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Effects Of Extrapolation Boundary Conditions On Subsonic Mems Flows Over A Flat PlateTurgut, Ozhan Hulusi 01 January 2006 (has links) (PDF)
In this research, subsonic rarefied flows over a flat-plate at constant pressure are investigated using the direct simulation Monte Carlo (DSMC) technique. An infinitely thin plate (either finite or semi-infinite) with zero angle of attack is considered. Flows with a Mach number of 0.102 and 0.4 and a Reynolds number varying between 0.063 and 246 are considered covering most of the transitional regime between the free-molecule and the continuum limits. A two-dimensional DSMC code of G.A. Bird is used to simulate these flows, and the code is modified to examine the effects of various inflow and outflow boundary conditions. It is observed that simulations of the subsonic rarefied flows are sensitive to the applied boundary conditions. Several extrapolation techniques are considered for the evaluation of the flow properties at the inflow and outflow boundaries. Among various alternatives, four techniques are considered in which the solutions are found to be relatively less sensitive. In addition to the commonly used extrapolation techniques, in which the flow properties are taken from the neighboring boundary cells of the domain, a newly developed extrapolation scheme, based on tracking streamlines, is applied to the outflow boundaries, and the best results are obtained using the new extrapolation technique together with the Neumann boundary conditions. With the new technique, the flow is not distorted even when the computational domain is small. Simulations are performed for various freestream conditions and computational domain configurations, and excellent agreement is obtained with the available experimental data.
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Caracterização experimental do campo de velocidade e campo acústico de um jato simples subsônico / Experimental characterization of velocity and acoustic fields of single-stream subsonic jetProença, Anderson Ramos 26 September 2013 (has links)
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The purpose of this work is to study and characterize aerodynamically a free jet operating at subsonic regime and identify its acoustic signature. This study aims to analyze fundamentally the turbulent structures and the total noise produced at different Mach numbers. This kind of research is crucial to the understanding of these mechanisms of noise generation and propagation, and it is extremely important for aeronautical applications, for instance, the jet engine exhaust. The research is done by analysing the data obtained in experiments using pitot tube, hot-wire anemometer and acoustic measurements. This work also describes the experimental procedures for each step of analysis, as well as the characteristics of jet noise facilities. The data from measurements with a pitot tube was used to study the mean velocity profiles. The average properties are also analyzed with an anemometry system, likewise used to study the turbulent intensity at eleven axial lines, ranging from the centerline to the edge of the nozzle (lipline). These results are compared with literature and has verified the accuracy of hot-wire anemometers for turbulent intensities lower than 15%. The aerodynamic data are obtained for Mach numbers 0.25, 0.50 and 0.75, from the nozzle exit to thirteen diameters in the direction of the jet. The acoustic study is carried out by analyzing the sound pressure level obtained at six positions in the far field, with observer angles ranging from 40 to 110º. In this campaign more velocities are studied with Mach numbers from 0.18 to 1.00 with step of 0.05 are described. A database with the sound pressure level as a function of frequency is constructed from this information. / O objetivo deste trabalho é estudar e caracterizar aerodinamicamente um jato livre operando em regime subsônico e identificar a assinatura acústica do mesmo. Esse estudo busca analisar fundamentalmente as estruturas turbulentas e o ruído total produzido em diferentes números de Mach. Tal estudo é crucial para o entendimento desses mecanismos de geração e propagação, e encontra extrema importância para aplicações aeronáuticas, como, por exemplo, a exaustão de motores a reação (jato). A investigação é feita através da análise dos dados obtidos em