On the Use of the Squire-Long Equation to Estimate Radial Velocities in Swirling Flows

2006 ◽  
Vol 129 (2) ◽  
pp. 209-217 ◽  
Author(s):  
Michel J. Cervantes ◽  
L. Håkan Gustavsson
Keyword(s):  
Boundary Conditions ◽  
Radial Velocity ◽  
Swirling Flow ◽  
Draft Tube ◽  
Three Dimensional ◽  
Swirling Flows ◽  
Laser Doppler Velocimeter ◽  
Test Case ◽  
Swirl Number ◽  
Experimental Values

A method to estimate the radial velocity in swirling flows from experimental values of the axial and tangential velocities is presented. The study is motivated by the experimental difficulties to obtain this component in a draft tube model as evidenced in the Turbine-99 IAHR∕ERCOFTAC Workshop. The method uses a two-dimensional nonviscous description of the flow. Such a flow is described by the Squire-Long equation for the stream function, which depends on the boundary conditions. Experimental values of the axial velocities at the inlet and outlet of the domain are used to obtain the boundary conditions on the bounded domain. The method consists of obtaining the equation related to the domain with an iterative process. The radial velocity profile is then obtained. The method may be applied to flows with a swirl number up to about Sw=0.25. The critical value of the swirl number depends on the velocity profiles and the geometry of the domain. The applicability of the methodology is first performed on a swirling flow in a diffuser with a half angle of 3deg at various swirl numbers, where three-dimensional (3D) laser Doppler velocimeter (LDV) velocity measurements are available. The method is then applied to the Turbine-99 test case, which consists in a model draft tube flow where the radial inlet velocity was undetermined. The swirl number is equal to Sw=0.21. The stability and the convergence of the approach is investigated in this case. The results of the pressure recovery are then compared to the experiments for validation.

Flow Measurements in a Model Burner—Part 2

1993 ◽  
Vol 115 (2) ◽  
pp. 309-316
Author(s):  
D. F. G. Dura˜o ◽  
M. V. Heitor ◽  
A. L. N. Moreira
Keyword(s):  
Laser Doppler Velocimetry ◽  
Swirling Flow ◽  
Laser Sheet ◽  
Three Dimensional ◽  
Swirling Flows ◽  
Dimensional Structure ◽  
Mixing Efficiency ◽  
Flow Measurements ◽  
Circular Jets ◽  
Turbulence Production

The isothermal swirling flow in the vicinity of a model oxy-fuel industrial burner is analyzed with laser-Doppler velocimetry together with laser-sheet visualization. The burner consists of a central axisymmetric swirling jet surrounded by sixteen circular jets, simulating the injection of oxygen in practical burners. The results extend those obtained for non-swirling flows, and presented in Part 1 of this paper, to the analysis of the dependence of the mixing efficiency of the burner assembly upon the swirl motion of the central jet and have the necessary detail to allow to assess the accuracy of calculation procedures of the flow in industrial burners. It is shown that swirl attenuates the three-dimensional structure typical of multijet flows in such a way that turbulence production and transport in the near burner zone are dominated by swirl-induced processes.

The entrainment envelope of dye-core vortices at submerged hydraulic intakes

2002 ◽  
Vol 29 (3) ◽  
pp. 400-408 ◽  
Author(s):  
E C Carriveau ◽  
R E Baddour ◽  
G A Kopp
Keyword(s):  
Water Surface ◽  
Laboratory Experiments ◽  
Swirling Flow ◽  
Three Dimensional ◽  
Swirling Flows ◽  
Surface Phenomenon ◽  
Acoustic Doppler Velocimeter ◽  
Velocity Measurements ◽  
Frazil Ice ◽  
Hydraulic Intake

Each winter in Canada, operational difficulties are encountered at various water works resulting from intake blockages caused by frazil ice entrainment. In a lake setting, frazil is a surface phenomenon, the strong downward current produced by a swirling flow, with an intake vortex present, provides a mechanism by which frazil is transported from the water surface to the submerged intake below. Laboratory experiments were conducted to study the entrainment envelope associated with swirling and non-swirling flows into submerged water intakes. Three-dimensional velocity measurements were made with an acoustic Doppler velocimeter. The results clearly show that the entrainment envelope for swirling flow is several times larger than that for non-swirling flow. This paper details, for a given set of conditions, the differences in the non-swirling and swirling flow entrainment envelopes and emphasizes the potential difficulties with frazil ice that vortices can cause at intakes.Key words: vortex, dye-core vortex, submerged hydraulic intake, entrainment envelope, three-dimensional velocity measurements, acoustic Doppler velocimeter.

