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 RANS MODELLING OF CROSS-SHORE SEDIMENT TRANSPORT AND MORPHODYNAMICS IN THE SWASH-ZONE

2020 ◽  
pp. 14
Author(s):  
Joost Kranenborg ◽  
Geert Campmans ◽  
Niels Jacobsen ◽  
Jebbe van der Werf ◽  
Robert McCall ◽  
...  
Keyword(s):  
Sediment Transport ◽  
Numerical Model ◽  
Navier Stokes ◽  
Swash Zone ◽  
Rans Equations ◽  
Model Based ◽  
Numerical Studies ◽  
Reynolds Averaged Navier Stokes ◽  
Averaged Models

Most numerical studies of sediment transport in the swash zone use depth-averaged models. However, such models still have difficulty predicting transport rates and morphodynamics. Depth-resolving models could give detailed insight in swash processes but have mostly been limited to hydrodynamic predictions. We present a depth-resolving numerical model, based on the Reynolds Averaged Navier-Stokes (RANS) equations, capable of modelling sediment transport and morphodynamics in the swash zone.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/PB8Vs0LJq88

scholarly journals Reynolds-averaged Navier–Stokes equations with explicit data-driven Reynolds stress closure can be ill-conditioned

2019 ◽  
Vol 869 ◽  
pp. 553-586 ◽  
Author(s):  
Jinlong Wu ◽  
Heng Xiao ◽  
Rui Sun ◽  
Qiqi Wang
Keyword(s):  
Reynolds Stress ◽  
Condition Number ◽  
Stokes Equations ◽  
Plane Channel ◽  
Channel Flows ◽  
Data Driven ◽  
Navier Stokes ◽  
Rans Equations ◽  
Reynolds Averaged Navier Stokes ◽  
Stress Models

Reynolds-averaged Navier–Stokes (RANS) simulations with turbulence closure models continue to play important roles in industrial flow simulations. However, the commonly used linear eddy-viscosity models are intrinsically unable to handle flows with non-equilibrium turbulence (e.g. flows with massive separation). Reynolds stress models, on the other hand, are plagued by their lack of robustness. Recent studies in plane channel flows found that even substituting Reynolds stresses with errors below 0.5 % from direct numerical simulation databases into RANS equations leads to velocities with large errors (up to 35 %). While such an observation may have only marginal relevance to traditional Reynolds stress models, it is disturbing for the recently emerging data-driven models that treat the Reynolds stress as an explicit source term in the RANS equations, as it suggests that the RANS equations with such models can be ill-conditioned. So far, a rigorous analysis of the condition of such models is still lacking. As such, in this work we propose a metric based on local condition number function for a priori evaluation of the conditioning of the RANS equations. We further show that the ill-conditioning cannot be explained by the global matrix condition number of the discretized RANS equations. Comprehensive numerical tests are performed on turbulent channel flows at various Reynolds numbers and additionally on two complex flows, i.e. flow over periodic hills, and flow in a square duct. Results suggest that the proposed metric can adequately explain observations in previous studies, i.e. deteriorated model conditioning with increasing Reynolds number and better conditioning of the implicit treatment of the Reynolds stress compared to the explicit treatment. This metric can play critical roles in the future development of data-driven turbulence models by enforcing the conditioning as a requirement on these models.

A Navier–Stokes Analysis of Airfoils in Oscillating Transonic Cascades for the Prediction of Aerodynamic Damping

1997 ◽  
Vol 119 (1) ◽  
pp. 77-84 ◽  
Author(s):  
R. S. Abhari ◽  
M. Giles
Keyword(s):  
Numerical Study ◽  
Three Dimensional ◽  
Outer Region ◽  
Navier Stokes ◽  
Compressor Cascade ◽  
Time Step ◽  
Aerodynamic Damping ◽  
Transonic Compressor ◽  
Standard Configuration ◽  
The Impact

An unsteady, compressible, two-dimensional, thin shear layer Navier–Stokes solver is modified to predict the motion-dependent unsteady flow around oscillating airfoils in a cascade. A quasi-three-dimensional formulations is used to account for the stream-wise variation of streamtube height. The code uses Ni’s Lax–Wendroff algorithm in the outer region, an implicit ADI method in the inner region, conservative coupling at the interface, and the Baldwin–Lomax turbulence model. The computational mesh consists of an O-grid around each blade plus an unstructured outer grid of quadrilateral or triangular cells. The unstructured computational grid was adapted to the flow to better resolve shocks and wakes. Motion of each airfoil was simulated at each time step by stretching and compressing the mesh within the O-grid. This imposed motion consists of harmonic solid body translation in two directions and rotation, combined with the correct interblade phase angles. The validity of the code is illustrated by comparing its predictions to a number of test cases, including an axially oscillating flat plate in laminar flow, the Aeroelasticity of Turbomachines Symposium Fourth Standard Configuration (a transonic turbine cascade), and the Seventh Standard Configuration (a transonic compressor cascade). The overall comparison between the predictions and the test data is reasonably good. A numerical study on a generic transonic compressor rotor was performed in which the impact of varying the amplitude of the airfoil oscillation on the normalized predicted magnitude and phase of the unsteady pressure around the airfoil was studied. It was observed that for this transonic compressor, the nondimensional aerodynamic damping was influenced by the amplitude of the oscillation.

