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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as OPTIMIZING TURBULENCE GENERATION FOR CONTROLLING PRESSURE RECOVERY IN SUBMARINE LAUNCHWAYS 171 Optimizing Turbulence Generation for Controlling Pressure Recovery in Submarine Launchways S.Jordan (Naval Undersea Warfare Center, USA) ABSTRACT Excess pressure recovered within submarine hull cavities can lead to unfavorable conditions for safe operation. A notable example would be the submarine vehicle launchway where the vehicle outlet and pump inlet are in far proximity along the hull. Inasmuch as the main outlet configuration is cylindrical, this topology permits insertion of periodic wall- mounted devices for controlling its pressure recovery capability. This control is centered on manifesting a pressure loss through turbulence ingestion caused by the rib's presence. Thus, the work herein presents a numerical investigation by the large-eddy simulation (LES) of periodic symmetric ribs with a rib height to rib spacing ratio of 5 in a cylindrical duct. The salient vortical structures produced by the rib's crests are shown as well as the turbulent statistics that comprise the new kinetic energy responsible for the pressure loss (or reduction in pressure recovery). A comparison of the predicted frictional coefficient with the at-sea measurements shows that the frictional coefficient is independent over Reynolds numbers spanning at least three orders-of-magnitude. INTRODUCTION Navy design engineers require strict control over the extent of pressure recovered inside submarine recessed hull cavities and vehicle launchways to insure successful undersea operations during reconnaissance and defense missions. In cases where the difference between the hydrodynamic performance of the submarine vehicle shutterway recess with respect to the pump inlet cavity promotes a reverse flow through the connecting launchway mechanism, an adverse pressure gradient pre-exists across the vehicle just prior to launch. This pressure difference must be overcome by the pump itself during start-up. Furthermore, given sufficient pressure difference, an initial breachward movement of the vehicle may occur that can result in unacceptable launch damage. The following work presents a flexible measure for controlling the level of pressure recovered in the submarine launchway to avoid the adverse launching conditions just described. Specifically, this measure involves placement of periodic ribs in the submarine cylindrical shutterway end of the vehicle launchway that can suitable minimize the level of the pressure recovered (or maximize pressure loss) of the internal flow. Roughening surfaces with small discrete ribs is thoroughly understood qualitatively for enhancing and controlling mass and heat transfer rates. This knowledge arose largely from the experimental and numerical investigations that demonstrated their importance in designing efficient ducts for mechanical systems such as aircraft engines and nuclear reactors. The ribs themselves are typically mounted periodically along the inner walls of the duct and generate new turbulent regions within the core streamwise flow. This enhanced turbulent activity greatly improves the mixing and/or cooling characteristics of the ribbed surface over the straight-walled duct. Generally, the accompanying pressure loss is viewed as a design penalty of the rib element, but as in the present application this consequence is an effective means for controlling the pressure gradient within the duct. The flow characteristics of ribbed-wall ducts in the fully rough regime (independent of Reynolds number) fall basically under one of two categories (Perry, 1969). Roughen surfaces with s/h>4 are termed “k-type” because the rib presence disturbs the core flow character (s/h denotes the pitch to height ratio of each rib element). Large-scale vortices shed from the rib crests whose structure remains intact while convected downstream by the core flow. By contrast, a roughened surface with s/h ≤4 signifies generation of confined vortical structures oscillating between the ribs with minimal influence on the core flow characteristics. Unlike the ‘k-type', the mean streamwise outer flow of this ‘d-type' roughness can be quantified by the logarithmic law (using inner variables) that extends down to the viscous sublayer along the rib crests. In the literature, one will find the authoritative version for attribution.