experimentos utilizando tubo de pitot, anemômetro de fio-quente e ensaios acústicos. Neste trabalho também são descritos os procedimentos experimentais de cada etapa de análise, bem como as características dos laboratórios utilizados para o estudo do ruído de jato. Com os dados provenientes das medições com tubo de pitot são estudados os perfis de velocidade média. As propriedades médias também são analisadas com o sistema de anemometria, que ainda é utilizado para estudo da intensidade turbulenta em onze linhas axiais, variando da linha de centro até a borda do bocal (lipline). Estes resultados são comparados com a literatura e é constatada a acurácia dos anemômetros de fio-quente para intensidades turbulentas menores que 15%. Os dados aerodinâmicos mencionados são obtidos para números de Mach 0,25, 0,50 e 0,75, a partir da saída do bocal até treze diâmetros na direção do jato. O estudo acústico é feito através da análise do nível de pressão sonora obtido em seis posições no campo distante, com ângulos de observação variando de 40 a 110º. Diferentes velocidades também foram analisadas, desta vez, com números de Mach de 0.18 a 1.00 com passo de 0.05. Um banco de dados com o nível de pressão sonora em função da frequência é construído a partir destas informações. / Mestre em Engenharia Mecânica
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An Experimental Study of the High-Lift System and Wing-Body Junction Wake Flow Interference of the NASA Common Research Model / En experimentell studie av flödesinterferensen mellan flygplanskropp och vinge för NASA's Common Research ModelBrundin, Desirée January 2017 (has links)
This thesis investigates the turbulent flow in the wake of the wing-body junction of the NASA Common Research Model to further reveal its complex vortical structure and to contribute to the reference database used for Computational Fluid Dynamics validation activities. Compressible flows near two wall-boundary layers occurs not only at the wing-body junction but at every control surface of an airplane, therefore increased knowledge about this complex flow structure could potentially improve the estimates of drag performance and control surface efficiency, primarily for minimizing the environmental impact of commercial flight. The airplane model is modified by adding an inboard flap to investigate the influence from the deflection on the vorticity and velocity field. Future flap designs and settings are discussed from a performance improvement point of view, with the investigated flow influence in mind. The experimental measurements for this thesis were collected using a Cobra Probe, a dynamic multi-hole pressure probe, for Reynolds numbers close to one million based on the wing root chord. A pre-programmed three-dimensional grid was used to cover the most interesting parts of the junction flow. The facility used for the tests is a 120 cm by 80 cm indraft, subsonic wind tunnel at NASA Ames Research Center’s Fluid Mechanics Lab, which provides an on-set flow speed of around Mach 0.15, corresponding to approximately 48 m/s. / Den här avhandlingen undersöker det turbulenta flödet runt övergången mellan flygplanskropp och vinge på en NASA Common Research Model för att vidare utforska den komplexa, tredimensionella strukturen av flödet och bidra till NASA’s officiella databas för jämförelser med simulerade flöden. Kompressibla flöden nära tvåväggsgränsskikt uppkommer inte bara vid övergången mellan flygplanskropp och vinge utan även vid varje kontrollyta på ett flygplan. Ökad kunskap om flödets beteende vid sådana områden kan därför bidra till en bättre uppskattning av prestanda och effektivitet av kontrollytorna och flygplanet i sin helhet, vilket kan bidra till minskad miljöpåverkan från kommersiell flygtrafik. Flygplansmodellen är modifierad genom montering av en vingklaff på den inre delen av vingen, detta för att undersöka hur olika vinklar på klaffarnas nedböjning påverkar flödets struktur och hastighetsfält. Framtida klaffdesigner och inställningar för ökad prestanda diskuteras även utifrån denna påverkan. Mätningarna i vindtunneln gjordes med en Cobra Probe, ett dynamisk tryckmätningsinstrument, speciellt designad för turbulenta och instabila flöden. Reynoldsnumren som generades av den subsoniska, indrags-vindtunneln var ungefär en miljon baserad på vingrotens längd, vilket motsvarar knappt en tiondel av normala flygförhållanden för samma flygplansmodell.
