the proposed FIA system were not statistically different from those obtained by titrimetry at the 95% confidence level. In addition, recoveries within 94 and 100% of spiked fertilizers were found. The relative standard deviation (n = 12) related to the phosphite-converted-phosphate peak alone was <= 3.5% for 800 mg L-1 P (phoshite) solution. Precision due to the differences of total phosphate and phosphate was 1.1% for 10 mg L-1 P (phosphate) + 3000 mg L-1 P (phosphite) solution. The sampling rate was calculated as 15 determinations per hour, and the reagent consumption was about 6.3 mg of KMnO4, 200 mg of (NH4)(6)Mo7O24 center dot 4H(2)O, and 40 mg of ascorbic acid per measurement.

Central nifedipine-induced alterations in salivary flow and compounds: Role of nitric oxide

The aim of this study was to examine the role of nifedipine and Nitric Oxide (NO) on salivary flow and compounds (salivary amylase, saliva total proteins, saliva calcium, sodium and potassium). Male Holtzman rats weighting 200-250 g were anesthetized with zoletil 50 mg kg -1 (tiletamine chloridrate 125.0 mg and zolazepan chloridrate 125.0 mg) into quadriceps muscle and stainless steel cannulas were implanted into their lateral ventricle of the brain (LV). Animals in divided group were injected with nifedipine (50 μg μL -1) alone and in combination with 7-nitroindazol (7-NIT) (40 μg μL -1), neuronal NO Sinthase Inhibitor (nNOSI) and Sodium Nitroprussate (SNP) (30 μg μL -1) NO donor agent. As a secretory stimuli, pilocarpine dissolved in isotonic was administered intraperitoneally (ip) at a dosage of 10 mg kg -1 body weight. Saliva was collected for 7 min with four cotton balls weighing approximately 20 mg each, two of which were placed on either side of the oral cavity, with the other two placed under the tongue. Nifedipine treatment induced a reduction in saliva secretion rate and concentration of amylase, total protein and calcium without changes in sodium and potassium concentration in comparison with controls. Co-treatment of animals with nifedipine and SNP retained flow rate and concentration of amylase, total protein and calcium in normal levels. Co-treatment of animals with nifedipine and 7-NIT potentiated the effect of nifedipine on the reduction of saliva secretion and concentrations of amylase, total protein and calcium. Nifedipine (dihydroperidine) calcium-channel blocker widely in use is associated with salivary dysfunction acting in the central nervous system structures. NO might be the mechanism for protective effect against the nifedipine-induce salivary dysfunction, acting in the CNS. © 2006 Asian Network for Scientific Information.