Effect of Wedge-Shaped Deflectors on Flow Fields of Dual-Stream Jets

Transcription

1 3th AIAA/CEAS Aeroacoustics Conference (8th AIAA Aeroacoustics Conference) AIAA Effect of Wedge-Shaed Deflectors on Flow Fields of Dual-Stream Jets Rebecca S. Shue * University of California, Irvine, CA, Khairul B. Zaman NASA Glenn Research Center, Cleveland, OH, 3 Dimitri Paamoschou University of California, Irvine, CA, The effect of wedge-shaed fan flow deflectors on the mean and turbulent flow-fields of dual-stream jets is investigated. Several wedge-shaed deflector concets were used to create asymmetry in the lume of a dual-stream jet issuing from a scaled down version of the NASA Glenn BB byass-ratio 8 turbofan nozzle. The deflector configurations comrised internal and external wedges with and without a ylon. Some external wedges incororated local extensions of the fan nacelle. All the deflectors reduced radial velocity gradients, magnitudes of eak Reynolds stresses, and eak turbulent kinetic energy beneath the jet centerlane, with an increase above the jet centerlane. A correlation was obtained between the maximum radial velocity gradient and the eak turbulent kinetic energy in the dominant noise source region. Nomenclature D = nozzle exit diameter k = turbulent kinetic energy = ( u + v + w ) u,v,w = axial, vertical, and sanwise velocity comonents in jet lume x,y,z = axial, vertical, and sanwise coordinates U = velocity at jet exit (.) = fluctuating value (.) = mean (time-averaged) value Subscrits f = secondary (fan) stream = rimary (core) stream = fixed axial location * Graduate Student Researcher, Deartment of Mechanical and Aerosace Engineering, Engineering Gateway, Irvine, CA , and visiting Graduate Student Researcher at NASA Glenn Research Center, through the Graduate Student Researchers Program (GSRP) fellowshi, AIAA Member. Aerosace Engineer, Proulsion Systems Division, Inlet and Nozzle Branch, Brookark Road, M.S. 86-7, Cleveland, OH 3, AIAA Associate Fellow. Professor, Deartment of Mechanical and Aerosace Engineering, Engineering Gateway, Irvine, CA , AIAA Associate Fellow. Coyright 7 by Rebecca Shue and Dimitri Paamoschou. Published by the, Inc., with ermission.

