Multi-Strip Numerical Analysis for Flexible Riser Response

2004 ◽  
Author(s):  
Karl W. Schulz ◽  
Trond S. Meling
Keyword(s):  
Flow Structure ◽  
Equations Of Motion ◽  
Solution Procedure ◽  
Navier Stokes ◽  
Coupled Flow ◽  
Time Step ◽  
Rans Equations ◽  
Coupling Strategy ◽  
Flow Configurations ◽  
The Time Domain

A multi-strip numerical method, combining solution of the incompressible Reynolds Averaged Navier-Stokes (RANS) equations with a finite-element structural dynamics response, has been developed to analyze the flow-structure interaction of long, flexible risers. This solution methodology combines a number of individual hydrodynamic simulations corresponding to individual axial strips along the riser section with a full 3D structural analysis to predict overall VIV loads and displacements. The hydrodynamic loading for each riser strip is derived from a 2D finite-volume discretization of the governing RANS equations which is applicable to both single and multiple riser configurations. The entire flow-structure solution procedure is carried out in the time domain via a loose coupling strategy, such that the hydrodynamic loads from each riser strip are summed to obtain the overall loading along the span of each riser. This loading is then used to integrate forward a single time-step in the riser equations of motion to obtain an updated riser displacement profile. Closure of the coupled flow-structure method is achieved by updating the riser displacements for each of the corresponding hydrodynamic strips in the next time-step integration. The developed multi-strip method is applied to a single bare riser subjected to both uniform and shear current profiles. The flow conditions and riser configuration were chosen to match the Marintek rotating rig experiments, and comparisons between experimental and numerical results are presented for several flow configurations and axial tensions. In addition, a parametric study is presented using 16, 32, and 64 hydrodynamic strips for a given flow configuration to ascertain the sensitivity of the results to the number of strips chosen.

scholarly journals On the Calculation of Propulsive Characteristics of a Bulk-Carrier Moving in Head Seas

2020 ◽  
Vol 8 (10) ◽  
pp. 786
Author(s):  
S. Polyzos ◽  
G. Tzabiras
Keyword(s):  
Navier Stokes ◽  
Bulk Carrier ◽  
Time Step ◽  
Towing Tank ◽  
Model Scale ◽  
Time Period ◽  
Unsteady Rans ◽  
Computational Fluid Dynamics Cfd ◽  
The Time Domain ◽  
Propeller Performance

The present work describes a simplified Computational Fluid Dynamics (CFD) approach in order to calculate the propulsive performance of a ship moving at steady forward speed in head seas. The proposed method combines experimental data concerning the added resistance at model scale with full scale Reynolds Averages Navier–Stokes (RANS) computations, using an in-house solver. In order to simulate the propeller performance, the actuator disk concept is employed. The propeller thrust is calculated in the time domain, assuming that the total resistance of the ship is the sum of the still water resistance and the added component derived by the towing tank data. The unsteady RANS equations are solved until self-propulsion is achieved at a given time step. Then, the computed values of both the flow rate through the propeller and the thrust are stored and, after the end of the examined time period, they are processed for calculating the variation of Shaft Horsepower (SHP) and RPM of the ship’s engine. The method is applied for a bulk carrier which has been tested in model scale at the towing tank of the Laboratory for Ship and Marine Hydrodynamics (LSMH) of the National Technical University of Athens (NTUA).

A Numerical Method for 3D Turbomachinery Aeroelasticity

2004 ◽  
Author(s):  
Paola Cinnella ◽  
Emanuele Cappiello ◽  
Pietro De Palma ◽  
Michele Napolitano ◽  
Giuseppe Pascazio
Keyword(s):  
Rigid Body ◽  
Numerical Method ◽  
Integral Form ◽  
Navier Stokes ◽  
Moving Grid ◽  
Time Step ◽  
Rans Equations ◽  
Standard Configuration ◽  
Reynolds Averaged Navier Stokes

This work provides an extension to 3D aeroelastic problems of a recently developed numerical method for turbomachinery aeroelasticity. The unsteady Euler or Reynolds-averaged Navier-Stokes (RANS) equations are solved in integral form, the blade passages being discretised using a deforming grid. The grid is regenerated at each time step using a novel methodology, that automatically avoids grid lines overlapping and guarantees the smoothness of the regenerated mesh. Firstly, the method has been validated versus the 2D 4th Aeroelastic Turbine Standard Configuration. Both inviscid and viscous turbulent computations have been performed, and the results previously obtained usind a different moving grid strategy have been recovered. In order to prove the robustness of the proposed deforming grid methodology, the same case has also been computed with the blade under-going large torsion displacements, the regenerated grid always preserving a good smoothness. Then, the methodology has been validated versus the 3D 4th Standard Aeroelastic Configuration, that involves a rigid body blade motion. Finally, a more severe 3D configuration, involving a clamped-beam-like blade deformation, has been considered.

scholarly journals Centrifugal Compressor Impeller Aerodynamics: A Numerical Investigation

