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Twenty-Third Symposium on Naval Hydrodynamics (2001)
Naval Studies Board (NSB)

Page
171
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Page
171
Front Matter (R1-R19)
Modern Seakeeping Computations for Ships (1-45)
Forces, Moment and Wave Pattern for Naval Combatant in Regular Head Waves (46-65)
New Green-Function Method to Predict Wave-Induced Ship Motions and Loads (66-81)
Validation of Time-Domain Prediction of Motion, Sea Load, and Hull Pressure of a Frigate in Regular Waves (82-97)
Ship Motions and Loads in Large Waves (98-111)
Prediction of Vertical-Plane Wave Loading and Ship Responses in High Seas (112-125)
Basic Studies of Water on Deck (126-142)
Second Order Waves Generated by Ship Motions (143-156)
Prediction of Nonlinear Motions of High-Speed Vessels in Oblique Waves (157-170)
Optimizing Turbulence Generation for Controlling Pressure Recovery in Submarine Launchways (171-180)
Hull Design by CAD/CFD Simulation (181-190)
Steady-State Hydrodynamics of High-Speed Vessels with a Transom Stern (191-205)
Practical CFD Applications to Design of a Wave Cancellation Multihull Ship (206-222)
Simulation of Ship Maneuvers Using Recursive Neural Networks (223-242)
Flow- and Wave-Field Optimization of Surface Combatants Using CFD-Based Optimization Methods (243-261)
Marine Propulsor Noise Investigations in the Hydroacoustic Water Tunnel 'G.T.H.' (262-283)
Propulsor Design Using Clebsch Formulation (284-300)
Unsteady Flow Quantities on Two-Dimensional Foils: Experimental and Numerical Results (301-313)
Hydrofoil Turbulent Boundary Layer Separation at High Reynolds Numbers (314-329)
Pressure Fluctuation on Finite Flat Plate Above Wing in Sinusoidal Gust (330-341)
Control of the Turbulent Wake of an Appended Streamlined Body (342-354)
Investigation of Global and Local Flow Details by a Fully Three-Dimensional Seakeeping Method (355-367)
Prediction of Wave Pressure and Loads on Actual Ships by the Enhanced Unified Theory (368-384)
Frequency Domain Numerical and Experimental Investigation of Forward Speed Radiation by Ships (385-401)
International Collaboration on Benchmark CFD Validation Data for Surface Combatant DTMB Model 5415 (402-422)
Validation of High Reynolds Number, Unsteady Multi-Phase CFD Modeling for Naval Applications (423-440)
Free Surface Viscous Flow Computation Around A Transom Stern Ship by Chimera Overlapping Scheme (441-456)
Anti-Roll Tank Simulations With A Volume of Fluid (VOF) Based Navier-Stokes Solver (457-473)
Validation of Tab Assisted Control Surface Computation (474-484)
Experimental and Numerical Investigation of the Flow Around the Appendices of a Whitbread 60 Sailing Yacht (485-492)
Propeller Wake Analysis by Means of PIV (493-510)
Experimental and Numerical Investigation of the Unsteady Flow Around a Propeller (511-526)
Simulation of Incompressible Viscous Flow Around a Ducted Propeller Using a RANS Equation Solver (527-539)
On Submerged Stagnation Points and Bow Vortices Generation (540-552)
Numerical Prediction of Scale Effects in Ship Stern Flows with Eddy-Viscosity Turbulence Models (553-568)
The Experimental and Numerical Study of Flow Structure and Water Noise Caused by Roughness of a Body (569-578)
Large-Eddy Simulations of Turbulent Wake Flows (579-598)
Instability of Partial Cavitation: A Numerical/Experimental Approach (599-615)
An Unsteady Three-Dimensional Euler Solver Coupled with a Cavitating Propeller Analysis Method (616-638)
On the Flow Structure, Tip Leakage Cavitation Inception and Associated Noise (639-653)
An Experimental Investigation of Cavitation Inception and Development of Partial Sheet Cavaties on Two-Dimensional Hydrofoils (654-669)
Modeling 3D Unsteady Sheet Cavities Using a Coupled UnRANS-BEM code (670-686)
Ship Wake Detectability in the Ocean Turbulent Environment (687-703)
An Experimental and Computational Study of the Effects of Propulsion on the Free-Surface Flow Astern of Model 5415 (704-712)
Breaking Waves in the Ocean and Around Ships (713-745)
