High Level Languages Implementation and Analysis of 3D Navier-Stokes Solvers

2011 ◽  
Vol 3 (3) ◽  
pp. 370-388
Author(s):  
Valerio Grazioso ◽  
Carlo Scalo ◽  
Giuseppe de Felice ◽  
Carlo Meola
Keyword(s):  
Stokes Equations ◽  
Complex Geometry ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Computationally Efficient ◽  
Flamelet Model ◽  
Advection Scheme ◽  
Variable Ordering ◽  
Pressure Variable ◽  
High Level

AbstractIn this work we introduce PRIN-3D (PRoto-code for Internal flows modeled by Navier-Stokes equations in 3-Dimensions), a new high level algebraic language (Matlab®) based code, by discussing some fundamental aspects regarding its basic solving kernel and by describing the design of an innovative advection scheme. The main focus was on designing a memory and computationally efficient code that, due to the typical conciseness of the Matlab coding language, could allow for fast and effective implementation of new models or algorithms. Innovative numerical methods are discussed in the paper. The pressure equation is derived with a quasi-segregation technique leading to an iterative scheme obtained within the framework of a global preconditioning procedure. Different levels of parallelization are obtainable by exploiting special pressure variable ordering patterns that lead to a block-structured Poisson-like matrix. Moreover, the new advection scheme has the potential of a controllable artificial diffusivity. Preliminary results are shown including a fully three-dimensional internal laminar flow evolving in a relatively complex geometry and a 3D methane-air flame simulated with the aid of libraries based on the Flamelet model.

Direct simulation of evolution and control of three-dimensional instabilities in attachment-line boundary layers

1995 ◽  
Vol 291 ◽  
pp. 369-392 ◽  
Author(s):  
Ronald D. Joslin
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Plate Boundary ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Computationally Efficient ◽  
Simulation Results ◽  
Dimensional Simulation ◽  
Attachment Line

The spatial evolution of three-dimensional disturbances in an attachment-line boundary layer is computed by direct numerical simulation of the unsteady, incompressible Navier–Stokes equations. Disturbances are introduced into the boundary layer by harmonic sources that involve unsteady suction and blowing through the wall. Various harmonic-source generators are implemented on or near the attachment line, and the disturbance evolutions are compared. Previous two-dimensional simulation results and nonparallel theory are compared with the present results. The three-dimensional simulation results for disturbances with quasi-two-dimensional features indicate growth rates of only a few percent larger than pure two-dimensional results; however, the results are close enough to enable the use of the more computationally efficient, two-dimensional approach. However, true three-dimensional disturbances are more likely in practice and are more stable than two-dimensional disturbances. Disturbances generated off (but near) the attachment line spread both away from and toward the attachment line as they evolve. The evolution pattern is comparable to wave packets in flat-plate boundary-layer flows. Suction stabilizes the quasi-two-dimensional attachment-line instabilities, and blowing destabilizes these instabilities; these results qualitatively agree with the theory. Furthermore, suction stabilizes the disturbances that develop off the attachment line. Clearly, disturbances that are generated near the attachment line can supply energy to attachment-line instabilities, but suction can be used to stabilize these instabilities.

1995 ASME Gas Turbine Award Paper: Development and Application of a Multistage Navier–Stokes Solver: Part I—Multistage Modeling Using Bodyforces and Deterministic Stresses

1998 ◽  
Vol 120 (2) ◽  
pp. 205-214 ◽  
Author(s):  
C. M. Rhie ◽  
A. J. Gleixner ◽  
D. A. Spear ◽  
C. J. Fischberg ◽  
R. M. Zacharias
Keyword(s):  
Stokes Equations ◽  
Pressure Ratio ◽  
Three Dimensional ◽  
Design Procedure ◽  
Potential Interaction ◽  
Theoretical Development ◽  
Navier Stokes ◽  
Radial Profiles ◽  
Compressor Performance ◽  
High Level

A multistage compressor performance analysis method based on the three-dimensional Reynolds-averaged Navier-Stokes equations is presented in this paper. This method is an average passage approach where deterministic stresses are used to ensure continuous physical properties across interface planes. The average unsteady effects due to neighboring blades and/or vanes are approximated using deterministic stresses along with the application of bodyforces. Bodyforces are used to account for the “potential” interaction between closely coupled (staged) rows. Deterministic stresses account for the “average” wake blockage and mixing effects both axially and radially. The attempt here is to implement an approximate technique for incorporating periodic unsteady flow physics that provides for a robust multistage design procedure incorporating reasonable computational efficiency. The present paper gives the theoretical development of the stress/bodyforce models incorporated in the code, and demonstrates the usefulness of these models in practical compressor applications. Compressor performance prediction capability is then established through a rigorous code/model validation effort using the power of networked workstations. The numerical results are compared with experimental data in terms of one-dimensional performance parameters such as total pressure ratio and circumferentially averaged radial profiles deemed critical to compressor design. This methodology allows the designer to design from hub to tip with a high level of confidence in the procedure.