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as OPTIMIZING TURBULENCE GENERATION FOR CONTROLLING PRESSURE RECOVERY IN SUBMARINE LAUNCHWAYS 172 many empirical relationships for approximating the frictional factor (pressure loss) of rib-roughened walls in the fully turbulent regime (see Fig. 1 and Table 1 for several of them). Unfortunately, given a specific rib height, the choice of its pitch for achieving an optimum frictional factor is not easily obtained using these relationships. By examining the origin of each relationship, one will see that the disparity among them arises principally from the various parameters chosen for each experiment such as the test section, h/D (or h/Dh) ratio and range of s/h ratios studied. Thus, the collapse of these relationships onto a unique expression for the frictional coefficient apparently requires redefining the s/h parameter. Alternatively, the choice of s/h for optimizing the pressure loss in the submarine shutterway must be based on the experimental measurements of Berger and Hau (1979). Although they did not report an empirical expression for the frictional coefficient, they produced quantitative local mean mass and heat transfer distributions within a roughened circular cylinder. They tested ribs 3≤s/h ≤10 which showed that the highest mean mass transfer coefficients were achieved for s/h=5 over a wide range of Reynolds numbers. Berger and Hau concluded that the ratio s/h=5 achieves favorable heat and mass transfer distributions because flow reattachment and separation occur simultaneously between subsequent ribs. Thus, the present paper is concerned with a ‘k-type' roughness having s/h=5 as an effective mechanism for maximizing the mean static pressure loss (or minimizing the mean pressure recovery) within a cylindrical duct. To ascertain the dominant turbulent physics that are responsible for producing the static pressure loss and the resulting frictional loss coefficient, a computation was conducted using the large-eddy simulation (LES) methodology. Since the energy-dominate scales of the turbulent field primarily attribute to the static pressure loss, LES is well-suited for this purpose. The impetus of the LES methodology is full resolution of the energy-bearing scales of the turbulent motion while modeling the smaller scales that tend towards homogeneous and isotropic conditions. The salient turbulent features of the flow are presented in this paper including its structure and statistical quantities that originate from the rib's presence. Although the present computations depict flow characteristics for a Reynolds number several orders of magnitude lower than full-scale, the mean pressure loss is verified by at-sea measurements taken from a full scale prototype test on-board a US Navy submarine. Figure 1. Empirical Relationships for Determining the Friction Factor for Rib -Roughened Ducts. Table 1. Parameters Determined for the Relationships in Fig. 1; β Author B C −0.24 Whitehead 0.41 4.50 6.53 −3.75 Webb 0.41 0.95 0.53 −3.75 1−h/Rh W&M 0.41 0.50 Hann 0.40 3.50 1.43 0.35 Karmon 0.40 1.20 ····· ···· ········· GOVERNING EQUATIONS AND SOLUTION METHOD To provide sufficient spatial resolution of the salient turbulent activity in the cylindrical duct, grid point clustering is necessary around the rib elements. Concurrently, application of a LES formulation to this grid topology requires proper transformation and filtering of the cylindrical coordinate form of the full-resolution equation system (incompressible Navier-Stokes and continuity equations) to a curvilinear coordinate famework. The procedure suggested by Jordan (1999) is followed herein where the first spatial operation is formal transformation of each term in the original equations. The transformed system appears as Continuity: (1) the authoritative version for attribution.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as OPTIMIZING TURBULENCE GENERATION FOR CONTROLLING PRESSURE RECOVERY IN SUBMARINE LAUNCHWAYS 173 Momentum [streamwise (x), radial (r), circumferential (θ)]: (2a) (2b) (2c) where each term is shown in its non-dimensional conservative form; and where The coefficients and denote the metrics and the Jacobian of the transformation, respectively. Filtering the above cylindrical system derives the LES formulation. Thus, the resultant grid-filtered equations in curvilinear coordinates for cylindrical geometries become Continuity: (3) Momentum: (4a) (4b) (4c) where the resolvable contravariant velocity components in the convective terms are defined; The subgrid scale (SGS) stress tensor is defined in contravariant form as According to Jordan (1999), the metric coefficients are considered as filtered because they are evaluated numerically at discrete points along the curvilinear lines (denoted by a tilde). The above LES system was time-advanced by a variant of the fractional-step method (Jordan and Ragab, 1996). This technique utilizes a semi-staggered discretization molecule that is reformulated in boundary-fitted cylindrical coordinates. The diffusive derivatives were time-advanced by the Crank-Nicolson scheme to eliminate the high viscous