Three-dimensional surges and recoveries in a numerical glacier model

1969 ◽  
Vol 6 (4) ◽  
pp. 979-986 ◽  
Author(s):  
William J. Campbell ◽  
Lowell A. Rasmussen
Keyword(s):  
Steady State ◽  
High Speed ◽  
Three Dimensional ◽  
Volume Transport ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Navier Stokes Equation ◽  
Total Recovery ◽  
Flow Equations ◽  
Bed Friction

The Navier–Stokes equation, integrated vertically to yield a two-dimensional transport equation, is combined with the three-dimensional continuity equation. By assuming a linear relation between volume transport and bottom shear stress, a system of numerically tractable differential equations is developed that contains a nonlinear surface slope term and a term in which horizontal frictional forces are stated explicitly. These equations, which are not based on perturbation analysis, are integrated directly on a high speed digital computer. The coefficient of each term in the flow equations is composed of physical parameters (gravity, density, viscosity); therefore, since no quantities such as ice velocities enter the equations, it is only necessary to specify an arbitrary bed configuration and a net-balance versus altitude curve to obtain a glacier solution.For two beds, valley and cirque, steady-state glacier solutions are found for a variety of bed and lateral frictional values. By reducing the bed friction coefficient for one year over the entire bed of the glacier, surges are induced in each of these cases. A reduction in bed friction to 5% of its original value yields a surge resembling typical observed surges. Interesting wave forms occur during the recovery. During the initial recovery, after the bed friction has been restored to its original value, height falls continue to occur even in the lower accumulation zone. The original steady-state shape is approached asymptotically, with total recovery taking hundreds of years.

Coriolis force influence on the AKA effect

2021 ◽  
Author(s):  
Peter Rutkevich ◽  
Georgy Golitsyn ◽  
Anatoly Tur
Keyword(s):  
Steady State ◽  
Stokes Equation ◽  
Nonlinear Equations ◽  
Coriolis Force ◽  
Large Scale ◽  
Fluid Velocity ◽  
Navier Stokes ◽  
Basic Solution ◽  
Navier Stokes Equation ◽  
Alpha Effect

<p>Large-scale instability in incompressible fluid driven by the so called Anisotropic Kinetic Alpha (AKA) effect satisfying the incompressible Navier-Stokes equation with Coriolis force is considered. The external force is periodic; this allows applying an unusual for turbulence calculations mathematical method developed by Frisch et al [1]. The method provides the orders for nonlinear equations and obtaining large scale equations from the corresponding secular relations that appear at different orders of expansions. This method allows obtaining not only corrections to the basic solutions of the linear problem but also provides the large-scale solution of the nonlinear equations with the amplitude exceeding that of the basic solution. The fluid velocity is obtained by numerical integration of the large-scale equations. The solution without the Coriolis force leads to constant velocities at the steady-state, which agrees with the full solution of the Navier-Stokes equation reported previously. The time-invariant solution contains three families of solutions, however, only one of these families contains stable solutions. The final values of the steady-state fluid velocity are determined by the initial conditions. After account of the Coriolis force the solutions become periodic in time and the family of solutions collapses to a unique solution. On the other hand, even with the Coriolis force the fluid motion remains two-dimensional in space and depends on a single spatial variable. The latter fact limits the scope of the AKA method to applications with pronounced 2D nature. In application to 3D models the method must be used with caution.</p><p>[1] U. Frisch, Z.S. She and P. L. Sulem, “Large-Scale Flow Driven by the Anisotropic Kinetic Alpha Effect,” Physica D, Vol. 28, No. 3, 1987, pp. 382-392.</p>

scholarly journals Development of a Three-Dimensional Geometry Optimization Method for Turbomachinery Applications

2004 ◽  
Vol 10 (5) ◽  
pp. 373-385
Author(s):  
Steffen Kämmerer ◽  
Jürgen F. Mayer ◽  
Heinz Stetter ◽  
Meinhard Paffrath ◽  
Utz Wever ◽  
...  
Keyword(s):  
Optimization Problem ◽  
Stokes Equations ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Optimization Techniques ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Flow Solver ◽  
Flow Simulations ◽  
Sensitivity Equations

This article describes the development of a method for optimization of the geometry of three-dimensional turbine blades within a stage configuration. The method is based on flow simulations and gradient-based optimization techniques. This approach uses the fully parameterized blade geometry as variables for the optimization problem. Physical parameters such as stagger angle, stacking line, and chord length are part of the model. Constraints guarantee the requirements for cooling, casting, and machining of the blades.The fluid physics of the turbomachine and hence the objective function of the optimization problem are calculated by means of a three-dimensional Navier-Stokes solver especially designed for turbomachinery applications. The gradients required for the optimization algorithm are computed by numerically solving the sensitivity equations. Therefore, the explicitly differentiated Navier-Stokes equations are incorporated into the numerical method of the flow solver, enabling the computation of the sensitivity equations with the same numerical scheme as used for the flow field solution.This article introduces the components of the fully automated optimization loop and their interactions. Furthermore, the sensitivity equation method is discussed and several aspects of the implementation into a flow solver are presented. Flow simulations and sensitivity calculations are presented for different test cases and parameters. The validation of the computed sensitivities is performed by means of finite differences.