A Numerical Method for Turbomachinery Aeroelasticity

2002 ◽  
Author(s):  
P. Cinnella ◽  
P. De Palma ◽  
G. Pascazio ◽  
M. Napolitano
Keyword(s):  
Numerical Method ◽  
Compressible Flows ◽  
State Of The Art ◽  
Second Order ◽  
The State ◽  
Turbine Cascade ◽  
Time Step ◽  
Difference Formula ◽  
Standard Configuration ◽  
Flow Through

This work provides an accurate and efficient numerical method for turbomachinery flutter. The unsteady Euler or Reynolds-averaged Navier–Stokes (RANS) equations are solved in integral form, the blade passages being discretised using a background fixed C-grid and a body-fitted C-grid moving with the blade. In the overlapping region data are exchanged between the two grids at every time step, using bilinear interpolation. The method employs Roe’s second-order-accurate flux difference splitting scheme for the inviscid fluxes, a standard second-order discretisation of the viscous terms, and a three-level backward difference formula for the time derivatives. The state-of-the-art second-order accuracy of numerical methods for unsteady compressible flows with shocks is thus carried over, for the first time to the authors knowledge, to flutter computations. The dual time stepping technique is used to evaluate the nonlinear residual at each time step, thus extending to turbomachinery aeroelasticity the state-of-the-art efficiency of unsteady RANS solvers. The code is proven to be accurate and efficient by computing the 4th Aeroelastic Standard Configuration, namely, the subsonic flow through a turbine cascade with flutter instability in the first bending mode, where viscous effect are found practically negligible. Then, the very severe 11th Aeroelastic Standard Configuration is computed, namely, the transonic flow through a turbine cascade at off-design conditions, where the turbulence model is found to be the critical feature of the method.

On the Numerical Prediction of Transitional Flows With Reynolds-Averaged Navier-Stokes and Scale-Resolving Simulation Models

2016 ◽  
Author(s):  
Filipe S. Pereira ◽  
Guilherme Vaz ◽  
Luís Eça ◽  
Sébastien Lemaire
Keyword(s):  
Boundary Layer ◽  
Mathematical Models ◽  
Navier Stokes ◽  
Turbulent Regime ◽  
Dimensionless Time ◽  
Time Step ◽  
Flow Physics ◽  
Transitional Flows ◽  
Eddy Simulation ◽  
Reynolds Averaged Navier Stokes

The present work investigates the transitional flow around a smooth circular cylinder at Reynolds number Re = 140,000. The flow is resolved using the viscous-flow solver ReFRESCO, and distinct mathematical models are applied to assess their ability to handle transitional flows. The selected mathematical models are the Reynolds-Averaged Navier-Stokes equations (RANS), Scale-Adaptive Simulation (SAS), Delayed Detached-Eddy Simulation (DDES), eXtra Large-Eddy Simulation (XLES) and Partially-Averaged Navier-Stokes (PANS) equations. The RANS equations are supplemented with the k–ω Shear-Stress Transport (SST) with and without the Local Correlation Transition Model (LCTM). The numerical simulations are carried out using structured grids ranging from 9.32 × 104 to 2.24 × 107 cells, and a dimensionless time-step of 1.50 × 10−3. As expected, the outcome demonstrates that transition from laminar to turbulent regime is incorrectly predicted by the k–ω SST model. Transition occurs upstream of the flow separation, which is typical of the supercritical regime and so the flow physics is incorrectly modelled. Naturally, all Scale-Resolving Simulation (SRS) models that rely on RANS to solve the boundary-layer, called hybrid models, will exhibit a similar trend. On the other hand, mathematical models capable to resolve part of the turbulence field in the boundary layer (PANS) lead to a better agreement with the experimental data. Furthermore, the k–ω SST LCTM is also able to improve the modelling accuracy when compared to the k–ω SST. Therefore, it might be a valuable engineering tool if its computational demands are considered (in the RANS context). Therefore, the results confirm that the choice of the most appropriate mathematical model for the simulation of turbulent flows is not straightforward and it may depend on the details of the flow physics.

