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Reynolds Averaged Navier Stokes Computations of Jet Flows Emanating From Turbofan Exhausts Turbofan Egzoz Cikisi Jet Akisinin Reynolds Averaged Navier Stokes Ile Hesaplanmasi
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REYNOLDS-AVERAGED NAVIER-STOKES COMPUTATIONS OF JET FLOWS EMANATING FROM TURBOFAN EXHAUSTS
A THESIS SUBMITTED TO THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES OF MIDDLE EAST TECHNICAL UNIVERSITY
SERPL KAYA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN AEROSPACE ENGINEERING
Approval of the Graduate School of Natural and Applied Sciences
Prof. Dr. Canan ZGEN Director I certify that this thesis satisfies all the requirements as a thesis for the degree of Master of Science.
Prof. Dr. . Hakk TUNCER Head of Department This is to certify that we have read this thesis and that in our opinion it is fully adequate, in scope and quality, as a thesis for the degree of Master of Science.
Prof. Dr. Yusuf ZYRK Supervisor Examining Committee Members Prof. Dr. Yusuf zyrk Prof. Dr. . Hakk Tuncer Assist. Prof. Dr. Ouz Uzol Dr. D. Funda Kurtulu Assist. Prof. Dr. Nilay Sezer Uzol (METU, AEE) (METU, AEE) (METU, AEE) (METU, AEE) (TOBB ETU, ME) ii
I hereby declare that all information in this document has been obtained and presented in accordance with academic rules and ethical conduct. I also declare that, as required by these rules and conduct, I have fully cited and referenced all material and results that are not original to this work.
Serpil KAYA
KAYA, Serpil M.S., Department of Aerospace Engineering Supervisor : Prof. Dr. Yusuf ZYRK
September 2008, 64 pages
This thesis presents the results of steady, Reynolds-averaged Navier-Stokes (RANS) computations for jet flow emanating from a generic turbofan engine exhaust. All computations were performed with commercial solver FLUENT v6.2.16. Different turbulence models were evaluated. In addition to turbulence modeling issues, a parametric study was considered. Different modeling approaches for turbulent jet flows were explained in brief, with specific attention given to the Reynolds-averaged Navier-Stokes (RANS) method used for the calculations.
First, a 2D ejector problem was solved to find out the most appropriate turbulence model and solver settings for the jet flow problem under consideration. Results of one equation Spalart-Allmaras, two-equation standart k-, realizable k-, k- and SST k- turbulence models were compared with the experimental data provided and also with the results of Yoder [21]. The results of SST k- and Spalart-Allmaras turbulence models show the best agreement with the experimental data. Discrepancy with the experimental data was observed at the initial growth region of the jet, but further downstream calculated results were closer to the measurements. Comparing the flow fields for these different turbulence models, it is seen that close to the onset of mixing section, turbulence dissipation was high for models other than SST k- and Spalart-Allmaras turbulence models. Higher levels of turbulent kinetic energy were present in the SST k- and SpalartAllmaras turbulence models which yield better results compared to other turbulence models. The results of 2D ejector problem showed that turbulence model plays an important role to define the real physics of the problem.
In the second study, analyses for a generic, subsonic, axisymmetric turbofan engine exhaust were performed. A grid sensitivity study with three different grid levels was done to determine grid dimensions of which solution does not change for the parametric study. Another turbulence model sensitivity study was performed for turbofan engine exhaust analysis to have a better understanding. In order to evaluate the results of different turbulence models, both turbulent and mean flow variables were compared. Even though turbulence models produced much different results for turbulent quantities, their effects on the mean flow field were not that much significant.
For the parametric study, SST k- turbulence model was used. It is seen that boundary layer thickness effect becomes important in the jet flow close to the lips of the nozzles. At far downstream regions, it does not affect the flow field. For different turbulent intensities, no significant change occurred in both mean and turbulent flow fields.
Keywords: Shear Layer, Axisymmetric Subsonic Jet, Reynolds-averaged Navier-Stokes, Jet Noise, Computational Fluid Dynamics, Turbulence, Ejector.
TURBOFAN EGZOZ IKII JET AKIININ REYNOLDS-AVERAGED NAVIER-STOKES LE HESAPLANMASI
KAYA, Serpil Yksek Lisans, Havaclk ve Uzay Mhendislii Blm Tez Yneticisi : Prof. Dr. Yusuf ZYRK
Eyll 2008, 64 sayfa
tezde
duraan,
Reynolds-averaged
Navier-Stokes
denklemleri
kullanlarak tipik bir turbofan egzoz kndaki jet aknn saysal zmleri sunulmutur. Tm hesaplamalar ticari yazlm FLUENT v6.2.16 kullanlarak yaplmtr. Farkl trblans modelleri kullanlarak yaplan deerlendirmeye ek olarak parametrik bir alma da yaplmtr. Trblansl jet aklarn modellemeye ilikin yaklamlar ksaca aklanm, almada kullanlan RANS metodu detayl olarak ilenmitir. lk olarak, iki boyutlu bir ejektr geometrisi iin zm yaplarak, jet akn modellemeye en uygun trblans modelinin seilmesi ve zc ayarlarnn viii
belirlenmesi istenilmitir. Bir denklemli Spalart-Allmaras, iki denklemli standart k-, realizable k-, k- ve SST k- trblans modelleri ile Yoderin [21] almasnn sonular deneysel veri ile karlatrlmtr. SST k- ve Spalart-Allmaras modelleri deneysel veriye en yakn sonular vermitir. Deneysel veri ile uyumazlk zellikle jetin ilk olumaya balad blgede grlmtr, jetin aa kesimlerinde sonular deneysel veri ile rtmektedir. Ak alanlar karlatrldnda, SST k- ve SpalartAllmaras haricindeki modeller, trblansl alan daha erken yok etmitir. SST k- ve Spalart-Allmaras modelleri ile elde edilen zmlerde ki trblans kinetik enerji seviyesinin daha yksek olduu grlmtr. ki boyutlu ejektr geometrisi iin yaplan almalar, trblans modeli belirlemenin problemin gerek fiziini yanstmas asndan ok nemli olduunu gstermitir. kinci bir alma olarak da gereki boyutlarda, ses alt hzdaki, tipik eksenel simetrik bir turbofan egzoz kndaki ak iin hesaplamalar yaplmtr. farkl seviyede hazrlanan zm alar ile yaplan almalarn sonular deerlendirilerek, parametrik alma iin uygun olan zm a belirlenmitir. Bu konfigrasyon iin de, sz konusu ak artlarnda, farkl trblans modelleri kullanlarak zmler alnmtr. Elde edilen sonular, ortalama ak deerleri ve trblans deikenlerine baklarak kyaslanmtr. Ortalama ak deerleri byk deiiklik gstermezken, trblans deikenlerinde farkllklar gzlemlenmitir. Parametrik alma iin SST k- trblans modeli kullanlmtr. Bu almada snr tabakas kalnlnn ve snr blgelerindeki trblans younluu deerlerinin aka olan etkisi incelenmitir. Snr tabakas kalnl zellikle llenin u ksmlarna yakn yerlerdeki jet akn etkilemitir. Aa kesimlerde ise etkisini yitirdii grlmtr. Trblans younluunun ise hem ortalama hem de trblans deerleri zerindeki etkisinin nemsiz olduu gzlemlenmitir. ix
Anahtar Kelimeler: Kayma Tabakas, Eksenel Simetrik Ses Alt Hzda Jet, Reynolds-averaged Navier-Stokes, Jet Grlts, Hesaplamal Akkanlar Dinamii, Trblans, Ejektr.
To the owner of everything, To My Parents, To KAYA and GLSEREN families
The author wishes to express his gratitude to Prof. Dr. Yusuf ZYRK for guiding this work. The author would also like to thank Assist. Prof. Dr. Ouz UZOL, Dr. D. Funda KURTULU for their help during the thesis work and also to all committee members. Special thanks go to the colleagues and friends of the author, Bra AKAY, Samih A. HAMID, N. Erkin OCER, zgr DEMR, Mustafa KAYA, Tahir TURGUT, Fatih KARADAL, Mehmet KARACA, Evrim DZEMEN, Ali AKTRK. This work wouldnt be done without the support of the authors altruistic parents ule, Hanifi KAYA, and dear sisters Serap, Seval and Sema. This study was supported for two terms by TBTAK (Turkish Research and Science Council). The author would like to thank for the financial support to TBTAK.
ACKNOWLEDGEMENTS ............................................................................ xii TABLE OF CONTENTS.............................................................................. xiii LIST OF TABLES......................................................................................... xv LIST OF FIGURES ..................................................................................... xvi CHAPTER 1.................................................................................................. 1 INTRODUCTION .......................................................................................... 1 1.1 1.2 1.3 Motivation ......................................................................................... 1 Literature Survey .............................................................................. 3 Objectives of the Present Research ................................................. 5
CHAPTER 2.................................................................................................. 7 THEORY OF TURBULENCE MODELING.................................................... 7 2.1 Turbulence Modeling and Simulation .................................................. 7 2.1.1 Direct Numerical Simulation (DNS)............................................... 8 2.1.2 Large Eddy Simulation (LES)........................................................ 8 2.1.3 Reynolds-averaged Navier-Stokes (RANS) .................................. 9 CHAPTER 3................................................................................................ 13 RANS CFD CALCULATIONS OF JET FLOWS .......................................... 13 3.1 RANS Computations for a 2D Ejector Nozzle ................................... 15 3.2.1 Problem Definition ...................................................................... 15 xiii
3.2.2 Computational Details................................................................. 17 3.2.2.1 Computational Grid.................................................................. 17 3.2.2.2 Boundary Conditions ............................................................... 18 3.2.3 Results and Discussion .............................................................. 19 3.3 Generic Turbofan Exhaust Analysis .................................................. 29 3.3.1 Problem Definition ...................................................................... 29 3.3.2 Computational Details................................................................. 30 3.3.2.1 Computational Grid.................................................................. 30 3.3.3.2 Boundary Conditions ............................................................... 33 3.4 Grid Sensitivity .................................................................................. 34 3.5 Turbulence Model Sensitivity............................................................. 37 3.6 Parametric Study............................................................................... 47 3.6.1 Effect of Boundary Layer Thickness on Turbulent Shear Layer.. 47 3.6.2 Effect of Turbulence Intensity ..................................................... 54 CONCLUSION............................................................................................ 59 REFERENCES ........................................................................................... 61
Table 3.1 Flow conditions for ejector nozzle [21]. Table 3.2 Grid Dimensions for three separate zones. Table 3.3 Flow conditions for generic turbofan dual stream engine nozzle. Table 3.4 Grid dimensions of zones.