2 I. Introduction his work is motivated by the advent of asymmetric dual-stream exhaust configurations for the suression of T airort community noise from turbofan engines. The secific method addressed here is the fan flow deflection (FFD) method, whereby aerodynamic devices are used to create asymmetry in the lume of a jet exiting an otherwise coaxial nozzle. The asymmetry causes noise reduction in the general direction of the deflection of the fan stream. To areciate the effect of the fan flow deflection, it is instructive to examine the rincial features of the mean flow of a coaxial jet, sketched in Fig.. They include the rimary otential core, of length x, and the generalized secondary core (GSC) which forms around the rimary core. The GSC is based on the outer two inflection oints, i and i 3, of the radial velocity rofile, which naturally form a loo. The end of the loo, at x=x GSC, signifies the transition of the velocity rofile from dual-stream to single-stream. For the velocity ratios considered here, the initial region of the core jet surrounded by the GSC can be treated as silent, in the sense that noise emission from the inner shear layer (between core and fan streams) is insignificant comared to the noise emission from the outer shear layer (between fan and ambient streams),. Downstream of the GSC, the core stream contains the dominant sources of jet noise. Our resent understanding of fan flow deflection is that it roduces two major effects: lengthening of the GSC, thereby silencing a greater ortion of the core flow; and/or reducing the radial velocity gradient ast the end of the GSC. 3, For x>x GSC, the maximum velocity gradient occurs on the locus of inflection oints i, as shown in Fig.. This work focuses on the reduction of the velocity gradient and its connection to changes in the turbulent velocity field. Two tyes of deflectors for creating asymmetry have been investigated so far: wedge-shaed deflectors mounted at the to of the nozzle, and airfoil-shaed vanes mounted at various azimuth angles -7. Both devices can be internal or external to the fan duct, although vanes are more aerodynamically efficient when laced in the subsonic environment inside the fan duct. Figure shows the lacement of the wedge-shaed deflector. Past studies have shown that wedge-shaed deflectors, installed on a fan nozzle with convergent streamlines, have the otential to reduce jet mixing noise significantly, articularly in the direction of eak emission, for a range of azimuth angles without crossover at high olar angles., Paamoschou and Shue noted a reduction in radial gradient of mean axial velocity comonent related to noise suression in the downward direction in asymmetric byass ratio jets. In an effort to understand directional noise suression due to a dearture from symmetry of dual-stream jets, this work examines in detail the flow field characteristics affected by that dearture, secifically changes in velocity gradients, turbulent kinetic energy, and Reynolds stresses. II. Exerimental Setu Exeriments were conducted in the CW-7 jet facility at NASA Glenn Research Center (GRC). Coannular flow is achieved via a secondary lenum chamber located just ustream of the nozzles. The secondary annular flow, sulied by four equally saced orts, is routed through a contoured interior and screens to rovide a uniform velocity rofile at the exit. The rimary Mach number at the exit was.8 and the secondary Mach number was.3. The secondary-to-rimary velocity ratio was.7 reresentative of the velocity ratio of a turbofan exhaust at takeoff condition. However, the magnitudes of the velocities were much lower than in a real engine to enable the use of hot-wire techniques. In all exeriments, air at room temerature was sulied to the searate-flow nozzle using a rimary blower and an auxiliary blower. The auxiliary blower was mounted on a by 8 suort, custom crafted so that the blower outlet was flush mounted with existing iing. A. Nozzle The NASA GRC BB nozzle has a byass ratio of aroximately 8 at tyical engine cycle conditions. A scaled down version of this nozzle, with fan diameter D f = 3.3 mm, was fabricated and used in the CW-7 facility. The Reynolds number of the jet, based on fan diameter, was. 6. Exit conditions are listed in Tables -3 for the baseline nozzle. The BB nozzle has convergent exit flow lines for the fan and core ducts, tyical of a realistic turbofan engine nozzle geometry. Figure 6 shows the radial coordinates of the BB nozzle. Photos of the nozzle are rovided in Fig. 7. B. Wedge and Pylon Configurations Five different wedge designs were tested with and without a ylon. The wedges without ylon comrised two external wedges (W and W ) and two internal wedges (W 3 and W ), as sketched in Fig. 3. W, W, and W 3 had half-angles of o. The height of the external wedge W was twice the fan exit height (Fig. 3a). External wedge W, shown in Fig. 3b, had a height equal to fan exit height at its aex, gradually increasing to. times the fan exit height at its base. The cross sections of the external wedges are shown in Fig.. The internal wedge W 3, Fig. 3c,