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 VIScous Vorticity Equation (VISVE) for Turbulent 2-D Flows with Variable Density and Viscosity

2020 ◽  
Vol 8 (3) ◽  
pp. 191 ◽  
Author(s):  
Spyros A. Kinnas
Keyword(s):  
Variable Viscosity ◽  
Variable Density ◽  
Vorticity Equation ◽  
Navier Stokes ◽  
Cavitating Flows ◽  
Rans Equations ◽  
Reynolds Averaged Navier Stokes

The general vorticity equation for turbulent compressible 2-D flows with variable viscosity is derived, based on the Reynolds-Averaged Navier-Stokes (RANS) equations, and simplified versions of it are presented in the case of turbulent or cavitating flows around 2-D hydrofoils.

scholarly journals Advances in Numerical Reynolds-Averaged Navier–Stokes Modelling of Wave-Structure-Seabed Interactions and Scour

2021 ◽  
Vol 9 (6) ◽  
pp. 611
Author(s):  
Pilar Díaz-Carrasco ◽  
Sergio Croquer ◽  
Vahid Tamimi ◽  
Jay Lacey ◽  
Sébastien Poncet
Keyword(s):  
Sediment Transport ◽  
Numerical Modelling ◽  
Review Paper ◽  
Fluid Phase ◽  
Wave Structure ◽  
Numerical Approach ◽  
Navier Stokes ◽  
Future Prospects ◽  
Rans Equations ◽  
Reynolds Averaged Navier Stokes

This review paper presents the recent advances in the numerical modelling of wave–structure–seabed interactions. The processes that are involved in wave–structure interactions, which leads to sediment transport and scour effects, are summarized. Subsequently, the three most common approaches for modelling sediment transport that is induced by wave–structure interactions are described. The applicability of each numerical approach is also included with a summary of the most recent studies. These approaches are based on the Reynolds-Averaged Navier–Stokes (RANS) equations for the fluid phase, and mostly differ in how they tackle the seabed response. Finally, future prospects of research are discussed.

Analysis of the Flow Around a Manoeuvring VLCC

2008 ◽  
Author(s):  
Roberto Muscari ◽  
Riccardo Broglia ◽  
Andrea Di Mascio
Keyword(s):  
Numerical Simulation ◽  
Rigid Body ◽  
Oral Presentation ◽  
Stokes Equations ◽  
Experimental Results ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations

This work describes the numerical simulation of a turning circle manoeuvre performed by the MOERI KVLCC2 induced by the rotation of the rudder. To this purpose, the Navier-Stokes equations are integrated, the hydrodynamical forces acting on the hull are computed and the hull is moved at each time step according to the rigid body equations. Because of the scarceness of experimental results for this kind of simulations, the validation of the proposed method is postponed to the oral presentation when the data from the SIMMAN 2008 Workshop (http://www.simman2008.dk/) will be available.

A Numerical Method for Turbomachinery Aeroelasticity

2004 ◽  
Vol 126 (2) ◽  
pp. 310-316 ◽  
Author(s):  
P. Cinnella ◽  
P. De Palma ◽  
G. Pascazio ◽  
M. Napolitano
Keyword(s):  
Numerical Method ◽  
Transonic Flow ◽  
Stokes Equations ◽  
Second Order ◽  
Turbine Cascade ◽  
Time Step ◽  
Difference Formula ◽  
Standard Configuration ◽  
Flow Through ◽  
Benchmark Solutions

This work provides an accurate and efficient numerical method for turbomachinery flutter. The unsteady Euler or Reynolds-averaged Navier-Stokes equations are solved in integral form, the blade passages being discretised using a background fixed C-grid and a body-fitted C-grid moving with the blade. In the overlapping region data are exchanged between the two grids at every time step, using bilinear interpolation. The method employs Roe’s second-order-accurate flux difference splitting scheme for the inviscid fluxes, a standard second-order discretisation of the viscous terms, and a three-level backward difference formula for the time derivatives. The dual-time-stepping technique is used to evaluate the nonlinear residual at each time step. The state-of-the-art second-order accuracy of unsteady transonic flow solvers is thus carried over to flutter computations. The code is proven to be accurate and efficient by computing the 4th Aeroelastic Standard Configuration, namely, the subsonic flow through a turbine cascade with flutter instability in the first bending mode, where viscous effect are found practically negligible. Then, for the very severe 11th Aeroelastic Standard Configuration, namely, transonic flow through a turbine cascade at off-design conditions, benchmark solutions are provided for various values of the inter-blade phase angle.

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