Figure 1.1 Maximum perceived noise levels for different components [7]. Figure 2.1 Time averaging of velocity. Figure 3.1 Schematic of the two-dimensional ejector nozzle [21]. Figure 3.3 Computational mesh for the 2D ejector. Figure 3.4 Residuals with iterations for SST k- turbulence model. Figure 3.5 Velocity profile for 2D ejector at x=0.0762 m. Figure 3.6 Velocity profile for 2D ejector at x=0.127 m. Figure 3.7 Velocity profile for 2D ejector at x=0.1778 m. Figure 3.8 Velocity profile for 2D ejector at x=0.2667 m. Figure 3.9 Total temperature for 2D ejector profile at x=0.0762 m. Figure 3.10 Total temperature for 2D ejector profile at x=0.2667 m. Figure 3.11 Axial velocity contours for the 2D ejector nozzle calculated with three different turbulence models Figure 3.12 Turbulent kinetic energy (m2/s2) contours for the 2D ejector nozzle calculated with three different turbulence models. Figure 3.13 Sketch of generic turbofan dual stream engine nozzle. Figure 3.14 Three-block computational grid for axsymmetric generic turbofan engine exhausts. Figure 3.15 Details of the computational mesh. Figure 3.16 Schematic of the boundary conditions. xvi
Figure 3.17 Comparison of axial velocity distribution at x=1, 2, 4, 8 m for 3 levels of grids. Figure 3.18 Comparison of turbulence intensity distribution at x=1, 2, 4, 8 m for 3 levels of grids. Figure 3.19 Schematic of the axial locations at which data are represented. Figure 3.20 Axial velocity distribution in radial direction at x=-1.7, -1.5, -0.2, 0 m for different turbulence models. Figure 3.21 Axial velocity distribution in radial direction at x=1, 2, 4, 8 m for different turbulence models. Figure 3.22 Axial velocity distribution in radial direction at x=25, 32 m for different turbulence models. Figure 3.23 Turbulent viscosity distribution in radial direction at x=-1.7, -1.5, 0.2, 0 m for different turbulence models. Figure 3.24 Axial velocity distribution in radial direction at x=-1.7, -1.5, -0.2, 0 m for different turbulent intensities. Figure 3.25 Turbulent viscosity distribution in radial direction at x=-1.7, -1.5, 0.2, 0 m for different turbulence models. Figure 3.26 Turbulent kinetic energy (m2/s2) contours with three turbulent models. Figure 3.27 Axial velocity distribution in radial direction at x=-1.7, -1.5, -0.2, 0 m for different nozzle wall lengths Figure 3.28 Axial velocity distribution in radial direction at x=4, 8, 25, 32 m for different nozzle wall lengths. Figure 3.29 Turbulent kinetic energy distribution in radial direction at x=-1.7, -1.5, -0.2, 0 m for different turbulence models.
Figure 3.30 Turbulent kinetic energy distribution in radial direction at x=4, 8, 25, 32 m for different nozzle wall lengths. Figure 3.31 Turbulent kinetic energy (m2/s2) contours for different boundary layer thickness configurations. Figure 3.32 Axial velocity distribution in radial direction at x=1, 2, 4, 8 m for different turbulent intensities. Figure 3.33 Axial velocity distribution in radial direction at x=25, 32 m for different turbulent intensities. Figure 3.34 Turbulent kinetic energy distribution in radial direction at x=1, 2, 4, 8 m for different turbulent intensities. Figure 3.35. Turbulent kinetic energy distribution in axial direction at x=25, 32 m for different turbulent intensities.
1.1 Motivation
The number of vehicles flying in air has been increasing very fast for both civilian transport and military operation purposes. One of the important things is to take many aspects into account while answering for this growing need. For example, higher performance vehicles are always required which might be possible with powerful engines, but it is important to keep in mind that powerful engines mostly come together with higher level of noise emission and some other atmospheric pollutants. Among these on noise emission levels there are restrictions and regulations set by international organizations which must be obeyed by aircraft manufacturers and airline operators.
There are many research programs including experimental, theoretical and computational investigations to reduce the level of noise and understand the associated complicated physical phenomena [1-6]. One of the intense research focuses in this area is to reduce the jet noise emanating from exhausts of the engines. However, most of todays large transport aircraft are powered by high bypass ratio turbofan engines. This type of engines has reduced jet speeds and consequently reduced jet noise levels. Nevertheless, 1
during especially take-off fan noise may be heard more than other noise components due to increased fan loadings. Fan noise propagates forward through the engine air intake and rearward through the bypass duct, and then radiate to far-field. As can be seen in the Figure 1.1 below, a significant amount of turbomachinery noise is radiated to the far-field through the core and fan exhaust compared to other components [7]. Sound waves exiting the bypass or core ducts radiate to far-field through the exhaust jets. These waves are refracted by the jets and some amplification effects occur during this process.
Total Fan Exhaust Core Exhaust Fan Inlet Combustion Core Airframe Turbine 60 70 80 90 100 110
Maximum perceived noise levels, dB
Figure 1.1 Maximum perceived noise levels for different components [7].
Considering the numerical studies, there are different approaches to predict the far field noise. One of the methods is to use a two-step calculation. First step is based on obtaining mean flow field and the second step corresponds to the prediction of acoustic propagation by using the linearized Euler equations [8-11]. This method brings the necessity of good representation of 2
the background turbulent jet flow field to predict the far-field noise accurately because of the interactions between the acoustic waves and the mean flow. These interactions may cause important refraction and amplification effects [8]. In this approach of predicting the turbomachinery noise radiation from engine exhaust, the required mean flow field is usually obtained by solving the Reynolds-averaged Navier-Stokes equations (RANS). Motivated by this, the present work studies several issues in computation of the mean turbulent flow field for a typical subsonic axisymmetric generic turbofan exhaust configuration, including the effects of turbulence modeling issues. In addition to that, a parametric study is conducted to have a better understanding of their influence on the turbulent jet flow field. One of the parameters is the boundary layer thickness developed inside the core and bypass ducts as well as on the external wall. The second parameter studied is the turbulence intensity at the core and bypass inlet boundaries.
1.2 Literature Survey
As mentioned before, one of the approaches to predict the far field sound is to solve the Euler equations linearized about the mean flow. The mean flow variables interacting with the turbulent structures should be resolved with enough accuracy in order to use as inputs for linearized Euler equations. In the literature, there are many studies for developing models or computational tools to represent the turbulent characteristics of jet flows. For example, Koch et al. [12] investigated subsonic axisymmetric separate flow jets with three flow solvers. Similar two-equation k- turbulence models were implemented in WIND, NPARC, and the CRAFT Navier-Stokes solvers. The results obtained from the three codes were generally in agreement with the experimental data. Their results show that the mixing rate was lower than that indicated by experimental results. The turbulent kinetic energy levels 3
were also lower, which corresponds to the slower mixing rate. Also, the maximum turbulent kinetic energy locations were predicted further downstream compared to the data. There are also many attempts to model the turbulence field by using different turbulence models ranging from algebraic to complex ones. However, there is not a universal model which can be generalized to a wide range of problems. For most jet applications linear two equation k- and k- models are typically used [13, 14]. Besides these linear models, a significant amount of work has been done in the area of advanced RANS models specifically for jets. Kenzakowski et al. [15] made simulations for noise prediction by using advanced turbulence modeling for a range of subsonic and supersonic 3D jets. They compared the data obtained by using advanced explicit algebraic stress model formulation (EASM/J) and an underlying k- turbulence model for a series of nozzles. Both heated and cold jets were considered. Flow field results for the cold jet cases indicate good agreement with available centerline data. Hot jet comparisons were also reasonable. Engblom et al. [16] investigated a series of hot and cold single flow subsonic nozzle flows including a baseline round nozzle and several chevron nozzles. The spreading toward the nozzle centerline was much lower than observed in experiments. Georgiadis et al. [17] investigated a reference subsonic lobed nozzle flow with linear two-equation and explicit algebraic stress turbulence models, and found similar trends. Additionally, far downstream, the computed far field mixing rate was predicted too high. This literature survey shows that, RANS turbulence models are not adequate for accurate prediction of jet flow details.
In addition to the modeling issues of the background flow, there are many studies to understand the physics of the jet flow and effects of some parameters. For example, Gao et al. [18] made a numerical study of nozzle 4
boundary layer thickness on axisymmetric supersonic jet screech tones. The axisymmetric Navier-Stokes equations and the two equation k- turbulence model were solved in the generalized curvilinear coordinate system. They chose a straight nozzle with several different initial boundary layer thicknesses. Their results showed that the nozzle boundary layer thickness has an important influence on the generation of supersonic jet screech tones. They concluded that increasing boundary layer thickness would be an effective way to reduce the supersonic jet screech tones. Viswanatham [19] also carried out a detailed parametric study of the noise from dual-stream jets. He evaluated the importance of the noise generated by primary and secondary shear layers. He aimed to understand principal radiation directions under different operating conditions. It is indicated that the secondary-to-primary jet velocity ratio was an important parameter for mixing noise while its effect is negligible on shock-associated noise. The shock-associated noise was found to be dependent on the geometric details of the nozzle.