3 used the same cross-section as the external wedges, Fig. a, and its contours were flush with the fan duct walls. Nacelle extensions of different geometries, Fig. c, were used to examine the effect of suressing the flow uwash over the short external wedge W, resulting in the arrangements shown in Fig. a. Pylon configurations comrised a wedge W that defined the interior ortion of the ylon, and external ylon half-wedges or flas. The crosssection of W was fast-diverging wedge dee inside the fan duct, with a half angle of roughly 3 o, with the sides becoming arallel to one another close to the fan exit, as shown in Fig. b. The external, ylon-mounted halfwedges had angles of 7 deg. relative to the ylon surface. Figure 6 lots the coordinates of the base nozzle and with wedges W W installed. Figure 7 shows hotograhs of the external wedge configurations tested, including the ylon with external half wedges. Wedges W W 3 were fabricated using Duraform EX lastic material. The ylon was constructed of three lastic ieces. The ensemble comrised an internal comonent (W ), terminating at the fan exit lane, an external comonent that was flush-mounted against the internal comonent, and two side-mounted half wedges (Fig.b). C. Velocity Measurements Two airs of crossed hot-wires, illustrated in Fig. 8, were used to survey the mean and fluctuating velocity comonents in the jet lume. One was in a u-v configuration, the other in a u-w configuration. The wires were saced.-mm aart, limiting the satial resolution to. mm in the y- and z-directions. The robes were mounted on a streamlined strut, visible in Fig. 7a, and the ositioning was automated under comuter control in all three directions. The two robes were located at the same y-location (vertical) and saced aart from one another by 3- mm in the z-direction (sanwise), Fig. 8. The ste size in the z-direction was chosen to be a submultile of the searation distance so that a shift of the u-v robe data by an integral number of stes matched the corresonding data from the u-w robe. With increasing axial distance, both the satial resolution and the samling rate were decreased. Smaller grid intervals were used where shar satial gradients were exected in the initial region of the jet. An exonential function was used to decrease the satial resolution with axial distance. In the x-direction, 6 data oints were acquired, sanning 8.3D f. Grid sacing in the x-direction started with a searation of.d f or 6.-mm between the first and second data oints and ended with a searation of.7d f between the last two data oints. The first data oint was taken.d f from the ti of the nozzle center lug in x and.6d f from the jet centerline in y, where the velocity was small. For each axial station, 9 data oints were collected along y, uniformly saced. At each axial station, the grid sacing in y was adjusted so that the outer grid oints formed an angle of.3º with the axis. The ustream-most osition used uniform intervals of.7d f (3.8-mm) and the furthest osition downstream used uniform intervals of.7d f (8.3-mm). For distances ustream of.8d f, the samling rate used was Hz, and for distances downstream of.8d f from the lug ti, the samling rate used was Hz. The ensemble size was. Thus, samling times of s or s were used deending on the axial location. At each grid oint, all three comonents of mean and RMS velocities were obtained. The Reynolds stresses u v and u w were also measured. In addition to the crossed wire surveys, a single wire was used searately to survey the nozzle exit boundary layers. The boundary layers were found to be nominally laminar and their characteristics are listed in Table 3; here, location refers to the inner layer of the rimary (core) nozzle, location refers to the outer layer of the rimary (core) nozzle, and location 3 refers to the inner layer of the secondary (fan) nozzle. III. Results A. Mean and RMS Velocity Fields Figure 9 shows the isocontours of the mean axial velocity, normalized by the rimary exit velocity, for the baseline jet and for the wedge configurations W W 3. Note the reduction in otential core for all the wedge cases, by examining the contour level ū(x,y,)/u =.9. Since the otential core length, x, rovides a scaling for the volume of turbulent mixing noise sources in jets, it is desirable to reduce it. Table lists otential core lengths for the baseline jet and for each asymmetric dual-stream jet, based on 9% of the rimary jet exit velocity U. The internal wedges are articularly effective in reducing x. In Fig. 9, cross-sectional slices of the jet lume are shown at the lug ti, x /D f =, and near the end of the rimary otential core, x /D f =. The values of x are referenced to the secondary (fan) nozzle exit lane. Uniformly reduced gradients beneath the jet centerlane are observed, similar to those reorted in Ref.. The cross-sectional slices at x /D f = for the two external wedges show that there is a wake region behind the wedge. Studies have shown that the drag for a wedge laced in a jet stream with the to surface exosed to ambient fluid is 7% less than the drag of the classical two-dimensional wedge roblem. 8 3

