Computational Fluid Dynamic Prediction of Noise From a Cold Turbulent Propane Jet

Numerical solutions of a turbulent jet flow are used to provide velocity information throughout a simple cold turbulent propane jet at a Reynolds number of 68,000. Predictions provided by the Reynolds-averaged Navier-Stokes simulations, based on a Reynolds stress turbulence model, are compared with experimental data available in the literature. The effect of the modelled inlet boundary conditions on the predicted flow field is described, and the discrepancy between the simulation results and experiment measurements is found to be less than the corresponding variations due to uncertainness in the experimental boundary conditions. In addition, these solutions are used as the basis for noise predictions for the jet based on Lighthill’s theory using the Goldstein broadband noise source formalization that postulates axisymmetric turbulence superposed on the mean flow. The latter model provides an aeroacoustic tool that is reasonable in identifying components or surfaces that generate significant amounts of noise, thereby providing opportunities for early design changes to aircraft and gas turbine components.

Download Full-text

Two-Level Brezzi-Pitkäranta Discretization Method Based on Newton Iteration for Navier-Stokes Equations with Friction Boundary Conditions

Abstract and Applied Analysis ◽

10.1155/2014/474160 ◽

2014 ◽

Vol 2014 ◽

pp. 1-14 ◽

Cited By ~ 1

Author(s):

Rong An ◽

Xian Wang

Keyword(s):

Boundary Conditions ◽

Iteration Method ◽

Numerical Solutions ◽

Stokes Equations ◽

Newton Iteration ◽

Navier Stokes ◽

Discretization Method ◽

Navier Stokes Equations ◽

Stabilized Finite Element Method ◽

The Stability

We present a new stabilized finite element method for Navier-Stokes equations with friction slip boundary conditions based on Brezzi-Pitkäranta stabilized method. The stability and error estimates of numerical solutions in some norms are derived for standard one-level method. Combining the techniques of two-level discretization method, we propose two-level Newton iteration method and show the stability and error estimate. Finally, the numerical experiments are given to support the theoretical results and to check the efficiency of this two-level iteration method.

Download Full-text

Numerical simulations of airflow in the human pharynx of OSAHS patients

Current Directions in Biomedical Engineering ◽

10.1515/cdbme-2016-0003 ◽

2015 ◽

Vol 1 (1) ◽

pp. 552-555

Author(s):

C. Kluck ◽

T.M. Buzug

Keyword(s):

Numerical Solutions ◽

Stokes Equations ◽

Fluid Dynamic ◽

Obstructive Sleep Apnea Patient ◽

Mandibular Advancement ◽

Navier Stokes ◽

Real Patient ◽

Dynamic Simulations ◽

Navier Stokes Equations ◽

Obstructive Sleep

AbstractAbstract: Computational Fluid Dynamic simulations are performed in real patient individual pharynx geometries of an Obstructive Sleep Apnea patient. The Navier-Stokes equations as well as the Reynolds Averaged Navier-Stokes equations and k − ∊ and k −ω turbulence models are used. The velocity profile and pressure distribution of the patient without any treatment and the patient wearing a mandibular advancement appliance are compared to each other. The simulation results for the different model conditions all lead to similar results showing the robustness of the numerical solutions. The pressure loss along the pharynx is lower in the presence of a mandibular appliance, which can indicate the reduction of OSAHS severity.

Download Full-text

Laminar and weakly turbulent oceanic gravity currents performing inertial oscillations

Ocean Science Discussions ◽

10.5194/osd-8-2001-2011 ◽

2011 ◽

Vol 8 (5) ◽

pp. 2001-2045

Author(s):

A. Wirth

Keyword(s):

