scholarly journals Improved Particle Trajectory Calculations Through Turbomachinery Affected by Coal Ash Particles

1981 ◽  
Author(s):  
B. Beecher ◽  
W. Tabakoff ◽  
A. Hamed
Keyword(s):  
Flow Field ◽  
Gas Turbines ◽  
Three Dimensional ◽  
Coal Ash ◽  
Two Dimensional ◽  
Flow Properties ◽  
Trajectory Calculations ◽  
Blade Thickness ◽  
Spline Fitting ◽  
Numerical Grid

Trajectories of small coal ash particles encountered in coal-fired gas turbines are calculated with an improved computer analysis currently under development. The analysis uses an improved numerical grid and mathematical spline-fitting techniques to account for three-dimensional gradients in the flow field and blade geometry. The greater accuracy thus achieved in flow field definition improves the trajectory calculations over previous two-dimensional models by allowing the small particles to react to radial variations in the flow properties. A greater accuracy thus achieved in the geometry definition permits particle rebounding in a direction perpendicular to the blade and flow path surfaces rather than in a two-dimensional plane. The improved method also accounts for radial variations in airfoil chord, stagger, and blade thickness when computing particle impact at a blade location.

Improved Particle Trajectory Calculations Through Turbomachinery Affected by Coal Ash Particles

1982 ◽  
Vol 104 (1) ◽  
pp. 64-68 ◽  
Author(s):  
B. Beacher ◽  
W. Tabakoff ◽  
A. Hamed
Keyword(s):  
Flow Field ◽  
Gas Turbines ◽  
Three Dimensional ◽  
Coal Ash ◽  
Two Dimensional ◽  
Flow Properties ◽  
Trajectory Calculations ◽  
Blade Thickness ◽  
Spline Fitting ◽  
Numerical Grid

Trajectories of small coal ash particles encountered in coal-fired gas turbines are calculated with an improved computer analysis currently under development. The analysis uses an improved numerical grid and mathematical spline-fitting techniques to account for three-dimensional gradients in the flow field and blade geometry. The greater accuracy thus achieved in flow field definition improves the trajectory calculations over previous two-dimensional models by allowing the small particles to react to radial variations in the flow properties. A greater accuracy thus achieved in the geometry definition permits particle rebounding in a plane perpendicular to the blade and flow path surfaces rather than in a two-dimensional plane. The improved method also accounts for radial variations in airfoil chord, stagger, and blade thickness when computing particle impact at a blade location.

Evaluation of the Theory for the Flow Pattern of a Hydrofoil of Finite Span

1960 ◽  
Vol 4 (01) ◽  
pp. 13-29
Author(s):  
Paul Kaplan ◽  
John P. Breslin ◽  
Winnifred R. Jacobs
Keyword(s):  
Surface Wave ◽  
Flow Field ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Limited Data ◽  
Flow Properties ◽  
Dimensional Theory ◽  
Finite Span ◽  
Wave Elevation ◽  
Experimental Values

Expressions for various properties of the flow field aft of a finite-span hydrofoil in smooth water are presented and discussed in this paper. Potential functions for the motion that have been derived previously on the basis of linearized free-surface theory serve as the basic terms from which the flow field is derived. Both two-dimensional and three-dimensional theories are used, and the expressions derived for the surface-wave elevation and downwash from the various theories are compared with experimental values. As a result of this study, it is shown that three-dimensional effects are of great importance and hence terms derived from the two-dimensional theory do not accurately represent the true flow properties. Recommended formulas, whose validity is demonstrated by the comparison with the limited data presented herein, are given for the evaluation of both the surface-wave amplitude and downwash.

Numerical and Experimental Investigation of Return Channel Vane Aerodynamics With Two-Dimensional and Three-Dimensional Vanes

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
A. Hildebrandt ◽  
F. Schilling
Keyword(s):  
Experimental Investigation ◽  
Flow Field ◽  
Static Pressure ◽  
Three Dimensional ◽  
Pressure Rise ◽  
Field Performance ◽  
Two Dimensional ◽  
Flow Angle ◽  
Overall Performance ◽  
Return Channel

The present paper deals with the numerical and experimental investigation of the effect of return channel (RCH) dimensions of a centrifugal compressor stage on the aerodynamic performance. Three different return channel stages were investigated, two stages comprising three-dimensional (3D) return channel blades and one stage comprising two-dimensional (2D) RCH vanes. The analysis was performed regarding both the investigation of overall performance (stage efficiency, RCH total pressure loss coefficient) and detailed flow-field performance. For detailed experimental flow-field investigation at the stage exit, six circumferentially traversed three-hole probes were positioned downstream the return channel exit in order to get two-dimensional flow-field information. Additionally, static pressure wall measurements were taken at the hub and shroud pressure and suction side (SS) of the 2D and 3D return channel blades. The return channel system overall performance was calculated by measurements of the circumferentially averaged 1D flow field downstream the diffuser exit and downstream the stage exit. Dependent on the type of return channel blade, the numerical and experimental results show a significant effect on the flow field overall and detail performance. In general, satisfactory agreement between computational fluid dynamics (CFD)-prediction and test-rig measurements was achieved regarding overall and flow-field performance. In comparison with the measurements, the CFD-calculated stage performance (efficiency and pressure rise coefficient) of all the 3D-RCH stages was slightly overpredicted. Very good agreement between CFD and measurement results was found for the static pressure distribution on the RCH wall surfaces while small CFD-deviations occur in the measured flow angle at the stage exit, dependent on the turbulence model selected.