4 Figures and deict isocontours of the RMS axial velocity fluctuation for the baseline jet and for all the isolated (without ylon) wedge configurations. It is noted that all the wedge configurations reduce the RMS levels below the jet centerlane and increase them above the jet centerlane. Internal wedges generally increase the RMS levels on the uer side of the jet much more than do external wedges. Thus, the enhanced mixing of the internal wedge, evident by the significant reduction of otential core length, comes at the exense of a large increase in turbulence levels at the to of the jet (Fig. d-e). Figure shows that a nacelle extension to the external wedge may further reduce turbulence intensity on the underside of the jet, with the tradeoff of increased levels on the uer side of the jet. B. Turbulent Kinetic Energy and Reynolds Stresses Figure shows isocontours of the mean velocity, turbulent kinetic energy, and Reynolds stress u v for the baseline jet and for the external wedge configurations W and W. Corresonding to a reduction in radial gradient in the downward direction, there is a reduction in eak turbulent kinetic energy (TKE) and a reduction in magnitude of eak Reynolds stress underneath the jet centerlane. There is a tradeoff of an increase in eak TKE and eak Reynolds stress above the jet centerlane. Tables and list the eak values of TKE and Reynolds stresses on the uer and lower half-lanes of the jet. Figure 3 shows the mean velocity, turbulent kinetic energy, and Reynolds stress u v isocontours for the baseline jet and the internal wedge configurations W 3 and W. The trends are similar, but more ronounced, as for the external wedges. Figure shows the mean velocity, turbulent kinetic energy, and Reynolds stress u v isocontours for the baseline jet and the internal ylon ortion W, with and without the external ylon, and with an external ylon and flas. The outer ylon increases the magnitude of the eak Reynolds stress beneath the jet by aroximately % when comared with the inner ortion W alone. The addition of external flas reduces the magnitude of the eak Reynolds stresses by about % relative to the configuration W + Pylon. Ref. 9 rovides a nice discussion on sensitivity of flow field to jet-ylon interaction. The external flas rovide a net reduction in the magnitude of eak Reynolds stress, suggesting the otential of external flas for noise suression on a searate-flow turbofan engine. With regard to the Reynolds stress u w, Table shows that the external wedges W, W, and W + Ca resulted in a decrease in its eak magnitude. This may indicate that the external wedges have better caability to reduce noise in the sideline direction, comared to the other configurations resented. Acoustic measurements are needed to confirm this. C. Correlation Between Turbulent Kinetic Energy and Radial Velocity Gradient We now discuss the connection between radial velocity gradient and turbulent kinetic energy. Figures and 6 lot the loci of inflection oints, axial distributions of the radial velocity gradient along inflection oint i on the underside of the jet (Fig.). Also shown are the axial distribution of eak TKE on the underside of the jet for all the configurations without the ylon. As mentioned in the introduction, the outer inflection oints, i and i 3, define the generalized secondary core (GSC). The maximum radial velocity gradient occurs on the inflection oint i ast the end of the GSC. Figure covers configurations W W, with the reference being the baseline nozzle. Figure 6 covers the W + Cas configurations and the reference is case W. We observe generally an elongation of the GSC beneath the jet centerlane and a shortening of the GSC above the jet centerlane. In the baseline jet, it is evident that there is some asymmetry in the flow desite ainstaking efforts to align the nozzle. Corresonding to the jet asymmetry, or the thickening of low-seed fluid underneath the jet, are reduced radial velocity gradients in the downward hemicylinder of the jet, and reduced eak TKE levels. Figure 7 shows a correlation between the radial gradient of the axial velocity comonent measured at the end of the GSC, defined as u( xgsc yi ) Df G =,,, y U () and the eak value of the turbulent kinetic energy. The correlation encomasses both the lower and uer sides of the jet. Because the baseline case was not erfectly symmetric, two oints are obtained for the baseline, one above, and one below the jet centerlane. A regression of the form k/u =.88G.6G +.9, is valid both above and below the jet centerlane. Since the eak turbulent kinetic energy can be thought of as a measure of how intense the turbulent mixing is, it is logical that it should also rovide a measure for turbulent mixing noise. Therefore, this correlation yields insight into the imortant mean flow arameter that will yield a correlation with noise. This is imortant, since a large number of exeriments have been conducted at UCI for which there are only mean flow measurements to be

