scholarly journals On the Kutta Condition in Compressible Flow over Isolated Airfoils

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 102 ◽  
Author(s):  
Farzad Mohebbi ◽  
Ben Evans ◽  
Mathieu Sellier
Keyword(s):  
Numerical Methods ◽  
Finite Difference Method ◽  
Compressible Flow ◽  
Stream Function ◽  
Compressible Flows ◽  
Accurate Method ◽  
Computational Domain ◽  
Kutta Condition ◽  
Trailing Edges ◽  
Comparison Of The Results

This paper presents a novel and accurate method to implement the Kutta condition in solving subsonic (subcritical) inviscid isentropic compressible flow over isolated airfoils using the stream function equation. The proposed method relies on body-fitted grid generation and solving the stream function equation for compressible flows in computational domain using finite-difference method. An expression is derived for implementing the Kutta condition for the airfoils with both finite angles and cusped trailing edges. A comparison of the results obtained from the proposed numerical method and the results from experimental and other numerical methods reveals that they are in excellent agreement, which confirms the accuracy and correctness of the proposed method.

Inviscid Flow Through a Cascade of Thick, Cambered Airfoils: Part 2—Compressible Flow

1973 ◽  
Vol 95 (3) ◽  
pp. 227-232 ◽  
Author(s):  
D. A. Frith
Keyword(s):  
Numerical Methods ◽  
Compressible Flow ◽  
Stream Function ◽  
Inviscid Flow ◽  
Two Dimensional ◽  
Regular Array ◽  
Unique Method ◽  
Flow Through ◽  
Grid Points ◽  
Inviscid Compressible Flow

Evaluation of two-dimensional, inviscid, compressible flow through a cascade of airfoils must involve numerical methods. Some of the associated problems are avoided if the flow field is mapped to the interior of a unit circle as the airfoil boundaries become grid points of the regular array in this domain. Further, far upstream and far downstream map to points in this circle so the uniform inlet and outlet flows are simply defined. For a solution obtained in terms of a stream function the compressible flow may be derived as a numerical perturbation from an analytical, incompressible stream function. A method incorporating these features is described in detail and some results for thick, cambered airfoils in cascade are presented. As supersonic patches can exist on the airfoils for high subsonic inlet Mach numbers, a unique method of relating the density to the stream function is employed in order to enable such flows to be calculated.

scholarly journals Study on the sound absorption behavior of multi-component polyester nonwovens: experimental and numerical methods

2018 ◽  
Vol 89 (16) ◽  
pp. 3342-3361 ◽  
Author(s):  
Tao Yang ◽  
Ferina Saati ◽  
Kirill V Horoshenkov ◽  
Xiaoman Xiong ◽  
Kai Yang ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Absorption Coefficient ◽  
Empirical Model ◽  
Surface Impedance ◽  
Sound Absorption ◽  
Low Frequency ◽  
Accurate Method ◽  
Small Error ◽  
Sound Absorption Coefficient ◽  
Acoustical Properties

This study presents an investigation of the acoustical properties of multi-component polyester nonwovens with experimental and numerical methods. Fifteen types of nonwoven samples made with staple, hollow and bi-component polyester fibers were chosen to carry out this study. The AFD300 AcoustiFlow device was employed to measure airflow resistivity. Several models were grouped in theoretical and empirical model categories and used to predict the airflow resistivity. A simple empirical model based on fiber diameter and fabric bulk density was obtained through the power-fitting method. The difference between measured and predicted airflow resistivity was analyzed. The surface impedance and sound absorption coefficient were determined by using a 45 mm Materiacustica impedance tube. Some widely used impedance models were used to predict the acoustical properties. A comparison between measured and predicted values was carried out to determine the most accurate model for multi-component polyester nonwovens. The results show that one of the Tarnow model provides the closest prediction to the measured value, with an error of 12%. The proposed power-fitted empirical model exhibits a very small error of 6.8%. It is shown that the Delany–Bazley and Miki models can accurately predict surface impedance of multi-component polyester nonwovens, but the Komatsu model is less accurate, especially at the low-frequency range. The results indicate that the Miki model is the most accurate method to predict the sound absorption coefficient, with a mean error of 8.39%.

scholarly journals Fluid Dynamics Android Application: An Efficient Semi-Implicit Solver for Compressible Flows

2019 ◽  
Author(s):  
Shivam Singhal ◽  
Yayati Gupta ◽  
Ashish Garg
Keyword(s):  
Fluid Dynamics ◽  
Numerical Methods ◽  
Language Learning ◽  
Compressible Flows ◽  
General Purpose ◽  
Android Application ◽  
Standard Atmosphere ◽  
Expansion Fan ◽  
Implicit Solver ◽  
Isentropic Flows