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Experimental and Numerical Study of Endwall Film CoolingMahadevan, Srikrishna 01 January 2015 (has links)
This research work investigates the thermal performance of a film-cooled gas turbine endwall under two different mainstream flow conditions. In the first part of the research investigation, the effect of unsteady passing wakes on a film-cooled pitchwise-curved surface (representing an endwall without airfoils) was experimentally studied for heat transfer characteristics on a time-averaged basis. The temperature sensitive paint technique was used to obtain the local temperatures on the test surface. The required heat flux input was provided using foil heaters. Discrete film injection was implemented on the test surface using cylindrical holes with a streamwise inclination angle of 35? and no compound angle relative to the mean approach velocity vector. The passing wakes increased the heat transfer coefficients at both the wake passing frequencies that were experimented. Due to the increasing film cooling jet turbulence and strong jet-mainstream interaction at higher blowing ratios, the heat transfer coefficients were amplified. A combination of film injection and unsteady passing wakes resulted in a maximum pitch-averaged and centerline heat transfer augmentation of ? 28% and 31.7% relative to the no wake and no film injection case. The second part of the research study involves an experimental and numerical analysis of secondary flow and coolant film interaction in a high subsonic annular cascade with a maximum isentropic throat Mach number of ? 0.68. Endwall (platform) thermal protection is provided using discrete cylindrical holes with a streamwise inclination angle of 30? and no compound angle relative to the mean approach velocity vector. The surface flow visualization on the inner endwall provided the location of the saddle point and the three-dimensional separation lines. Computational predictions showed that the leading-edge horseshoe vortex was confined to approximately 1.5% of the airfoil span for the no film injection case and intensified with low momentum film injection. At the highest blowing ratio, the film cooling jet weakened the horseshoe vortex at the leading-edge plane. The passage vortex was intensified with coolant injection at all blowing ratios. It was seen that increasing average blowing ratio improved the film effectiveness on the endwall. The discharge coefficients calculated for each film cooling hole indicated significant non-uniformity in the coolant discharge at lower blowing ratios and the strong dependence of discharge coefficients on the mainstream static pressure and the location of three-dimensional separation lines. Near the airfoil suction side, a region of coalesced film cooling jets providing close to uniform film coverage was observed, indicative of the mainstream acceleration and the influence of three-dimensional separation lines.
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Effects of Various Shaped Roughness Elements in Two-Dimensional High Reynolds Number Turbulent Boundary LayersBennington, Jeremy Lawrence 14 September 2004 (has links)
Modeling the effects of surface roughness is an area of concern in many practical engineering applications. Many current roughness models to this point have involved the use of empirical 'constants' and equivalent sand grain roughness. These underdeveloped concepts have little direct relationship to realistic roughness and cannot predict accurately and consistently the flow characteristics for different roughness shapes. In order to aid in the development of turbulence models, the present research is centered around the experimental investigation of seven various shaped single roughness elements and their effects on turbulence quantities in a two-dimensional turbulent boundary layer.
The elements under scrutiny are as follows: cone, cone with spatial variations equal to the smallest sublayer structure length scale, cone with spatial variations equal to 2.5 times the smallest sublayer structure length scale, Gaussian-shaped element, hemisphere, cube aligned perpendicular to the flow (cube at 90°), and a cube rotated 45° relative to the flow. The roughness element heights, k+, non-dimensionalized by the friction velocity (U_tau) of the approaching turbulent boundary layer, are 145, 145, 145, 145, 80, 98, and 98 respectively. Analysis of a three-dimensional fetch of the same Gaussian-shaped elements described previously was also undertaken. In order to analyze the complex flow fields, detailed measurements were obtained using a fine-measurement-volume (50 micron diameter) three-velocity component laser-Doppler velocimetry (LDV) system.
The data reveals the formation of a horseshoe vortex in front of the element, which induces the downwash of higher momentum fluid toward the wall. This 'sweep' motion not only creates high Reynolds stresses (v^2, w^2, -uv) downstream of the element, but also leads to higher skin-friction drag. Triple products were also found to be very significant near the height of the element. These parameters are important in regards to the contribution of the production and diffusion of the turbulent kinetic energy in the flow. The 'peakiness' of the roughness element was found to have a direct correlation to the production of circulation, whereas the spatial smoothing does not have an immense effect on this parameter. The peaked elements were found to have a similar trend in the decay of circulation in the streamwise direction. These elements tend to show a decay proportional to (x/d)^-1.12, whereas the cube elements and the hemisphere do not have a common trend.