stability restriction near the rib crests, while the non-linear terms were time-advanced by an explicit Adams-Bashforth scheme. Spatially, the convective derivatives were approximated by third-order-accurate upwind-biased finite differences with the diffusive terms discretized using standard second-order-accurate finite volume differences. The pressure-Poisson equation of the fractional-step procedure was also central differenced to the second order. Additional details of the solution methodology, along with several test cases, can be found in Jordan and Ragab (1996). DYNAMIC SUBGRID SCALE MODEL For the ribs computation, all of the turbulent scales removed by the filter operation were modeled by an eddy viscosity relationship modified for dynamic computation of the model coefficient (Smagorinsky, 1963), (Germano et al., 1991). The dynamic coefficient will give the correct asymptotic behavior of the turbulent stresses when approaching the rib walls and minimize SGS contributions in the low turbulent regions between subsequent ribs. The transformed form of the dynamic model is expressed as (5) where C is the dynamic coefficient and the filtered metric term is defined as the authoritative version for attribution.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as OPTIMIZING TURBULENCE GENERATION FOR CONTROLLING PRESSURE RECOVERY IN SUBMARINE LAUNCHWAYS 174 which transforms the trace of the SGS stress tensor. The turbulent eddy viscosity is defined as where and is the grid-filter width which is equal to the local grid spacing. The resolvable strain-rate field is expressed as with each term defined by (6a) (6b) (6c) where To preserve second-order accuracy in time, the Crank-Nicolson and Adams-Bashforth schemes were applied to the first and remaining components of the total viscous term, respectively. MODEL COEFFICIENT A unique expression for the model coefficient was derived by employing the procedures of Germano et al. (1991), Lilly (1992) and Jordan and Ragab (1998). The procedure requires test filtering the above governing LES equations for cylindrical geometries. This third spatial operation produces resolvable tensors similar to those obtained by Jordan and Ragab (1998) for generalized curvilinear coordinate systems. Specifically, two tensors arise that entail a modified Reynolds stress (7) and a modified Leonard stress (8) The second overbar in these definitions indicate the test filter operation. Both tensors and are evaluated in the computation by explicitly filtering the cylindrical and the contravariant velocity components of the resolved field. The identity for the Leonard term in this curvilinear coordinate system has an identical form to that originally derived by Jordan and Ragab (1998). Using the same eddy viscosity relationship, modeling the modified Reynolds stress tensor becomes (9) Substituting this relationship into the above identity along with the expression for the SGS stress field defines the modified Leonard term in the computational space as (10a) (10b) where the filter width ratio is If we now follow the least-squares minimization procedure of Lilly (1992), the model coefficient is uniquely given by (11) As noted earlier, this expression gives both positive and negative values for the dynamic coefficient through the product Positive coefficients denote forward scatter of energy from the coarse to the finer turbulent scales whereas the negative values indicate backscatter or energy transfer locally up the cascade. To insure computational stability, the negative coefficients were truncated to zero. Thus, in those regions of the flow the truncation error of convective term acted as the SGS model. Explicit filtering by a box-type filter was performed along the curvilinear lines in the computational space. The filter itself is identical in form to its Cartesian counterpart but requires transformation of the physical variable the authoritative version for attribution. before and after filtering. In the present application, a filter width ratio of α=2 gave acceptable model performance. RESULTS AND DISCUSSION The following section presents and discusses the turbulent statistics of a roughened cylindrical duct by square ribs placed periodically at s/h=5. According to the space limitations of the submarine launchway under consideration herein, the maximum permissible height to diameter ratio (h/D) of each rib is 0.1. Thus, the