scholarly journals Numerical simulation of the dimensional transformation of atomization in a supersonic aerodynamic atomization dust-removing nozzle based on transonic speed compressible flow

2020 ◽  
Vol 7 (3) ◽  
pp. 597-610 ◽  
Author(s):  
Tian Zhang ◽  
Deji Jing ◽  
Shaocheng Ge ◽  
Jiren Wang ◽  
Xiangxi Meng ◽  
...  
Keyword(s):  
Flow Field ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Three Dimensional Model ◽  
Speed Flow ◽  
Complex Process ◽  
Study Results ◽  
Laval Nozzles

Abstract To simulate the transonic atomization jet process in Laval nozzles, to test the law of droplet atomization and distribution, to find a method of supersonic atomization for dust-removing nozzles, and to improve nozzle efficiency, the finite element method has been used in this study based on the COMSOL computational fluid dynamics module. The study results showed that the process cannot be realized alone under the two-dimensional axisymmetric, three-dimensional and three-dimensional symmetric models, but it can be calculated with the transformation dimension method, which uses the parameter equations generated from the two-dimensional axisymmetric flow field data of the three-dimensional model. The visualization of this complex process, which is difficult to measure and analyze experimentally, was realized in this study. The physical process, macro phenomena and particle distribution of supersonic atomization are analyzed in combination with this simulation. The rationality of the simulation was verified by experiments. A new method for the study of the atomization process and the exploration of its mechanism in a compressible transonic speed flow field based on the Laval nozzle has been provided, and a numerical platform for the study of supersonic atomization dust removal has been established.

Axial Transport Effects on Natural Convection Inside of an Open-Ended Annulus

1991 ◽  
Vol 113 (3) ◽  
pp. 627-634 ◽  
Author(s):  
K. Vafai ◽  
J. Ettefagh
Keyword(s):  
Temperature Distribution ◽  
Flow Field ◽  
Three Dimensional ◽  
Transient Behavior ◽  
Temperature Fields ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Subsequent Effect ◽  
Transport Effects ◽  
Temperature And Velocity Fields

The present work centers around a numerical three-dimensional transient investigation of the effects of axial convection on flow and temperature fields inside an open-ended annulus. The transient behavior of the flow field through the formation of a three-dimensional flow field and its subsequent effect on the temperature distribution at different axial locations within the annulus were analyzed by both finite difference and finite element methods. The results show that the axial convection has a distinctly different influence on the temperature and velocity fields. It is found that in the midportion of the annulus a two-dimensional assumption with respect to the temperature distribution can lead to satisfactory results for Ra<10,000. However, such an assumption is improper with respect to the flow field. Furthermore, it is shown that generally the errors for a two-dimensional assumption in the midportion of the annulus are less at earlier times (t<50Δt) during the transient development of the flow and temperature fields.

Three-Dimensional Time-Resolved Flow Field in the First and Last Turbine Stage of a Heavy Duty Gas Turbine: Part II — Interpretation of Blade Pressure Fluctuations

2000 ◽  
Author(s):  
Martin von Hoyningen-Huene ◽  
Wolfram Frank ◽  
Alexander R. Jung
Keyword(s):  
Flow Field ◽  
Gas Turbine ◽  
Gas Turbines ◽  
Pressure Fluctuations ◽  
Three Dimensional ◽  
Potential Interaction ◽  
Heavy Duty ◽  
Turbine Stage ◽  
Count Ratio ◽  
Heavy Duty Gas Turbine

Unsteady stator-rotor interaction in gas turbines has been investigated experimentally and numerically for some years now. Most investigations determine the pressure fluctuations in the flow field as well as on the blades. So far, little attention has been paid to a detailed analysis of the blade pressure fluctuations. For further progress in turbine design, however, it is mandatory to better understand the underlying mechanisms. Therefore, computed space–time maps of static pressure are presented on both the stator vanes and the rotor blades for two test cases, viz the first and the last turbine stage of a modern heavy duty gas turbine. These pressure fluctuation charts are used to explain the interaction of potential interaction, wake-blade interaction, deterministic pressure fluctuations, and acoustic waveswith the instantaneous surface pressure on vanes and blades. Part I of this two-part paper refers to the same computations, focusing on the unsteady secondary now field in these stages. The investigations have been performed with the flow solver ITSM3D which allows for efficient simulations that simulate the real blade count ratio. Accounting for the true blade count ratio is essential to obtain the correct frequencies and amplitudes of the fluctuations.