A model equation is proposed for a drag correlation common to all roughness elements. This equation takes into account the viscous drag and pressure drag terms in the calculation of the actual drag due to the roughness elements presence in the boundary layer. The size, shape, frontal and wetted surface areas of the roughness elements are related to one another via this model equation. Flow drawings related to each element are presented which gives rise to a deeper understanding of the physics of the flow associated with each roughness element. / Master of Science
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An Experimental Study of Turbulent Boundary Layers Subjected to High Free-stream Turbulence EffectsOrsi Filho, Edgar 06 January 2006 (has links)
The work presented in this thesis was on nominally two-dimensional turbulent boundary layers at zero pressure gradient subjected to high free-stream turbulent intensities of up to 7.9% in preparations for high free-stream turbulence studies on three-dimensional boundary layers, which will be done in the future in the Aerospace and Ocean Engineering Boundary Layer Wind Tunnel at Virginia Tech. The two-dimensional turbulent flow that will impinge three-dimensional bodies needed to be characterized, before the three-dimensional studies can be made. An active turbulence generator designed to create high free-stream turbulence intensities in the wind tunnel was tested and modified in order to obtain the lowest possible mean flow non-uniformities. A seven-hole pressure probe was used to obtain planes of mean velocity measurements. A three-component state of the art laser-Doppler velocimeter (LDV) was used to obtain mean and fluctuating velocities. Previous high free-stream turbulence studies have been reviewed and are discussed, and some of the previously published data of other authors have been corrected. Based on the measurements obtained with the LDV, it was also determined that the semi-log law of the wall is valid for high free-stream turbulence cases, but with different constants than the ones proposed by Coles, where the constants for the high free-stream cases may be dependent on the turbulence intensity. For the first time, the skin friction coefficient (Cf) was deduced from the viscous sublayer. The difference between the U_tau obtained in the viscous sublayer mean velocity profile and the U_tau obtained in the semi-log layer was 1.5%. The skin friction coefficient was determined to increase by 10.5% when the two-dimensional turbulent boundary layer was subjected to high free-stream turbulence effects. Spectral data obtained with the LDV, were compared to the von Kármán model spectrum and to the Pope's model spectrum, where the von Kármán spectrum was proven to fit the spectral data slightly better than the Pope's spectrum. Finally, the Hancock-Bradshaw-Blair parameter obtained for this experiment agreed very well with previously published data. / Master of Science
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Objekt-relationsmappning i datacentrerad applikation / Object-Relational Mapping in a Data-Centric ApplicationÖjebo, Erik January 2009 (has links)
<p>Denna rapport presenterar en undersökning av sex olika objekt-relationsmappningsramverk, nämligen Entity Framework, LINQ to SQL, NHibernate, Castle ActiveRecord, MyGeneration Doodads och Subsonic. Undersökningen redogör för styrkor och svagheter hos de olika ramverken samt diskuterar när respektive ramverk är lämpligt att använda.</p><p>De ramverk som bedömdes vara mest intressanta var NHibernate och Entity Framework, då de erbjuder flexibel mappning mellan domänmodellen och det underliggande databasschemat samt god tillgång till dokumentation och litteratur.</p><p>Undersökningen användes som grund för att besluta vilket av de aktuella ramverken som skulle användas vid en omskrivning av en existerande applikation för IT-konsultföretaget Sogeti. Det ramverk som ansågs mest lämpligt för applikationen var NHibernate.</p> / <p>This report presents a study of six different object-relational mapping frameworks, namely Entity Framework, LINQ to SQL, NHibernate, Castle ActiveRecord, MyGeneration Doodads and Subsonic. The study describes the strengths and weaknesses of the various frameworks and discusses when each framework is appropriate to use.</p><p>The frameworks that were judged to be the most interesting were NHibernate and Entity Framework, since they provide flexible mapping between the domain model and the underlying database schema as well as good availability of documentation and literature.</p><p>The study was used as a basis for deciding which of the frameworks that should be used in a rewrite of an existing application for the IT consulting company Sogeti. The framework that was considered the most appropriate for the application was NHibernate.</p>