Numerical and Experimental Study of the Wave Breaking Generated by a Submerged Hydrofoil (746-761)
The Numerical Simulation of Ship Waves Using Cartesian Grid Methods (762-779)
Radiation Loads on a Cylinder Oscillating in Pycnocline (780-791)
Wave Resistance Computations - A Comparison of Different Approaches (792-804)
Computations of Nonlinear Turbulent Free Surface Flows Using the Parallel Uncle Code (805-819)
Submarine Maneuverability Assessment Using Computational Fluid Dynamic Tools (820-832)
Simulation of UUV Recovery Hydrodynamics (833-847)
Reynolds-Averaged Modeling of High-Froude-Number Free Surface Jets (848-862)
On Roll Hydrodynamics of Cylinders Fitted with Bilge Keels (863-880)
Combining Accuracy and Effciency with Robustness in Ship Stern Flow Computation (882-896)
An Unstructured Multielement Solution Algorithm for Complex Geometry Hydrodynamic Simulations (897-909)
Ship Stern Flow Calculations on Overlapping Composite Grids (910-926)
Study on the Prediction of Flow Characteristics Around a Ship Hull (927-940)
Analysis of Turbulence Free-Surface Flow Around Hulls in Shallow Water Channel by a Level-Set Method (941-956)
A Design Tool for High Speed Ferries Washes (957-967)
Flow Around Ships Sailing in Shallow Water - Experimental and Numerical Results (968-982)
Ship Stability Study in the Coastal Region: New Coastal Wave Model Coupled with a Dynamic Stability Model (983-992)
Waves and Forces Caused by Oscillation of a Floating Body Determined Through a Unified Nonlinear Shallow-Water Theory (993-1005)

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Optimizing Turbulence Generation for Controlling Pressure Recovery in Submarine Launchways S. Jordan (NavalUnderseaWarfareCenter,USA) ABSTRACT E cess pressure recovered withm submarin hull cavities c m lead b u favorable conditions for safe operation A notable example would be the submarin vehicle Izmmchway when She vehicle outlet Ed pump inlet are m far proximity along the h 11 h~zsmuch as th mam outlet co figuration is cylind ical, this topology p mmits insertion of p riodic wall-mounted devices for controlling its pa ssure recovery capability This control is centered on m mifesting z pressure loss though turbulence ingestion caused by the he's presen Thus, She work herein presents z mmmerical m- e tigation by the Izrge~ddy simulation DIES) of periodic symmetric ribs with z nib height to nib spacing ratio of 5 m z cylind ical duct The salient cortical structures produced by the rib's on sts are shown as w 11 as the turbulent statistics hat comprise the n w kin tic en rgy nsponsible for the pnssure loss (or red ction in pressure recovery) A comparison of She predicted frictional coefficient with the zt-sez measur merits shows flat the Fictional coefhcient is independent over Rey olds mmmbers sparming It least th ee crders-of-magnitude INTRODUCTION NO y design engineers require trict conhol over the extent of pressure recoven d insid submarin recessed hull cavities Ed vehicle kunchways to Insure successful underset operations during reconnaissance Ed delense missi ms in cases where She differed e betw en the hyd odynamic performance of the submarin vehicle shutterway n cess with respect to the pump inlet cavity promotes z reverse flow th ough She com cting I muchway mech mism, m adverse pressure a. dient pa Exists across the vehicle just prior to I much This pressure differed e must be overcome by She pump itself dmmg tart~p Funh n ore, given sufficient pressure differ e, m initial breachward movement of the vehicle may occur that m result in unacceptable hunch damage The following work presents z flexible measure for conhollmg She level of pressun recovered in the submarin I muchway to avoid the adverse hunching conditions just described Specifically, f is measure in olves plac merit of periodic ribs in the submarin cylmd ical shutte way end of the vehicle kunchway that m suitable minimize She level of the pressure recovered (or maximize pressure loss) of She Eternal flow Roughening surfaces with small discnte ribs is thoroughly under tood