Vorticity Modeling of Blade Wakes behind Isolated Annular Blade-Rows: Induced Disturbances in Swirling Flows

1981 ◽  
Vol 103 (2) ◽  
pp. 279-287 ◽  
Author(s):  
C. S. Tan
Keyword(s):  
Swirling Flow ◽  
Three Dimensional ◽  
Stagnation Pressure ◽  
Swirling Flows ◽  
Axial Distance ◽  
Free Vortex ◽  
Blade Row ◽  
Type 3 ◽  
Theoretical Considerations ◽  
Type Potential

A general analysis is proposed for studying the fluid-mechanical behavior of blade wakes from an annular blade-row in highly swirling flow. The coupling between the centrifugal force and the vorticity, which is inherent to highly swirling flows, can significantly modify the wake behavior from that in a two-dimensional situation. In steady flow, theoretical considerations show that a blade wake consists primarily of two distinct types of vorticity: (1) trailing vorticity shed from the blade due to a spanwise variation in blade circulation; and (2) vorticity associated with defects in stagnation pressure (or rotary stagnation in relative coordinate system). Three types of disturbances can be identified in the resulting three-dimensional disturbance field: (1) the exponentially decaying type (potential, irrotational), (2) the purely convected type (rotational), and (3) the nonconvected type (both rotational and irrotational parts). Type (3) arises because of the interaction of centrifugal and Coriolis forces with (1) and (2). It is found that near the blade row the nonconvected disturbances grow linearly in magnitude with the axial distance. However, although those nonconvected disturbances associated with the trailing vorticity (also called Beltrami vorticity) persist for moderate distances downstream, they eventually decay inversely with the axial distance, irrespective of the types of swirl distribution. In contrast, those parts of nonconvected disturbances which are induced by the vorticity caused by (rotary) stagnation pressure defects persist indefinitely downstream for any type of swirl other than free-vortex. In the limit of free-vortex swirl, all disturbances decay at least inversely with the axial distance downstream.

Factorial Design Applied to CFD

2004 ◽  
Vol 126 (5) ◽  
pp. 791-798 ◽  
Author(s):  
Michel J. Cervantes ◽  
T. Fredrik Engstro¨m
Keyword(s):  
Boundary Conditions ◽  
Factorial Design ◽  
Draft Tube ◽  
Turbulence Models ◽  
Test Case ◽  
Unknown Boundary ◽  
Experimental Uncertainty ◽  
Complex Flow ◽  
Input Parameters ◽  
Unknown Boundary Conditions

Factorial design, a statistical method widely used for experiments, and its application to CFD are discussed. The aim is to propose a systematic, objective, and quantitative method for engineers to design a set of simulations in order to evaluate main and joint effects of input parameters on the numerical solution. The input parameters may be experimental uncertainty on boundary conditions, unknown boundary conditions, grid, differencing schemes, and turbulence models. The complex flow of the Turbine-99 test case, a hydropower draft tube flow, is used to illustrate the method, where four factors are chosen to perform a 24 factorial design. The radial velocity at the inlet (not measured) is shown to have an important influence on the pressure recovery (7%) and the energy loss factor (49%).

Calculation of Intake-Fan-Bypass Interaction With a Fan Similarity Model

2018 ◽  
Author(s):  
Mauro Carnevale ◽  
Feng Wang ◽  
Luca di Mare
Keyword(s):  
Boundary Conditions ◽  
Three Dimensional ◽  
Coupled System ◽  
Design Stage ◽  
Modern Trend ◽  
Test Case ◽  
Operation Condition ◽  
Present Contribution ◽  
Aero Engines ◽  
Very High

Modern trend in installation design is moving towards very high-bypass ratio turbofans. Very high-bypass turbofans represent an effective way of improving the propulsive efficiency of civil aero-engines. Such engines require larger and heavier nacelles, which partially offset the gains in specific fuel consumption. The penalty associated with a larger installation can be mitigated by adopting thinner walls for the nacelle and by shortening the intake section. Such inlet sections are characterized by more restrictive operation condition because they are more prone to separation at high incidence flight conditions. Moreover, in short nacelle installations the by-pass guide vanes and pylon are closer to the fan blades and consequently the distortion due to potential effects induced by the presence of the pylon and non-axisymmetric OGV stage play a significant role in terms of unsteady interaction in the entire system. It is mandatory to consider the inlet, fan, bypass and pylon as a unique coupled system also at the design stage, for assessment of fan force. This kind of assessment is usually carried on by expensive URANS calculation. The factors leading to high computational demands are the spatial resolution required in the fan domain and the time resolution required to sample the fan blade passing frequency. Large savings are therefore possible if simplifications are introduced which relax the resolution requirements in the fan passages and change the nature of the computation into a steady-state computation for the ducts. The present contribution documents a simplified fan model for fan-intake computations based on the solution of the double linearization problem for unsteady, transonic flow past a cascade of thin aerofoils with finite mean load. The coupling with the intake flow and the bypass is performed by using the flow patterns at fan face and fan exit as boundary conditions for the fan model and computing circumferentially non-uniform boundary conditions for the intake and the bypass from the fan model. The computation of the flow in the intake, bypass and pylon is therefore reduced to a steady problem, whereas the computation of the flow in the fan is reduced to one steady problem and a set of linearised models in the frequency domain. The model is applied to a well-documented test case and compares favourably with experimental data and much more expensive three-dimensional, time domain computations.