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Objekt-relationsmappning i datacentrerad applikation / Object-Relational Mapping in a Data-Centric ApplicationÖjebo, Erik January 2009 (has links)
Denna rapport presenterar en undersökning av sex olika objekt-relationsmappningsramverk, nämligen Entity Framework, LINQ to SQL, NHibernate, Castle ActiveRecord, MyGeneration Doodads och Subsonic. Undersökningen redogör för styrkor och svagheter hos de olika ramverken samt diskuterar när respektive ramverk är lämpligt att använda. De ramverk som bedömdes vara mest intressanta var NHibernate och Entity Framework, då de erbjuder flexibel mappning mellan domänmodellen och det underliggande databasschemat samt god tillgång till dokumentation och litteratur. Undersökningen användes som grund för att besluta vilket av de aktuella ramverken som skulle användas vid en omskrivning av en existerande applikation för IT-konsultföretaget Sogeti. Det ramverk som ansågs mest lämpligt för applikationen var NHibernate. / This report presents a study of six different object-relational mapping frameworks, namely Entity Framework, LINQ to SQL, NHibernate, Castle ActiveRecord, MyGeneration Doodads and Subsonic. The study describes the strengths and weaknesses of the various frameworks and discusses when each framework is appropriate to use. The frameworks that were judged to be the most interesting were NHibernate and Entity Framework, since they provide flexible mapping between the domain model and the underlying database schema as well as good availability of documentation and literature. The study was used as a basis for deciding which of the frameworks that should be used in a rewrite of an existing application for the IT consulting company Sogeti. The framework that was considered the most appropriate for the application was NHibernate.
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Experimental And Computational Investigations Of Underexpanded Jets From Elliptical Sonic NozzlesRajakuperan, E 03 1900 (has links)
Three dimensional nozzles and jet flows have attracted the attention of many researchers due to their potential application to many practical devices. Rectangular nozzles are considered for short/vertical take off and landing aircrafts for achieving powered lift. Axisymmetric nozzles with lobes, tabs or slots and elliptical nozzles are considered for noise reduction in aircrafts and mixing augmentation in airbreathing rockets. Interaction of supersonic jets with solid
surface, as in the case of retro and ullage rockets in launch vehicles and interaction of multiple jets as in the case of launch vehicles with multiple booster rockets/multiple nozzle engines are of practical importance. Design of rockets and aircrafts employing these nozzles needs the understanding of the structure and behaviour of the complex three dimensional supersonic jets issuing from these nozzles. The problem is so complex that different investigators have addressed only some specific aspects of the problem and there is much more to be done to fully understand these flows. For example, in the case of rectangular nozzle with semi circular ends (known as elliptical nozzle), the investigations have been limited to a single nozzle of aspect ratio 3,0 and pressure ratio (ratio of the total pressure to ambient pressure) 3.0. Further, the measurements were made in the far field subsonic region beyond a distance of 20 times the equivalent nozzle radius (RJ.
For the present study, the elliptical sonic nozzle of the type mentioned above was chosen, as it offered simplicity for manufacturing and carrying out computations, but has all the complex features associated with the three dimensional jets. A systematic study to understand the mean flow structure and the effect of important governing parameters like
ratio and pressure ratio on the flow development process of the jet issuing from Navier-Stokes equations.
