scholarly journals Fast identification of transonic buffet envelope using computational fluid dynamics

2019 ◽  
Vol 91 (2) ◽  
pp. 309-316 ◽  
Author(s):  
Jernej Drofelnik ◽  
Andrea Da Ronch ◽  
Matteo Franciolini ◽  
Andrea Crivellini
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Turbulent Flow ◽  
Stokes Equations ◽  
Aircraft Design ◽  
Navier Stokes ◽  
Swept Wing ◽  
Navier Stokes Equations ◽  
Content Type ◽  
Preliminary Aircraft Design

Purpose This paper aims to present a numerical method based on computational fluid dynamics that allows investigating the buffet envelope of reference equivalent wings at the equivalent cost of several two-dimensional, unsteady, turbulent flow analyses. The method bridges the gap between semi-empirical relations, generally dominant in the early phases of aircraft design, and three-dimensional turbulent flow analyses, characterised by high costs in analysis setups and prohibitive computing times. Design/methodology/approach Accuracy in the predictions and efficiency in the solution are two key aspects. Accuracy is maintained by solving a specialised form of the Reynolds-averaged Navier–Stokes equations valid for infinite-swept wing flows. Efficiency of the solution is reached by a novel implementation of the flow solver, as well as by combining solutions of different fidelity spatially. Findings Discovering the buffet envelope of a set of reference equivalent wings is accompanied with an estimate of the uncertainties in the numerical predictions. Just over 2,000 processor hours are needed if it is admissible to deal with an uncertainty of ±1.0° in the angle of attack at which buffet onset/offset occurs. Halving the uncertainty requires significantly more computing resources, close to a factor 200 compared with the larger uncertainty case. Practical implications To permit the use of the proposed method as a practical design tool in the conceptual/preliminary aircraft design phases, the method offers the designer with the ability to gauge the sensitivity of buffet on primary design variables, such as wing sweep angle and chord to thickness ratio. Originality/value The infinite-swept wing, unsteady Reynolds-averaged Navier–Stokes equations have been successfully applied, for the first time, to identify buffeting conditions. This demonstrates the adequateness of the proposed method in the conceptual/preliminary aircraft design phases.

Development of SIMPLE-Like Algorithms for Incompressible Navier-Stokes Equations in Liquid Processing of Materials

2012 ◽  
Vol 184-185 ◽  
pp. 944-948 ◽  
Author(s):  
Hai Jun Gong ◽  
Yang Liu ◽  
Xue Yi Fan ◽  
Da Ming Xu
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Stokes Equations ◽  
Simple Algorithm ◽  
Navier Stokes ◽  
Incompressible Fluid Flow ◽  
Numerical Accuracy ◽  
Simple Scheme ◽  
Navier Stokes Equations ◽  
Computational Fluid Dynamics Cfd

For a clear and comprehensive opinion on segregated SIMPLE algorithm in the area of computational fluid dynamics (CFD) during liquid processing of materials, the most significant developments on the SIMPLE algorithm and its variants are briefly reviewed. Subsequently, some important advances during last 30 years serving as increasing numerical accuracy, enhancing robustness and improving efficiency for Navier–Stokes (N-S) equations of incompressible fluid flow are summarized. And then a so-called Direct-SIMPLE scheme proposed by the authors of present paper introduced, which is different from SIMPLE-like schemes, no iterative computations are needed to achieve the final pressure and velocity corrections. Based on the facts cited in present paper, it conclude that the SIMPLE algorithm and its variants will continue to evolve aimed at convergence and accuracy of solution by improving and combining various methods with different grid techniques, and all the algorithms mentioned above will enjoy widespread use in the future.

Computational analysis of turbulent flow through an eccentric annulus under different temperature conditions

2018 ◽  
Vol 28 (9) ◽  
pp. 2189-2207 ◽  
Author(s):  
Erman Ulker ◽  
Sıla Ovgu Korkut ◽  
Mehmet Sorgun
Keyword(s):  
Turbulent Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Content Type ◽  
Non Linear ◽  
Fully Developed Turbulent Flow ◽  
Effects Of Temperature ◽  
Eccentric Annuli ◽  
Pipe Rotation

Purpose The purpose of this paper is to solve Navier–Stokes equations including the effects of temperature and inner pipe rotation for fully developed turbulent flow in eccentric annuli by using finite difference scheme with fixing non-linear terms. Design/methodology/approach A mathematical model is proposed for fully developed turbulent flow including the effects of temperature and inner pipe rotation in eccentric annuli. Obtained equation is solved numerically via central difference approximation. In this process, the non-linear term is frozen. In so doing, the non-linear equation can be considered as a linear one. Findings The convergence analysis is studied before using the method to the proposed momentum equation. It reflects that the method approaches to the exact solution of the equation. The numerical solution of the mathematical model shows that pressure gradient can be predicted with a good accuracy when it is compared with experimental data collected from experiments conducted at Izmir Katip Celebi University Flow Loop. Originality/value The originality of this work is that Navier–Stokes equations including temperature and inner pipe rotation effects for fully developed turbulent flow in eccentric annuli are solved numerically by a finite difference method with frozen non-linear terms.

