Evaluation of Secondary Flow between Rotating Concentric Spheres Using a Perturbation Method

2021 ◽  
Vol 412 ◽  
pp. 49-72
Author(s):  
R. Leticia Corral Bustamante ◽  
Antonino H. Pérez ◽  
Alfredo L. Márquez
Keyword(s):  
Perturbation Method ◽  
Secondary Flow ◽  
Analytical Method ◽  
Analytic Solution ◽  
Previous Analysis ◽  
Secondary Flows ◽  
Newtonian Flow ◽  
New Approach ◽  
Concentric Spheres ◽  
Method Show

A new approach to evaluate the Newtonian flow between concentric rotating spheres is introduced in this paper. A general analytic solution to the problem is deduced using a perturbation method that takes into account the primary and secondary flows produced between the spheres, as well as an alternative analytical method. In order to exemplify the results of the previous analysis, six particular cases were studied. The results of the perturbation method show that under certain circumstances the secondary flow is no negligible, as is usually considered, but it is comparable to the value of the primary one. While the analytical method allows us to simulate the flow with results very similar to those of other authors.

Evaluation of Secondary Flow Between Rotating Concentric Spheres Using a Perturbation Method

2001 ◽  
Author(s):  
R. L. Corral ◽  
A. Pérez ◽  
A. Márquez
Keyword(s):  
Perturbation Method ◽  
Secondary Flow ◽  
Analytic Solution ◽  
Previous Analysis ◽  
Secondary Flows ◽  
Newtonian Flow ◽  
New Approach ◽  
Concentric Spheres

Abstract A new approach to evaluate the Newtonian flow between concentric rotating spheres is introduced in this paper. A general analytic solution to the problem is deduced using a perturbation method that takes into account the primary and secondary flows produced between the spheres. In order to exemplify the results of the previous analysis, six particular cases were studied. The results show that under certain circumstances the secondary flow is no negligible, as is usually considered, but it is comparable to the value of the primary one.

scholarly journals A Review of Numerical Simulations of Secondary Flows in River Bends

Water ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 884
Author(s):  
Rawaa Shaheed ◽  
Abdolmajid Mohammadian ◽  
Xiaohui Yan
Keyword(s):  
Numerical Modeling ◽  
Numerical Simulations ◽  
Secondary Flow ◽  
Cross Section ◽  
Turbulence Models ◽  
Main Flow ◽  
Secondary Flows ◽  
River Bends ◽  
River Cross Section ◽  
River Bend

River bends are one of the common elements in most natural rivers, and secondary flow is one of the most important flow features in the bends. The secondary flow is perpendicular to the main flow and has a helical path moving towards the outer bank at the upper part of the river cross-section, and towards the inner bank at the lower part of the river cross-section. The secondary flow causes a redistribution in the main flow. Accordingly, this redistribution and sediment transport by the secondary flow may lead to the formation of a typical pattern of river bend profile. It is important to study and understand the flow pattern in order to predict the profile and the position of the bend in the river. However, there are a lack of comprehensive reviews on the advances in numerical modeling of bend secondary flow in the literature. Therefore, this study comprehensively reviews the fundamentals of secondary flow, the governing equations and boundary conditions for numerical simulations, and previous numerical studies on river bend flows. Most importantly, it reviews various numerical simulation strategies and performance of various turbulence models in simulating the flow in river bends and concludes that the main problem is finding the appropriate model for each case of turbulent flow. The present review summarizes the recent advances in numerical modeling of secondary flow and points out the key challenges, which can provide useful information for future studies.

scholarly journals A New Approach for Approximate Solution of ADE: Physical-Based Modeling of Carriers in Doping Region

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 458
Author(s):  
Leobardo Hernandez-Gonzalez ◽  
Jazmin Ramirez-Hernandez ◽  
Oswaldo Ulises Juarez-Sandoval ◽  
Miguel Angel Olivares-Robles ◽  
Ramon Blanco Sanchez ◽  
...  
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Analytic Solution ◽  
Order Differential Equation ◽  
Electric Circuit ◽  
New Approach ◽  
In Doping ◽  
Electric Behavior ◽  
Spatio Temporal ◽  
Physical Phenomena

The electric behavior in semiconductor devices is the result of the electric carriers’ injection and evacuation in the low doping region, N-. The carrier’s dynamic is determined by the ambipolar diffusion equation (ADE), which involves the main physical phenomena in the low doping region. The ADE does not have a direct analytic solution since it is a spatio-temporal second-order differential equation. The numerical solution is the most used, but is inadequate to be integrated into commercial electric circuit simulators. In this paper, an empiric approximation is proposed as the solution of the ADE. The proposed solution was validated using the final equations that were implemented in a simulator; the results were compared with the experimental results in each phase, obtaining a similarity in the current waveforms. Finally, an advantage of the proposed methodology is that the final expressions obtained can be easily implemented in commercial simulators.