scholarly journals RUBBLE MOUND BREAKWATER OVERTOPPING: ESTIMATION OF THE RELIABILITY OF A 3D NUMERICAL SIMULATION

2012 ◽  
Vol 1 (33) ◽  
pp. 8 ◽  
Author(s):  
Luca Cavallaro ◽  
Fabio Dentale ◽  
Giovanna Donnarumma ◽  
Enrico Foti ◽  
Rosaria E. Musumeci ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Complex Geometry ◽  
Fluid Dynamic ◽  
Complete Solution ◽  
Three Dimensional ◽  
Design Tool ◽  
Physical Models ◽  
Navier Stokes ◽  
Free Boundaries ◽  
Navier Stokes Equations

Until recently, physical models were the only way to investigate into the details of breakwaters behavior under wave attack. From the numerical point of view, the complexity of the fluid dynamic processes involved has so far hindered the direct application of Navier-Stokes equations within the armour blocks, due to the complex geometry and the presence of strongly non stationary flows, free boundaries and turbulence. In the present work the most recent CFD technology is used to provide a new and more reliable approach to the design analysis of breakwaters, especially in connection with run-up and overtopping. The solid structure is simulated within the numerical domain by overlapping individual virtual elements to form the empty spaces delimited by the blocks. Thus, by defining a fine computational grid, an adequate number of nodes is located within the interstices and a complete solution of the full hydrodynamic equations is carried out. In the work presented here the numerical simulations are carried out by integrating the three-dimensional Reynolds Average Navier-Stokes Equations coupled with the RNG turbulence model and a Volume of Fluid Method used to handle the dynamics of the free surface. The aim of the present work is to investigate the reliability of this approach as a design tool. Two different breakwaters are considered, both located in Southern Sicily: one a typical quarry stone breakwater, another a more complex design incorporating a spill basin and an armoured layer made up by Coreloc® blocks.

High Fidelity Simulation of Safety Relief Valve Internal Flows

2015 ◽  
Author(s):  
Yunchao Yang ◽  
Alexis Lefebvre ◽  
Ge-Cheng Zha ◽  
Qing-Feng Liu ◽  
Jun Fan ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Complex Geometry ◽  
Three Dimensional ◽  
Weno Scheme ◽  
Inlet Pressure ◽  
Navier Stokes ◽  
Implicit Time ◽  
Complex Flow ◽  
Relief Valve ◽  
Expansion Waves

This paper presents a numerical methodology and simulation for three-dimensional transonic flow in Safety Relief Valves. Simulation of safety relief valve flows is very challenging due to complex flow paths, high pressure variation, supersonic flow with shock and expansion waves, boundary layers, etc. The 3D unsteady Reynolds averaged Navier-Stokes (URANS) equations with one-equation Spalart-Allmaras turbulence model is used. A fifth order WENO scheme for the inviscid flux and a second order central differencing for the viscous terms are employed to discretize the Navier-Stokes equations. The low diffusion E-CUSP scheme used as the approximate Riemann solver suggested by Zha et al. is utilized with the WENO scheme to evaluate the inviscid fluxes. Implicit time marching method with 2nd order temporal accuracy using Gauss-Seidel line relaxation is employed to achieve a fast convergence rate. Parallel computing is implemented to save wall clock simulation time. The valve flows with air under different inlet pressures and temperatures are successfully simulated for the full geometry with all the fine leakage channels. A 3D mesh topology is generated for the complex geometry. Detailed simulations of air flow are accomplished with inlet gauge pressure 0.5MPa and 2.1MPa. The simulated air mass flow rate agrees excellently with the experimental results with an error of 0.26% for the inlet pressure of 0.5Mpa, and an error of 2.5% for the inlet pressure of 2.1MPa. The shock waves and expansion waves downstream of the orifice are very well resolved.

Annular and spiral patterns in flows between rotating and stationary discs

2001 ◽  
Vol 434 ◽  
pp. 65-100 ◽  
Author(s):  
E. SERRE ◽  
E. CRESPO DEL ARCO ◽  
P. BONTOUX
Keyword(s):  
Stokes Equations ◽  
Rotation Axis ◽  
Three Dimensional ◽  
Fourier Method ◽  
Navier Stokes ◽  
Type I ◽  
Boundary Layer Flows ◽  
Navier Stokes Equations ◽  
Rotation Rates ◽  
High Level

