Instability of erodible beds

1970 ◽  
Vol 42 (2) ◽  
pp. 225-244 ◽  
Author(s):  
Frank Engelund
Keyword(s):  
Mathematical Model ◽  
Internal Friction ◽  
Potential Flow ◽  
Transport Mechanism ◽  
Flow Analysis ◽  
Two Dimensional ◽  
Alluvial Channel ◽  
The Stability ◽  
Vorticity Transport ◽  
Erodible Beds

The stability of a sand bed in an alluvial channel is investigated by a two-dimensional mathematical model, based on the vorticity transport equation. The model takes account of the internal friction and describes the non-uniform distribution of the suspended sediment. It turns out that the inclusion of the friction and of a definite model of the sediment transport mechanism leads to results rather different from those obtained previously by potential-flow analysis.

On the development of dunes in erodible channels

1974 ◽  
Vol 64 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Jørgen Fredsøe
Keyword(s):  
Stability Analysis ◽  
Order Approximation ◽  
Experimental Fact ◽  
Bed Load ◽  
Two Dimensional ◽  
Alluvial Channel ◽  
Load Transport ◽  
Bed Load Transport ◽  
The Stability ◽  
Vorticity Transport

A two-dimensional stability analysis of the flow in a straight alluvial channel has been carried out, using the vorticity transport equation. In the analysis an attempt has been made to account for the influence of gravity on bed-load transport, and this turned out to change the stability quite significantly.In the case of instability, the further growth of the dunes has been investigated using a second-order approximation, This nonlinear theory explains the experimental fact that the dunes very soon become asymmetric.

scholarly journals Design and Testing of Swept and Leaned Outlet Guide Vanes to Reduce Stator-Strut-Splitter Aerodynamic Flow Interactions

1998 ◽  
Author(s):  
A. R. Wadia ◽  
P. N. Szucs ◽  
K. L. Gundy-Burlet
Keyword(s):  
Dimensional Analysis ◽  
Test Performance ◽  
Potential Flow ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Angle Distribution ◽  
Two Dimensional ◽  
Guide Vanes ◽  
Flow Interactions ◽  
Design And Testing

Large circumferential varying pressure levels produced by aerodynamic flow interactions between downstream stators and struts present a potential noise and stability margin liability in a compression component. These interactions are presently controlled by tailoring the camber and/or stagger angles of vanes neighboring the fan frame struts. This paper reports on the design and testing of a unique set of swept and leaned fan outlet guide vanes (OGVs) that do not require this local tailoring even though the OGVs are closely coupled with the fan frame struts and splitter to reduce engine length. The swept and leaned OGVs not only reduce core-duct diffusion, but they also reduce the potential flow interaction between the stator and the strut relative to that produced by conventional radial OGVs. First, the design of the outlet guide vanes using a single bladerow three-dimensional viscous flow analysis is outlined. Next, a two-dimensional potential flow analysis was used for the coupled OGV-frame system to obtain a circumferentially non-uniform stator stagger angle distribution to further reduce the upstream static pressure disturbance. Recognizing the limitations of the two-dimensional potential flow analysis for this highly three-dimensional set of leaned OGVs, as a final evaluation of the OGV-strut system design, a full three-dimensional viscous analysis of a periodic circumferential sector of the OGVs, including the fan frame struts and splitter, was performed. The computer model was derived from a NASA-developed code used in simulating the flow field for external aerodynamic applications with complex geometries. The three-dimensional coupled OGV-frame analysis included the uniformly-staggered OGVs configuration and the variably-staggered OGVs configuration determined by the two-dimensional potential flow analysis. Contrary to the two-dimensional calculations, the three-dimensional analysis revealed significant flow problems with the variably-staggered OGVs configuration and showed less upstream flow non-uniformity with the uniformly-staggered OGVs configuration. The flow redistribution in both the radial and tangential directions, captured fully only in the three-dimensional analysis, was identified as the prime contributor to the lower flow non-uniformity with the uniformly-staggered OGVs configuration. The coupled three-dimensional analysis was also used to validate the design at off-design conditions. Engine test performance and stability measurements with both uniformly- and variably-staggered OGVs configurations with and without the presence of inlet distortion confirmed the conclusions from the three-dimensional analysis.