5 correlated with the noise measurements. The direct correlation between the mean flow arameter measured at the end of the generalized secondary core and the eak turbulent kinetic energy suggests that it may be ossible to obtain a correlation, a toic of future research. In constructing correlations with the acoustics, the gradient arameter u G = ( x y,) x, GSC i, () y may be more hysical because it is based on the otential core length, x, which defines roughly the extent of the core noise sources. Figure 8 shows a romising correlation. Hoefully, this arameter may be used to correlate downward reductions in overall sound ressure level, although current models are still reliminary. One of the remaining challenges in obtaining a robust correlation between acoustics and mean flow will be to extend the rocedure to include the azimuthal variations of the velocity gradient and of the GSC. IV. Conclusions Flow field surveys at NASA Glenn Research Center were conducted in an effort to understand and quantify the effects of wedge-shaed fan flow deflectors on the mean and turbulent velocity fields of dual-stream jets. A large variety of such deflectors was tested on a scaled-down version of the GRC BB nozzle, including internal and external wedges. We focused on the distributions of radial velocity gradients, eak turbulent kinetic energy, and eak Reynolds stresses, on the jet lane of symmetry. Crossed hot-wire measurements revealed reductions of the aforementioned arameters on the underside of the jet and increases on the uer side of the jet. External wedges rovided significant downward reduction in turbulence levels with the least amount of uward increases. The exeriments were instrumental in establishing a link between the asymmetry of the mean velocity field and the reduction in eak turbulent kinetic energy and eak Reynolds stresses. Reduced velocity gradients were correlated with reduced turbulent kinetic energy levels. This correlation is hoed to hel in the develoment of models connecting noise reduction to the distortion of the mean flow. Through comutational flow field redictions, it would enable the efficient design of next-generation aircraft engine nozzles with directional noise suression caabilities. Acknowledgments We would like to acknowledge the diligent work of Jeff Hamman in rearing the jet facility for the exeriments. Thanks are due to Henry Haskins of NASA LARC for hel with the ylon design. The first author would like to acknowledge the NASA Graduate Student Researchers Program (GSRP) fellowshi, which facilitated this research oortunity. References Paamoschou, D., New Method for Jet Noise Suression in Turbofan Engines, AIAA Journal, Vol., No.,,. -3. Fisher, M.J., Preston, G.A., and Bryce, W.D., A Modelling of the Noise from Simle Coaxial Jets, Part : With Unheated Primary Flow, Journal of Sound and Vibration, Vol. 9, No. 3, 998, Paamoschou, D., Mean Flow and Acoustics of Dual-Stream Jets, AIAA Paer -, resented at the nd AIAA Aerosace Sciences Meeting, January, Reno, NV. Paamoschou, D., and Shue, R.S., Effect of Nozzle Geometry on Jet Noise Reduction using Fan Flow Deflectors, AIAA Paer 6-77, resented at the th AIAA/CEAS Aeroacoustics Conference, Cambridge, MA, May 8-, 6. Paamoschou, D., Fan Flow Deflection in Simulated Turbofan Exhaust, AIAA Journal, Vol., No., 6, Zaman, K.B.M.Q., Bridges, J. E., and Paamoschou, D., Offset Stream Technology Comarison of Results from Exeriments Conducted at UCI and GRC, AIAA Paer 7-38, January 7. 7 Henderson, B., Norum, T. and Bridges, J. E., An MDOE Assessment of Nozzle Vanes for High Byass Ratio Jet Noise Reduction, AIAA Paer 6-3, resented at the th AIAA/CEAS Aeroacoustics Conference, Cambridge, MA, May 8-, 6. 8 Paamoschou, D. Vu, A., and Johnson, A.J., Aerodynamics of Wedge-Shaed Deflectors for Jet Noise Reduction, AIAA Paer 6-36, resented at the th AIAA Alied Aerodynamics Conference, June 6, San Francisco, CA. 9 Birch, S.F., Lyubimov, D.A., Buchshtab, P.A., Secundov, A.N. and Yakubovsky, K.Y., Jet-Pylon Interaction Effects, AIAA Paer -38, th Aeroacoustics Meeting, Monterey, CA, 3- May,. U