1990 ◽  
Author(s):  
Daniel J. Dorney ◽  
Roger L. Davis
Keyword(s):  
Centrifugal Compressor ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Elliptic Partial Differential Equation ◽  
Solution Procedure ◽  
Design Flow ◽  
Navier Stokes ◽  
Impeller Blade ◽  
Compressor Impeller ◽  
Rotor Stator Interaction

A three-dimensional, Navier-Stokes analysis is presented for the prediction of viscous flows through centrifugal impellers. Based on the Navier-Stokes rotor/stator interaction procedure developed by Rai, the present analysis uses a zonal grid methodology to discretize the impeller flow field and to facilitate the relative motion of the impeller. A blade surface oriented O-grid generated from an elliptic partial differential equation solution procedure is patched into an algebraically generated H-grid which is used to discretize the inlet, exit and blade-to-blade regions. The equations of motion are integrated using a spatially third-order accurate, implicit, iterative, upwind, finite difference, time-marching technique. Predicted results are presented for flow through a low speed centrifugal compressor impeller operating at design flow conditions. Comparison of these predicted results with experimental data demonstrates the capability of this procedure to predict impeller blade loading and provide insight into the secondary flow structure within the impeller blade passage.

Dissipative, forced turbulence in two-dimensional magnetohydrodynamics

1977 ◽  
Vol 17 (3) ◽  
pp. 369-398 ◽  
Author(s):  
David Fyfe ◽  
David Montgomery ◽  
Glenn Joyce
Keyword(s):  
Vector Potential ◽  
Spectral Power ◽  
Equations Of Motion ◽  
Power Laws ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Dynamo Action ◽  
Time Step ◽  
Forced Turbulence ◽  
External Forces

The equations of motion for turbulent two-dimensional magnetohydrodynamic flows are solved in the presence of finite viscosity and resistivity, for the case in which external forces (mechanical and/or magnetic) act on the fluid. The goal is to verify the existence of a magnetohydrodynamic dynamo effect which is represented mathematically by a substantial back-transfer of mean square vector potential to the longest allowed Fourier wavelengths. External forces consisting of a random part plus a fraction of the value at the previous time step are employed, after the manner of Lilly for the Navier–Stokes case. The regime explored is that for which the mechanical and magnetic Reynolds numbers are in the region of 100 to 1000. The conclusions are that mechanical forcing terms alone cannot lead to dynamo action, but that dynamo action can result from either magnetic forcing terms or from both mechanical and magnetic forcing terms simultaneously. Most real physical cases seem most accurately modelled by the third situation. The spatial resolution of the 32 × 32 calculation is not adequate to test accurately the predictions of the spectral power laws previously arrived at on the basis of the assumption of simultaneous cascades of energy and vector potential. Some speculations are offered concerning possible relations between turbulent cascades and the ‘disruptive instability’.

The stability of unsteady axisymmetric incompressible pipe flow close to a piston. Part 1. Numerical analysis

1971 ◽  
Vol 50 (4) ◽  
pp. 625-644 ◽  
Author(s):  
J. H. Gerrard
Keyword(s):  
Stokes Equations ◽  
Equations Of Motion ◽  
Circular Cross Section ◽  
Cylindrical Tube ◽  
Navier Stokes ◽  
Ring Vortex ◽  
Random Disturbance ◽  
Time Step ◽  
Continuity Equations ◽  
Starting Flow

A numerical solution of the Navier-Stokes equations of motion by means of finite-difference forms of the vorticity and continuity equations is presented. This is applied to the study of the flow of an incompressible fluid produced by the motion from rest of a piston in a cylindrical tube of circular cross-section.Experiments at high Reynolds number indicated the presence in the starting flow of a ring vortex which was not reproduced by computation. Iteration to determine the stream function was not found to be necessary to achieve 1% accuracy. Omitting iteration is equivalent to only slightly disturbing the flow. An additional random disturbance applied to the flow at each time step was found to result in the production of the ring vortex.

scholarly journals Three-Dimensional Elastodynamic Analysis Employing Partially Discontinuous Boundary Elements

Algorithms ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 129
Author(s):  
Yuan Li ◽  
Ni Zhang ◽  
Yuejiao Gong ◽  
Wentao Mao ◽  
Shiguang Zhang
Keyword(s):  
Side Effect ◽  
Domain Boundary ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Integration Scheme ◽  
Computational Accuracy ◽  
Time Step ◽  
Corner Points ◽  
Discontinuous Elements ◽  
The Time Domain

Compared with continuous elements, discontinuous elements advance in processing the discontinuity of physical variables at corner points and discretized models with complex boundaries. However, the computational accuracy of discontinuous elements is sensitive to the positions of element nodes. To reduce the side effect of the node position on the results, this paper proposes employing partially discontinuous elements to compute the time-domain boundary integral equation of 3D elastodynamics. Using the partially discontinuous element, the nodes located at the corner points will be shrunk into the element, whereas the nodes at the non-corner points remain unchanged. As such, a discrete model that is continuous on surfaces and discontinuous between adjacent surfaces can be generated. First, we present a numerical integration scheme of the partially discontinuous element. For the singular integral, an improved element subdivision method is proposed to reduce the side effect of the time step on the integral accuracy. Then, the effectiveness of the proposed method is verified by two numerical examples. Meanwhile, we study the influence of the positions of the nodes on the stability and accuracy of the computation results by cases. Finally, the recommended value range of the inward shrink ratio of the element nodes is provided.