qualitatively for etch ing Ed conholling mass Ed heat t msfer rates This k owledge arose k gely fiom She experimental Ed mmmerical investigations that demonstrated then importance in designing efficient ducts for mech mical systems such as zucraft engin s Ed mmclear reactors The ribs Themselves are t pically mounted periodically along She i mer walls of th duct Ed generate n w turbulent regions withm the core sheamwise flow This erJkmced t rbulent activity greatly improves She mixing Ed or cooling characteristics of the ribbed surface over the traight walled duct Gen .. fly, the zccomp Eying pa ssure loss is viewed as z design penalty of the nib el ment, but as m the pose t application f is consequen e is m effective me ms for controlling She pressun gradient within the duct The flow characteristics of ribbed wall ducts in the fully rough regime (independent of Rey olds mmmt:erl fall basically under on of two categories IPmrz, 1969) Roughen surfaces with sh > 4 are termed 'k-type" bec mse She rib pa sen e disturbs the con flow character (s h d notes th pit h to height ratio of each rib element) l~rge-scale vortices shed from the rib cre ts whose shucture remains Intact whi e convected downsheam by the core flow By contrast, z roughen d surface with s h < 4 signifies gen ration of cordin d cortical struct res oscillating 1 en een th ribs with minimal i fluen e on She core flow characteristics Unlike the k-t pe', She mean .- ~ zmwise outer flow of this 'd -type' roughness c m be qmsnrhied by the logarithmic kw (using imler variables) that extends down to the viscous subbyer along She rib costs in She literature, on will find

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m my empirical relationships for approximating the frictional factor pressme loss) of rib~oughened walls m the fully turbulent regime (see Fig I Ed Table I for several of th m) U fort mutely, given ~ specific rib height, She choice of its pitch for achieving m optimum frictional factor is not easily obtained using these relationships By examming the origin of each relationship, one will see that She disparity among th m arises principally from the various parameters chosen for each experiment such as She te t section, h D (or h/D ) ratio Ed r mge of s h ratios st died Thus, the collapse of These relationships onto ~ unique expression for the f ictional coefficient apparently reveres red fining She s h parameter Alternatively, the choice of s h for optimi ing the pressme loss in th submarine shutte way must be based on She e perimental measurements of Berger Ed Hhu (1979) Although they did not report m empu ical expression for She frictional coefficient, they produced quantitative local me m mass Ed heat t msfer dishibutions within ~ roughened circular cylinder They tested ribs 3 < s/h < 10 which showed Chat the highest me m mass h msfer coetllcifftrs were achieved for h = 5 over ~ wide r we of Rey olds mmmbers Berger Ed Hhu concluded font She ratio s h = 5 achieves favorable heat Ed mass tr msfer distributions 1 e. mse flow reattachment Ed separation occur simult meouslybetw en subsequent ribs Thus, the present pap r is concerned with ~ 'k- type' roughness having sh = 5 as m effective loss (or minimi i g the me m pressure recovery) withm ~ cylind ical duct To asce tam the domi mt turbulent physics that me responsible for producing the static pressure loss Ed She resulting fiictiomal loss coefhcie t, ~ computation was conducted using the k Shoddy simulation LE3 1 methodology Since the energy-domim~te scales of the t rbulent field primarily attribute to th tatic poet me loss, LES is w 11-suited for this purpose The impet s of the LES methodology is f 11 resolution of the energybearmg scales of the turbulent motion while mod hng the smaller scales font tend towards homogeneous Ed isotropic conditions The salient turbulent featmes of She flow are presented in this paper Including its struct He Ed statistical quantities font on noble fiom She rib's presence Aldhough She prese t computations depict flow characteristics for ~ Rey olds mmmber se- eras orders of magnitude low r f m f 11-scale, She me m pressme loss is verified by at-sea met tuemem3 taken fiom ~ full scale prototype test onboard ~ US Na y submarine 0.1 _ 1 - (3~\ 3 ~` .