On the Application of a Linearized Unsteady Potential-Flow Analysis to Fan-Tip Cascades

1986 ◽  
Vol 108 (1) ◽  
pp. 59-67
Author(s):  
W. J. Usab ◽  
J. M. Verdon
Keyword(s):  
Potential Flow ◽  
Vibrational Frequency ◽  
Numerical Solutions ◽  
Flow Analysis ◽  
Experimental Measurements ◽  
Two Dimensional ◽  
Good Qualitative Agreement ◽  
Blade Loading ◽  
Unsteady Aerodynamic ◽  
Flow Phenomena

A linearized potential flow analysis, which accounts for the effects of nonuniform steady flow phenomena on the unsteady response to prescribed blade motions, has been applied to five two-dimensional cascade configurations. These include a flat-plate cascade and three cascades which are representative of the tip sections of current fan designs. Here the blades are closely spaced, highly staggered, and operate at low mean incidence. The fifth configuration is a NASA Lewis cascade of symmetric biconvex airfoils for which experimental measurements are available. Numerical solutions are presented that clearly illustrate the effects and importance of blade geometry and mean blade loading on the linearized unsteady response at high subsonic inlet Mach number and high blade-vibrational frequency. In addition, a good qualitative agreement is shown between the analytical predictions and experimental measurements for the cascade of symmetric biconvex airfoils. Finally, recommendations on the research needed to extend the range of application of linearized unsteady aerodynamic analyses are provided.

scholarly journals A Mathematical Model of the Transition from the Normal Hematopoiesis to the Chronic and Accelerated Acute Stages in Myeloid Leukemia

2020 ◽  
Author(s):  
Lorand Gabriel Parajdi ◽  
Radu Precup ◽  
Eduard Alexandru Bonci ◽  
Ciprian Tomuleasa
Keyword(s):  
Mathematical Model ◽  
Stem Cells ◽  
Bone Marrow ◽  
Stability Analysis ◽  
Myeloid Leukemia ◽  
Transition Process ◽  
Two Dimensional ◽  
The Stability ◽  
Theoretical Results

A mathematical model given by a two - dimensional differential system is introduced in order to understand the transition process from the normal hematopoiesis to the chronic and accelerated acute stages in chronic myeloid leukemia. A previous model of Dingli and Michor is refined by introducing a new parameter in order to differentiate the bone marrow microenvironment sensitivities of normal and mutant stem cells. In the light of the new parameter, the system now has three distinct equilibria corresponding to the normal hematopoietic state, to the chronic state, and to the accelerated acute phase of the disease. A characterization of the three hematopoietic states is obtained based on the stability analysis. Numerical simulations are included to illustrate the theoretical results.

scholarly journals A Two-Dimensional Mathematical Model of Heat Propagation Equations and Their Significance for Soil Temperature

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 478 ◽  
Author(s):  
Anis Dhahbi ◽  
Salah Boulaaras ◽  
Taha Radwan ◽  
Nadia Mezouar ◽  
Khaled Zennir ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Soil Temperature ◽  
Heat Propagation ◽  
Two Dimensional ◽  
Mathematical Problems ◽  
Different Depths ◽  
Spatial Method ◽  
The Stability ◽  
Academic Year ◽  
Real Experimental Data

In the context of the development of the research project (Boulaaras et al.) which was supported by the Deanship of Scientific Research of Qassim University under the Project No. 1140 during the academic year 2016/1437, this research will introduce a two dimensional mathematical model based on the finite elements spatial method combined with a finite differences time scheme applied to the diffusion equations. This model will be applied in the hypothetical example where the obtained results will be compared with the real experimental data. Such a comparison will allow to predict the soil temperature for different depths and at different time periods according to certain conditions on the weather and take into account the stability conditions of the used numerical method. It’s worthy of note that some of the concreted mathematical problems will be addressed by the experimental scientific theories of functional analysis and then the numerical simulation of the theoretical study will be provided thanks to sophisticated methods with more convergence and stability. This mathematical model would be reduced by means of physical measurement and also in charge of the physical cost.