Mathematical Models ◽

Numerical Solutions ◽

Stokes Equations ◽

Gravity Current ◽

Boussinesq Approximation ◽

Turbulent Fluxes ◽

Navier Stokes ◽

Small Scale ◽

Mean Flow ◽

Inertial Oscillations

Abstract. The small scale dynamics of a weakly turbulent oceanic gravity current is determined. The gravity current considered is initially at rest and adjusts by performing inertial oscillations to a geostrophic mean flow. The dynamics is explored with a hierarchy of mathematical models. The most involved are the fully 3-D Navier-Stokes equations subject to the Boussinesq approximation. A 1-D and 0-D mathematical model of the same gravity current dynamics are systematically derived. Using this hierarchy and the numerical solutions of the mathematical models, the turbulent dynamics at the bottom and the interface is explored and their interaction investigated. Three different regimes of the small scale dynamics of the gravity current are identified, they are characterised by laminar flow, coherent roll vortices and turbulent dynamics with coherent streaks and bursts. The problem of the rectification of the turbulent fluxes, that is how to average out the fluctuations and calculate their average influence on the flow is considered. It is shown that two different regimes of friction are superposed, an Ekman friction applies to the average geostrophic flow and a linear friction, not influenced by rotation, to the inertial oscillations. The combination of the two makes the bulk friction non-local in time for the 0-D model. The implications of the results for parametrisations of the Ekman dynamics and the small scale turbulent fluxes in the planetary boundary layer are discussed.

Download Full-text

RIP CURRENTS ON A BARRED BEACH

Coastal Engineering Proceedings ◽

10.9753/icce.v33.currents.38 ◽

2012 ◽

Vol 1 (33) ◽

pp. 38

Author(s):

Andrea Ruju ◽

Pablo Higuera ◽

Javier L. Lara ◽

Inigo J. Losada ◽

Giovanni Coco

Keyword(s):

Boundary Conditions ◽

Stokes Equations ◽

Numerical Study ◽

Three Dimensional ◽

Wave Generation ◽

Dimensional Structure ◽

Navier Stokes ◽

Rip Currents ◽

Mean Flow ◽

Forcing Mechanisms

This work presents the numerical study of rip current circulation on a barred beach. The numerical simulations have been carried out with the IH-FOAM model which is based on the three dimensional Reynolds Averaged Navier-Stokes equations. The new boundary conditions implemented in IH-FOAM have been used, including three dimensional wave generation as well as active wave absorption at the boundary. Applying the specific wave generation boundary conditions, the model is validated to simulate rip circulation on a barred beach. Moreover, this study addresses the identification of the forcing mechanisms and the three dimensional structure of the mean flow.

Download Full-text

On the Numerical Behavior of RANS-Based Transition Models

Journal of Fluids Engineering ◽

10.1115/1.4045576 ◽

2020 ◽

Vol 142 (5) ◽

Cited By ~ 2

Author(s):

Rui Lopes ◽

Luís Eça ◽

Guilherme Vaz

Keyword(s):

Boundary Conditions ◽

Numerical Solutions ◽

Turbulence Models ◽

Discretization Error ◽

Navier Stokes ◽

Laminar Separation ◽

Aft Model ◽

Transition Models ◽

Distinct Features ◽

Naca 0012

Abstract A comparison of several Reynolds-averaged Navier–Stokes (RANS) based transition models is presented. Four of the most widespread models are selected: the γ−Reθ, γ, amplification factor transport (AFT), and kT−kL−ω models, representative of different modeling approaches. The calculations are performed on several geometries: a flat plate, the Eppler 387 and NACA 0012 two-dimensional (2D) airfoils at two angles of attack, and the SD7003 wing. Distinct features such as the influence of the inlet boundary conditions, discretization error, and modeling error are discussed. It is found that all models present a strong sensitivity to the turbulence quantities inlet boundary conditions, and with the exception of the AFT model, are severely influenced by the decay of turbulence predicted by the underlying turbulence model. This makes the estimation of modeling errors troublesome because these quantities are rarely reported in experiments. Despite not having specific terms in their formulation to deal with separation-induced transition, both the AFT and kT−kL−ω models manage to predict it for the Eppler 387 foil, although presenting higher numerical uncertainty than the remaining models. However, both models show difficulties in the simulation of flows at Reynolds numbers under 105. The γ−Reθ and γ models are the most robust alternatives in terms of iterative and discretization error. The use of RANS compatible transition models allows for laminar flow and features such as laminar separation bubbles to be reproduced and can lead to greatly improved numerical solutions when compared to simulations performed with standard turbulence models.