~N : _ Webb (iill1 - _ __ WaSSel ~ MrIlS (~979) 1 10 100 p/h Figme I Empu ical Relationships for Dere mini g the Fricti m Factor for Rib Roughened Ducts Table I Parameters Determined for the Relationships mFig 1; f =2[ltu(r/h)+uy 3] 2, oh =C(r/h)t 04 04 041 04C 04 _ _ E r 11 450 _ t 375 t 375 l tC 3 50 _ tC 1 20 Go 3 653 024 5 053 I of. O. 50 1 43 0 35 GOVERNING METHOD EQUATIONS AND SOLUTION To provide sufhcie t patial resolution of She salient turbulent activity in She cylind ical duct, grid point clustering is necessary around the rib elements Concunently, application of ~ LES formulation to this grid topology reduces proper h m formation Ed filtering of th cylmd i 91 coordinate form of She full - resolution equation system nncomp~ , Ale Navier- Stokes Ed contimmity equations) to ~ curvilmear coordinate famework The procedure suggested by Jord m (1999) is follow d herein where She fu st patial operation is formal h m fommation of each term in the original equations The h msfommed system appears as Contimmity: at/ q (1)

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Moment m [she tmwise (x), radMI (r), cl cumfet ntMI (3)]: a r~pV~ aT¢t iq j V~ a r\rZ: p at ak ak +~[J7gk aV~] a ~ ~ J-v ~v~ = r a [k¢~ P + I ~ a |~gk~aVr 1| rV +2aF¢tV~ 1 ar,/ Vd ali::,qiV9+EVv~= aTk~tP +Re[a~k(Fg a ~ | r([V~ 2 )¢k |] whet each temm is show t m its non-dimensiorul conservativefomm; xj=(x,r,0), qj=(rv~ ,ve) md gt =hj~t~, where hj =(r J.4r) he coefficients (t~ md ~/; dertote the metrics md the Jacobi m of fhe tt msformation, respectively Filtermg fhe ~hove cylind icM sy tem derives the LES fommuLtion hus, the t sultmt grid-frltered equctions m curvilmear coordit~tes for cylind icM geometries become Contimmity: au+av+aw=0 a; a~ a: Momentum: a r~ a T7}~ a R/~ p D at a~k a k a~k + I a (~gk aVx | aW au}v, ~_ _ a~-~}~ a t Rel4(~ a ~ r(~' (k (3) (48) (4b) a r`~0 +a U~:v~ ~VIVC = aF¢9 P+a~k (2a) +Re~(~g a¢J r(~vs 2 a k 1 where the resolvable conttavari mt velocity compot nts (U}) m fhe convective terms are defn d; U}=~/~}~ qj he subgrid scMe (SGS) shess tensor t ~' is defmed in conttavari mt form es t }=U} v~ U}v~ Accord6ng to Jord m (1999), fhe metric coefficients are considered es filtered bee mse fhey me evalllated mmmericMly et discrete pomts Mong the curvilit ar Imes(denotedbyatilde) he ctove LES sy tem was time~dvanced by c vari mt of the fractiot~l- tep method (Jordan md Rag~h, 1996) his techmiqtt utilizes c s ml-staggered disct ti ction molecule that is refommuLted in boundary-frtted cylind icM coordit~tes he diff sive derivatives w t time ~dvanced by fhe Crcr~k-Nicolson scheme to elimit~te fhe high viscous stability re triction t ar fhe rib rrests, while fhe non-lmear terms w t time tdvanced by m explicit Adtms- Bcshforfh scheme SpatMlly, the convective derivative s w re cpproximate d by fhir d -or de t accu rcte upwindbiased fmite differet es wifh fhe dfffusive terms discretized using st mdard second-order-accurcte finte volume dfffet t es he Pt ssure-Poisson equction of fhe fractiot~l-step procedure was Mso cenhM differet d to the second order Addbtiot~1 det tils of fhe solution medhodology, along wifh several test cases, c m be found in Jord m md Rcgab (1996) DYNAMIC SUBGRID SCALE MODEL For the nbs comput ttion. Ml of fhe turbulent scMes removed by the filter opemtion w re modeled by m eddy viscosity rektionship modified for dyt tmic computation of the model coeffrcient (Smcgormsky, 1963), (Germ mo et M, 1991) he dynamic coefficient will give the conect csymptotic behavior of the turbulent stt sses when cpproaching fhe nb wMls md minimize SGS conhibutions in the low turbulent regions betweert tbsequent ribs he tt msfcrmed form of the dyt tmic model is expt ssed es t ~'+1/~g,i'7~ =2C~ S S,} (5) where C is the dynamic coefficient md the frltered mehic term 5} is defit d ~s S}=~/:S,dj~=s~.

