Analysis of the Leakage Behavior of Francis Turbines and Its Impact on the Hydraulic Efficiency—A Validation of an Analytical Model Based on Computational Fluid Dynamics Results

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Jürgen Schiffer ◽  
Helmut Benigni ◽  
Helmut Jaberg
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Pressure Distribution ◽  
Analytical Model ◽  
Analytical Approach ◽  
Analytical Calculation ◽  
Francis Turbine ◽  
Centrifugal Pumps ◽  
Present Contribution ◽  
Disk Friction

The present contribution addresses the analysis of the leakage behavior of a small hydro Francis turbine using an analytical approach, which was validated based on the results of computational fluid dynamics (CFD). For a custom-designed Francis turbine with a specific speed of nq = 41.9 rpm, the flow chambers resulting from the labyrinth geometry were added to a traditional full CFD model of the turbine and numerical simulations were performed for several operation points ranging from part load (Qmin = 0.5 × Qopt) to over load (Qmax = 1.3 × Qopt). Consequently, the single losses occurring in the runner seals on crown and band side as well as the pressure distribution within the runner side spaces could be evaluated and compared to the results gained with an analytical approach, which was originally developed to calculate the leakage flow of centrifugal pumps. The comparison of the pressure distribution achieved with the numerical simulation and the analytical calculation shows that both approaches match well if the angular velocity of the fluid ωFluid trapped in the runner side spaces is calculated in an appropriate way. Furthermore, the achieved results demonstrate that the use of the analytical model enables the calculation of the disk friction and leakage losses with sufficient accuracy. This paper contributes to the improvement of the performance prediction of Francis turbines based on combined numerical and analytical calculations.

scholarly journals Journal Bearing: An Integrated CFD-Analytical Approach for the Estimation of the Trajectory and Equilibrium Position

2020 ◽  
Vol 10 (23) ◽  
pp. 8573
Author(s):  
Franco Concli
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Pressure Distribution ◽  
Equilibrium Position ◽  
Analytical Approach ◽  
Journal Bearing ◽  
Cfd Model ◽  
Cavitation Model ◽  
Computational Fluid Dynamics Cfd ◽  
The Mathematical Model

For decades, journal bearings have been designed based on the half-Sommerfeld equations. The semi-analytical solution of the conservation equations for mass and momentum leads to the pressure distribution along the journal. However, this approach admits negative values for the pressure, phenomenon without experimental evidence. To overcome this, negative values of the pressure are artificially substituted with the vaporization pressure. This hypothesis leads to reasonable results, even if for a deeper understanding of the physics behind the lubrication and the supporting effects, cavitation should be considered and included in the mathematical model. In a previous paper, the author has already shown the capability of computational fluid dynamics to accurately reproduce the experimental evidences including the Kunz cavitation model in the calculations. The computational fluid dynamics (CFD) results were compared in terms of pressure distribution with experimental data coming from different configurations. The CFD model was coupled with an analytical approach in order to calculate the equilibrium position and the trajectory of the journal. Specifically, the approach was used to study a bearing that was designed to operate within tight tolerances and speeds up to almost 30,000 rpm for operation in a gearbox.

scholarly journals Rapid pivot feeding in pipefish: flow effects on prey and evaluation of simple dynamic modelling via computational fluid dynamics

2008 ◽  
Vol 5 (28) ◽  
pp. 1291-1301 ◽  
Author(s):  
Sam Van Wassenbergh ◽  
Peter Aerts
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Analytical Model ◽  
Dynamic Modelling ◽  
Head Rotation ◽  
Theoretical Models ◽  
Cfd Simulations ◽  
Deceleration Phase ◽  
Computational Fluid Dynamics Cfd ◽  
Flow Effects

Most theoretical models of unsteady aquatic movement in organisms assume that including steady-state drag force and added mass approximates the hydrodynamic force exerted on an organism's body. However, animals often perform explosively quick movements where high accelerations are realized in a few milliseconds and are followed closely by rapid decelerations. For such highly unsteady movements, the accuracy of this modelling approach may be limited. This type of movement can be found during pivot feeding in pipefish that abruptly rotate their head and snout towards prey. We used computational fluid dynamics (CFD) to validate a simple analytical model of cranial rotation in pipefish. CFD simulations also allowed us to assess prey displacement by head rotation. CFD showed that the analytical model accurately calculates the forces exerted on the pipefish. Although the initial phase of acceleration changes the flow patterns during the subsequent deceleration phase, the accuracy of the analytical model was not reduced during this deceleration phase. Our analysis also showed that prey are left approximately stationary despite the quickly approaching pipefish snout. This suggests that pivot-feeding fish need little or no suction to compensate for the effects of the flow induced by cranial rotation.

scholarly journals Derivation of Global Parametric Performance of Mixed Flow Hydraulic Turbine Using CFD