Download Full-text

The hybrid Euler–Lagrange procedure using an extension of Moffatt's method

Journal of Fluid Mechanics ◽

10.1017/s0022112010002867 ◽

2010 ◽

Vol 661 ◽

pp. 45-72 ◽

Cited By ~ 9

Author(s):

A. M. SOWARD ◽

P. H. ROBERTS

Keyword(s):

Fluid Dynamic ◽

Fluid Motion ◽

Large Eddy Simulations ◽

Navier Stokes ◽

Constant Density ◽

Mean Flow ◽

Tensor Calculus ◽

Inviscid Incompressible Fluid ◽

Large Eddy ◽

The Mean

The hybrid Euler–Lagrange (HEL) description of fluid mechanics, pioneered largely by Andrews & McIntyre (J. Fluid Mech., vol. 89, 1978, pp. 609–646), has had to face the fact, in common with all Lagrangian descriptions of fluid motion, that the variables used do not describe conditions at the coordinate x, upon which they depend, but conditions elsewhere at some displaced position xL(x, t) = x + ξ(x, t), generally dependent on time t. To address this issue, we employ ‘Lie dragging’ techniques of general tensor calculus to extend a method introduced by Moffatt (J. Fluid Mech., vol. 166, 1986, pp. 359–378) in the fluid dynamic context, whereby the point x is dragged to xL(x, t) by a ‘fictitious steady flow’ η*(x, t) in a unit of ‘fictitious time’. Whereas ξ(x, t) is a Lagrangian concept intimately linked to the location xL(x, t), the ‘dragging velocity’ η*(x, t) has an essentially Eulerian character, because it describes the fictitious velocity at x itself. For the case of constant-density fluids, we show, using solenoidal η*(x, t) instead of solenoidal ξ(x, t), how the HEL theory can be cast into Eulerian form. A useful aspect of this Eulerian development is that the mean flow itself remains solenoidal, a feature that traditional HEL theories lack. Our method realizes the objective sought by Holm (Physica D, vol. 170, 2002, pp. 253–286) in his derivation of the Navier–Stokes–α equation, which is the basis of one of the methods currently employed to represent the sub-grid scales in large-eddy simulations. His derivation, based on expansion to second order in ξ, contained an error which, when corrected, implied a violation of Kelvin's theorem on the constancy of circulation in inviscid incompressible fluid. We show that this is rectified when the expansion is in η* rather than ξ, Kelvin's theorem then being satisfied to all orders for which the expansion converges. We discuss the implications of our approach using η* for the Navier–Stokes–α theory.

Download Full-text

Thermoacoustic Stability of Quasi-One-Dimensional Flows–Part I: Analytical and Numerical Formulation

Journal of Turbomachinery ◽

10.1115/1.1791288 ◽

2004 ◽

Vol 126 (4) ◽

pp. 637-644 ◽

Cited By ~ 5

Author(s):

Dilip Prasad ◽

Jinzhang Feng

Keyword(s):

Boundary Conditions ◽

Numerical Solutions ◽

Problem Formulation ◽

Mean Flow ◽

Sonic Point ◽

Impedance Boundary ◽

One Dimensional ◽

Natural Modes ◽

Local Wave ◽

Numerical Formulation

A numerical method is developed for transient linear analysis of quasi-one-dimensional thermoacoustic systems, with emphasis on stability properties. This approach incorporates the effects of mean flow variation as well as self-excited sources such as the unsteady heat release across a flame. Working in the frequency domain, the perturbation field is represented as a superposition of local wave modes, which enables the linearized equations to be integrated in space. The problem formulation is completed by specifying appropriate boundary conditions. Here, we consider impedance boundary conditions as well as those relevant to choked and shocked flows. For choked flows, the boundary condition follows from the requirement that perturbations remain regular at the sonic point, while the boundary conditions applicable at a normal shock are obtained from the shock jump conditions. The numerical implementation of the proposed formulation is described for the system eigenvalue problem, where the natural modes are sought. The scheme is validated by comparison with analytical and numerical solutions.

Download Full-text

Prediction of Combustion Noise in a Model Combustor Using a Network Model and a LNSE Approach

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.4038026 ◽

2017 ◽

Vol 140 (4) ◽

Cited By ~ 1

Author(s):

Wolfram C. Ullrich ◽

Yasser Mahmoudi ◽

Kilian Lackhove ◽

André Fischer ◽

Christoph Hirsch ◽

...