scholarly journals Viscous Potential Flow Analysis of Electroaerodynamic Instability of a Liquid Sheet Sprayed with an Air Stream

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Mukesh Kumar Awasthi ◽  
Vineet K. Srivastava ◽  
M. Tamsir
Keyword(s):  
Electric Field ◽  
Potential Flow ◽  
Thin Sheet ◽  
Flow Analysis ◽  
Liquid Sheet ◽  
Liquid Stream ◽  
Viscous Potential Flow ◽  
Two Fluids ◽  
Air Stream ◽  
The Stability

The instability of a thin sheet of viscous and dielectric liquid moving in the same direction as an air stream in the presence of a uniform horizontal electric field has been carried out using viscous potential flow theory. It is observed that aerodynamic-enhanced instability occurs if the Weber number is much less than a critical value related to the ratio of the air and liquid stream velocities, viscosity ratio of two fluids, the electric field, and the dielectric constant values. Liquid viscosity has stabilizing effect in the stability analysis, while air viscosity has destabilizing effect.

Design and Testing of Swept and Leaned Outlet Guide Vanes to Reduce Stator–Strut–Splitter Aerodynamic Flow Interactions

1999 ◽  
Vol 121 (3) ◽  
pp. 416-427 ◽  
Author(s):  
A. R. Wadia ◽  
P. N. Szucs ◽  
K. L. Gundy-Burlet
Keyword(s):  
Dimensional Analysis ◽  
Potential Flow ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Angle Distribution ◽  
Two Dimensional ◽  
Guide Vanes ◽  
Flow Interactions ◽  
Design And Testing ◽  
Flow Nonuniformity

Large circumferentially varying pressure levels produced by aerodynamic flow interactions between downstream stators and struts present a potential noise and stability margin liability in a compression component. These interactions are presently controlled by tailoring the camber and/or stagger angles of vanes neighboring the fan frame struts. This paper reports on the design and testing of a unique set of swept and leaned fan outlet guide vanes (OGVs) that do not require this local tailoring even though the OGVs are closely coupled with the fan frame struts and splitter to reduce engine length. The swept and leaned OGVs not only reduce core-duct diffusion, but they also reduce the potential flow interaction between the stator and the strut relative to that produced by conventional radial OGVs. First, the design of the outlet guide vanes using a single blade row three-dimensional viscous flow analysis is outlined. Next, a two-dimensional potential flow analysis was used for the coupled OGV–frame system to obtain a circumferentially nonuniform stator stagger angle distribution to reduce the upstream static pressure disturbance further. Recognizing the limitations of the two-dimensional potential flow analysis for this highly three-dimensional set of leaned OGVs, as a final evaluation of the OGV–strut system design, a full three-dimensional viscous analysis of a periodic circumferential sector of the OGVs, including the fan frame struts and splitter, was performed. The computer model was derived from a NASA-developed code used in simulating the flow field for external aerodynamic applications with complex geometries. The three-dimensional coupled OGV–frame analysis included the uniformly staggered OGV configuration and the variably staggered OGV configuration determined by the two-dimensional potential flow analysis. Contrary to the two-dimensional calculations, the three-dimensional analysis revealed significant flow problems with the variably staggered OGV configuration and showed less upstream flow nonuniformity with the uniformly staggered OGV configuration. The flow redistribution in both the radial and tangential directions, captured fully only in the three-dimensional analysis, was identified as the prime contributor to the lower flow nonuniformity with the uniformly staggered OGV configuration. The coupled three-dimensional analysis was also used to validate the design at off-design conditions. Engine test performance and stability measurements with both uniformly and variably staggered OGV configurations with and without the presence of inlet distortion confirmed the conclusions from the three-dimensional analysis.