1.3 Objectives of the Present Research
The primary goal of this research is to understand the influence of boundary layer thickness and turbulence intensity on the jet flow development issuing from the exhaust of generic turbofan engine geometry. The flow at the inlet boundaries of the engine geometry is subsonic. The flows from the core and the bypass ducts mix and a shear layer develops. Also a highly developed shear layer occurs due to gradients through the flow from bypass duct and co-external flow. Since turbulence plays an important role on the propagation of acoustic waves in these mixing shear layers, it is crucial to model the turbulent flow field accurately. The mean flow and turbulence properties in the jet plume were determined from Computational Fluid 5
Dynamics (CFD) analysis using the Reynolds-averaged Navier-Stokes (RANS) equations. Different turbulence models were used to close the RANS equations and a sensitivity analysis was made.
The thesis is organized as follows. In Chapter 2, different approaches to simulate such turbulent jet flows are explained. Special focus is given on the Reynolds-averaged Navier-Stokes (RANS) modeling with brief explanations on two other approaches; Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES). Chapter 3 is dedicated to the details of the RANS CFD analysis for two different problems. First one is a 2D ejector problem with experimental data [20, 21]. The aim to solve this problem is to asses the flow solver and solver settings and compare with the experimental data. All computational details are given. To have a better understanding, turbulence model sensitivity study is also conducted for this case. The second problem is a subsonic, axisymmetric generic turbofan engine nozzle with realistic dimensions and operating conditions. The goal is to conduct a study to understand the influence of some parameters on the mean flow field which might cause different noise level predictions. The proposed parameters can be listed as the effect of boundary layer thickness, and influence of turbulence intensity at the inlet boundaries. Also, discussions for the grid and turbulence model sensitivity are provided. The concluding remarks are presented in the final section.
THEORY OF TURBULENCE MODELING
2.1 Turbulence Modeling and Simulation
To simulate turbulent flows, many computational approaches and models have been proposed and many are in use [22-28]. However, it is difficult to develop an accurate theory or universal model for all types of turbulent flows. In turbulent flows, the velocity field is three dimensional, time dependent, and random. The largest turbulent motions are almost as large as the characteristics width of the flow. Since the characteristic lengths change with the boundary geometry, the largest turbulent motions are specific to problem under consideration. As a result, there is a large range of time scales and length scales. Relative to the largest scales, the smallest timescale decreases as Re-1/2 and the smallest length scale as Re-3/4 [29]. Therefore, resolving all the length and time scales of turbulent flows is a difficult task.
As mentioned above, there are different simulation approaches to model a turbulent flow field. Direct numerical simulation (DNS), large eddy simulation (LES), and Reynolds-averaged Navier-Stokes (RANS) are used to calculate the turbulent flows. In this study, calculations were carried out by using only 7
RANS modeling, since the computational cost of DNS and LES is too high for Reynolds number on the order of 1.5 million. For the sake of completeness, brief explanations were also presented for DNS and LES methods.
2.1.1 Direct Numerical Simulation (DNS) In direct numerical simulation (DNS), the time dependent Navier-Stokes equations are solved and all of the relevant length scales in the turbulent flow are resolved. Since the time history of the entire unsteady turbulent flow field is known, no turbulence modeling is required. It is conceptually the simplest approach and provides the best accuracy. However, since all length scales and time scales have to be resolved, DNS is computationally expensive. The computational cost increases so rapidly with Reynolds number, therefore this approach is currently limited to flows with low-tomoderate Reynolds numbers, on the order of 3,000-4,000 for turbulent jets [29]. As a result, this approach is not feasible for the high Reynolds number application of modern jet engines.
2.1.2 Large Eddy Simulation (LES) In large eddy simulation, the larger three-dimensional unsteady turbulent motions are directly resolved, whereas effects of the smaller scale motions are modeled. A spatial filter is applied to remove the small scales that are not resolved by the grid [29]. Because the large scale unsteady motions are represented explicitly, LES gives accurate and reliable results. However, presently it is not practical to perform LES calculations for Reynolds numbers that are consistent with modern jet engines, which can be on the order of 10 million. When the internally mixed flow region is included, near 8
solid wall boundaries grid resolution becomes higher which increase the computational cost significantly. Therefore, LES approach is also not applicable for the real jet problems.
2.1.3 Reynolds-averaged Navier-Stokes (RANS) The turbulent motion could be easily included into the Navier-Stokes equations. Statistical methods are used to average the fluctuating properties of flow in the turbulent case. To obtain the mean values, there are different averaging techniques such as time, spatial and ensemble averaging. For homogenous turbulence with uniform turbulent flow in all directions, spatial averaging is used. For stationary turbulence on the average, does not vary with time, time averaging is used. But ensemble averaging is the most suitable averaging for flows decaying in time. For the flows that engineers mostly deal with, time averaging is used. Time averaging yields an average and a fluctuating part for a certain variable. These parts could be represented as the part of the instantaneous parameter, for example, velocity.
ui ( x, t ) = Ui ( x) + ui( x, t )
(2.1 )
Here ui ( x, t ) is expressed as the instantaneous velocity with, U i ( x ) ; average and ui ( x, t ) fluctuating part.
Figure 2.1 Time averaging of velocity.
If this instantaneous velocity given in Equation 2.1 is added into the NavierStokes equations and then time averaging is applied, so called Reynolds Averaged Navier-Stokes (RANS) equations are obtained.
U i U i P ' ' + U j = + 2 S ji u j ui t x j xi x j
( 2.2 )
The quantity u j ui is known as the Reynolds-stress tensor. In order to
determine the mean-flow properties of the turbulent flow, the value of the Reynolds stress tensor should be found. The mean flow variables could be solved (or computed) in the same manner as Navier-Stokes equations, but the Reynolds stress tensor must be modeled.
Prandtl suggested a model for the eddy viscosity in which the eddy viscosity is dependent on the kinetic energy of turbulent fluctuations, k. It was the first introduction of one-equation turbulence model. Kinetic energy per unit mass is described and related to the Reynolds stress tensor as,
k=
2 2 1 '2 u + v ' + w' 2
ii = ui ' ui ' = 2 k
Implementation of this relation into Reynolds stress tensor resulted in a transport equation for the turbulent kinetic energy,
U i k k k 1 1 ' ' ' ' +U j = ij + ui ui u j P ' u j ( 2.4 ) { t x x x j x 2 4 3 2 3 14 244j 4 3 1 2 3 DISSIPATION 4 4j 1 3 14 244 14 4 2j TURBULENT MOLECULAR PRESSURE SUBSTANTIAL PRODUCTION TRANSPORT DIFFUSION DERIVATIVE DIFFUSION
Each term has a different meaning regarding the turbulent flow. Production term could be regarded as the mechanism of kinetic energy of the mean flow turning into turbulent kinetic energy where as dissipation appears to be the term describing the turbulent kinetic energy dissipated as thermal energy. Last three diffusion terms could be explained as the turbulent energy diffusion by fluids natural molecular transport, diffusion by turbulent fluctuations and turbulent transport from pressure and velocity fluctuations in the order of appearance.
The turbulence models do not involve a length scale. Since the turbulent viscosity includes a velocity and a length scale (on dimensional grounds, the
2 kinematic viscosity appears to be in m
that is the product of a velocity
and a length scale), the models without involving a length scale are regarded as incomplete.
Kolmogorov introduced the first complete turbulence model by presenting a time scale known as the rate of dissipation of energy in unit volume and time and represented as . The absent length scale is provided by k
k is analogue to the dissipation rate . This success of additional
equation showed up as the introduction of two-equation turbulence models. Since the dissipation term in the k equation is evaluated by another transport for , the model is complete. Second equation appears as,
+U j = 2 + t x j x j
T x j
Later Wilcox [29] had modified the Kolmogorovs equation and formed new correlations. Given the basic RANS formulation with one and two equation formulas, Reference 29 should be referred as a source for detail explanations.
RANS CFD CALCULATIONS OF JET FLOWS
For many years, Reynolds-averaged Navier-Stokes (RANS) methods have been used to calculate turbulent jet flow fields. The reason behind the common usage of RANS methods is the low computational cost for industrial flows compared to higher order methods like large eddy simulation (LES) or direct numerical simulation (DNS). RANS methods replace all turbulent fluid dynamics effects with a turbulence model. However, such turbulence models have limitations. For jets with significant three-dimensionality, compressibility, and high temperature streams, turbulence models are not capable to yield accurate results [30, 31]. CFD analysis based on the RANS equations uses models for the turbulence that employ many ad hoc assumptions and empirically determined coefficients. Typically, these models cannot be applied with confidence to a class of flow for which they have not been validated.
In this chapter, comparisons of the RANS calculations with different turbulence models, mostly used in literature for jet flows were made. First part of the chapter includes the computational results for a 2D ejector nozzle test case found from literature. It is aimed to set the proper solver settings and once comparable results with the measurements were achieved, similar boundary conditions and solver settings were applied to the generic turbofan 13
engine exhaust flow analyses in the second part. Before making a parametric study on the generic turbofan engine exhaust flow, different turbulence models have been evaluated for the sake of better understanding of the sensitivity of the solution to turbulence modeling. Besides the turbulence model variation, a grid study was performed to find out the grid dimensions of which solution does not change. Choosing the turbulence model and grid, a study was performed to understand the influence of some parameters on the flow physics.
The parametric study includes two issues. First one aims to understand effect of the different boundary layer thicknesses on the developing shear layers from the core and bypass ducts. Second item is related with the effect of turbulence intensity values at the bypass, core and free stream inlet boundaries which are unknown prior to analyses in most of real applications.