scholarly journals New Approach to the Planetary Theory

1979 ◽  
Vol 81 ◽  
pp. 69-72 ◽  
Author(s):  
Manabu Yuasa ◽  
Gen'ichiro Hori
Keyword(s):  
Perturbation Method ◽  
Canonical Form ◽  
Equations Of Motion ◽  
Disturbing Function ◽  
Averaging Principle ◽  
The Sun ◽  
Planetary Theory ◽  
New Approach ◽  
Canonical Perturbation ◽  
Relative Coordinates

A new approach to the planetary theory is examined under the following procedure: 1) we use a canonical perturbation method based on the averaging principle; 2) we adopt Charlier's canonical relative coordinates fixed to the Sun, and the equations of motion of planets can be written in the canonical form; 3) we adopt some devices concerning the development of the disturbing function. Our development can be applied formally in the case of nearly intersecting orbits as the Neptune-Pluto system. Procedure 1) has been adopted by Message (1976).

scholarly journals Incidence Angle and Pitch-Chord Effects on Secondary Flows Downstream of a Turbine Cascade

1992 ◽  
Author(s):  
A. Perdichizzi ◽  
V. Dossena
Keyword(s):  
Flow Field ◽  
Secondary Flow ◽  
Incidence Angle ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Pressure Probe ◽  
Turbine Cascade ◽  
Oil Flow ◽  
Secondary Velocity ◽  
Secondary Flow Field

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 degrees, 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% 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 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.

scholarly journals The Design of an Improved Endwall Film-Cooling Configuration

1998 ◽  
Author(s):  
S. Friedrichs ◽  
H. P. Hodson ◽  
W. N. Dawes
Keyword(s):  
Secondary Flow ◽  
Film Cooling ◽  
Large Scale ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Aerodynamic Loss ◽  
Cooling Flow ◽  
High Static Pressure ◽  
Endwall Film Cooling ◽  
Aerodynamic Losses

The endwall film-cooling cooling configuration investigated by Friedrichs et al. (1996, 1997) had in principle sufficient cooling flow for the endwall, but in practice, the redistribution of this coolant by secondary flows left large endwall areas uncooled. This paper describes the attempt to improve upon this datum cooling configuration by redistributing the available coolant to provide a better coolant coverage on the endwall surface, whilst keeping the associated aerodynamic losses small. The design of the new, improved cooling configuration was based on the understanding of endwall film-cooling described by Friedrichs et al. (1996, 1997). Computational fluid dynamics were used to predict the basic flow and pressure field without coolant ejection. Using this as a basis, the above described understanding was used to place cooling holes so that they would provide the necessary cooling coverage at minimal aerodynamic penalty. The simple analytical modelling developed in Friedrichs et al. (1997) was then used to check that the coolant consumption and the increase in aerodynamic loss lay within the limits of the design goal. The improved cooling configuration was tested experimentally in a large scale, low speed linear cascade. An analysis of the results shows that the redesign of the cooling configuration has been successful in achieving an improved coolant coverage with lower aerodynamic losses, whilst using the same amount of coolant as in the datum cooling configuration. The improved cooling configuration has reconfirmed conclusions from Friedrichs et al. (1996, 1997); firstly, coolant ejection downstream of the three-dimensional separation lines on the endwall does not change the secondary flow structures; secondly, placement of holes in regions of high static pressure helps reduce the aerodynamic penalties of platform coolant ejection; finally, taking account of secondary flow can improve the design of endwall film-cooling configurations.

scholarly journals Secondary Flow Control in Low Aspect Ratio Vanes Using Splitters

2016 ◽  
Author(s):  
Christopher Clark ◽  
Graham Pullan ◽  
Eric Curtis ◽  
Frederic Goenaga
Keyword(s):  
Kinetic Energy ◽  
Aspect Ratio ◽  
Secondary Flow ◽  
Current Practice ◽  
Leading Edge ◽  
Horseshoe Vortex ◽  
Secondary Flows ◽  
Optimization Approach ◽  
Flow Strength ◽  
Low Aspect Ratio