scholarly journals An Advance-Tracing Boundary Element Method in the Time Domain for Solving the Radiating Problem of an Arbitrary Obstacle Accelerating Randomly

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Jui-Hsiang Kao
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Time Domain ◽  
Boundary Integral ◽  
Normal Velocity ◽  
Time Step ◽  
Random Acceleration ◽  
The Time Domain ◽  
First Time ◽  
Element Method

This research develops an Advance-Tracing Boundary Element Method in the time domain to calculate the waves that radiate from an immersed obstacle moving with random acceleration. The moving velocity of the immersed obstacle is multifrequency and is projected along the normal direction of every element on the obstacle. The projected normal velocity of every element is presented by the Fourier series and includes the advance-tracing time, which is equal to a quarter period of the moving velocity. The moving velocity is treated as a known boundary condition. The computing scheme is based on the boundary integral equation in the time domain, and the approach process is carried forward in a loop from the first time step to the last. At each time step, the radiated pressure on each element is updated until obtaining a convergent result. The Advance-Tracing Boundary Element Method is suitable for calculating the radiating problem from an arbitrary obstacle moving with random acceleration in the time domain and can be widely applied to the shape design of an immersed obstacle in order to attain security and confidentiality.

scholarly journals Statistical Uncertainty of DNS in Geometries without Homogeneous Directions

2021 ◽  
Vol 11 (4) ◽  
pp. 1399
Author(s):  
Jure Oder ◽  
Cédric Flageul ◽  
Iztok Tiselj
Keyword(s):  
Channel Flow ◽  
A Priori ◽  
Time Integration ◽  
Navier Stokes ◽  
Statistical Uncertainty ◽  
Time Step ◽  
Order Of Magnitude ◽  
Averaging Time ◽  
The Individual ◽  
Time Required

In this paper, we present uncertainties of statistical quantities of direct numerical simulations (DNS) with small numerical errors. The uncertainties are analysed for channel flow and a flow separation case in a confined backward facing step (BFS) geometry. The infinite channel flow case has two homogeneous directions and this is usually exploited to speed-up the convergence of the results. As we show, such a procedure reduces statistical uncertainties of the results by up to an order of magnitude. This effect is strongest in the near wall regions. In the case of flow over a confined BFS, there are no such directions and thus very long integration times are required. The individual statistical quantities converge with the square root of time integration so, in order to improve the uncertainty by a factor of two, the simulation has to be prolonged by a factor of four. We provide an estimator that can be used to evaluate a priori the DNS relative statistical uncertainties from results obtained with a Reynolds Averaged Navier Stokes simulation. In the DNS, the estimator can be used to predict the averaging time and with it the simulation time required to achieve a certain relative statistical uncertainty of results. For accurate evaluation of averages and their uncertainties, it is not required to use every time step of the DNS. We observe that statistical uncertainty of the results is uninfluenced by reducing the number of samples to the point where the period between two consecutive samples measured in Courant–Friedrichss–Levy (CFL) condition units is below one. Nevertheless, crossing this limit, the estimates of uncertainties start to exhibit significant growth.

The inlet flow structure of a conceptual open-nose supersonic drone

2021 ◽  
pp. 095441002098304
Author(s):  
Eiman B Saheby ◽  
Xing Shen ◽  
Anthony P Hays ◽  
Zhang Jun
Keyword(s):  
Flow Structure ◽  
Stokes Equations ◽  
Fluid Dynamic ◽  
Three Dimensional ◽  
Computational Fluid Dynamic Simulation ◽  
Navier Stokes ◽  
Ansys Fluent ◽  
Navier Stokes Equations ◽  
Aerodynamic Efficiency ◽  
Performance Effects

This study describes the aerodynamic efficiency of a forebody–inlet configuration and computational investigation of a drone system, capable of sustainable supersonic cruising at Mach 1.60. Because the whole drone configuration is formed around the induction system and the design is highly interrelated to the flow structure of forebody and inlet efficiency, analysis of this section and understanding its flow pattern is necessary before any progress in design phases. The compression surface is designed analytically using oblique shock patterns, which results in a low drag forebody. To study the concept, two inlet–forebody geometries are considered for Computational Fluid Dynamic simulation using ANSYS Fluent code. The supersonic and subsonic performance, effects of angle of attack, sideslip, and duct geometries on the propulsive efficiency of the concept are studied by solving the three-dimensional Navier–Stokes equations in structured cell domains. Comparing the results with the available data from other sources indicates that the aerodynamic efficiency of the concept is acceptable at supersonic and transonic regimes.

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