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which t msforms th trace of the SGS shess tensor The t rbulent eddy viscosity is defmed as VT =CA2 s wh re |s| = Am; md A is She grid- filter width which is equal to th loch grid spacing The resolvable shMn~cte field (51~) is expressed as s ~ = HAS Sit with each term define d by ~ 21~ a: i ~ S -S} = I I`Ug}4 a ~ + fits a: 21 |pv, + 2 aJ~k vs -S} = I~`f~g} OCR for page 175
Figure 2. Stretched Grid Generated for the Rib-walled Duct Computation; 64x141x401 (O,r,x directions). Table 2. Geometry and Steady-state Flow Parameters of the LES Computation. | h/R ~;;;~ (a) Figure 3. Isosurfaces of Streamwise Vorticity; (a) Max 2.4, Min 1.6; (b) Max.-1.2, Min.-2.0 pitch to diameter ratio of each rib for the present LES computation is s/D = 0.5. Proper resolution of the turbulent vorticity near the rib walls requires respective boundary stretching of the grid points. Choice of the first field point is difficult to justify 'a-priori' because the classic law-of-the-wall profile is not expected along any of the duct walls (expect perhaps near the rib crests). Typically, the first field point in wall units should be on the order of y+ < 5. Using this criterion as a requirement on the instantaneous level, the grid cluster was suitably adjusted before collection of the LES results took place for evaluating the steady-state turbulent statistics. The final grid reached for the cylindrical rib application housed 65x141x401 points in the circumferential (0), radial (r), and streamwise directions (x), respectively, as shown in Fig. 2 with simulation parameters listed in Table 2. The grid is orthogonal, but boundary-fitted to all no-slip walls. First point spacing around the ribs is 0.013 (scaled by h). Along the cylinder walls in the trough region the first point spacing is 0.021. Highest mean values for y+ were found along the rib crests and typically were y+ = 0~1~. Although the instantaneous flow is obviously non- periodic, the computation assumed statistical steady- state homogeneous characteristics at each subsequent rib and trough section. Thus, periodic boundary conditions were used in the streamwise as well as the circumferential direction. The grid spacing in the circumferential direction was uniform over O < 0 < 2~. The Reynolds number (Re) based on streamwise velocity can not be specifically controlled a-priori. But using the statistical steady-state results that were time-averaged over T = 32, Re = 3310 which is based on the rib height and mean centerline streamwise velocity (Uc). Numerical stability allowed the computation to be time-advanced at AT = 0.001; T = tUC/h. We begin studying the flow characteristics of the rib-wall duct by illustrating the isosurfaces of the streamwise vertical structure throughout the ribbed- walled cylinder in Fig. 3. While positive magnitudes are plotted in the lower half of the duct (Fig. 3a), negative isosurfaces are shown in the upper half (Fig. 3b). Away from the walls near the duct core, both figures clearly indicate elongated self-similar structures that are periodic and appear to originate near the rib crests. In the trough regions the same periodicity is apparent, but the structural shape and location of the specific vortices differ in each region. Obese same characteristics can be seen in Fig. 4 where the streamwise contours of the circumferential vorticity (~) are plotted on a plane of constant 0 (0= ~/23. This figure clearly indicates that the streamwise vertical structures shown in the previous figure do indeed originate at the rib crests and require about two periodic lengths before fully convected radially to the primary duct core. These structures house the maximum and minimum magnitudes of circumferential vorticity in the entire duct flow. Between these salient

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:N Figure 4. Contours of Circumferential Vorticity; Max 5.O, Min-6.O, Incr. 1.0. (b) Figure 5. Contours of Streamwise Vorticity; (a) Rib Mid-plane, Max 3.2, Min-2.4, Incr. 0.2; (b) 1/2h Plane Downstream of Rib, Max 4.O, Min-4.O, Incr. 0.4 streamwise structures, a secondary low-vorticity flow exits, but the origin of these secondary structures is not readily obvious in Figs. 3 and 4. Lastly, the distribution of circumferential vorticity in both trough regions reveals little similarity and contributes modestly to the primary vertical flow. Instantaneous contours of the streamwise vorticity (~) on the first rib mid-plane and on a second plane that is itch downstream of the first rib are shown in Fig. 5. Positive streamwise vorticity is given by the solid contours whereas the negative values are plotted as dashed lines. On the mid-plane, a circumferential cluster of streamwise structures is clearly evident that was vertically convected approximately one rib height since their origin along the previous rib crest. A second cluster can be observed near the primary core flow. Unlike their lower counterpart, these latter structures only fluctuate in position while being convected downstream by the dominant streamwise velocity component. The plane downstream of the first rib (Fig. 5b) shows the same lower cluster of streamwise structures as seen in the previous plane. In addition, this plane reveals the circumferential cluster of streamwise vorticity that was produced just upstream along the rib crest. Careful look at their circumferential distribution shows pairs of vertical structures of alternating sign. This observation suggests that these structures are pairs of counter- rotating streamwise vorticity. Lastly, the streamwise vorticity in the trough region of this figure is of little consequence. Their magnitudes are comparatively low and do not appear to communicate strongly with the core flow. Specifically, the streamwise structures that are generated along the rib crest do not enter into the trough region. We can explore the above claim of counter- rotating vertical pairs by showing the circumferential distribution of the vorticity magnitude (Q=4C3o2+c3r2+c3x2 ~ near the first rib crest. The instantaneous isosurfaces of magnitude Q = 2 that are shown in the lower half of the duct in Fig. 6 do indeed confirm this observation. Six pairs of vertical structures are clearly evident that appear symmetric about the crest streamwise centerline. Moreover, the chief content of vorticity in these structures originates only at the rib's leading edge. Figure 6. Isosurfaces of Streamwise Vorticity; Q =2.0.