It is proposed that the length of the core and bypass nozzle changing the boundary layer thickness at the lip of the nozzles might have a significant influence on the developed shear layer. For jet simulations finite domain is used to decrease the computational cost. Therefore, influence of the thickness of the boundary layer has been neglected. In a recent study, it was shown that it has a significant effect on the screech tones of supersonic jet [18]. In this study, main concern is to see the influence of boundary layer thickness for subsonic jets. For this aim, length of the core and bypass duct walls were doubled. Both the mean and the turbulent state variables were compared for different boundary layer thicknesses.
A second parametric study was performed for different turbulent intensities. The turbulent intensities at the inflow boundaries are usually not well known and the values are estimated in analyses. In order to see the sensitivity of the flow to the turbulence intensity, the results of the parametric study were evaluated.
3.1 RANS Computations for a 2D Ejector Nozzle
In this section, it is aimed to determine if the RANS calculations can capture the experimentally observed jet flow development for the 2D ejector geometry. Different turbulent models were chosen for the computations and the one which shows the best agreement with the measurements was used to further examine details of the developing dual stream jets for the generic turbofan engine exhaust problem.
3.2.1 Problem Definition The turbulent flow through a two-dimensional ejector nozzle consisted of a slot type primary nozzle and a two-dimensional mixing section was tested by Gilbert and Hill [20] as shown schematically in Figure 3.1. The experimental setup consists of a rectangular variable area channel formed by symmetrically contoured upper and lower walls and the two flat sidewalls. The widths of both the primary nozzle discharge slot and the mixing section were 0.2032 m. Other dimensions of the system were shown in Figure 3.1. Suction slots were placed in the corners of the mixing section to prevent flow separation.
In this flow, the turbulent mixing occurs between the primary jet and entrained secondary air. Another feature of the problem is the interaction with the wall boundary layers. The experimental data to be used for comparison purposes consists of velocity and temperature measurements at several axial locations. The inflow conditions used in the numerical computations were listed in the Table 3.1.
Table 3.1 Flow conditions for ejector nozzle [21]. Pt (Pa) Secondary Inlet Primary Nozzle Downstream 101559.7 246349.6 92734.5(static) Tt (K) 305.6 357.8 305.6 Mach number 0.2 0.07
Figure 3.1 Schematic of the two-dimensional ejector nozzle [21].
As shown in Table 3.1, the temperature gradient is not high between the primary nozzle and secondary inlet whereas a high pressure difference occurs. The flow in the primary nozzle is very slow compared to the secondary inlet. Therefore, we expect a highly developed shear layer between the two streams. Comparisons were made between the FLUENT v6.2.16 realizable k-, standard k-, Shear Stress Transport (SST) k-, Spalart-Allmaras turbulence models and the experimental results. Also, the results found from the literature obtained with the WIND solver were presented [21].
3.2.2 Computational Details The fluid flow was simulated by solving steady, compressible, 2D, Reynoldsaveraged Navier-Stokes equations using an implicit, coupled, second order, up-wind flux-difference splitting finite volume scheme and with variable turbulence models. The computational grid and the boundary conditions were explained in the following sections.
3.2.2.1 Computational Grid Due to the symmetric nature of the ejector nozzle and mixing section, only half of the ejector was modeled numerically. The 131x121 mesh of Georgiadis, Chitsomboon, and Zhu [32] was used in these calculations. Only format of the grid was modified in order to make it compatible with FLUENT v6.2.16. The grid was packed to solid surfaces such that the first point of the wall corresponded to a y+ between 0.1 and 1.6, depending on the flow conditions as can be shown in the Figure 3.2. The viscous sublayer was resolved well. The grid was composed from three blocks for the primary 17
inflow, secondary inflow and mixing regions. Relative size of each block was shown in Table 3.2.
Table 3.2 Grid Dimensions for three separate zones. Axial Direction Primary Nozzle Secondary Flow Mixing Section 31 31 101 Radial Direction 41 71 121
Figure 3.2 Wall y+ values for the nozzle and upper contoured walls.
3.2.2.2 Boundary Conditions A schematic of the boundary conditions that are applied to each region of the computational grid was shown in Figure 3.3. No slip condition was 18
applied at wall boundaries, and walls were assumed to be adiabatic. Pressure inlet boundary condition was used for the primary nozzle and secondary flow inlets; total pressures and total temperatures were specified. Pressure outlet boundary condition was applied to the downstream boundary, flow parameters were extrapolated from the interior. Symmetry boundary condition, zero gradients were typically specified on the centerline. Even though not shown in the figure, no slip boundary condition was applied on the ejector wall.
Figure 3.3 Computational mesh for the 2D ejector.
3.2.3 Results and Discussion As mentioned earlier, different turbulent models were used in the calculations. The results of the standard k-, realizable k-, Spalart-Allmaras and the SST k- turbulence models in FLUENT v6.2.16 code were compared with the experimental data. The results carried out with WIND k- turbulence model by Yoder [21] was also compared with the FLUENT v6.2.16 results.
For the FLUENT v6.2.16 solutions, total 26000 iterations were done to have a converged solution. Numerical stability problem appeared at the first 19
iterations due to developing shear layer between the primary and secondary flows. Courant number (CFL) was gradually increased to have a better convergence. First 8000 iterations were run with a CFL of 0.5, the next 4000 iterations with a CFL of 1, next 4000 with 2 and rest iterations were run by setting CFL to 3. Continuity, axial velocity, momentum and energy residuals for SST k- turbulence model are shown in the Figure 3.4, as representative. The residuals of the variables dropped four to seven orders of magnitude, which is enough to assume a converged solution.
Figure 3.4 Residuals with iterations for SST k- turbulence model.
Figure 3.5, Figure 3.6, Figure 3.7 and Figure 3.8 show the axial velocity profiles obtained by using different turbulence models at x= 0.0762 m, 0.127 m, 0.1778 m and 0.2667 which were measured relative to the primary nozzle exit plane and the vertical positions relative to the centerline. The vertical positions were nondimensionalized by the local half-duct length.
In literature, for most of the jet flow problems k- model has been used in RANS calculations. However, for the given problem as can be seen from Figure 3.5 to Figure 3.8, FLUENT v6.2.16 SST k- and Spalart-Allmaras turbulence models produce closer results to the experimental data. Except at x=0.2667 m, all turbulence models underpredict the axial velocity distribution. The velocity peak at the centerline was overpredicted for all turbulence models under consideration.
As can be seen in Figure 3.5, at x=0.0762 m , at the first axial station, all turbulence models of FLUENT v6.2.16 code and k- model with compressibility correction of WIND code underpredict the axial velocity in the mixing shear layer. The realizable k- turbulence model of FLUENT v6.2.16 code and k- model of the WIND code give comparable results. In the mixing shear layer they underpredict the velocity distribution and give higher peak velocities at the centerline. At x=0.127 m, there is still discrepancy with the experimental data. The trend for the axial velocity profile is similar at x=0.0762 m. All models underpredict velocity in the mixing layer and higher peaks at the centerline. However, agreement with the experimental data at this station is better compared to x=0.0762 m which is closer to the mixing section. Here, again SST k- and Spalart-Allmaras turbulence models yield the best results.
At farther downstream, at x=0.1778 m, the results are in good comparison with the experimental data. There is still a discrepancy between the WIND results and the experiment; however, SST k- turbulence model result matches with the experimental data well. Spalart-Allmaras turbulence model
slightly overpredicts compared to the experimental data and the SST k- turbulence model results.
Comparing the total temperature profiles at two axial locations; (1) close to the lip of the nozzle and (2) at the downstream region, again there is a mismatch with the experimental data. Figure 3.9 and Figure 3.10 show the total temperature profiles at x=0.0762 m and x=0.266 meters, respectively. It is interesting to note neither SST k- nor Spalart-Allmaras turbulence models show no significant improvement compared to standard k- model as in the case of axial velocity distribution. Looking the contour plots for the x velocity and turbulent kinetic energy, the difference in the solutions can be understood better. Figure 3.11 shows the x axial velocity distribution for three different turbulence models. As can be seen, the flow in the primary nozzle accelerates in the convergent sections of the ejector such that it exceeds the speed at the secondary inlet. At the lip of the ejector, two streams start to mix composing the shear layer. The potential core lengths can be observed clearly in Figure 3.11. As shown, realizable k- and standard k- turbulence models yield similar results whereas the potential core length is shorter for SST k- turbulence model.
Similar to velocity distribution, turbulent kinetic energy profiles also shed light on the reasons for the different solutions. As shown in Figure.3.12, the turbulent kinetic energy diffuses in the downstream region more in the SST k- turbulence model compared to realizable and standard k- turbulence models. There is higher level of turbulent kinetic energy in close regions where mixing starts for the SST k- turbulence model. In realizable and standard k- turbulence models, this kinetic energy is dissipated. 22
Velocity Profile at x=0.0762 m
0 0 50 100 150 200 250 300 350 400
Velocity (m/s)
Experiment WIND k-epsilon [21] FLUENT Realizable k-epsilon FLUENT Standart k-epsilon FLUENT SST k-omega FLUENT Spalart-Allmaras
Figure 3.5 Velocity profile for 2D ejector at x=0.0762 m.
Velocity Profile at x=0.127 m
0 0 50 100 150 200 250 300 350
Figure 3.6 Velocity profile for 2D ejector at x=0.127 m.
0 0 50 100 150 200 250 300
Experiment WIND k-epsilon [21]
FLUENT Realizable k-epsilon FLUENT Standart k-epsilon
FLUENT SST k-omega FLUENT Spalart-Allmaras
Total Temperature Profile at x=0.0762 m
Total Temperature (K)
FLUENT SST k-omega FLUENT Spallart-Allmaras
Figure 3.9 Total temperature for 2D ejector profile at x=0.0762 m.
Figure 3.10 Total temperature for 2D ejector profile at x=0.2667 m (10.5 in).