Study of three-dimensional unsteady Oseen flow

1978 ◽  
Vol 86 (4) ◽  
pp. 609-622 ◽  
Author(s):  
S. Murata ◽  
Y. Miyake ◽  
Y. Tsujimoto ◽  
F. Yamamoto
Keyword(s):  
Flow Field ◽  
External Force ◽  
Three Dimensional ◽  
Velocity Fields ◽  
Applied Force ◽  
Two Dimensional ◽  
Uniform Velocity ◽  
Pressure Fields ◽  
Oseen Flow ◽  
Impulsive Pressure

In the present paper, it is intended to give the elementary solutions of three-dimensional unsteady Oseen flow when unsteady concentrated lift and/or drag is applied in the flow field. It is shown that the pressure fields due to concentrated impulsive lift and/or drag can be represented by an impulsive pressure doublet in the direction of the applied force and the corresponding velocity fields by diffusing free doublets in the direction of the external force that are shed from the location of the force application and convected downstream with otherwise uniform velocity. It is also confirmed that combination of the elementary solutions given in the present paper yields the two-dimensional ones.

Extension of the Prandtl–Batchelor theorem to three-dimensional flows slowly varying in one direction

2010 ◽  
Vol 654 ◽  
pp. 351-361 ◽  
Author(s):  
M. SANDOVAL ◽  
S. CHERNYSHENKO
Keyword(s):  
Flow Field ◽  
Small Parameter ◽  
Order Approximation ◽  
Three Dimensional ◽  
Inviscid Limit ◽  
Two Dimensional ◽  
Leading Order ◽  
Dimensional Flow ◽  
Two Dimensional Flow

According to the Prandtl–Batchelor theorem for a steady two-dimensional flow with closed streamlines in the inviscid limit the vorticity becomes constant in the region of closed streamlines. This is not true for three-dimensional flows. However, if the variation of the flow field along one direction is slow then it is possible to expand the solution in terms of a small parameter characterizing the rate of variation of the flow field in that direction. Then in the leading-order approximation the projections of the streamlines onto planes perpendicular to that direction can be closed. Under these circumstances the extension of the Prandtl–Batchelor theorem is obtained. The resulting equations turned out to be a three-dimensional analogue of the equations of the quasi-cylindrical approximation.

A two-dimensional boundary layer encountering a three-dimensional hump

1977 ◽  
Vol 83 (1) ◽  
pp. 163-176 ◽  
Author(s):  
F. T. Smith ◽  
R. I. Sykes ◽  
P. W. M. Brighton
Keyword(s):  
Boundary Layer ◽  
Constant Width ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Flow Properties ◽  
Nonlinear Motion ◽  
Dimensional Boundary ◽  
Incompressible Boundary ◽  
Insight Into ◽  
Steady Laminar

A shallow three-dimensional hump disturbs the two-dimensional incompressible boundary layer developed on an otherwise flat surface. The steady laminar flow is studied by means of a three-dimensional extension of triple-deck theory, so that there is the prospect of separation in the nonlinear motion. As a first step, however, a linearized analysis valid for certain shallow obstacles gives some insight into the flow properties. The most striking features then are the reversal of the secondary vortex motions and the emergence of a ‘corridor’ in the wake of the hump. The corridor stays of constant width downstream and within it the boundary-layer displacement and skin-friction perturbation are much greater than outside. Extending outside the corridor, there is a zone where the surface fluid is accelerated, in contrast with the deceleration near the centre of the corridor. The downstream decay (e.g. of displacement) here is much slower than in two-dimensional flows.

scholarly journals Measurement of Lagrangian Trajectories in a 3 L Stirred Tank Reactor using 4D Particle Tracking Velocimetry with Shake-the-Box

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Jürgen Fitschen ◽  
Alexandra Von Kameke ◽  
Sebastian Hofmann ◽  
Marko Hoffmann ◽  
Michael Schlüter
Keyword(s):  
Flow Field ◽  
Particle Tracking ◽  
Particle Tracking Velocimetry ◽  
Three Dimensional ◽  
Field Measurements ◽  
Stirred Tank ◽  
Two Dimensional ◽  
Scientific Publications ◽  
Stirred Tank Reactor ◽  
Tank Reactor

Stirred tank reactors are widely used in the chemical industry and bioprocess engineering and, consequently, a large number of scientific publications deal with the characterization of those apparatuses. However, there is very little information about the flow conditions. This is mostly due to the fact that these apparatuses are generally made of stainless steel, which restricts optical access. Furthermore, three-dimensional flow field measurements are still not trivial and involve costly equipment, therefore, investigations often reduce to two-dimensional PIV measurements. Nevertheless, recent works (Rosseburg et al., 2018; Taghavi and Moghaddas, 2020; Kuschel et al., 2021) impressively show the formation of compartments which hinder and delay mixing. However, these measurements are based either on instantaneous concentration profiles by means of pLIF measurements or on a two-dimensional projection of the system and thus do not allow conclusions about the development of the three dimensional compartments and the exchange rates between the compartments. In this work, for the first time, instantaneous flow field measurements with high spatial and temporal resolution are performed in the entire volume of a 3L stirred tank reactor based on 4D particle tracking velocimetry. The highly resolved particle trajectories further allow detailed Lagrangian analysis of the mixing dynamics inside the reactor, data that was previously inaccessible.

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