scholarly journals A Massively Parallel Hybrid Finite Volume/Finite Element Scheme for Computational Fluid Dynamics

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2316
Author(s):  
Laura Río-Martín ◽  
Saray Busto ◽  
Michael Dumbser
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Finite Element ◽  
Mach Number ◽  
Finite Volume ◽  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Massively Parallel ◽  
Navier Stokes ◽  
Navier Stokes Equations

In this paper, we propose a novel family of semi-implicit hybrid finite volume/finite element schemes for computational fluid dynamics (CFD), in particular for the approximate solution of the incompressible and compressible Navier-Stokes equations, as well as for the shallow water equations on staggered unstructured meshes in two and three space dimensions. The key features of the method are the use of an edge-based/face-based staggered dual mesh for the discretization of the nonlinear convective terms at the aid of explicit high resolution Godunov-type finite volume schemes, while pressure terms are discretized implicitly using classical continuous Lagrange finite elements on the primal simplex mesh. The resulting pressure system is symmetric positive definite and can thus be very efficiently solved at the aid of classical Krylov subspace methods, such as a matrix-free conjugate gradient method. For the compressible Navier-Stokes equations, the schemes are by construction asymptotic preserving in the low Mach number limit of the equations, hence a consistent hybrid FV/FE method for the incompressible equations is retrieved. All parts of the algorithm can be efficiently parallelized, i.e., the explicit finite volume step as well as the matrix-vector product in the implicit pressure solver. Concerning parallel implementation, we employ the Message-Passing Interface (MPI) standard in combination with spatial domain decomposition based on the free software package METIS. To show the versatility of the proposed schemes, we present a wide range of applications, starting from environmental and geophysical flows, such as dambreak problems and natural convection, over direct numerical simulations of turbulent incompressible flows to high Mach number compressible flows with shock waves. An excellent agreement with exact analytical, numerical or experimental reference solutions is achieved in all cases. Most of the simulations are run with millions of degrees of freedom on thousands of CPU cores. We show strong scaling results for the hybrid FV/FE scheme applied to the 3D incompressible Navier-Stokes equations, using millions of degrees of freedom and up to 4096 CPU cores. The largest simulation shown in this paper is the well-known 3D Taylor-Green vortex benchmark run on 671 million tetrahedral elements on 32,768 CPU cores, showing clearly the suitability of the presented algorithm for the solution of large CFD problems on modern massively parallel distributed memory supercomputers.

The approximation method in the problem on a flow of viscous fluid around a thin plate

2019 ◽  
Vol 91 (6) ◽  
pp. 807-813
Author(s):  
Yanina Berdnik ◽  
Alexey Beskopylny
Keyword(s):  
Viscous Fluid ◽  
Thin Plate ◽  
Approximation Method ◽  
Stokes Equations ◽  
Aircraft Design ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Research Approach ◽  
Navier Stokes Equations ◽  
Content Type

Purpose The paper aims to obtain an effective solution to the problem on a flow of viscous fluid around a thin plate using a new approximation method based on the exact Navier–Stokes equations. Also, correction factors are proposed to improve the obtained solution at high Reynolds numbers. Design/methodology/approach The paper has opted for a method that is based on an approximation scheme for certain perturbations concerning the velocity of the oncoming unperturbed flow behind a leading edge of the plate as a zero approximation step. The perturbations are assumed to be small, far from the plate when compared to the basic flow to justify the linearization. Numerical methods are used for the integral equations at each approximation step. Findings This paper provides the friction force coefficient compared with the classical Blasius solution and the ANSYS results. Also, some diagrams of the velocity distribution in the flow are presented. The first and second approximation steps provide a sufficiently high degree of accuracy. Research limitations/implications Because of the chosen research approach, the results may lack accuracy for low and average Reynolds numbers. Thus, researchers are encouraged to improve the proposed method further. Practical implications The paper includes implications for the development of an aircraft design or a wind turbine design considering a wing as a thin plate at the first approximation. Originality/value This paper provides a new approximation method based on the exact Navier–Stokes equations, in contrast to the known solutions.

scholarly journals Spectral Wave Explicit Navier-Stokes Equations for wave-structure interactions using two-phase Computational Fluid Dynamics solvers

2021 ◽  
Vol 221 ◽  
pp. 108513
Author(s):  
Zhaobin Li ◽  
Benjamin Bouscasse ◽  
Guillaume Ducrozet ◽  
Lionel Gentaz ◽  
David Le Touzé ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Stokes Equations ◽  
Wave Structure ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations

Computational fluid dynamics prediction of hydrodynamic forces on a manoeuvring ship including effects of dynamic sinkage and trim