Figure 3.11 Axial velocity (m/s) contours for the 2D ejector nozzle calculated with three different turbulence models. 26
Figure 3.12 Turbulent kinetic energy (m2/s2) contours for the 2D ejector nozzle calculated with three different turbulence models.
For the simulations, no values at the boundaries were given for turbulent variables in the experiment. In the simulations 2% of turbulence intensity was assumed. As shown in SST k- results, higher level of turbulence at the mixing region occurs, which results in better agreement with the experimental measurements.
To conclude, there is a deficiency for accurate prediction of the initial jet growth region. At further downstream regions, results get closer to the experimental data. Comparing the different turbulence models, SST k- and Spalart-Allmaras turbulence models are the most promising to yield better results. For SST k- turbulence model, turbulence intensity can be defined directly as boundary condition whereas it is not possible for Spalart-Allmaras turbulence model. Since a parametric study concerning the turbulence intensity will be conducted, SST k- turbulence model is chosen to be proper for further calculations of the second turbofan dual stream jet flow problem.
3.3 Generic Turbofan Exhaust Analysis
3.3.1 Problem Definition Realistic geometry and engine conditions were chosen to enhance the usefulness of the data obtained. The effects of boundary layer thickness and the turbulence intensity on turbulent shear layers emanating from the exhaust of the turbofan were evaluated in the presence of an external coflowing stream.
Figure 3.13 Sketch of generic turbofan dual stream engine nozzle. The conditions at the inflow boundaries were given in Table 3.3, below. The flow in the core is high temperature with a higher level of turbulence while the flow in the fan is at higher pressure, lower temperature and at higher speed. There are high velocity and pressure gradient between the fan stream and the external co-flowing stream composing the shear layer.
Given the total values at the inflow boundaries, the static values were calculated by using isentropic relations to apply as boundary conditions.
Table 3.3 Flow conditions for generic turbofan dual stream engine nozzle. Core Pt (Pa) Tt (K) Mach Turbulence intensity 140000 720 0.68 10% Fan 165000 300 0.85 6% Free stream 106000 287 0.22 1%
3.3.2 Computational Details For the background turbulent shear flow computations, as in the validation case, FLUENT 6.2.16 was used. The computational grid was constructed by using CFD-GEOM program. The details for the computational grid, boundary conditions were given in the following parts. The fluid flow was simulated by solving steady, compressible, axisymmetric, Reynolds-averaged NavierStokes equations using an implicit, segregated, second order, up-wind fluxdifference splitting finite volume scheme and with various turbulence models.
3.3.2.1 Computational Grid As mentioned above, the grid was created in CFD-GEOM program. This is a multiblock grid, with 3 blocks as shown in Figure 3.14, below. The domain extends 50 radius in axial direction and 30 radius in radial direction. The extent in the axial direction is enough to have a developed shear layer and far enough in the radial direction to apply far field boundary condition. Since the problem is axisymmetric, only half of the model was meshed to save computational time.
Table 3.4 Grid dimensions of zones. Axial Direction Zone1 (Core flow) Zone2 (Fan flow) Zone3 (Free stream) 747 1013 981 Radial direction 101 101 211
Grid dimensions for different zones were shown in Table 3.4. As can be seen, the grid is sufficiently fine in the axial direction to resolve the rapid changes occurring in the shear layer. Especially, in the interior region of the zones the grid lines were packed near the primary and secondary shear layers. The grid was also clustered near the solid boundaries so that giving a y+ of 1. This value corresponds to wall normal grid spacing of 10-6 m for the flow conditions under consideration. This resolution is proper for all the turbulence models applied here. The close view of the grid was shown in the Figure 3.15.
Figure 3.14 Three-block computational grid for axsymmetric generic turbofan engine exhausts.
Figure 3.15 Details of the computational mesh.
3.3.3.2 Boundary Conditions A schematic of the boundary conditions that are applied to each region of the computational grid was shown in Figure 3.16. No slip condition was applied at wall boundaries, and walls were assumed to be adiabatic. Pressure inlet boundary condition was used for the core, bypass stream inlets and at free stream inlets; total pressures and total temperatures were specified. Free stream boundary condition was used on the outer boundaries to represent the simulated flight stream, and the inflow Mach number was specified. Pressure outlet boundary condition was applied to the downstream boundary, flow parameters were extrapolated from the interior. Axis boundary condition, i.e., zero gradients was typically specified on the centerline.
Figure 3.16 Schematic of the boundary conditions.
When the realizable k-, k- and SST k- turbulence models were selected, the turbulence intensity and turbulent viscosity ratios were specified at the inflow and free stream boundaries. For all of the turbulence models stated, 33
these values were specified using the following assumptions: (1) the core and bypass streams had an inflow turbulence intensity of 6% and 10%, respectively, (2) the free stream had an inflow turbulence intensity of 2%, (3) the core and bypass streams had a turbulence viscosity ratio of 100, and free stream had a turbulent viscosity ratio of 10. Those values correspond to fully turbulent flows. These values are typical for the background turbulence levels in jet flow experiments.
3.4 Grid Sensitivity
Three levels of grids were created to find out the grid independent solution. They were labeled as coarse, medium and fine grids. The coarse grid was built by decreasing one of every other two grid lines in the axial and radial directions. Fine grid was made by increasing the grid dimensions in the axial direction only. For all three levels, height of the first cell was kept constant to make sure the viscous sub layer is well resolved near the wall regions for all the grids. The medium grid for the generic turbofan engine nozzle contains 384,751 cells grid points. As shown in the Figure 3.17 below, at four different axial locations velocity profiles were compared for three levels of grid. The turbulence intensity profiles for all grid levels were shown in the Figure 3.18. The velocity profiles essentially do not vary between the medium and fine grid levels, whereas there is a slight difference with the coarse grid. When we look at the turbulence intensity profiles, as can be seen there is a discrepancy for all three level grids at the downstream regions x=4 m and x=8 m where primary flow mixes with the secondary fan flow. Since mean flow quantities do not vary and the aim is not to validate but to understand the effects of some parameters, further grid sensitivity analyses were not performed. The medium level great was used for further analyses. 34
Axial Velocity at x=1 m
Figure 3.17 Comparison of axial velocity distribution at x=1, 2, 4, 8 m for 3 levels of grids. 35
Turbulence Intensity at x=1 m
Figure 3.18 Comparison of turbulence intensity distribution at x=1, 2, 4, 8 m for 3 levels of grids. 36
3.5 Turbulence Model Sensitivity
This section aims to compare four different turbulence models to get a better understanding the influence of turbulence modeling on the complex shear flow. Spalart-Allmaras, realizable k-, k- and Shear Stress Transport (SST) k- turbulence models of FLUENT solver were chosen to assess the modeling issue.
Spalart-Allmaras turbulence model solves the single transport equation for a modified turbulent viscosity which is used to compute turbulent stresses and so on. It is relatively simple compared to the other turbulence models. The two-equation turbulence models were developed and calibrated for room temperature, low Mach number, and plane mixing layer. For high temperature jet flows, the standard turbulence models lack the ability to predict the observed increase in the growth rate of mixing layer. Realizable k- turbulence model solves two other transport equations for turbulent kinetic energy and dissipation rates. It is mostly chosen for simulating shear flows, jet flows. It has also some empirical constants derived from experiments. Even though those constants are suitable for most of the fully turbulent flows, calibration might be necessary. K- turbulence model incorporates modifications for low-Reynolds-number effects, compressibility, and shear flow spreading. It predicts free shear flow spreading rates that are in close agreement with measurements for far wakes, mixing layers, and plane, round, and radial jets, and is thus applicable to wall-bounded flows and free shear flows. The shear-stress transport (SST) k- model was developed to effectively bring together the robust and accurate formulation of the k- model in the near-wall region with the free-stream independence of the k- model in the far field. To achieve this, the k- model is converted
into a k- formulation. The SST k- model is similar to the standard k- model, but includes some refinements [33]:
In order to evaluate the results, the axial velocity and turbulence viscosity profiles for different turbulence models were plotted. The axial locations where profiles were plotted were shown in the Figure 3.19, below.
Figure 3.19 Schematic of the axial locations at which data are represented.
As shown in the Figure 3.20 and Figure 3.21, axial velocity profiles at upstream of x=4 m do not vary much with the turbulence model used. It is interesting to note that SST k- and Spalart-Allmaras models produce slightly different results at the very close mixing region of the bypass and free stream flows where the gradients are higher compared to shear layer developed from the core and bypass ducts. However, especially at locations downstream of x=4 m turbulence models start to give different results. The results of Spalart-Allmaras and SST k- models are comparable with each other. Also, k- and k- models give similar results within each other. However, as can be seen in Figure 3.22, at locations further downstream (x=25 m and 32 m), k- turbulence model results become very different compared to other three models. It produces higher values for axial velocity. 38
K- turbulence model differs from the SST k- model in terms of its closure coefficients which are obtained by calibrating experimental data. Other than that, a cross-diffusion derivative term is included to k- formulation to obtain SST k- model [32]. These two refinements to k- model make the difference between the results. Taking the results obtained from the 2D ejector case into account, k- model closure coefficients should be recalibrated to get comparable results with other models. At further downstream regions, turbulence modeling does not have a strong influence on axial velocity distributions. As shown in the Figure 3.23 and Figure 3.24, turbulent viscosity distribution variation for different turbulence models cannot be ignored. The SST k- model yields higher values while the lowest turbulent viscosities were obtained from k- turbulence model at the mixing region of the bypass flow and free stream. Comparing the turbulent kinetic energies sheds light on reason for difference. As shown in Figure 3.26, k- turbulence model yields longer potential core length and lower turbulent kinetic energy levels. SST k- turbulence model gives higher turbulent kinetic energy compared to k- turbulence model especially close to onset of free stream and bypass flow mixing region. Also, the potential core length is longer for SST k- turbulence model than k- turbulence model.