6 Table GRC BB Nozzle Parameters Quantity Primary Secondary Nozzle diameter (mm) Plug diameter (mm). - Li thickness (mm).7 - Protrusion (mm).3 - Table GRC BB Nozzle Exit Conditions Quantity Primary Secondary Velocity (m/s) 63.. Mach number.8.3 Byass ratio -.67 Table 3 GRC BB Nozzle Boundary Layer Surveys Boundary Layer Survey Location Momentum thickness, δ (in.) Dislacement thickness, δ (in.). Inner Primary Nozzle.7.. Outer Primary Nozzle Inner Fan Nozzle.7.7 Shae factor, δ /δ Maximum turbulence, u max /U.7.7. Table Peak TKE and Mean Flow Field Parameters GRC Exeriment Peak k/u Below Peak k/u Above * G Below * G Above x GSC / D f Below x GSC / D f Above x / D f Baseline W W W W W+Ca W+Ca W+Ca Table Peak Reynolds Stresses GRC Exeriment Peak u v /U Below (-) u( x ) * GSC, yi, G = y D U Peak u v /U Peak u w /U Above (+) (-) f Peak u w /U (+) Baseline W W W+Ca W W W+Pylon W+Pylon+Flas

7 y Secondary Shear Layer Secondary Core U f PrimaryShear Layer x U Primary Core z x rot i 3 x GSC i i i x Fig. Primary otential core length, x, generalized secondary core (GSC) length, x GSC, and rotrusion of inner nozzle, x rot. The GSC is formed by outer inflection oints i and i 3. Maximum velocity gradient is considered on i for x x GSC. Fig. Wedge-shaed deflector and thickened low seed region underneath the jet centerlane. 7

8 a) c) b) d) Fig. 3 Wedge-shaed deflector configurations. a) W b) W c) W 3 and d) W. H = 6.83 mm is the fan exit height. 3 o a) B=.mm b).mm c) L=9.mm Ca Ca Ca 3 Fig. Cross-sections of a) W, W, and W 3 ; b) W ; and c) three cas (to views). W + Ca W + Ca W + Ca3 Fig. a) Ca configurations tested. b) W + ylon + external fla. 8

9 a) y (mm) x (mm) b) y (mm) x (mm) c) y (mm) x (mm) d) y (mm) x (mm) Fig. 6 Radial coordinates for the CW7 BB nozzle with a) W ; b) W ; c) W 3 ; and d) W. 9

10 a) d) b) e) c) f) Fig. 7 Photos of a) GRC CW-7 jet facility with BB nozzle. Crossed hot-wire robes mounted on an arm attached to a 3D traversing mechanism are in the foreground. b) W ; c) W ; d) W + Ca ; e) W + Ca 3; f) W + Pylon + Flas. z = 3 mm u-v robe u-w robe Fig. 8 Illustration of u-v and u-w crossed hot-wire robe, showing searation in the z-direction.

11 a) u(x,y,)/u contours from. to u, /. -. contours from. to.9 x /D = f u, /. -. contours from. to.9 x /D = f b) W u(x,y,)/u contours from. to u, / W. -. contours from. to.9 x /D = f u, / W. -. contours from. to.9 x /D = f c) W u(x,y,)/u contours from. to u, / W. -. contours from. to.9 x /D = f u, / W. -. contours from. to.9 x /D = f d) W3 u(x,y,)/u contours from. to u, / W3. -. contours from. to.9 x /D = f u, / W3. -. contours from. to.9 x /D = f Fig. 9 Isocontours of mean axial velocity on the lanes z=, =, and =. a) Baseline nozzle; b) external wedge W ; c) external wedge W ; and d) internal wedge W 3.

12 a) a) b) b) c) c) d) d) e) Fig. RMS axial velocity fluctuation on the lane z= for: a) W ; b) W + Ca ; c) W + Ca ; and d) W + Ca 3. Fig. RMS axial velocity fluctuation on the lane z= for: a) baseline nozzle; b) W ; c) W ; d) W 3 ; and e) W.

13 u, /. -. contours from. to.9 x /D = f.8.6. u, / W. -. contours from. to.9 x /D = f.8.6. u, / W. -. contours from. to.9 x /D = f k(x,y,z)/u contours from.3 to. x /D = f x -3. k(x,y,z)/u contours from.3 to.6 W x /D = f x -3. k(x,y,z)/u contours from.3 to.9 W x /D = f x '( x, y u' v, contours from -.3 to.37 x /D = f ( ) x -3 W - - u' v' x a) b) c), y, z. -. U contours from -.39 to.7 x /D = f ( ) x -3 W - - u' v' x, y, z. -. U contours from -. to. x /D = f x Fig. Cross-sectional isocontours at = of mean velocity (to), turbulent kinetic energy (middle), and Reynolds stress (bottom). a) Baseline nozzle; b) W ; and c) W. 3