Effects of inlet cavitation on swirling flow in draft-tube cone

2018 ◽  
Vol 35 (4) ◽  
pp. 1694-1705
Author(s):  
Jing Yang ◽  
Qingjuan Hu ◽  
Zhengwei Wang ◽  
Jinghuan Ding ◽  
Xianyu Jiang
Keyword(s):  
Boundary Condition ◽  
Flow Field ◽  
Unsteady Flow ◽  
Vortex Flow ◽  
Swirling Flow ◽  
Draft Tube ◽  
Francis Turbine ◽  
Cavitation Flow ◽  
Swirl Number ◽  
Content Type

Purpose For Francis turbine, the vortex flow in the draft tube plays an important role in the safe and efficient operating of hydraulic turbine. The swirling flow produced at the blade trailing edge at off-design conditions has been proved to be the fundamental reason of the vortex flow. Exploring the swirling flow variations in the non-cavitation flow and cavitation flow field is an effective way to explain the mechanism of the complex unsteady flow in the draft tube. Design/methodology/approach The swirling flow in different cavitation evolution stages of varying flow rates was studied. The swirl number, which denotes the strength of the swirling flow, was chosen to systematically analyze the swirling flow changes with the cavitation evolutions. The Zwart–Gerber–Blemari cavitation model and SST turbulence model were used to simulate the two-phase cavitating flow. The finite volume method was used to discrete the equations in the unsteady flow field simulation. The Frozen Rotor Stator scheme was used to transfer the data between the rotor-stator interfaces. The inlet total pressure was set to inlet boundary condition and static pressure was set to outlet boundary condition. Findings The results prove that the mutual influences exist between the swirling flow and cavitation. The swirling flow was not only affected by the load but also significantly changed with the cavitation development, because the circumferential velocity decrease and axial velocity increase presented with the cavitation evolution. At the high load conditions, the system stability may improve with the decreasing swirling flow strength. Research limitations/implications Further experimental and simulation studies still need to verify and estimate the reasonability of the swirling flow seen as the cavitation inception signal. Originality/value One interesting finding is that the swirl number began to change as the inception cavitation appeared. This is meaningful for the cavitation controlling in the Francis turbine.

scholarly journals Vorticity Modelling of Blade Wakes Behind Isolated Annular Blade-Rows: Induced Disturbances in Swirling Flows

1980 ◽  
Author(s):  
C. S. Tan
Keyword(s):  
Coordinate System ◽  
Swirling Flow ◽  
Three Dimensional ◽  
Stagnation Pressure ◽  
Swirling Flows ◽  
Two Dimensional ◽  
Blade Row ◽  
Theoretical Considerations ◽  
Type Potential ◽  
Disturbance Field

A general analysis is proposed for studying the fluid-mechanical behavior of blade wakes from an annular blade-row in highly swirling flow. The coupling between the centrifugal force and the vorticity, which is inherent to highly swirling flows, can significantly modify the wake behavior from that in a two-dimensional situation. In steady flow, theoretical considerations show that a blade wake consists primarily of two distinct types of vorticity: a) trailing vorticity shed from the blade due to a span wise variation in blade circulation, and b) vorticity associated with defects in stagnation pressure (or rotary stagnation in relative coordinate system). Three types of disturbances can be identified in the resulting three-dimensional disturbance field: a) the exponentially decaying type (potential, irrotational), b) the purely convected type (rotational), and c) the non-convected type (both rotational and irrotational parts).

Asymmetric Swirling Flows in Turbomachine Annuli

1978 ◽  
Vol 100 (4) ◽  
pp. 618-629 ◽  
Author(s):  
E. M. Greitzer ◽  
T. Strand
Keyword(s):  
Experimental Investigation ◽  
Swirling Flow ◽  
Three Dimensional ◽  
Swirling Flows ◽  
Experimental Measurements ◽  
Strongly Coupled ◽  
Flow Disturbances ◽  
Different Types ◽  
Theoretical Predictions ◽  
Good Agreement

An analytical and experimental investigation of asymmetric annular swirling flows is presented. It is shown that, in contrast to the situation in nonswirling flow, the different types of flow disturbances (pressure and vorticity) are not separable in a swirling flow but are strongly coupled. The flows that occur due to this coupling are inherently three-dimensional and exhibit new features not seen in the nonswirling case. The theoretical predictions are in good agreement with experimental measurements carried out in an annular swirl rig.

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