Low aspect ratio vanes, often the result of overall engine architecture constraints, create strong secondary flows and high endwall loss. In this paper, a splitter concept is demonstrated that reduces secondary flow strength and improves stage performance. An analytic conceptual study, corroborated by inviscid computations, shows that the total secondary kinetic energy of the secondary flow vortices is reduced when the number of passages is increased and, for a given number of vanes, when the inlet endwall boundary layer is evenly distributed between the passages. Viscous computations show that, for this to be achieved in a splitter configuration, the pressure-side leg of the low aspect ratio vane horseshoe vortex, must enter the adjacent passage (and not “jump” in front of the splitter leading edge). For a target turbine application, four vane designs were produced using a multi-objective optimization approach. These designs represent: current practice for a low aspect ratio vane; a design exempt from thickness constraints; and two designs incorporating splitter vanes. Each geometry is tested experimentally, as a sector, within a low-speed turbine stage. The vane designs with splitters geometries were found to reduce the measured secondary kinetic energy, by up to 85%, to a value similar to the design exempt from thickness constraints. The resulting flowfield was also more uniform in both the circumferential and radial directions. One splitter design was selected for a full annulus test where a mixed-out loss reduction, compared to the current practice design, of 15.3% was measured and the stage efficiency increased by 0.88%.

The Mechanics of the Secondary Flows of Viscoelastic Fluids in Non-Circular Straight Tubes and the Mean Transversal Field in Pulsating Flows

2000 ◽  
Author(s):  
Dennis A. Siginer ◽  
Mario F. Letelier
Keyword(s):  
Secondary Flow ◽  
Cross Sections ◽  
Viscoelastic Fluids ◽  
Secondary Flows ◽  
Novel Approach ◽  
Transversal Field ◽  
Time Domains ◽  
Viscoelastic Liquids ◽  
First Time ◽  
Secondary Flow Field

Abstract A survey of secondary flows of viscoelastic liquids in straight tubes is given including recent work pointing at striking analogies with transversal deformations associated with the simple shearing of solid materials. The importance and implications of secondary flows of viscoelastic fluids in heat transfer enhancement are explored together with the difficulties in detecting weak secondary flows (dilute, weakly viscoelastic solutions) in a laboratory setting. Recent new work by the author and colleagues which explores for the first time the structure of the secondary flow field in the pulsating flow of a constitutively nonlinear simple fluid, whose structure is defined by a series of nested integrals over semi-infinite time domains, in straight tubes of arbitrary cross-sections is summarized. The transversal field arises at the second order of the perturbation of the nonlinear constitutive structure, and is driven by first order terms which define the linearly viscoelastic longitudinal flow in the hierarchy of superposed linear flows stemming from the perturbation of the constitutive structure. Arbitrary conduit contours are obtained through a novel approach to the concept of domain perturbation. Time averaged, mean secondary flow streamline contours are presented for the first time for triangular, square and hexagonal pipes.

Second Vane Total Pressure Loss Due to Endwall Iceform Contouring

2008 ◽  
Author(s):  
Ronald S. LaFleur
Keyword(s):  
Heat Transfer ◽  
Secondary Flow ◽  
Pressure Loss ◽  
Total Pressure ◽  
Aerodynamic Drag ◽  
Pressure Coefficient ◽  
Secondary Flows ◽  
Total Pressure Loss ◽  
Surface Shape ◽  
Exit Plane

The iceformation design method generates an endwall contour, altering the secondary flows that produce elevated endwall heat transfer load and total pressure losses. Iceformation is an analog to regions of metal melting where a hot fluid alters the isothermal surface shape of a part as it is maintained by a cooling fluid. The passage flow, heat transfer and geometry evolve together under the constraints of flow and thermal boundary conditions. The iceformation concept is not media dependent and can be used in analogous flows and materials to evolve novel boundary shapes. In the past, this method has been shown to reduce aerodynamic drag and total pressure loss in flows such as diffusers and cylinder/endwall junctures. A prior paper [1] showed that the Reynolds number matched iceform geometry had a 24% lower average endwall heat transfer than the rotationally symmetric endwall geometry of the Energy Efficiency Engine (E3). Comparisons were made between three endwall geometries: the ‘iceform’, the ‘E3’ and the ‘flat’ as a limiting case of the endwall design space. This paper adds to the iceformation design record by reporting the endwall aerodynamic performances. Second vane exit flow velocities and pressures were measured using an automated 2-D traverse of a 1.2 mm diameter five-hole probe. Exit plane maps for the three endwall geometries are presented showing the details of the total pressure coefficient contours and the velocity vectors. The formation of secondary flow vortices is shown in the exit plane and this results in an impact on exit plane total pressure loss distribution, off-design over- and under-turning of the exit flow. The exit plane contours are integrated to form overall measures of the total pressure loss. Relative to the E3 endwall, the iceform endwall has a slightly higher total pressure loss attributed to higher dissipation of the secondary flow within the passage. The iceform endwall has a closer-to-design exit flow pattern than the E3 endwall.

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