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(a): vx Contours Max 0.16, Min O.O, Incr. 0.02 (b) vr Contours Max O.1O, Min O.O, Incr. 0.005 (c) q2 Contours Max 3.4e-04, Min O.O, Incr. 1.7e-05 , , (d) vx vr Contours Max 0.007, Min-0.002, Inc 4.5e-04 f ....... (e) Cp Contours Max le-03, Min O.O, Incr. 5e-05 Figure 7. Contours of the Steady-state Fluctuating Quantities; (a) Streamwise Velocity (vx ), (b) Radial Velocity (vr ), (c) Kinetic Energy (q2), (d) Reynolds , , , Stress (vx vr ), Pressure Coefficient (Cp ~ Figure 8. Mean Streamlines (T =32) The duct's turbulent statistics of velocity and pressure scaled by the mean bulk velocity (Ub) are given in Fig. 7. These root-mean square (rms) contours depict circumferential averages as well as time averages over T = 32. They include the resolved as well as the SGS model contributions. The periodicity of each quantity in the trough and core sections of the duct justifies imple meeting periodic boundary conditions in the streamwise direction as well as the total time required to reach statistical steady-state. Interestingly, the normal fluctuations reach their highest values along narrow bands within the core flow. Highest stre amwise fluctuations (vx//Ub~mls peak approximately 2h above the rib crests whereas the radial component (vr//Ub~mls attains its maximum about 1/2h into the core flow (Figs. 7a and 7b, respectively). By comparing the relative rms values of these normal components, the streamwise fluctuations clearly dominate the turbulent activity. This fact is supported by the scaled kinetic energy distributions shown in Fig. 7c. Contours of the streamwise Reynolds stress component (U/V//Ub2) indicate a much wider band distribution of dominant magnitudes with peak values occurring at approximately h above the rib crests (Fig. 7d). Unlike the velocity quantities, pressure fluctuations (Cp/) peak locally at the leading edge of the rib's crest (Fig. 7e). Pockets can also 1r observed about h above the rib's crest, but their values are less than 1/3 of peak. Finally, minimal turbulent activity is shown in the trough and centerline regions of the duct, which were not unexpected characteristics for this type of flow.