The experimental study revealed many interesting flow features. It was found that the Underexpanded jet issuing from elliptical sonic nozzle spreads rapidly in the minor axis plane while it maintains almost constant width or contracts in the major axis plane. However, the gross spreading of this jet is much higher compared to the axisymmetric jet. The higher spreading rates experienced in the minor axis plane compared to the major axis plane of this 'et, results in the jet width in the minor axis plane to become higher than that in the major axis plane. The longitudinal location, where this occurs is called the axis switching location. This kind of axis switching phenomenon is known to exist for subsonic elliptical jets. However, for the present supersonic jets, the axis switching locations are much closer to the nozzle exit compared to the subsonic cases reported. It was further found that this location strongly depends on the pressure and aspect ratios. A critical pressure ratio was found to exist for each nozzle at which the axis switching location is the farthest. Above the critical pressure ratio, the axis switching location was observed to move upstream with the increase in the pressure ratio and is controlled by the
complex interactions of shock and expansion waves near the nozzle exit. Below the critical pressure ratio, the axis switching location moves upstream with the decrease in pressure ratio and is controlled by some kind of instability in the minor axis plane.
The shock structure present in the underexpanded jet from an elliptical nozzle was also observed to depend on both pressure and aspect ratios. For some aspect ratios and pressure ratios, the shock pattern observed in both the major and minor axis planes are similar to that of an axisymmetric jet, where the incident barrel shock and the Mach reflection (from the edges of the Mach disk) are present. But for all other cases, this shock
continues to be seen only in the major axis plane. Whereas, in the minor axis plane, the incident shock is absent in the shock pattern.
Detailed measurement in the jet cross sectional planes, for the case of aspect ratio 2.0 nozzle, shows that the cross sectional shape changes along the length and it becomes almost a circle at the axis switching location. Further downstream, the jet spreads rapidly in the minor axis plane whereas no significant change in the width of the jet in the major axis plane is observed. Far downstream, the jet boundary appears like a distorted ellipse with its major and minor dimensions lying respectively in the minor and major axis planes of the nozzle. The elongated shape of the jet cross sections at locations downstream of the axis switching point gives the impression that the entire flow in the major axis plane is turned towards the minor axis plane. This effect appears to be predominant at high pressure ratios.
The computed near field shock structure in the planes of symmetry, pitot pressure distributions, cross sectional shape of the jet and the spreading pattern agree very well with the experimental results. In addition to this, the present computational method gives the detailed near field flow structure including the azimuthal extent of the incident shock, cross flow details and distributions of flow variables. It is shown that the present inviscid methodology can also predict the axis switching point accurately if it occurs before the formation of the Mach disk and it demonstrates that the jet growth phenomenon in the near field, atleast, is mainly controlled by the inviscid flow process. The computed results have shown that changes in the jet cross sectional shape in the near field is caused mainly by the interaction of compression and expansion waves with each other and with the constant pressure boundary. The inviscid method seems to be able to capture the complicated secondary cross flow structure (indicating presence of longitudinal vortices) of the elliptical jet.
The complex mean flow structure in the near field region of the jet issuing from elliptical nozzles and the effect of nozzle aspect ratio and pressure ratio on the structure are brought out clearly in the present study. The mechanism governing the spreading and the axis switching characteristics are also brought out. Thus the present experimental and computational investigations give a comprehensive understanding of the mean flow structure of the underexpanded jets issuing from elliptical nozzles. Further studies are required to understand the other aspects of the elliptical jets as well as other three-dimensional jets. Some of these studies are identified for future work.
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Large Eddy Simulation of Free and Impinging Subsonic Jets and their Sound FieldsSubramanian, G January 2014 (has links) (PDF)
Evaluating aerodynamic noise from aircraft engines is a design stage process, so that it conform to regulations at airports. Aerodynamic noise is also a principal source of structural vibration and internal noise in short/vertical take off and landing and rocket launches. Acoustic loads may be critical for the proper functioning of electronic and mechanical components. It is imperative to have tools with capability to predict noise generation from turbulent flows. Understanding the mechanism of noise generation is essential in identifying methods for noise reduction.
