Local Loss Coefficient Research Articles

SPRINKMOD - pressure and discharge simulation model for pressurized irrigation systems. 3. Sensitivity to lateral hydraulic parameters and leakage

A computer model, SPRINKMOD, was tested with field data collected from a simple sprinkler irrigation system in operation. The original data for laterals and the amount and way leakage is considered were modified to evaluate the model sensitivity. The model predicted the pump station flow rate within 2% and the pump station pressure head within 5% with the original data collected. For this irrigation system, no practical effect was observed in the system operating point by changing the lateral pipe characteristics, lateral leakage amount and distribution, lateral pipe roughness and lateral local loss coefficient for flow past a riser outlet. The amount of leakage had more effect on the model simulation of pressure heads than the way leakage was considered, localized or distributed along the laterals. The use of a variable local loss coefficient, K r, along the 350-m hand-move laterals had a negligible effect on both system operating point and distribution of pressure heads along the laterals.

SPRINKMOD - pressure and discharge simulation model for pressurized irrigation systems. 2. Case study

A computer model, SPRINKMOD, was tested with field data collected from a complex sprinkler irrigation system in operation. The original data collected were adjusted in order to calibrate the model for the irrigation system. Five modifications were made in the original data so that the model sensitivity could be evaluated. The model predicted the system operating point with less than 1% error, after some adjustments in the data. The relative mean standard error was 4.1% for the upstream pressure heads and 2.1% for the downstream pressure heads of all laterals analyzed together. Measurement of pressure and discharge at pump stations along with a reasonable estimate of leakage appears to be essential for simulation of old systems. Adjustments made to pipe wall thickness and pipe roughness were not as important as the adjustments made to the lateral valves closure in getting SPRINKMOD to simulate pressure heads that were close to the measured values. For long laterals, like center pivot laterals, a variable local loss coefficient for flow past a riser outlet worked better than a fixed value of 0.3.

A general correlation for the local loss coefficient in Newtonian axisymmetric sudden expansions

Results from numerical simulations and guidance from an approximated corrected-theory, developed by Oliveira and Pinho (1997), (Oliveira, P.J. and Pinho, F.T. 1997. Pressure drop coeAcient of laminar Newtonian flow in axisymmetric sudden expansions. Int. J. Heat and Fluid flow 18, 518‐529) have been used to arrive at a correlation expressing the irreversible loss coeAcient for laminar Newtonian flow in axisymmetric sudden expansions. The correlation is valid for the ranges 1.5 < D2/D1 < 4 and 0.5 < Re < 200 with errors of less than 5%, except for 25 < Re < 100 where the error could be as much as 7%. The recirculation bubble length is also presented for the same range of conditions and the pressure recovery coeAcient was calculated for Reynolds numbers above 15. ” 1998 Elsevier Science Inc. All rights reserved.

Modeling and numerical simulation of oscillatory two-phase flows, with application to boiling water nuclear reactors

This paper is concerned with the analysis of dynamics and stability of boiling channels and systems. The specific objectives are 2-fold. One of them is to present the results of a study aimed at analyzing the effects of various modeling concepts and numerical approaches on the transient response and stability of parallel boiling channels. The other objective is to investigate the effect of closed-loop feedback on stability of a boiling water reactor (BWR). Various modeling and computational issues for parallel boiling channels are discussed, such as: the impact of the numerical discretization scheme for the node containing the moving boiling boundary on the convergence and accuracy of computations, and the effects of subcooled boiling and other two-phase flow phenomena on the predictions of marginal stability conditions. Furthermore, the effects are analyzed of local loss coefficients around the recirculation loop of a boiling water reactor on stability of the reactor system. An apparent paradox is explained concerning the impact of changing single-phase losses on loop stability. The calculations have been performed using the DYNOBOSS computer code. The results of DYNOBOSS validation against other computer codes and experimental data are shown.

Pressure drop coefficient of laminar Newtonian flow in axisymmetric sudden expansions

Laminar flow of a Newtonian fluid in an axisymmetric pipe expansion has been studied numerically by means of the finite-volume approach. Predicted values of some of the overall flow characteristics, such as recirculation length, its strength, and centre location, were compared with available experimental data and correlations, and good agreement was found. The purpose of the work was to evaluate the pressure-loss coefficient C l for a range of Reynolds numbers and to compare the results with existing simplified theory, which is based on a one-dimensional (1-D) overall balance of energy and momentum. Considerable differences were found, which lead us to formulate corrected theoretical equations in the scope of the 1-D approximation. These corrections were evaluated from the numerical results and accounted for three effects: (1) differing actual and fully developed wall friction; (2) distortion of velocity profiles from the parabolic shape at the sudden expansion section; and (3) nonuniformity of pressure at the expansion plane. Predicted values of the loss coefficient agreed to within 4% with the corrected theory and were found to be proportional to the inverse of the Reynolds number for Re ≤ 17.5 [with effect (3) above predominant and accounting for up to 85% of C l ] and approximately constant for Re > 17.5 [with effect (1) above predominant and accounting for 20% of C l ]. Finally, a correlation for calculating the local loss coefficient as a function of the Reynolds number for the 1:2.6 sudden expansion and fully developed conditions is proposed.