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Ott o.' :~ o 0.5 1.0 1.5 2.0 u/Uc Figure 9. Separated Free-shear Layer Growth in the Duct Trough Region. 20 _ Go 1 5 _ ~ ~ o u+=2.,:-' Spalding (196~—~f~~ ~— [it ~ 4~) ,hy3 ~ ('T - X'^ ci.~] ~ _ 1 0 , yplus . . . . 1 0 0 Figure 10. Streamwise Mean Velocity Profile at the Rib Mid-Point in Local Wall Units. Like the turbulent rms quantities, the mean streamlines displayed in Fig. 8 support statistical steady-state similarity when averaged over time T = 32. In the mean, the flow remains attached to the rib crests, which indicates a 'd-type' flow behavior in contrast to the 'k-type' unsteady characteristics as described above. Moreover, this observation suggests that the rib periodicity s/h = 5 is actually within a transition phase from a steady 'd-type' flow behavior to one that is purely 'k-type'. Although the streamlines deflect into the trough region, they do not indicate reattachment. This fact leads to a favorable pressure gradient over the rib crests, which inhibits separation on this surface. We can explore deeper into these conclusions by noting that the growth of the separated free-shear layer in the trough region is linear as given in Fig. 9. Using four inflection points, this layer grows according to Ar/Ax=0.174. Thus, the shear layer grows only 2/3 h between subsequent ribs. A profile of the mean streamwise velocity ~ vx ~ in wall units is plotted in Fig. 10 at the rib crest mid -point along with the law-of-the- wall relationship (using the local inner variables) and Spalding's formula (Spalding, 1961~. Overall, the profile is symbolic of a favorable pressure gradient along the rib crest. Up to y+ < 4, the rib profile follows the classic linear sublayer relationship (u+ = y+) using the local inner variables. Above this point, two distinct relationships are suggested that intersect at about = . These latter profiles require further attention, but will not be investigated in the present . . ( ,lscusslon. As emphasized earlier, the argument for placing periodic ribs in the cylindrical duct is to introduce a pressure loss at the core through turbulent ingestion. Using the mean pressure gradient from the LES results at the duct centerline, a friction coefficient (f = 0.6) was calculated; f = 2Ap/pU2(D/~), where L is the length of the duct. This value was subsequently verified by a full-scale test on-board a US Navy submarine to insure its independence on Reynolds number. Specifically, three at-sea measurement groupings were recorded that gave consistent friction coefficients of f = 0.56+0.04 over 3X106 < Re < 5x106. Thus, although the at-sea measurements were taken at Reynolds numbers that were three orders-of-magnitude higher that the present LES results, the calculated frictional coefficients remain essentially unchanged. This agreement illustrates the fact that when the salient turbulent physics stay consistent over a wide range of Re, LES becomes a useful design tool for realistic topologies as well as practical flows. CONCLUSIVE REMARKS The present work demonstrates control of the pressure recovered in a cylindrical duct through the pressure losses introduced by newly generated turbulent activity from periodic ribs mounted along the internal walls. Given a rib spacing to rib height ratio of s/h = 5 and respectively to the duct diameter (h/D = 0.1), the frictional coefficient (f =0.6) is constant over Reynolds numbers ranging from 3x103 to 5x106; based on the rib height and the duct centerline mean velocity. While the unsteady predictions show separated flow beginning shortly after the rib's leading edge, the steady-state streamlines remained attached to the rib crests. These observations depict characteristics that are purely neither 'd-type' nor 'k-type' roughness. The instantaneous LES results also show distinct large- scale counter-rotating vertical structures originating principally at the rib's leading edge, then convected vertically to their streamwise position in the core flow after two periodic lengths. The tough regions between subsequent ribs do not communicate extensively with the core flow and therefore contribute very little to the mean pressure loss. Both the normal and Reynolds stresses reach peak at different radii with the core flow. The streamwise

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normal st~ess clearly dominstes contributions to the kinetic energy of the core flow Conversely, the pressure fluctuatiom attsm fheir maximum near the nb crest lesding edge Finally, the scaled separated shear Isyer dow tresm of the nb gr ws st s mte of Ar/Ax = 0 174 This growfh rste shows thst the flow remsins detached withm the trough region Conversely, doove the nb crests the treamwise velocity profile in local wsll units indLcstes s non-separstmg flow under s favorstle pressure grsdient The profile only follows the im r subbyer rektionship for turbulent boundary Isyers up toy <4 Ae knowledge me nt s The mfhor md investigstor of fhis work grstef lly ack owledges fhe combmed support of the Office of Nsval Research Dr L Patrick Pmtell, progmm of hcer), fhe Naval Ses Systems Comm md (Cd, R. Schulz, PMS 350) md fhe in-house