In sum, it can be said that resolving the wall bounded regions are comparable for each turbulence model. Variation between the results obtained from different turbulent models occurs if the flow gradients are strong. We see that the variation is pronounced in the mixing region of fan and free stream flows at which high gradients are present. At further downstream, the gradients become smaller and turbulence modeling does not change the results much other than the k- turbulence model.
Axial Velocity at x=-1.7 m
Figure 3.20 Axial velocity distribution in radial direction at x=-1.7,-1.5, -0.2, 0 m for different turbulence models. 40
Figure 3.21 Axial velocity distribution in radial direction at x=1, 2, 4, 8 m for different turbulence models. 41
Axial Velocity at x=25 m
Figure 3.22 Axial velocity distribution in radial direction at x=25, 32 m for different turbulence models. One should be careful while determining the turbulence model that will be used and if necessary calibration should be made to represent the real physics of the flow better.
Turbulent Viscosity at x=-1.7 m
Turbulent Viscosity at x=0 m
Figure 3.23 Turbulent viscosity distribution in radial direction at x=-1.7, -1.5, 0.2, 0 m for different turbulence models. 43
Figure 3.24 Turbulent viscosity distribution in radial direction at x=1, 2, 4, 8 m for different turbulence models. 44
Turbulent Viscosity at x=25 m
Figure 3.25 Turbulent viscosity distribution in radial direction at x=25, 32 m for different turbulence models.
Figure 3.26 Turbulent kinetic energy (m2/s2) contours with three turbulent models.
3.6 Parametric Study
In this part, the flow physics has been explained before discussing the influence of the parameters on the flow field. The feature of shear layer composed by a dual stream nozzle depends on thermodynamic parameters; pressure, temperature in the primary and secondary flows, velocity ratio of secondary flow to the primary flow and also geometric parameters [19]. Other than the parameters listed above, it is proposed that turbulence intensity, thickness of the boundary layer might have an impact to the mixing. Change in the mean flow field also modifies the behavior of the sound waves passing through the shear layer and therefore an evaluation to see the effects of these parameters on the background turbulent flow field is useful.
3.6.1 Effect of Boundary Layer Thickness on Turbulent Shear Layer As pointed out before, propagated noise levels and propagation direction are strongly influenced by the background turbulent flow field. In industrial simulations, only representative values are used at the inlet locations. Upstream nozzle geometry is not included in analyses which results in uncertainties in specifying the mean and turbulent flow profiles at the boundaries. It is very much important to include both the geometric and the flow conditions details as realistic as possible for the sake of obtaining accurate results. It is known that shear layer is associated with the flow field inside the nozzle; therefore any change for the nozzle boundary layer can significantly impact downstream mixing and change the direction and amplification of the sound waves propagated through the turbulent jet.
To see the influence of the boundary layer thickness, two more cases were evaluated. For the first case, only length of the core nozzle wall length was doubled, in the second case bypass and core nozzle walls were extended two times. The total values at the inlet boundaries were kept constant; in other words, the loss due to boundary layer was assumed to be negligible for longer walls. The static values at the inlet boundaries were calculated from isentropic relations.
For the simulations SST k- turbulence model was used due to results obtained for 2D ejector nozzle problem in the first part. Axial velocity and turbulent viscosity profiles at different axial locations were plotted for comparison.
Doubling the wall lengths result in roughly 1.8 times thicker boundary layer at the lip of the nozzles. Doing so, as plotted in Figure 3.27 there is a slight variation in the axial velocity distribution between the generic nozzle and the longer nozzles. The impact of boundary layer thickness on the mean velocity field is slightly more pronounced at downstream regions. The change in turbulent field is more distinguishing compared to the mean flow. As shown in the turbulent kinetic energy profile plots, change starts to occur in the wall bounded regions of core duct flow with thicker boundary layer and it affects the mixing regions. The influence of the boundary layer thickness loses its importance at the further downstream regions, namely after x=32 m. It is interesting to note that, increasing both the fan and core duct lengths does not change the results; in other words, the influence of boundary layer thickness in the core duct is eliminated due to effects of thicker boundary layer thickness in the fan flow as can be seen from the plots below.
Figure 3.27 Axial velocity distribution in radial direction at x=-1.7, -1.5, -0.2, 0 m for different nozzle wall lengths. 49
Figure 3.28 Axial velocity distribution in radial direction at x=4, 8, 25, 32 m for different nozzle wall lengths. 50
Turbulent Kinetic Energy at x=-1.7 m
Turbulent Kinetic Energy at x=0 m
Figure 3.29 Turbulent kinetic energy distribution in radial direction at x=-1.7, 1.5, -0.2, 0 m for different nozzle wall lengths. 51
Turbulent Kinetic Energy at x=25 m
Figure 3.30 Turbulent kinetic energy distribution in axial direction at x=4, 8, 25, 32 m for different nozzle wall lengths. 52
Figure 3.31 Turbulent kinetic energy (m2/s2) contours for different boundary layer thickness configurations.
3.6.2 Effect of Turbulence Intensity Another uncertainty in computing turbulent flows is the unknown value of turbulence quantity at the boundaries. However, they are needed for simulations as inputs. In this section effect of the turbulence intensity was compared, again SST k- turbulence model was used in the computations. The turbulence intensity both in the fan and core streams were doubled and decreased to half. In other words, 3%, 6% and 12% turbulence intensity values were used as parameters.
As shown in the Figure 32, different turbulent intensities do not affect the axial velocity distribution; however, there is a slight influence is observed at downstream locations as can be seen in the Figure 33. Similar trend occurs for the turbulent kinetic energy distribution as shown in the Figure 34 and Figure 35, below. According to the results, turbulent flow field is slightly influenced only at downstream regions of x=25 m and further downstream locations.
Figure 3.32 Axial velocity distribution in radial direction at x=1, 2, 4, 8 m for different turbulent intensities. 55
Figure 3.33 Axial velocity distribution in radial direction at x=25, 32 m for different turbulent intensities.
Figure 3.34 Turbulent kinetic energy distribution in radial direction at x=1, 2, 4, 8 m for different turbulent intensities. 57
Figure 3.35. Turbulent kinetic energy distribution in axial direction at x=25, 32 m for different turbulent intensities.
In this study, jet flow emanating from a turbofan engine exhaust was computed by using Reynolds-averaged Navier-Stokes method with different turbulence models of FLUENT solver. Turbulence modeling issues and a parametric study were considered.
First, a 2D ejector problem was solved to find out the most appropriate turbulence model. The results of 2D ejector problem showed that turbulence model plays an important role to define the real physics of the problem. All four turbulence models; Spalart-Allmaras, realizable k-, k- and SST k- used here lack to predict accurately especially the initial jet growth region. The models should be carefully evaluated and necessary modifications should be done. For example, calibrating the constants used in the models can be a choice to have better results.
For the parametric study, SST k- turbulence model was used by taking the turbulence model sensitivity studies for both ejector and turbofan engine exhaust analyses results into account. It is seen that boundary layer thickness effect becomes important in the jet flow close to the lips of the nozzles. At far downstream regions, it does not affect the flow field. For different turbulent intensities, no significant change occurred in both mean 59
and turbulent flow fields. However, higher intensities might be possible for real engine conditions which might impact the flow characteristics.
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Three Navier-Stokes Solvers for an Axisymmetric Separate Flow Jet, AIAA Paper 2002-0672,2002. [13] Thies A. T., Tam C. K. W., Computation of Turbulent Axisymmetric and Nonaxisymmetric Jet Flows Using the k-epsilon Model, AIAA Journal 1996; 34(2):309-16. [14] Morgans R. C., Dally B. B., Nathan G. J., Lanspeary P. V., Fletcher D. F., Application of the Revised Wilcox k- Turbulence Model to a Jet in Coflow, 6-8 December, 1999. [15] Kenzakowski D. C., Kannepalli C., Jet Simulation for Noise Prediction Using Advanced Turbulence Modeling, AIAA-2005-3086. [16] Engblom W. A., Khavaran A., Bridges J.E., Numerical Prediction of Chevron Nozzle Noise Reduction Using Wind-MGBK Methodology, AIAA Paper 2004-2979, 2004. [17] Georgiadias N. J., Rumsey C. L., Yoder D. A., Zaman KBMQ., Turbulence Modeling Effects on Calculation of Lobed Nozzle Flowfields, J. of Propulsion and Power, 2006, 22(3):567-75. [18] Gao J. H., Li X. D., A Numerical Study of Nozzle Boundary Layer Thickness on Axisymmetric Supersonic Jet Screech Tones, AIAA-20062675. 62
[19] Viswanatham K., Parametric Study of Noise from Dual-Stream Nozzles, J. Fluid Mechanics, Vol. 521, pp. 35-68, 2004. [20] Gilbert G. B., Hill P. G., Analysis and Testing of two-Dimensional Slot Nozzle Ejectors with Variable Area Mixing Sections, NASA-CR-2251, May 1973. [21] NPARC Alliance CFD Verification and Validation Website. [22] Spalart, P. R., Jou, W.-H., Stretlets, M., and Allmaras, S. R. (1997), Comments on the Feasibility of LES for Wings and on the Hybrid RANS/LES Approach, Advances in DNS/LES, Proceedings of the First AFOSR International Conference on DNS/LES. [23] Launder, B. E., Reece, G. J. and Rodi, W. (1975), Progress in the Development of a Reynolds-Stress Turbulent Closure Journal of Fluid Mechanics, Vol. 68(3), pp. 537-566. [24] Menter, F. R. (1993), Zonal Two Equation k- Turbulence Models for Aerodynamic Flows, AIAA Paper 93-2906. [25] Strelets, M. (2001), Detached Eddy Simulation of Massively Separated Flows, AIAA 2001-0879. [26] Wilcox, D.C. (1988), Re-assessment of the scale-determining equation for advanced turbulence models, AIAA Journal, vol. 26, pp. 1414-1421. [27] Germano, M., Piomelli, U., Moin, P. and Cabot, W. H. (1991), A dynamic sub-grid scale eddy viscosity model, Physics of Fluids, A(3): pp. 1760-1765, 1991. [28] Spalart, P. R. and Allmaras, S. R. (1992), A One-Equation Turbulence Model for Aerodynamic Flows, AIAA Paper 92-0439. [29] Pope S. B., Turbulent Flows.