Pressure drop coefficient of laminar Newtonian flow in axisymmetric sudden expansions

Laminar flow of a Newtonian fluid in an axisymmetric pipe expansion has been studied numerically by means of the finite-volume approach. Predicted values of some of the overall flow characteristics, such as recirculation length, its strength, and centre location, were compared with available experimental data and correlations, and good agreement was found. The purpose of the work was to evaluate the pressure-loss coefficient Cl for a range of Reynolds numbers and to compare the results with existing simplified theory, which is based on a one-dimensional (1-D) overall balance of energy and momentum. Considerable differences were found, which lead us to formulate corrected theoretical equations in the scope of the 1-D approximation. These corrections were evaluated from the numerical results and accounted for three effects: (1) differing actual and fully developed wall friction; (2) distortion of velocity profiles from the parabolic shape at the sudden expansion section; and (3) nonuniformity of pressure at the expansion plane. Predicted values of the loss coefficient agreed to within 4% with the corrected theory and were found to be proportional to the inverse of the Reynolds number for Re ≤ 17.5 [with effect (3) above predominant and accounting for up to 85% of Cl] and approximately constant for Re > 17.5 [with effect (1) above predominant and accounting for 20% of Cl]. Finally, a correlation for calculating the local loss coefficient as a function of the Reynolds number for the 1:2.6 sudden expansion and fully developed conditions is proposed.

Incidence Angle and Pitch–Chord Effects on Secondary Flows Downstream of a Turbine Cascade

This paper describes the results of an experimental investigation of the three-dimensional flow downstream of a linear turbine cascade at off-design conditions. The tests have been carried out for five incidence angles from −60 to +35 deg, and for three pitch-chord ratios: s/c = 0.58, 0.73, 0.87. Data include blade pressure distributions, oil flow visualizations, and pressure probe measurements. The secondary flow field has been obtained by traversing a miniature five-hole probe in a plane located at 50 percent of an axial chord downstream of the trailing edge. The distributions of local energy loss coefficients, together with vorticity and secondary velocity plots, show in detail how much the secondary flow field is modified both by incidence and by cascade solidity variations. The level of secondary vorticity and the intensity of the crossflow at the endwall have been found to be strictly related to the blade loading occurring in the blade entrance region. Heavy changes occur in the spanwise distributions of the pitch-averaged loss and of the deviation angle, when incidence or pitch–chord ratio is varied.

Mach Number Effects on Secondary Flow Development Downstream of a Turbine Cascade

The results of an investigation of the three-dimensional flow downstream of a transonic turbine cascade are presented. The investigation was carried out for a wide range of Mach numbers, extending from M2is = 0.2 up to 1.55. Measurements were made in five planes at different axial locations downstream of the trailing edge (covering more than one chord length), by using a miniaturized five-hole probe especially designed for transonic flows. The results are presented in terms of local loss coefficient, vorticity, and secondary velocity plots; these plots give a detailed picture of the secondary flow development downstream of the cascade and show how flow compressibility influences the vortex configuration. As Mach number increases, the passage vortex is found to migrate toward the endwall and secondary flow effects are more confined in the endwall region. The pitchwise mass averaged loss and flow angle distributions along the blade height appear to be affected by the expansion ratio; at high Mach number both underturning and overturning angles are found to be smaller than in low velocity flows. Overall losses, vorticity, and secondary kinetic energy versus Mach number are also presented and discussed.

An Approximate Treatment of Flow in Branches and Bends

Flow in channel branches and bends is analysed by using elementary hydraulic theory. The results are expressions for the local loss coefficients. The primary purpose is to explore the simplified flow processes in the two flow elements. The theoretical solutions match observations well qualitatively but need improvement if quantitative agreement with observations is to be obtained.

Gravity-Driven Flow and Heat Transfer in a Spent Nuclear Fuel Storage Pool

The GFLOW code analyzes a three-dimensional rectangular porous medium by dividing the porous medium into a number of nodes or cells specified by the user. The finite difference form of the fluid conservation equations is solved for each node by application of a modified “marker and cell” numerical technique. The existence of spent nuclear fuel in any node is modeled by using a porosity value less than unity in that node and by including a surface heat transfer term in the fluid energy equation. In addition, local pressure losses due to grid spaces or other planar flow obstructions can be modeled by local loss coefficients. Heat conduction in the fuel is simulated by a fast running implicit finite difference model of the fuel, gap, and clad regions of the fuel rod.

Analyse théorique-expérimentale de l'écoulement réel dans les pompes assoradiales

The paper presents a numerical method for non-isoentropic through flow calculation in centrifugal and mixed-flow pump impellers. The analysis of incompressible fluid motion is done following Wu's general theory on 82 type surface. In particular, one of the motion equations is substituted by the geometrical condition for the flow to follow the prescribed 82 surface. Besides the flow is assumed to take place in presence of a dissipative force field locally opposite to the relative velocity vector and tangent to the stream line. Combining the basic equations of continuity, entropy production, energy and motion, defining the local geometry of the stream surface S2 (angles lambda and mu) and the stream function ψ it is possible to derive the final flow equation of the type δ2ψ/δr2 + δ2ψ/δz2 = q1 +qE ) (7) where q1 depends on velocity components and on S2 geometry and qE depends on the entropy production inside the fluid flow. The equation of stream surface is obtained starting from the blade geometry and considering its distortion due to the slip effect. For the expression of entropy gradient a local loss coefficient n ψ is defined as a ratio between the rise of total pressure in the real flow conditions and the rise of total pressure in isoentropic flow. In this way it is possible to evaluate the therm qE if a preceding isoentropic flow calculation is available. The computer numerical model for the through flow calculation perforrns the following steps : a) defmition of 82 geometry starting from the impeller geometric data and considering the slip effect. b) Iterative solution of equation (7) in the isoentropic case (qE = 0) c) Evaluation of entropy field. d) Iterative solution of equation (7) in its complete form. In the step a) three-dimensional parametric splines are used for surface representation. The discretization of the problem is done using finite element technique with isoparametric, rectangular elements (8 nodes). The solution of non-linear equation (7) is performed using Galerkin's weighted residual method. The paper finally shows an example of through flow calculation in a mixed-flow pump for the design conditions and for two off-design working points. The computed results are compared with experimental measurements.