14 u, /. -. contours from. to.9 x /D = f.8.6. u, / W3. -. contours from. to.9 x /D = f.8.6. u, / W. -. contours from. to.9 x /D = f k(x,y,z)/u contours from.3 to. x /D = f x -3. k(x,y,z)/u contours from.3 to.8 W3 x /D = f x -3. k(x,y,z)/u contours from.3 to.8 W x /D = f x '( x, y u' v, contours from -.3 to.37 x /D = f x '( x, y u' v, W3. -. contours from -.33 to.3 x /D = f x '( x, y u' v, W. -. contours from -.38 to.9 x /D = f x a) b) c) Fig. 3 Cross-sectional isocontours at = of mean velocity (to), turbulent kinetic energy (middle), and Reynolds stress (bottom). a) Baseline nozzle; b) W 3 ; and c) W.

15 u, / W. -. contours from. to.9 x /D = f.8.6. u, / W + Pylon. -. contours from. to.9 x /D = f.8.6. u, / W + Pylon + Flas. -. contours from. to.9 x /D = f k(x,y,z)/u contours from.3 to.8 W x /D = f x -3. k(x,y,z)/u contours from.3 to.6 W + Pylon x /D = f x -3. k(x,y,z)/u contours from.3 to.79 W + Pylon + Flas x /D = f x '( x, y u' v, W. -. contours from -.38 to.9 x /D = f x '( x, y u' v, contours from -. to. W + Pylon x /D = f x '( x, y u' v, contours from -.36 to. W + Pylon + Flas x /D = f x a) b) c) Fig. Cross-sectional isocontours at = of mean velocity (to), turbulent kinetic energy (middle), and Reynolds stress (bottom). a) W; b) W + Pylon; and c) W + Pylon + Flas.

16 a) ū(x,y,)/ ymax (Df/U) k(x,y,) max / U b) W ū(x,y,)/ ymax (Df/U) k(x,y,) max / U c) W ū(x,y,)/ ymax (Df/U) k(x,y,) max / U d) W ū(x,y,)/ ymax (Df/U) k(x,y,) max / U e) W ū(x,y,)/ ymax (Df/U) k(x,y,) max / U Fig. Inflectional loci showing GSC below jet and GSC above jet (left); maximum radial gradient of the axial comonent of velocity (middle); and maximum turbulent kinetic energy below jet centerlane (right). a) Baseline; b) W ; c) W ; d) W 3 ; and e) W.. ( Baseline ; Wedge Cases ). 6

17 a) W ū(x,y,)/ ymax (Df/U) k(x,y,) max / U b) W + Ca ū(x,y,)/ ymax (Df/U) k(x,y,) max / U c) W + Ca ū(x,y,)/ ymax (Df/U) f k(x,y,) max / U d) W + Ca ū(x,y,)/ ymax (Df/U) k(x,y,) max / U Fig. 6 Inflectional loci showing GSC below jet and GSC above jet (left); maximum radial gradient of the axial comonent of mean velocity (middle); and maximum turbulent kinetic energy below jet centerlane (right). a) W ; b) W + Ca ; c) W + Ca ; d) W + Ca 3. ( W ; W + Cas ). 7

18 x -3 Peak k vs. G Below & Above Jet Centerline k(x,y,) max /U.. BASE W W W 3 W W ca W ca W ca3... u( xgsc, yi ) D, f G = y U Fig. 7 Correlation of eak TKE versus velocity gradient G, valid below and above the jet centerlane. G is measured at x=x GSC, and it is non-dimensionalized using D f. A second-order olynomial fit is also lotted. x -3 Peak k vs. G Below Jet Centerline k(x,y,) max /U BASE W W W 3 W W ca W ca W ca3 6 8 u( xgsc, yi ) x, G = y U Fig. 8 Correlation of eak TKE versus velocity gradient G for the lower half of the jet. G is calculated at x=x GSC, and it is non-dimensionalized using x. 8