Keyword(s):

Stokes Equations ◽

Hybrid Approach ◽

Noise Spectrum ◽

Broadband Noise ◽

Combustion Noise ◽

Noise Model ◽

Navier Stokes ◽

Minor Importance ◽

Mean Flow ◽

Statistical Noise

The reduction of pollution and noise emissions of modern aero engines represents a key concept to meet the requirements of the future air traffic. This requires an improvement in the understanding of combustion noise and its sources, as well as the development of accurate predictive tools. This is the major goal of the current study where the low-order thermo-acoustic network (LOTAN) solver and a hybrid computational fluid dynamics/computational aeroacoustics approach are applied on a generic premixed and pressurized combustor to evaluate their capabilities for combustion noise predictions. LOTAN solves the linearized Euler equations (LEE) whereas the hybrid approach consists of Reynolds-averaged Navier–Stokes (RANS) mean flow and frequency-domain simulations based on linearized Navier–Stokes equations (LNSE). Both solvers are fed in turn by three different combustion noise source terms which are obtained from the application of a statistical noise model on the RANS simulations and a post-processing of incompressible and compressible large eddy simulations (LES). In this way, the influence of the source model and acoustic solver is identified. The numerical results are compared with experimental data. In general, good agreement with the experiment is found for both the LOTAN and LNSE solvers. The LES source models deliver better results than the statistical noise model with respect to the amplitude and shape of the heat release spectrum. Beyond this, it is demonstrated that the phase relation of the source term does not affect the noise spectrum. Finally, a second simulation based on the inhomogeneous Helmholtz equation indicates the minor importance of the aerodynamic mean flow on the broadband noise spectrum.

Download Full-text

Numerical Computation of the Heat Transfer and Fluid Mechanics in the Laminar Wall Jet and Comparison to the Self-Similar Solutions

Heat Transfer, Volume 2 ◽

10.1115/imece2004-61701 ◽

2004 ◽

Cited By ~ 2

Author(s):

Johnny Issa ◽

Alfonso Ortega

Keyword(s):

Boundary Conditions ◽

Analytical Solutions ◽

Numerical Solutions ◽

Fluid Dynamic ◽

Wall Jet ◽

Temperature Profiles ◽

Computational Domain ◽

Two Dimensional ◽

Self Similar ◽

Laminar and weakly turbulent oceanic gravity currents performing inertial oscillations

Ocean Science ◽

10.5194/os-8-301-2012 ◽

2012 ◽

Vol 8 (3) ◽

pp. 301-317

Author(s):

A. Wirth

Keyword(s):

Mathematical Models ◽

Numerical Solutions ◽

Stokes Equations ◽

Gravity Current ◽

Boussinesq Approximation ◽

Turbulent Fluxes ◽

Navier Stokes ◽

Small Scale ◽

Mean Flow ◽

Inertial Oscillations

Abstract. The small scale dynamics of a weakly turbulent oceanic gravity current is determined. The gravity current considered is initially at rest and adjusts by performing inertial oscillations to a geostrophic mean flow. The dynamics is explored with a hierarchy of mathematical models. The most involved are the fully 3-D Navier-Stokes equations subject to the Boussinesq approximation. A 1-D and 0-D mathematical model of the same gravity current dynamics are systematically derived. Using this hierarchy and the numerical solutions of the mathematical models, the turbulent dynamics at the bottom and the interface is explored and their interaction investigated. Three different regimes of the small scale dynamics of the gravity current are identified, they are characterised by laminar flow, coherent roll vortices and turbulent dynamics with coherent streaks and bursts. The problem of the rectification of the turbulent fluxes, that is, how to average out the fluctuations and calculate their average influence on the flow, is considered. It is shown that two different regimes of friction are superposed, an Ekman friction applies to the average geostrophic flow and a linear friction, not influenced by rotation, to the inertial oscillations. The combination of the two makes the bulk friction non-local in time for the 0-D model. The implications of the results for parametrisations of the Ekman dynamics and the small scale turbulent fluxes in the planetary boundary layer are discussed.

Download Full-text