The computing power of smartphones has not received considerable attention in the mainstream education system. Most of the education-oriented smartphone applications (apps) are limited to general purpose services like Massive Open Online Courses (MOOCs), language learning, and calculators (performing basic mathematical calculations). Greater potential of smartphones lies in educators and researchers developing their customized apps for learners in highly specific domains. In line with this, we present Fluid Dynamics, a highly accurate Android application for measuring flow properties in compressible flows. This app can determine properties across the stationary normal and oblique shock, moving normal shock and across Prandtl $-$ Meyer expansion fan. This app can also measure isentropic flows, Fanno flows, and Rayleigh flows. The functionality of this app is also extended to calculate properties in the atmosphere by assuming the International Standard Atmosphere (ISA) relations and also flows across the Pitot tube. Such measurements are complicated and time-consuming since the relations are implicit and hence require the use of numerical methods, which give rise to repetitive calculations. The app is an efficient semi-implicit solver for gas dynamics formulations and uses underlying numerical methods for the computations in a graphical user interface (GUI), thereby easing and quickening the learning of concerned users. The app is designed for the Android operating system, the most ubiquitous and capable surveillance platform, and its calculations are based on JAVA based code methodology. In order to check its accuracy, the app's results are validated against the existing data given in the literature.

scholarly journals A comparative analysis of methods: mimetics, finite differences and finite elements for 1-dimensional stationary problems

2021 ◽  
Vol 8 (1) ◽  
pp. 1-11
Author(s):  
Abdul Abner Lugo Jiménez ◽  
Guelvis Enrique Mata Díaz ◽  
Bladismir Ruiz
Keyword(s):  
Numerical Methods ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Difference Method ◽  
Initial Conditions ◽  
Stationary Regime ◽  
Heat Transfer Fluid ◽  
Mimetic Finite Difference Method ◽  
Linear Differential

Numerical methods are useful for solving differential equations that model physical problems, for example, heat transfer, fluid dynamics, wave propagation, among others; especially when these cannot be solved by means of exact analysis techniques, since such problems present complex geometries, boundary or initial conditions, or involve non-linear differential equations. Currently, the number of problems that are modeled with partial differential equations are diverse and these must be addressed numerically, so that the results obtained are more in line with reality. In this work, a comparison of the classical numerical methods such as: the finite difference method (FDM) and the finite element method (FEM), with a modern technique of discretization called the mimetic method (MIM), or mimetic finite difference method or compatible method, is approached. With this comparison we try to conclude about the efficiency, order of convergence of these methods. Our analysis is based on a model problem with a one-dimensional boundary value, that is, we will study convection-diffusion equations in a stationary regime, with different variations in the gradient, diffusive coefficient and convective velocity.

Comparison of numerical methods for the solution of viscous incompressible and low Mach number compressible flow

2018 ◽  
Vol 174 ◽  
pp. 167-178
Author(s):  
Monika Balázsová ◽  
Jan Česenek ◽  
Miloslav Feistauer ◽  
Petr Sváček ◽  
Jaromír Horáček
Keyword(s):  
Mach Number ◽  
Numerical Methods ◽  
Compressible Flow ◽  
Low Mach Number

Numerical Investigation of the Compressible Flow Through a Turbine Center Frame Duct

2018 ◽  
Author(s):  
Li-Wei Chen ◽  
Christian Wakelam ◽  
Jonathan Ong ◽  
Andreas Peters ◽  
Andrea Milli ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Numerical Investigation ◽  
Compressible Flow ◽  
Flow Behavior ◽  
Computational Domain ◽  
Turbulent Structures ◽  
Curvature Effects ◽  
Eddy Simulation ◽  
Static Pressure Distribution

Numerical investigation of the compressible flow in the Turbine Center Frame (TCF) duct was carried out using a Reynolds-averaged Navier-Stokes (RANS) method, and a Hybrid RANS/Large Eddy Simulation (HLES) method, i.e. Stress-Blended Eddy Simulation (SBES). The reference Reynolds number based on the TCF inlet condition is 530,000, and the inlet Mach number is 0.41. It is found that the boundary layer flow behavior is very sensitive to the incoming turbulence characteristics, so the upstream grid used to generate turbulence in the experiment is also included in the computational domain. Results have been validated carefully against experimental data, in terms of static pressure distribution on hub and casing walls, total pressure and Mach number profiles on the TCF measurement planes, as well as over-all pressure loss coefficient. Further, various fundamental mechanisms dictating the intricate flow phenomena, including concave and convex curvature effects, interactions between inlet turbulent structures and boundary layer, and turbulent kinetic energy budget, have been studied systematically. The current study is to evaluate the performance of HLES method for TCF flows and develop a further understanding of unsteady flow physics in the TCF duct. The results obtained in this work provide physical insight into the mechanisms relevant to the turbine intercase or TCF duct flows subjected to complex inlet disturbances.