scholarly journals Modeling and Simulating Asymmetrical Conductance Changes in Gramicidin Pores

2014 ◽  
Vol 2 (1) ◽  
Author(s):  
Shixin Xu ◽  
Minxin Chen ◽  
Sheereen Majd ◽  
Xingye Yue ◽  
Chun Liu
Keyword(s):  
Mathematical Model ◽  
Lipid Membranes ◽  
Membrane Surface ◽  
Gramicidin A ◽  
Enzymatic Reactions ◽  
Computational Domain ◽  
Two Dimensional ◽  
Fem Method ◽  
Conductance Changes ◽  
The Stability

Abstract Gramicidin A is a small and well characterized peptide that forms an ion channel in lipid membranes. An important feature of gramicidin A (gA) pore is that its conductance is affected by the electric charges near the its entrance. This property has led to the application of gramicidin A as a biochemical sensor for monitoring and quantifying a number of chemical and enzymatic reactions. Here, a mathematical model of conductance changes of gramicidin A pores in response to the presence of electrical charges near its entrance, either on membrane surface or attached to gramicidin A itself, is presented. In this numerical simulation, a two dimensional computational domain is set to mimic the structure of a gramicidin A channel in the bilayer surrounded by electrolyte. The transport of ions through the channel is modeled by the Poisson-Nernst-Planck (PNP) equations that are solved by Finite Element Method (FEM). Preliminary numerical simulations of this mathematical model are in qualitative agreement with the experimental results in the literature. In addition to the model and simulations, we also present the analysis of the stability of the solution to the boundary conditions and the convergence of FEM method for the two dimensional PNP equations in our model.

scholarly journals A Mathematical Model of the Transition from Normal Hematopoiesis to the Chronic and Accelerated-Acute Stages in Myeloid Leukemia

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 376
Author(s):  
Lorand Gabriel Parajdi ◽  
Radu Precup ◽  
Eduard Alexandru Bonci ◽  
Ciprian Tomuleasa
Keyword(s):  
Mathematical Model ◽  
Stem Cells ◽  
Bone Marrow ◽  
Stability Analysis ◽  
Myeloid Leukemia ◽  
Transition Process ◽  
Two Dimensional ◽  
The Stability ◽  
Theoretical Results

A mathematical model given by a two-dimensional differential system is introduced in order to understand the transition process from the normal hematopoiesis to the chronic and accelerated-acute stages in chronic myeloid leukemia. A previous model of Dingli and Michor is refined by introducing a new parameter in order to differentiate the bone marrow microenvironment sensitivities of normal and mutant stem cells. In the light of the new parameter, the system now has three distinct equilibria corresponding to the normal hematopoietic state, to the chronic state, and to the accelerated-acute phase of the disease. A characterization of the three hematopoietic states is obtained based on the stability analysis. Numerical simulations are included to illustrate the theoretical results.

The Effect of Radius Change on Two-Dimensional Cascade Solutions

1985 ◽  
Author(s):  
Joseph R. Caspar ◽  
David E. Hobbs
Keyword(s):  
Potential Flow ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Rotating Frame ◽  
Steady Flows ◽  
Two Dimensional ◽  
Potential Solution ◽  
Radius Variation ◽  
Stators And Rotors ◽  
Euler Solution

The effects of varying radius along a streamsurface are included in a two dimensional blade-to-blade potential flow analysis of turbomachinery rotors and stators in order to model better three dimensional effects. On a cylindrical streamsurface, flows in rotors can be treated as steady flows in the rotating frame; the rotation can be ignored. On a streamsurface with varying radius, however, the flow, even in the rotating frame, is not potential. Thus the physical flow is related to a non-physical, potential flow for calculation purposes. Computed results for compressor stators and rotors show that the potential solution agrees well with an Euler solution, that effects of radius variation are very important for both stators and rotors, and that effects of radius contouring and of rotation can also be important.

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