Lsborstory Independent Research Progrsm Mr R. Philips) st the Naval Underses Warfare C nter REFERENCES Berger, P. P. md Hsu, K P. (1 979), 'Local Msss/Hest Tr m fer Distribution m Surfaces Roughened with Small Square R'bs,' Journol of Heot Mass Tronsfer, Vol. 22, pp 1645-1656 Germano, M, Piomelli, U. Moin, P. md Cnbot W. H. (1991), 'A Dynsmic Subgrid-Scale Eddy Viscosity Model,' Physics ofFluid ,A 3,pp 1760-1765 Jordm, SA, (1999), 'A Large-Eddy Simulstion Methodology m Generalized Curvilinear Coordim~tes,' Journol of Comput tionol Physics, Vol. 14S, pp 322- 340 Jord m, S. A md Rsgsb, S. A, (1996), 'A E hcient Practiorul-Step Techmique for Unstesdy Th ee- Dimensiom~l Plows,' Journol of Computotionol Physics, Vol. 127, pp 218 225 Jord m, 5 A md Rsgdo, 5 A, (1998), "A Large-Eddy Simubtion of th Near Wake of s Cucukr Cylmder," Journol of Fluid Engineering, Vol. 120, pp 243-253 Karmm, T. Von, (1930), Nochr Ges Wiss Goett Moth Phys Kl, pp SS-76 Lilly, DK, (1992), 'A Proposed Modfficstion of fhe Gemm mo Subgrid-Scale Closure Method,' Phy ics of Fluids,A 4,pp 633-635 Peny, AE, Schofield, WH md Joube t, P. N. (1969), 'Rough Wsll Turbulent Boundary Lsyers,' Journol of Fluid Mechonics, Vol. 37, pp 383-413 Smagorinsky, J. (1963), 'General Cucubtion E periments with the Primitive Equstions, l The Bssic E periment," Monthy WeotherReview, Vol. 91, pp 99- 164 Wsssel, A T. md Mills, A P. (1979), 'Cslculstion of Varistle Property Turbulent Priction in Tubes with Hest T msfer m Rough Pipes,' ASME Journol of Heot Transfer,Vol 101,pp 469-474 Webb, R. L, E kert, E R. G md Goldstem, R. I (1971), 'Hest T msfer md Priction in Tubes with Repeated- Rib Roughmess' Intemotionol Joumol of Heot md Mass Tronsfer, Vol. 14, pp 601-618 Whitehesd, AW, (1976), 'The Efects of Suface Roughmg on Pluid Plow md Hest T msfer,' Ph. D Thesis, Queff~ Mary College, Umvers ity of London

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DISCUSSION I C lik We t Vi ginic University, USA Periodic boundary conditions w re used in the sheamwise direction This implies i fmite mmmber of ribs How w 11 does this assumption co terence. with the dom cm developing flow over c fmite mmmber of ribs is questionable But useful i formation c m still be deduced from LES bee mse She dom i mt vorticcl sh uctmes will be periodic, bee mse there me generated vie separation of the flow et the sharp edge of She ribs DISCUSSION S. Cordier Bcssin d'esscis des Crones, France Could you please explain how c periodic sh eamwise boudary condition c m be use d to simulate the turbulencegenerction or vorticity generation in the heal system? Were tests performed with m me th m one rib present m the computational domain? AUTHOR'S REPLY First of all, let me thank Dr C lik md Dr Cordier for then comments md interest m the paper Both discussions question the use of periodic boundary conditions in the streamwise direction of the ribbed duct for representing c series of ribs that ingest new turbulent structures into the core flow The mew r to this question rests on justifying c correct set of flow conditions et these open boundaries bee mse Hey depend on the physics outside She flow domain This dependence is satisfied when setting These faces es periodic, but the turbulence is assumed to be statistically homogeneous or statistically periodic Sufficient separation of these boundaries is critical, where 'opnori' t ~ led e is Required of th two-pomt conelation length of the periodic streamwise stmct res in She case of subsequent ribs, the con canon length is simply She rib's pit h But for simpler geometries such es the turbulent charmel flow, the channel length mu t be et least twice the integral scale of the turbulence in the sheamwise direction The present LES computation tested the periodicity of the duct flow by simulating two ribs On She mst mtaneous level, periodic vorticcl stmctures w re computed within the core flow that on nailed along the lecdmg edge of previous rib Rest These stmctures w re convected Radially towards She duct center over two periodic lengths to reach Heir streamwise position The instmtmeous stmct res withm the trough regions, how ver, showed discernible differences Thus, the trough regions sufficiently guided the computation towards statistical stecdy-state given periodic boundary conditions along She inlet md outlet faces Previous date es w 11 es f 11-sccle measurements taken of the present design show that the flow's memory from nomperiodic inlet conditions occurs only over the first two ribs This length appears mdependent of She present rmge of Rey olds mmmbers md scales closme of the separated shear Dyers Nat me growing radially towards She duct centerline Thus, the present LES computation, which employs streamwise periodic boundary conditions, mimics the actual prototype design fiom the third rib md beyond Direct comparisons of the mean flow date taken from She full-sccle prototype md the present computation proved this point Given c target centerline pressure loss of c prototype design for the submarine I muchway, These LES results provide the requited design length plus two cdditiorurl ribs

Representative terms from entire chapter:

pressure loss