Lighthill (1952) and Lighthill (1954) provided the first explanation for the mechanism of aerodynamic noise generation and a procedure to estimate the radiated sound field. Many such procedures, known as acoustic analogies are used for estimating the radiated sound field in terms of the turbulent fluid flow properties. In these methods, the governing equations of the fluid flow are rearranged into two parts, the acoustic sources and the propagation terms. The noise source terms and propagation terms are different in different approaches. A good description of the turbulent flow field and the noise sources is required to understand the mechanism of noise generation.
Computational aeroacoustics (CAA) tools are used to calculate the radiated far field noise. The inputs to the CAA tools are results from CFD simulations which provide details of the turbulent flow field and noise sources. Reynolds-Averaged Navier Stokes (RANS) solutions can be used as inputs to CAA tools which require only time-averaged mean quantities. The output of such tools will also be mean quantities. While complete unsteady turbulent flow details can be obtained from Direct Numerical Simulation (DNS), the computation is limited to low or moderate Reynolds number flows. Large eddy simulations (LES) provide accurate description for the dynamics of a range of large scales. Most of the kinetic energy in a turbulent flow is accounted by the large-scale structures. It is also the large-scale structures which accounts for the maximum contribution towards the radiated sound field. The results from LES can be used as an input to a suitable CAA tool to calculate the sound field.
Numerical prediction of turbulent flow field, the acoustic sources and the radiated sound field is at the focus of this study. LES based on explicit filtering method is used for the simulations. The method uses a low-pass compact filter to account for the sub-grid scale effects. A one-parameter fourth-order compact filter scheme from Lele (1992) is used for this purpose. LES has been carried out for four different flow situations: (i) round jet (ii) plane jet (iii) impinging round jet and (iv) impinging plane jet. LES has been used to calculate the unsteady flow evolution of these cases and the Lighthill’s acoustic sources. A compact difference scheme proposed by Hixon & Turkel (1998) which involves only bi-diagonal matrices are used for evaluating spatial derivatives. The scheme provides similar spectral resolution as standard tridiagonal compact schemes for the first spatial derivatives. The scheme is computationally less intensive as it involves only bi-diagonal matrices. Also, the scheme employs only a two-point stencil.
To calculate the radiated sound field, the Helmholtz equation is solved using the Green’s function approach, in the form of the Kirchhoff-Helmholtz integral. The integral is performed over a surface which is present entirely in the linear region and covers the volume where acoustic sources are present. The time series data of pressure and the normal component of the pressure gradient on the surface are obtained from the CFD results. The Fourier transforms of the time series of pressure and pressure gradient are then calculated and are used as input for the Kirchhoff-Helmholtz integral.
The flow evolution for free jets is characterised by the growth of the instability waves in the shear layer which then rolls up into large vortices. These large vortical structures then break down into smaller ones in a cascade which are convected downstream with the flow. The rms values of the Lighthill’s acoustic sources showed that the sources are located mainly at regions immediately downstream of jet break down. This corresponds to the large scale structures at break down.
The radiated sound field from free jets contains two components of noise from the large scales and from the small scales. The large structures are the dominant source for the radiated sound field. The contribution from the large structures is directional, mainly at small angles to the downstream direction. To account for the difference in jet core length, the far field SPL are calculated at points suitably shifted based on the jet core length. The peak value for the radiated sound field occurs between 30°and 35°as reported in literature.
Convection of acoustic sources causes the radiated sound field to be altered due to Doppler effect. Lighthills sources along the shear layer were examined in the form of (x, t) plots and phase velocity pattern in (ω, k) plots to analyse for their convective speeds. These revealed that there is no unique convective speeds for the acoustic sources. The median convective velocity Uc of the acoustic sources in the shear layer is proportional to the jet velocity Uj at the center of the nozzle as Uc ≈ 0.6Uj.