[30] Lele S. K., Compressibility Effects on Turbulence, Annual Reviews in. Fluid Mechanics, 1994, 26:211-54. [31] Georgiadis N. J., Debonis J. R., Navier-Stokes Analysis for Turbulent Jet Flows with Application to Aircraft Exhaust Nozzles, Prog. Aerospace Sci (2007), doi: 10.1016/j.paerosci.2006.12.001. [32] http://www.grc.nasa.gov/WWW/wind/valid/eject/eject.cgd [33] Fluent Users Manual.
Navier–Stokes Equations
Reynolds Number
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The success of the IRC®is due in no small part to its design flexibility. Battery or mains-powered, the IRC®can use batteries as back-up power to mains supply if required. The sensor can be pipe, wall or ceiling mounted, surface-mounted or recessed to conceal the unit and reduce the risk of vandalism.


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Long-Short Momentum Down 9% and Other Tales of a Shocked Market
Stock Markets Jun 05, 2020 11:45AM ET
© Reuters. Long-Short Momentum Down 9% and Other Tales of a Shocked Market
CUK
NCLH
(Bloomberg) -- The latest U.S. jobs report will go down in history as the data that shocked economists. And the market.
Forecasts for a drop of 7.5 million in payrolls were met with the reality of a 2.5 million increase in May, supporting the view that the word's largest economy may be more resilient than previously thought. A stock market already up 40% in a record period of time rallied further, with particular pockets going haywire.
From a blowup in the momentum factor trade to a surge in small-cap shares, here's a sample of what was happening under the equity market's surface Friday.
Winners Turn Losers
The momentum factor, which in essence bets that the recent winners will keep on winning, got pummeled Friday. At its lows, a Dow Jones market neutral momentum portfolio that goes long the highest momentum stocks and shorts those with the least momentum dropped 9% -- the worst day since at least 2002.
"The nature of the rally has changed," said Brian Nick, chief investment strategist for Nuveen. "The stocks that had momentum have lost it. If this keeps going then the new momentum will be value. Everything has happened fast in 2020, it's very much in keeping with that."
The index pared some of its losses to 6.5%, but still posted the largest decline in a decade.
Smaller Is Better
Small-cap stocks surged on prospects of a faster economic rebound, sending the Russell 2000 up as much as 4.6%. The risk-on tone was evident in the large-cap arena too, with an equal-weight version of the S&P 500 that gives Coty (NYSE:COTY) Inc. just as much weight as Microsoft Corp (NASDAQ:MSFT). rising 4.3% at one point.
The equal-weight benchmark is up close to 10% this week, its best period versus the classic market-cap weighted index in two decades.
"If we want to make sense of the market move, we need to not just look at the S&P or the Nasdaq but look beyond that," said Willie Delwiche, an investment strategist at Baird. "Areas that lagged for years that made much more substantial lows are coming back as the economy transitions from worse-than-expected data to better-than-expected data."
Airlines Fly, Cruise Ships Sail
Some of the best-performing stocks Friday were airlines and cruise lines. They were hit hard in the coronavirus stock crash and arguably stand to be among the first in line to benefit from a return to economic normal. American Airlines (NASDAQ:AAL) Group Inc. was up 26%, extending its 41% record gain on Thursday.
Norwegian Cruise Line (NYSE:NCLH) Holdings, Carnival (NYSE:CUK) Corp., United Airlines Holdings (NASDAQ:UAL) Inc. and Royal Caribbean (NYSE:RCL) Cruises Ltd. were all up at least 15%.
Energized Energy
Among 11 S&P 500 sectors, energy was the best performing Friday, up more than 7%. Occidental Petroleum Corp (NYSE:OXY). rose 23%, while Apache Corp (NYSE:APA). and Noble Energy Inc (NASDAQ:NBL). also added more than 12%.
"It's all about the future and we are coming out of the storm," said Bryce Doty, senior portfolio manager at Sit Investment Associates. "It was a terrible storm that caused widespread destruction. Everything from this point on will be 'less bad' and even turn positive. Huge sentiment shift."
©2020 Bloomberg L.P.


Op-Ed: Hits and Misses in the ..
The Post Salon will host a special organizing meeting Sunday, March 13, 2 p.m. – 4 p.m., to prepare for the April 5 City Council meeting, where the council will consider passing a housing state of emergency to temporarily freeze some rents and halt most evictions in Oakland.
Organizers say it will take a united and outspoken community to win the housing state of emergency and pass new laws in the next two or three months that will protect the right of renters to stay in the city.
The growing coalition so far includes Qilombo Community Center, the Oakland Tenants Union, Oakland Alliance, participants in the Oakland Post Salon, Wellstone Democratic Renewal Club, John George Democratic Club and the Block by Block Organizing Network.
The meeting will be held at Geoffrey's Inner Circle, 410 14th St. in downtown Oakland. For information call (510) 287-8200.


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Avian Control Bird Repellent is a patent-pending, EPA-registered liquid bird repellent that helps you efficiently repel undesirable birds without harming the birds, people or other animals. It can be sprayed or fogged on and around a variety of surfaces, structures and crops. Use to solve bird problems in agricultural, commercial, airport and residential applications. Spray on grapes, apples, wild rice, sunflowers, etc. Fog to disperse geese, coots, starlings, crows, seagulls, pigeons and more.
How Does Avian Control Repellent work?
Avian Control Bird Repellent is a Contact Repellent. The target birds must inhale or ingest the repellent to get the repellent effect.
Avian Control Bird Repellent uses the proven effective Methyl Anthranilate (MA) to temporarily irritate a bird's trigeminal nerve system 1 causing discomfort, stress and disorientation. When the bird leaves the treated area, the discomfort subsides. It soon learns that the location and/or treated object equals irritation and stays away.
Note 1: Trigeminal nerve transmits the information sensed by a bird's eyes, nose and beak to the brain where the information is interpreted. Temporarily irritating this nerve with the MA in Avian Control causes the bird irritation, stress and disorientation. This dissipates when the bird leaves the treated areas and/or stops ingesting or inhaling the repellent.
The Avian Control repellent can be sprayed or fogged in most locations where birds gather. Here are a few specific applications for the repellent.
Prevent birds from loitering in parking lots, landscaping, gardens, etc.
When used as directed, the repellent is safe around people, plants, pets and structures.
Longer lasting results than previous repellents.
Also highly effective for Agricultural, Airport, Dairy Barns and other applications.
How long will an application of Avian Control Repellent last?
For outdoor direct spray applications, Avian Control can last from 10 to 14 days depending upon the frequency and severity of local rain. Experience has shown that an application interval of 10 days is ideal. Avian Control is resistant to irrigation and most light to moderate rains. Very heavy rains may wash Avian Control off of your plants and will require re-application.
Always refer to the Avian Control Product Label for more details.
Note 5: If you do not have an agricultural surfactant, you may substitute a dishwashing detergent such as Dawn, Palmolive or Joy.
For small areas, use a fine spray. Keep the solution well mixed. Make sure the intended surfaces/objects are completely coated by the repellent mix. You will have to reapply every 7 to 14 days or after each mowing. Reapplication may be necessary after heavy rainfall or flooding.
Ground Applications Mix repellent with water at a ratio of 1 part repellent to 10 to 20 parts water (1:10 or 1:20) depending on vegetation density. Use an agricultural surfactant to help ensure even coverage. Apply at a rate of 25 to 100 gallons of mix per acre.
Aerial Applications (fixed and/or rotary wing aircraft) Mix repellent with water at a ratio of 1 part repellent to 10 to 20 parts water (1:10 or 1:20) depending on vegetation density. Use an agricultural surfactant to help ensure even coverage. Apply at a rate of 25 to 100 gallons of mix per acre.
Why Use Avian Control® for Dairy Barns?
Long-lasting results – up to two weeks with one spray!
*Note: CA and NY do not allow application of repellent to animal feedstuffs.
Lower the health risks associated with barn swallows invading your dairy barns by preventing barn swallow nesting altogether with Avian Control®, today. Ensure your livestock, water and feed is bird and contaminate-free all year long by ordering now!
EcoBird 4.0 Fogging Bird Repellent is a Methyl Anthranilate (MA) based bird repellent that is applied with pulse jet thermal foggers, mechanical cold foggers and aerosol generators.
An EPA Registered liquid bird repellent that helps repel pest birds without harming them. It can be sprayed or fogged outdoors.
Commercial grade, 4 gallon (15 liter) Bak-Pak hand pump sprayer is designed for professional use and features 3 different nozzles for all types of spraying applications.


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Film & TV, Movies
Hope the "Stars Align" for Edge of Tomorrow Sequel: Emily Blunt
Written by R Abhishek Vishnu on March 10, 2020
Emily Blunt is no ordinary name when it comes to Hollywood. The actress has seen a recent surge of successful movies like "A Quiet Place" and "Mary Poppins Returns" to name a few and has been the recipient of the Golden Globes and Screen Actors Guild Award.
In a recent interview with Indiewire, she revealed that she hopes that the "stars align" for her, director Doug Liman, and co-star Tom Cruise to move forward on the project.