Code Verification of a Pressure-Based Solver for Subsonic Compressible Flows

2020 ◽  
Vol 5 (4) ◽  
Author(s):  
João Muralha ◽  
Luís Eça ◽  
Christiaan M. Klaij
Keyword(s):  
Compressible Flow ◽  
Incompressible Flow ◽  
Compressible Flows ◽  
Simple Algorithm ◽  
Code Verification ◽  
Weighted Interpolation ◽  
Number Range ◽  
Flow Solver ◽  
Manufactured Solutions ◽  
Method Of Manufactured Solutions

Abstract Although most flows in maritime applications can be modeled as incompressible, for certain phenomena like sloshing, slamming, and cavitation, this approximation falls short. For these events, it is necessary to consider compressibility effects. This paper presents the first step toward a solver for multiphase compressible flows: a single-phase compressible flow solver for perfect gases. The main purpose of this work is code verification of the solver using the method of manufactured solutions. For the sake of completeness, the governing equations are described in detail including the changes to the SIMPLE algorithm used in the incompressible flow solver to ensure mass conservation and pressure–velocity–density coupling. A manufactured solution for laminar subsonic flow was therefore designed. With properly defined boundary conditions, the observed order of grid convergence matches the formal order, so it can be concluded that the flow solver is free of coding mistakes, to the extent tested by the method of manufactured solutions. The performance of the pressure-based SIMPLE solver is quantified by reporting iteration counts for all grids. Furthermore, the use of pressure–weighted interpolation (PWI), also known as Rhie–Chow interpolation, to avoid spurious pressure oscillations in incompressible flow, though not strictly necessary for compressible flow, does show some benefits in the low Mach number range.

Multi-Model Formulation for Compressible Multiphysics and Multiphase Flows: An Efficient Coupling Algorithm

2009 ◽  
Author(s):  
Julien Verhaegen ◽  
Jacques Massoni ◽  
Eric Daniel
Keyword(s):  
Multiphase Flows ◽  
Compressible Flows ◽  
Computational Domain ◽  
Two Phase ◽  
Riemann Solvers ◽  
Two Fluids ◽  
Wave Patterns ◽  
Efficient Coupling ◽  
Coupling Algorithm ◽  
Short Times

A coupling between a general multiphase flows model and a two-phase dilute flow model is presented. Both models are based on Eulerian approach (two fluids models) and compressible flows are considered. This coupling permits to solve problems in which a multiphase description (involving N phases) is necessary to obtain a good physical behavior of the flow on short times: it corresponds to a given location on the computational domain. Then the flow is developing and far from the location of the initial establishment of the flow, a simpler model can be used, for example a dilute two-phase model one. A methodology for coupling both models is necessary in order to get efficient calculations and a physical consistency. This coupling is not only a challenge regarding the computing resources or the programming. We also require that the wave patterns are correctly transmitted through the coupling interface. We then developed specific Riemann solvers that allow the transmission of acoustic or material waves. We also require the preservation of the conservative quantities such as mass, momentum and energy. The method is checked on ID case: propagation of uniform flows, shock tubes. Multidimensional problem are also presented, showing the efficiency of the coupling methodology regarding CPU time.

Study of Afterburning in Solid Rocket Booster Jet: Towards a Model for Afterburning in Large Eddy Simulations

2014 ◽  
Author(s):  
Adèle Poubeau ◽  
Roberto Paoli ◽  
Daniel Cariolle
Keyword(s):  
Three Dimensional ◽  
Axial Direction ◽  
Large Eddy Simulations ◽  
Chemical Mechanism ◽  
Computational Domain ◽  
Time Step ◽  
Simple Method ◽  
Large Eddy ◽  
Solid Rocket ◽  
Comparison Of The Results

This paper focuses on two decisive steps towards Large Eddy Simulation of a solid rocket booster jet. First, three-dimensional Large Eddy Simulations of a non-reactive booster jet including the nozzle were obtained at flight conditions of 20 km of altitude. A particularly long computational domain (400 nozzle exit diameters in the jet axial direction) was simulated, thanks to an innovative local time-stepping method via coupling multi instances of a fluid solver. The dynamics of the jet is analysed and comparison of the results with previous knowledge validates the simulations and confirms that this computational setup can be applied for Large Eddy Simulations of a reactive booster jet. The second part of this paper details the implementation of a simple method to study the hot plume chemistry. Despite its limitations, it is accurate enough to observe the various steps of the chemical mechanism and assess the effect of uncertainties of the rate parameters on chlorine reactions. It was also used to reduce the set of chemical reactions into a short scheme involving a minimum of species and having a limited impact on the physical time step of the Large Eddy Simulations.

Sign in / Sign up

Export Citation Format

Share Document