Cylinder rolling on a wall at low Reynolds numbers

2011 ◽  
Vol 685 ◽  
pp. 461-494 ◽  
Author(s):  
Alain Merlen ◽  
Christophe Frankiewicz
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Flow Around A Cylinder ◽  
Low Reynolds Numbers ◽  
Initial Location ◽  
Upstream Pressure ◽  
Small Reynolds Numbers ◽  
Onset Of Cavitation

AbstractThe flow around a cylinder rolling or sliding on a wall was investigated analytically and numerically for small Reynolds numbers, where the flow is known to be two-dimensional and steady. Both prograde and retrograde rotation were analytically solved, in the Stokes regime, giving the values of forces and torque and a complete description of the flow. However, solving Navier–Stokes equation, a rotation of the cylinder near the wall necessarily induces a cavitation bubble in the nip if the fluid is a liquid, or compressible effects, if it is a gas. Therefore, an infinite lift force is generated, disconnecting the cylinder from the wall. The flow inside this interstice was then solved under the lubrication assumptions and fully described for a completely flooded interstice. Numerical results extend the analysis to higher Reynolds number. Finally, the effect of the upstream pressure on the onset of cavitation is studied, giving the initial location of the phenomenon and the relation between the upstream pressure and the flow rate in the interstice. It is shown that the flow in the interstice must become three-dimensional when cavitation takes place.

scholarly journals The Rise and Fall of α-Model Viscosity

1996 ◽  
Vol 158 ◽  
pp. 111-114
Author(s):  
F. V. Hessman ◽  
C. Obach
Keyword(s):  
Steady State ◽  
Stokes Equation ◽  
Accretion Disks ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Averaged Models

AbstractFor nearly two decades, our only useful model for the viscosity in accretion disks has been the so-called ‘α-model’. However, it has become clear that the simplest models –in which α is constant – are inadequate to explain the range of behaviours seen in real disks. We show that the properties of steady-state, vertically-averaged models can be determined without any assumptions other than that the disks obey the classical Navier-Stokes equation. These solutions have derived values of α which vary with radius by many orders of magnitude even in small CV disks.

scholarly journals Numerical and Experimental Study of Flow Field between the Main Hull and Demi-Hull of a Trimaran

2020 ◽  
Vol 8 (12) ◽  
pp. 975
Author(s):  
Cong Sun ◽  
Chunyu Guo ◽  
Chao Wang ◽  
Lianzhou Wang ◽  
Jianfeng Lin
Keyword(s):  
Flow Field ◽  
High Speed ◽  
Light Transmission ◽  
Transmission Rate ◽  
Laser Sheet ◽  
Three Dimensional ◽  
Wake Flow ◽  
Navier Stokes ◽  
Unsteady Wake ◽  
Real Flow

The interactions between the main hull and demi-hull of trimarans have been arousing increasing attention, and detailed circumferential flow fields greatly influence trimaran research. In this research, the unsteady wake flow field of a trimaran was obtained by Reynolds-Averaged Navier-Stokes (RANS) equations on the basis of the viscous flow principles with consideration of the heaving and pitching of the trimaran. Then, we designed an experimental method based on particle-image velocimetry (PIV) and obtained a detailed flow field between the main hull and demi-hull of the trimaran. A trimaran model with one demi-hull made of polycarbonate material with 90% light transmission rate and a refractive index 1.58 (close to that of water 1.33) was manufactured as the experiment sample. Using polycarbonate material, the laser-sheet light-source transmission and high-speed camera recording problems were effectively rectified. Moreover, a nonstandard calibration was added into the PIV flow field measurement system. Then, we established an inverse three-dimensional (3D) distortion coordinate system and obtained the corresponding coordinates by using optics calculations. Further, the PIV system spatial mapping was corrected, and the real flow field was obtained. The simulation results were highly consistent with the experimental data, which showed the methods established in this study provided a strong reference for obtaining the detailed flow field information between the main hull and demi-hull of trimarans.

NONLINEAR EVOLUTION OF TURBULENT COHERENT STRUCTURES IN CHANNEL FLOWS

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1539-1542
Author(s):  
ZHANG LI ◽  
DENGBIN TANG ◽  
LINLIN GUO
Keyword(s):  
Coherent Structures ◽  
Nonlinear Evolution ◽  
Three Dimensional ◽  
Channel Flows ◽  
Navier Stokes ◽  
Theoretic Model ◽  
Compact Difference Scheme ◽  
Navier Stokes Equation ◽  
Turbulent Coherent Structures ◽  
Dimensional Coupling

The generation and the development of turbulent coherent structures in channel flows are investigated by using numerical simulation of Navier-Stokes equation and the theoretic model of turbulent coherent structures built up by the flow stability theories. The three-dimensional coupling compact difference scheme with high accuracy and resolution developed can be applied to the calculative region including points near the boundary. The results computed show nonlinear evolution process and characteristics of Reynolds stress, stream-wise vortices and span-wise vorticities, especially the nonlinear interactions between different coherent structures.

Unsteady Flow at the Outlet of the High Specific Speed Centrifugal Compressor Impeller

1984 ◽  
Author(s):  
Fumikata Kano ◽  
Takafumi Shirakami
Keyword(s):  
Unsteady Flow ◽  
Centrifugal Compressor ◽  
Coal Gasification ◽  
Three Dimensional ◽  
Axial Direction ◽  
Navier Stokes ◽  
Meridional Plane ◽  
Mixed Flow ◽  
Navier Stokes Equation ◽  
Specific Speed

The unsteady flow at the outlet of the high specific speed mixed flow Impeller was studied. The specific speed is 500 (m3/min)1/2 · rpm · m−3/4. The flow is strongly influenced by the impeller blading. The other hand, the flow influences the performance of the stationary vanes downstream of the impeller. The flow path at the outlet of the mixed flow impeller is inclined to the axial direction and is curved in the meridional plane. The study was carried out to develop the 30 MW centrifugal compressor. This compressor is used in the field of the coal gasification, the geothermal power generation, etc. The distributions of flow velocity, pressure and temperature of three dimensional flow were measured using a high sensitive pressure transducer and a total temperature probe. The flow was surveyed across the entire passage at about ten axial locations including endwall boundary layer. A theoretical analysis was also carried out using the linearized Navier-Stokes equation.

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