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as OPTIMIZING TURBULENCE GENERATION FOR CONTROLLING PRESSURE RECOVERY IN SUBMARINE LAUNCHWAYS 175 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. Figure 2. Stretched Grid Generated for the Rib-walled Duct Computation; 64x141x401 (θ, r, x directions). Table 2. Geometry and Steady-state Flow Parameters of the LES Computation. h/R s ∆ymin y+ Rec 0.23 5h 0.013h 0.75 3310 Figure 3. Isosurfaces of Streamwise Vorticity; (a) Max 2.4, Min 1.6; (b) Max. − 1.2, Min. −2.0 The final grid reached for the cylindrical rib application housed 65x141x401 points in the circumferential (θ), 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+= O(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 0≤θ≤ 2π. 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 ∆T=0.001; T=tUc/h. We begin studying the flow characteristics of the rib-wall duct by illustrating the isosurfaces of the streamwise vortical 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. These same characteristics can be seen in Fig. 4 where the streamwise contours of the circumferential vorticity (ωθ) are plotted on a plane of constant θ (θ= π/2). This figure clearly indicates that the streamwise vortical 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 the authoritative version for attribution. vorticity in the entire duct flow. Between these salient

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as OPTIMIZING TURBULENCE GENERATION FOR CONTROLLING PRESSURE RECOVERY IN SUBMARINE LAUNCHWAYS 176 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 vortical flow. Figure 4. Contours of Circumferential Vorticity; Max 5.0, Min −6.0, Incr. 1.0. 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 4.0, Min −4.0, Incr. 0.4 Instantaneous contours of the streamwise vorticity (ω x) on the first rib mid-plane and on a second plane that is 1/2h 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 vortical 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 vortical pairs by showing the circumferential distribution of the near the first rib crest. The instantaneous isosurfaces of magnitude Ω=2 that are vorticity magnitude shown in the lower half of the duct in Fig. 6 do indeed confirm this observation. Six pairs of vortical 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. the authoritative version for attribution. Figure 6. Isosurfaces of Streamwise Vorticity; Ω =2.0.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as OPTIMIZING TURBULENCE GENERATION FOR CONTROLLING PRESSURE RECOVERY IN SUBMARINE LAUNCHWAYS 177 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 implementing 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 Streamwise fluctuations (vx′/Ub)rms peak approximately 2h above the rib crests whereas the radial component (vr′/Ub)rms 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 be 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. the authoritative version for attribution.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as OPTIMIZING TURBULENCE GENERATION FOR CONTROLLING PRESSURE RECOVERY IN SUBMARINE LAUNCHWAYS 178 Figure 9. Separated Free-shear Layer Growth in the Duct Trough Region. 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 ∆r/ ∆x=0.174. Thus, the shear layer grows only 2/3h between subsequent ribs. A profile of the mean streamwise velocity ( ) 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 discussion. 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; 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 OCR for page 171
About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as OPTIMIZING TURBULENCE GENERATION FOR CONTROLLING PRESSURE RECOVERY IN SUBMARINE LAUNCHWAYS 179 normal stress clearly dominates contributions to the kinetic energy of the core flow. Conversely, the pressure fluctuations attain their maximum near the rib crest leading edge. Finally, the scaled separated shear layer downstream of the rib grows at a rate of ∆r/∆x=0.174. This growth rate shows that the flow remains detached within the trough region. Conversely, above the rib crests the streamwise velocity profile in local wall units indicates a non-separating flow under a favorable pressure gradient. The profile only follows the inner sublayer relationship for turbulent boundary layers up to y+<4. ACKNOWLEDGEMENTS The author and investigator of this work gratefully acknowledges the combined support of the Office of Naval Research (Dr. L.Patrick Purtell, program officer), the Naval Sea Systems Command (Cdr, R. Schulz, PMS 350) and the In-house Laboratory Independent Research Program (Mr. R.Philips) at the Naval Undersea Warfare Center. REFERENCES Berger, F.P.. and Hau, K.F., (1979), ‘Local Mass/Heat Transfer Distribution on Surfaces Roughened with Small Square Ribs,' Journal of Heat Mass Transfer, Vol. 22, pp. 1645–1656. Germano, M., Piomelli, U., Moin, P., and Cabot W.H., (1991), ‘A Dynamic Subgrid-Scale Eddy Viscosity Model,' Physics of Fluids, A. 3, pp. 1760– 1765. Jordan, S.A., (1999), ‘A Large-Eddy Simulation Methodology in Generalized Curvilinear Coordinates,' Journal of Computational Physics, Vol. 148, pp. 322–340. Jordan, S.A. and Ragab, S.A., (1996), ‘An Efficient