Simulations of the round jet at Mach number 0.9 were used for validating the LES approach. Five different cases of the round jet were used to understand the effect of Reynolds number and inflow perturbation on the flow, acoustic sources and the radiated sound field. Simulations were carried out for an Euler and LES at Reynolds number 3600 and 88000 at two different inflow perturbations. The LES results for the mean flow field, turbulence profiles and SPL directivity were compared with DNS of Freund (2001) and experimental data available in literature. The LES results showed that an increase in inflow forcing and higher Reynolds number caused the jet core length to reduce. The turbulent energy spectra showed that the energy content in smaller scale is higher for higher Reynolds number.
LES of plane jets were carried out for two different cases, one with a co-flow and one without co-flow. LES of plane jets were carried out to understand the effect of co-flow on the sound field. The plane jets were of Mach number 0.5 and Reynolds number of 3000 based on center-line velocity excess at the nozzle. This is similar to the DNS by Stanley et al. (2002). It was identified that the co-flow leads to a reduction in turbulence levels. This was also corroborated by the turbulent energy spectrum plots. The far field radiation for the case without co-flow is higher over all angles. The contribution from the low frequencies is directional, mainly towards the downstream direction. The range of dominant convective velocities of the acoustic sources were different along shear layers and center-line.
The plane jet results were also used to bring out a qualitative comparison of flow and the radiation characteristics with round jets. For the round jet, the center-line velocity decays linearly with the stream-wise distance. In the plane jet case, it is the square of the center-line velocity excess which decays linearly with the stream-wise distance. The turbulence levels at any section scales with the center-line stream-wise velocity. The decay of turbulence level is slower for the plane jet and hence the acoustic sources are present for longer distance along the downstream direction.
Subsonic impinging jets are composed of four regions, the jet core, the fully developed jet, the impingement zone and the wall jet. The presence of the second region (fully developed free jet) depends on the distance of the wall from the nozzle and the length of the jet core. In impinging jets, reflection from the wall and the wall jet are additional sources of noise compared to the free jets. The results are analysed for the contribution of the different regions of the flow towards the radiated sound field. LES simulations of impinging round jets and impinging plane jet were carried out for this purpose. In addition, the results have been compared with equivalent free jets. The directivity plots showed that the SPL levels are significantly higher for the impinging jets at all angles. For free jets, a typical time scale for the acoustic sources is the ratio of the nozzle size to the jet velocity. This is ro/Uj for round jets and h/Uj for plane jets. For impinging jets, the non-dimensionlised rms of Lighthill’s source indicates that the time scale for acoustic sources is the ratio of the height of the nozzle from the wall to the jet velocity be L/Uj.
LES of impinging round jets was carried out for two cases with different inflow perturbations. The jets were at Reynolds number of 88000 and Mach number of 0.9, same as the free jet cases. The impingement wall was at a distance L = 24ro from the nozzle exit. For impinging round jets, the SPL levels are found to be higher than the equivalent free jets. From the SPL levels and radiated noise spectra it was shown that the contribution from the large scale structures and its reflection from the wall is directional and at small angles to the wall normal. The difference in the range of angles where the radiation from the large scale structures were observed shows the significance of refraction of sound waves inside the flow. The rms values of the Lighthill’s sources indicate two dominant regions for the sources, just downstream of jet breakdown and in the impingement zone.
The LES of impinging plane jet was done for a jet of Mach number 0.5 and Reynolds number of 6000. The impingement wall was at a distance L = 10h from the nozzle exit. The radiated sound field appears to emanate from this impingement zone. The directivity and the spectrum plots of the far field SPL indicate that there is no preferred direction of radiation from the impingement zone. The Lighthill’s sources are concentrated mainly in the impingement zone. The rms values of the sources indicate that the peak values occur in the impingement zone.
The results from the different flow situations demonstrates the capability of LES with explicit filtering method in predicting the turbulent flow and radiated noise field. The method is robust and has been successfully used for moderate Reynolds number and an Euler simulation. An important feature is that LES can be used to identify acoustic sources and its convective speeds. It has been shown that the Lighthill source calculations, the calculated sound field and the observed radiation patterns agree well. An explanation for these based on the different turbulent flow structures has also been provided.
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