2017 ◽  
Vol 233 (1) ◽  
pp. 251-266 ◽  
Author(s):  
Yi Liu ◽  
Lu Zou ◽  
Zao-Jian Zou
Keyword(s):  
Fluid Dynamics ◽  
Experimental Data ◽  
Computational Fluid Dynamics ◽  
Stokes Equations ◽  
Hydrodynamic Forces ◽  
Numerical Error ◽  
Navier Stokes ◽  
Container Ship ◽  
Navier Stokes Equations ◽  
Sinkage And Trim

Understanding the manoeuvring performance of a ship requires accurate predictions of the hydrodynamic forces and moments on the ship. In the present study, the hydrodynamic forces and moments on a manoeuvring container ship at various rudder and drift angles are numerically predicted by solving the unsteady Reynolds-averaged Navier–Stokes equations. The effects of dynamic sinkage and trim on the hydrodynamic forces are first investigated together with a grid dependency study to estimate the numerical error and uncertainty caused by grid discretization, and with a validation study combining the experimental data. The results show that the effect of dynamic sinkage and trim is non-negligible, since including it improves the hydrodynamic force predictions and reduces the numerical error and uncertainty, and the averaged error and uncertainty are smaller than the other computational fluid dynamics results where sinkage and trim were fixed with given values from model tests. Therefore, it is included in the subsequent systematic simulations regarding the influence of rudder and drift angles. The computed forces, moments and rudder coefficients at different rudder and drift angles on the container ship are compared with the benchmark model test data. From the computations, all the predicted quantities are in satisfactory agreement with the experimental data. The details of the flow filed and hydrodynamic forces, such as pressure distributions, transverse force distributions along the hull, velocity contours, streamlines and wave patterns are presented and discussed, and a deep insight into the physical mechanism in the hydrodynamic forces on a manoeuvring ship is obtained.

Rapid gust response simulation of large civil aircraft using computational fluid dynamics

2017 ◽  
Vol 121 (1246) ◽  
pp. 1795-1807 ◽  
Author(s):  
P. Bekemeyer ◽  
R. Thormann ◽  
S. Timme
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Stokes Equations ◽  
Lift Coefficient ◽  
Computational Cost ◽  
Aircraft Design ◽  
Navier Stokes ◽  
Surface Pressure Distribution ◽  
Wide Range ◽  
Civil Aircraft

ABSTRACTSeveral critical load cases during the aircraft design process result from atmospheric turbulence. Thus, rapidly performable and highly accurate dynamic response simulations are required to analyse a wide range of parameters. A method is proposed to predict dynamic loads on an elastically trimmed, large civil aircraft using computational fluid dynamics in conjunction with model reduction. A small-sized modal basis is computed by sampling the aerodynamic response at discrete frequencies and applying proper orthogonal decomposition. The linear operator of the Reynolds-averaged Navier-Stokes equations plus turbulence model is then projected onto the subspace spanned by this basis. The resulting reduced system is solved at an arbitrary number of frequencies to analyse responses to 1-cos gusts very efficiently. Lift coefficient and surface pressure distribution are compared with full-order, non-linear, unsteady time-marching simulations to verify the method. Overall, the reduced-order model predicts highly accurate global coefficients and surface loads at a fraction of the computational cost, which is an important step towards the aircraft loads process relying on computational fluid dynamics.

A viscous blade body force model for computational fluid dynamics–based throughflow analysis of axial compressors

2021 ◽  
pp. 095441002199955
Author(s):  
Jian Li ◽  
Jinfang Teng ◽  
Mingmin Zhu ◽  
Xiaoqing Qiang
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Stokes Equations ◽  
Skin Friction Coefficient ◽  
Navier Stokes ◽  
Force Model ◽  
Navier Stokes Equations ◽  
Design Speed ◽  
Airfoil Cascade ◽  
Throughflow Model

In recent years, the computational fluid dynamics (CFD) techniques have attracted enormous interest in the throughflow calculations, and one of the major concerns in the CFD-based throughflow method is the modeling of blade forces. In this article, a viscous blade force model in the CFD-based throughflow program was proposed to account for the loss generation. The throughflow code is based on the axisymmetric Navier–Stokes equations. The inviscid blade force is determined by calculating a pressure difference between the pressure and suction surfaces, and the viscous blade force is related to the local kinetic energy through a skin friction coefficient. The viscous blade force model was validated by a linear controlled diffusion airfoil cascade, and the results showed that it can correctly introduce the loss into the CFD-based throughflow model. Then, the code was applied to calculate the transonic NASA rotor 67, and the calculated results were in good agreement with the measured results, which showed that the calculated shock losses reduce the dependence of the throughflow calculation on the empirical correlation. Last, the 3.5-stage compressor P&W3S1 at 85%, 100%, and 105% of the design speed was performed to demonstrate the reliability of the viscous blade force model in a multistage environment. The results showed that the CFD-based throughflow method can easily predict the spanwise mixing due to the inclusion of the turbulence model, and predicted results were in acceptable agreement with the experimental results. In a word, the proposed viscous blade force model and CFD-based throughflow model can achieve the throughflow analysis with an acceptable level of accuracy and a little time-consuming.

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