"I think there's an idea, that he (Doug Liman) says is great, And he says this guy came in and cracked the case. How the stars will all align for us to be able to do it. I don't know. I hope they do. "
Doug Liman had earlier revealed a picture of Robinson and producer Alison Winter alongside a pair of massive whiteboards that appear to be filled with the predictably wild story beats of a sequel.
How many whiteboards is too many? #LiveDieRepeat2
A post shared by Doug Liman (@dougliman) on Jan 14, 2020 at 11:21am PST
Emily went on to say that she's far from being blindly optimistic and that the first movie meant the world to her even though it admittedly 'broke her body in half.'
"I absolutely adored it. It broke my body in half, but I'd be willing to do it again to work with those boys who I love. So let's see."
The actress then went on to joke about how Tom and herself would be really old and getting in on the years by the time a sequel is actually confirmed.
"Tom and I are going to be 70 before we make another one. It's going to look a bit weird. We'll have to do a real flashforward one. We'll go full 'Irishman,' it'll be the 'Irishman' version of 'Edge of Tomorrow.' Who knows? I hope, I'm going to talk to Doug about it [at the 'A Quiet Place: Part II' premiere]."
With all this said and done, we really hope the stars do align for the actors and the director despite all their scheduling conflicts where they all meet for a nice warm dinner and come to a final decision where they're just like "Fought Aliens before. Let's fight them again."
Emily Blunt's A Quiet Place: Part II and Jungle Cruise are set to hit the theatres on March 20th and July 24th respectively.
R Abhishek Vishnu


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Startup tackles incontinence with bladder-sensing wearable
San Francisco-based Lir Scientific is developing a new wearable device, called Brightly, that tracks the user's bladder fullness to help remind people to urinate. Lir Scientific hopes the device will replace adult diapers.
Brightly is a patch, worn on the abdomen, that notifies the user with either a sound or vibration when it senses that the user needs to urinate. The device will also send an alert to the user's smartphone via Bluetooth that reminds them to use the restroom, according to a post from Wired. The patch has a swappable battery so that users can wear it for as long as they want.
The company's CEO and cofounder, Jean Rintoul, previously worked at Emotiv, which has developed EEG headsets, as well as activity tracker company Basis Science, which was later acquired by Intel.
Rintoul told Wired that she created a prototype device while at HAX, a hardware accelerator that has offices in San Francisco and Shenzhen, China. She also said she expects the device to sell for $400, which is much less expensive than other devices used in hospitals currently.
Rintoul explained that moving forward, she plans to launch pilots with urologists and in hospitals to test Brightly further. In hospitals, she added, the device could help alert nurses to when patients need to urinate, which would prevent them from getting bed sores from wetting the bed. Other uses cases for the device, she said, include medical imaging and measuring lung expansion.
Last year, researchers Professor Takayasu Sakurai and Professor Takao Someya from the University of Tokyo developed a flexible, disposable sensor for adult diapers. The sensor, which can detect moisture, humidity and pressure, is printed on plastic film and will transmit information wirelessly.
adult diaper sensor, Brightly, incontinence, Lir Scientific


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Ira Glass and the OC
You guys know that I love Ira Glass and want to be his intern. Or boss. Or friend. Or peer whom he respects and buys quirky-thoughtful birthday presents for. I found his confession of loving The O.C. totally endearing. He and his wife always watch it and when the theme song comes on they sing it out loud together. They know it's nerdy, but they love it. I love it! I have never seen The O.C. (is it good? Should I TIVO?) But Christian and I are like this with Law and Order. It's the comfort food of TV. It's always on. It follows a predictable pattern. I know to expect an unexpected ending. And when it starts. . . Christian and I sing along in parts: "Bow bow" "Duh duh duh duh duh." "Bow bow." "Duh duh duh duh duh" "Deedle leedle leedle leedle leeee!" And so on. I'm not a fan of SVU but I have grown to love Criminal Intent. At first I was an L&O purist. I just look back at myself and laugh!
One day before we got hip to Criminal Intent, Christian's mother told us about a whole episode. She talked about Detective Goren and how he's like a modern-day Sherlock Holmes. The details were lost on us because when someone is telling you about a show you don't watch (and I have done this to people with whole SEASONS of Lost and Heroes) you kind of, oh what's the phrase? Don't care.
Then we started watching Criminal Intent during the writer's strike and found out that he is like Sherlock Holmes. He's brilliant! His partner, Eames, is the only person who really gets him. Christian loves Eames and understands their relationship the way I really understood the relationship between Mulder and Scully. Unlike Scully, who has gotten much thinner over the years, Detective Goren just gets fatter and fatter. He's also a little pigeon-toed. His mom is Rita Moreno. His dad is a serial killer. He once gave his no-good brother his coat. One time I looked Bobby Goren up on Wikipedia and I was proud to find that there was not a single fact about him there that I didn't already know. You really get to know a person watching them on TV ten times a week.
Which is to say nothing of my real favorite, Mike Logan or the show's new host, Jeff Goldblum. Anyway, Ira Glass was watching The O.C. and one of the characters mentioned his radio show, This American Life. "Is that the show where those hipster know-it-alls talk about how fascinating ordinary people are?" Can you imagine? I can imagine. I can imagine tuning in to Criminal Intent after the murder set up, when Goren and Eames come on the scene. Eames would be all, "How about that blog Every Day I Write the Book. . . Ever heard of it?" And Goren would reply, "Is that the one where the stay-at-home lamester talks about how thrilling ethnocentrism is?" And I would die a little.
So what did Ira Glass say? Did he laugh? Did he feel stupid? Did you ever watch This American Life (the TV show)?
He thought it was funny and surreal. I just got the DVD of the TV show. It's really good.
Sue 9:28 PM
The first season of the OC rocks. The others are worthless. Beyond worthless.
I can't believe I just left a comment with the word "rocks" in it. I think that officially makes me ninety.
I share your very great love for Ira Glass.
Did you get the episode where the Mormon guy paints pictures of Jesus? (who is super hot in real life. The model, not the Lord.)
Kacy 10:34 PM
I saw that--I was going to mention it in my last comment. It's such a great story.
Heidi 11:14 PM
I think I started watching Lost after you told me all about the first season and pestered Neil (while he had an alarmed look on his face) about his thoughts on it. Yeah, I'm pretty sure that is why I started watching it.
I loved the OC. The first season might be one of the most brilliant to ever air on TV. It lost it's way the next couple, but the final season it was back, way back, and then it got canceled.
I still go back and watch episodes, and I never watch old TV (Well, The Cosby Show and The OC.)
You can watch it here, on hulu, and it's awesome. I miss it, I really do. I bet Ira misses it too.
Its way. Not it's. I was so excited about an O.C. discussion that I mistaked all over your comments.
Eliza 10:00 AM
I watched the first season, then lost interest after that since Anna (my favorite) moved away. Then I watched the last few episodes of the final season. Yowsa, I was not prepared for that ending.
Anyway, I really liked the first season of The OC and I really like Ira Glass.
I also like Ira Flatow, but I don't think it's as cool to like him.
Me plus 3 Hecks 10:27 AM
I think I now know why I feel connected to your blog--it's the Law and Order harmony. Perfect. I feel exactly the same about the spin-offs and everything. Except my favorite person is Sam Waterston--I have very seriously considered naming a child McCoy because of him. Yup. Pretty great.
Oh. And I think the OC makes me feel like my brain is dripping out of my ear. So good luck with that.
Ashlyn 2:37 PM
Thank god you are back to posting. After spending 2-3 full days a few weeks ago reading all your archives, I was having serious withdrawal issues after your recent blogging hiatus.
I'm so delighted by these new posts, I can hardly stand it! I'm so happy for Ira Glass. And I also watched the OC. Delightful first season.
Kaylynn 7:13 AM
Wouldn't it be better if Ira Glass mentioned you? Or maybe that has already happened and I missed it. My favorite Ira Glass episode is all about Mr. Rogers, not really an ordinary person.
Julienne 1:54 PM
I was so lost reading this post. Do you think I should watch more TV so that I can be in the loop? I honestly have never watched any of those shows, although I have heard of one- Law and Order.
Right Sue, the first season of the oc is awesome.Gr8 storyline and characters are taken very good..i have seen full episodes of oc and never missed it any episode.


Today, I am ready to share them with you…the full blown story and how you can make them. Helping you have a little fun in your home with arts and crafts….and your children!
A couple of years ago, a friend of mine gave me this cute book: Jumbo Book of Basics -For Kindergarten. It's a fun book with cute activities for a great year of kindergarten. Alas, I have failed to use it very much…but, now that my little guy is really starting to show some interest in learning, I've been pulling it out more.
Recently, I came upon this REALLY cute and fun way of making Easter Eggs…though, they are not just easter eggs, they are BIG Dinosaur Eggs made out of Paper Mache.
And…I'm going to share the steps with you here!!!
Allow your dinosaur eggs to dry…. And…it may be helpful to find the Mommy Dinosaur to take care of the eggs…. Too much paste will take the eggs a LONG time to dry…so a little extra protection is never a bad thing!
Once they are dry…Paint away!
WE had a ton of fun making these…the best part was making them with friends.
This is too cool! Just love it! 🙂 I know my kids would go bonkers with this! Thanks for sharing!
Lisa, we did have a lot of fun….we made these with some very dear friends….and took two weeks to make them….
Words cannot express how much I love this! 🙂 Adore!
So, then, you'll have to show me when you get here! Hope you're safe and getting some rest!
These look like fun! I think they might be on the agenda this weekend!
These are great! maybe you can link them up this week with our Wednesday linky!!
I LOVE your new blog design!! So clean and fresh!!
Theresa, thanks!!!! I will link them up and they were fun to make!
Wow! These are very cool! I haven't tried paper mache with my girls yet…I really think they'd like it.
Susan, Thanks! I had it ready for last week…..but, definitely understood waiting and working through Pinterest Concerns.
What a wonderful project. It looks like lots of fun.