Different instabilities of the boundary layer flows that appear in the cavity between stationary and rotating discs are investigated using three-dimensional direct numerical simulations. The influence of curvature and confinement is studied using two geometrical configurations: (i) a cylindrical cavity including the rotation axis and (ii) an annular cavity radially confined by a shaft and a shroud. The numerical computations are based on a pseudo-spectral Chebyshev–Fourier method for solving the incompressible Navier–Stokes equations written in primitive variables. The high level accuracy of the spectral methods is imperative for the investigation of such instability structures. The basic flow is steady and of the Batchelor type. At a critical rotation rate, stationary axisymmetric and/or three-dimensional structures appear in the Bödewadt and Ekman layers while at higher rotation rates a second transition to unsteady flow is observed. All features of the transitions are documented. A comparison of the wavenumbers, frequencies, and phase velocities of the instabilities with available theoretical and experimental results shows that both type II (or A) and type I (or B) instabilities appear, depending on flow and geometric control parameters. Interesting patterns exhibiting the coexistence of circular and spiral waves are found under certain conditions.

scholarly journals The curled wake model: a three-dimensional and extremely fast steady-state wake solver for wind plant flows

2021 ◽  
Vol 6 (2) ◽  
pp. 555-570
Author(s):  
Luis A. Martínez-Tossas ◽  
Jennifer King ◽  
Eliot Quon ◽  
Christopher J. Bay ◽  
Rafael Mudafort ◽  
...  
Keyword(s):  
Steady State ◽  
Wind Power ◽  
Power Plants ◽  
Stokes Equations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Computationally Efficient ◽  
Mean Power ◽  
Wake Model

Abstract. Wind turbine wake models typically require approximations, such as wake superposition and deflection models, to accurately describe wake physics. However, capturing the phenomena of interest, such as the curled wake and interaction of multiple wakes, in wind power plant flows comes with an increased computational cost. To address this, we propose a new hybrid method that uses analytical solutions with an approximate form of the Reynolds-averaged Navier–Stokes equations to solve the time-averaged flow over a wind plant. We compare results from the solver to supervisory control and data acquisition data from the Lillgrund wind plant obtaining wake model predictions which are generally within 1 standard deviation of the mean power data. We perform simulations of flow over the Columbia River Gorge to demonstrate the capabilities of the model in complex terrain. We also apply the solver to a case with wake steering, which agreed well with large-eddy simulations. This new solver reduces the time – and therefore the related cost – it takes to simulate a steady-state wind plant flow (on the order of seconds using one core). Because the model is computationally efficient, it can also be used for different applications including wake steering for wind power plants and layout optimization.

Potential-Flow Modeling for Data Center Applications

2011 ◽  
Author(s):  
Christopher M. Healey ◽  
James W. VanGilder ◽  
Zachary R. Sheffer ◽  
Xuanhang Simon Zhang
Keyword(s):  
Data Center ◽  
Potential Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Wall Friction ◽  
Navier Stokes ◽  
Computationally Efficient ◽  
Navier Stokes Equations ◽  
Comprehensive Comparison ◽  
Efficient Alternative

Potential-flow-based airflow and heat transfer models have been proposed as a computationally efficient alternative to the Navier-Stokes Equations for predicting the three-dimensional flow field in data center applications. These models are simple, solve quickly, and capture much of the fluid flow physics, but ignore buoyancy and frictional effects, i.e., rotationality, turbulence, and wall friction. However, a comprehensive comparison of the efficiency and accuracy of these methods versus more sophisticated tools, like CFD, is lacking. The main contribution of this paper is a study of the performance of potential-flow methods compared to CFD in eight layouts inspired by actual data center configurations. We demonstrate that potential-flow methods can be helpful in data center design and management applications.

scholarly journals DETERMINATION OF ACOUSTIC CHARACTERISTICS OF FULL-SCALE SAMPLE OF SINGLE LAYERED HONEYCOMB LINER BASED ON NUMERICAL SIMULATION

Akustika ◽  
2019 ◽  
Vol 32 ◽  
pp. 182-188 ◽  
Author(s):  
Igor Khramtsov ◽  
Oleg Kustov ◽  
Vadim Palchikovskiy
Keyword(s):  
Numerical Simulation ◽  
Stokes Equations ◽  
Complex Geometry ◽  
Three Dimensional ◽  
Single Layer ◽  
Normal Incidence ◽  
Full Scale ◽  
Navier Stokes ◽  
Acoustic Characteristics ◽  
Good Agreement

The acoustic characteristics of a full-scale sample of an actual single-layer liner are determined by numerical simulation of physical processes in normal incidence interferometer. Numerical simulation is performed based on solving the unsteady Navier-Stokes equations with allowance for compressibility in three-dimensional statement. It is noted the good agreement of the acoustic characteristics of the liner sample obtained in numerical simulation and in experiment. It is shown that conducting numerical simulation on single cell sample of the liner also gives results that are in good agreement with the experiment. It allows predicting the acoustic characteristics of samples of locally reacting liners with a more complex geometry in further.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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