1970 ◽  
Vol 7 ◽  
pp. 60-64 ◽  
Author(s):  
Ruchi Khare ◽  
Vishnu Prasad Prasad ◽  
Sushil Kumar
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Numerical Solutions ◽  
Guide Vane ◽  
Hydraulic Turbine ◽  
Francis Turbine ◽  
Mixed Flow ◽  
Flow Equations ◽  
Laboratory Setup ◽  
Wide Range

The testing of physical turbine models is costly, time consuming and subject to limitations of laboratory setup to meet International Electro technical Commission (IEC) standards. Computational fluid dynamics (CFD) has emerged as a powerful tool for funding numerical solutions of wide range of flow equations whose analytical solutions are not feasible. CFD also minimizes the requirement of model testing. The present work deals with simulation of 3D flow in mixed flow (Francis) turbine passage; i.e., stay vane, guide vane, runner and draft tube using ANSYS CFX 10 software for study of flow pattern within turbine space and computation of various losses and efficiency at different operating regimes. The computed values and variation of performance parameters are found to bear close comparison with experimental results.Key words: Hydraulic turbine; Performance; Computational fluid dynamics; Efficiency; LossesDOI: 10.3126/hn.v7i0.4239Hydro Nepal Journal of Water, Energy and EnvironmentVol. 7, July, 2010Page: 60-64Uploaded date: 31 January, 2011

Direct Design of Ducts

2003 ◽  
Vol 125 (1) ◽  
pp. 158-165 ◽  
Author(s):  
A. Ashrafizadeh ◽  
G. D. Raithby ◽  
G. D. Stubley
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Pressure Distribution ◽  
Design Method ◽  
Three Dimensional ◽  
Viscous Flows ◽  
Simple Extension ◽  
Two Dimensional ◽  
Direct Design ◽  
Dependent Variables

This paper describes a method for calculating the shape of duct that leads to a prescribed pressure distribution on the duct walls. The proposed design method is computationally inexpensive, robust, and a simple extension of existing computational fluid dynamics methods; it permits the duct shape to be directly calculated by including the coordinates that define the shape of the duct wall as dependent variables in the formulation. This “direct design method” is presented by application to two-dimensional ideal flow in ducts. The same method applies to many problems in thermofluids, including the design of boundary shapes for three-dimensional internal and external viscous flows.

Pump Grooved Seals: A Computational Fluid Dynamics Approach to Improve Bulk-Flow Model Predictions

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Tingcheng Wu ◽  
Luis San Andrés
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Mechanical Energy ◽  
Bulk Flow ◽  
Dynamic Force ◽  
Centrifugal Pumps ◽  
Force Coefficients ◽  
Damping Coefficients ◽  
Groove Seal ◽  
Rectangular Groove

In multiple stage centrifugal pumps, balance pistons, often comprising a grooved annular seal, equilibrate the full pressure rise across the pump. Grooves in the stator break the evolution of fluid swirl and increase mechanical energy dissipation; hence, a grooved seal offers a lesser leakage and lower cross-coupled stiffness than a similar size uniform clearance seal. To date, bulk-flow modelbulk-flow models (BFMs) expediently predict leakage and rotor dynamic force coefficients of grooved seals; however, they lack accuracy for any other geometry besides rectangular. Note that scalloped and triangular (serrated) groove seals are not uncommon. In these cases, computational fluid dynamics (CFD) models seals of complex shape to produce leakage and force coefficients. Alas, CFD is not yet ready for routine engineer practice. Hence, an intermediate procedure presently takes an accurate two-dimensional (2D) CFD model of a smaller flow region, namely a single groove and adjacent land, to produce stator and rotor surface wall friction factors, expressed as functions of the Reynolds numbers, for integration into an existing BFM and ready prediction of seal leakage and force coefficients. The selected groove-land section is well within the seal length and far away from the effects of the inlet condition. The analysis takes three water lubricated seals with distinct groove shapes: rectangular, scalloped, and triangular. Each seal, with length/diameter L/D = 0.4, has 44 grooves of shallow depth dg ∼ clearance Cr and operates at a rotor speed equal to 5,588 rpm (78 m/s surface speed) and with a pressure drop of 14.9 MPa. The method validity is asserted when 2D (single groove-land) and three-dimensional (3D) (whole seal) predictions for pressure and velocity fields are compared against each other. The CFD predictions, 2D and 3D, show that the triangular groove seal has the largest leakage, 41% greater than the rectangular groove seal does, albeit producing the smallest cross-coupled stiffnesses and whirl frequency ratio (WFR). On the other hand, the triangular groove seal has the largest direct stiffness and damping coefficients. The scalloped groove seal shows similar rotordynamic force coefficients as the rectangular groove seal but leaks 13% more. For the three seal groove types, the modified BFM predicts leakage that is less than 6% away from that delivered by CFD, whereas the seal stiffnesses (both direct and cross-coupled) differ by 13%, the direct damping coefficients by 18%, and the added mass coefficients are within 30%. The procedure introduced extends the applicability of a BFM to predict the dynamic performance of grooved seals with distinctive shapes.

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