Fractional-Step Technique for Unsteady Three-Dimensional Flows,' Journal of Computational Physics, Vol. 127, pp. 218–225. Jordan, S.A. and Ragab, S.A., (1998), “A Large-Eddy Simulation of the Near Wake of a Circular Cylinder,” Journal of Fluids Engineering, Vol. 120, pp. 243–253. Karman, T.Von, (1930), Nachr. Ges. Wiss. Goett. Math-Phys. Kl., pp. 58–76. Lilly, D.K., (1992), ‘A Proposed Modification of the Germano Subgrid-Scale Closure Method,' Physics of Fluids, A. 4, pp. 633–635. Perry, A.E., Schofield, W.H. and Joubert, P.N., (1969), ‘Rough Wall Turbulent Boundary Layers,' Journal of Fluid Mechanics, Vol. 37, pp. 383–413. Smagorinsky, J., (1963), ‘General Circulation Experiments with the Primitive Equations, I. The Basic Experiment,” Monthy Weather Review, Vol. 91, pp. 99–164. Wassel, A.T. and Mills, A.F., (1979), ‘Calculation of Variable Property Turbulent Friction in Tubes with Heat Transfer in Rough Pipes,' ASME Journal of Heat Transfer, Vol. 101, pp. 469–474. Webb, R.L., Eckert, E.R.G. and Goldstein, R.J. (1971), ‘Heat Transfer and Friction in Tubes with Repeated-Rib Roughness' International Journal of Heat and Mass Transfer, Vol. 14, pp. 601–618. Whitehead, A.W., (1976), ‘The Effects of Surface Roughing on Fluid Flow and Heat Transfer,' Ph.D. Thesis, Queen Mary College, University of London. the authoritative version for attribution.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as OPTIMIZING TURBULENCE GENERATION FOR CONTROLLING PRESSURE RECOVERY IN SUBMARINE LAUNCHWAYS 180 DISCUSSION I.Celik West Virginia University, USA Periodic boundary conditions were used in the streamwise direction. This implies infinite number of ribs. How well does this assumption conferences with the domain developing flow over a finite number of ribs is questionable. But useful information can still be deduced from LES because the dominant vortical structures will be periodic, because there are generated via separation of the flow at the sharp edge of the ribs. DISCUSSION S.Cordier Bassin d'essais des Carnes, France Could you please explain how a periodic streamwise boudary condition can be used to simulate the turbulencegeneration or vorticity generation in the real system? Were tests performed with more than one rib present in the computational domain? AUTHOR'S REPLY First of all, let me thank Dr. Celik and Dr. Cordier for their comments and interest in the paper. Both discussions question the use of periodic boundary conditions in the streamwise direction of the ribbed duct for representing a series of ribs that ingest new turbulent structures into the core flow. The answer to this question rests on justifying a correct set of flow conditions at these open boundaries because they depend on the physics outside the flow domain. This dependence is satisfied when setting these faces as periodic, but the turbulence is assumed to be statistically homogeneous or statistically periodic. Sufficient separation of these boundaries is critical, where ‘a-priori' knowledge is required of the two-point correlation length of the periodic streamwise structures. In the case of subsequent ribs, the correlation length is simply the rib's pitch. But for simpler geometries such as the turbulent channel flow, the channel length must be at least twice the integral scale of the turbulence in the streamwise direction. The present LES computation tested the periodicity of the duct flow by simulating two ribs. On the instantaneous level, periodic vortical structures were computed within the core flow that originated along the leading edge of previous rib crest. These structures were convected radially towards the duct center over two periodic lengths to reach their streamwise position. The instantaneous structures within the trough regions, however, showed discernible differences. Thus, the trough regions sufficiently guided the computation towards statistical steady-state given periodic boundary conditions along the inlet and outlet faces. Previous data as well as full-scale measurements taken of the present design show that the flow's memory from non- periodic inlet conditions occurs only over the first two ribs. This length appears independent of the present range of Reynolds numbers and scales closure of the separated shear layers that are growing radially towards the duct centerline. Thus, the present LES computation, which employs streamwise periodic boundary conditions, mimics the actual prototype design from the third rib and beyond. Direct comparisons of the mean flow data taken from the full-scale prototype and the present computation proved this point. Given a target centerline pressure loss of a prototype design for the submarine launchway, these LES results provide the required design length plus two additional ribs. the authoritative version for attribution.