Proceedings of the Sixth International Conference on Numerical Ship Hydrodynamics (1994) / Chapter Skim
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Session 8- Viscous Flow: Applications 1
Session 8- Viscous Flow: Applications 1
Pages 407-454
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From page 409... ...
The distributions of transverse forces along the hull and the integrated moments about the center of buoyancy are computed and comparisons with the measurements are made. INTRODUCTION Purely for mathematical interest, the inviscid flow about a body of revolution has long since been formulated and studied in detail.
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From page 410... ...
BOUNDARY CONDITION The computational domain defined by a CO grid extends from two loony lengths upstream of the nose to two body lengths downstream of the tail in the longitudinal direction, and two loopy lengths from the body axis in the radial direction. On the loony surface, the no-slip condition 410
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From page 411... ...
In order to predict multiple secondary crossbow separations at high incidence angle, modification was made such that the turbulence length scale of the outer region is determined by the viscous vorticity imbedded in the boundary layer and not the inviscid vorticity shed from the separation line. The modified model has been successfully used in several occasions to compute the turbulent flows over bodies of revolution at an incidence angle (7,16,17~.
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From page 412... ...
The transverse forces along the hull at several incidence angles are shown in Figure 4. Notice that the integration of the areas underneath the curves gives the total normal forces acting on the hull.
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From page 413... ...
Vatsa, V.N., "viscous Flow Solutions for Slender Bodies of Revolution at Incidence," Computers Fluids, Vol.20, No..30, 1991, pp.313,320 18. Gee, K., Cummings, R.M., and S chid, L.B., "Turbulence Model Effects on Separated Flow about a Prolate Spheroid," AIAA Journal Vol.30 No.3 1992, pp.655-664 , , , 19.
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From page 414... ...
(b) Potential Flow Solution .4o 0 0.2 0.4 0.6 0.8 1.0 x/L Figure 2.
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From page 415... ...
ou 0 5 10 1520 0 5 Distance from nose, feet 1 2° Pitch ret °\Lof 1 50 0.50 O.OC 1 5° Pitch 'of, ~ oaf 40, Distance from nose, feet 1.50 6° Pitch ~9° Pitch 1.00 ; 0.50 0.00 ~ -o.sa 10 15 20 C 1 .50 0.00 5 10 15 20 Figure 4. Transverse force along hull at incidences 415 ~ oT oN.
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From page 416... ...
_~ Figure 5. Transverse force coefficients 6 12 15 18 -- -r Gnd# 1 : 79x81x83 Gnd # 2 : 79xl 11x83 0.150 J ~, 0.1 00 .
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From page 417... ...
However, the methods fail to describe the flow at the half-radius position. NOMENCLATURE constant of proportionality for the eddy viscosity k turbulence kinetic energy Lpp length between forward perpendiculars r radial length from propeller axis RD radius of grid domain R propeller radius Us tangential fluid velocity Ux axial fluid velocity at propeller plane UOO free-stream fluid velocity w Taylor wake fraction wit average circumferential wake fraction w2 volumetric mean wake fraction x longitudinal distance perpendicular turbulence diffusion rate angle between propeller radius and horizontal radius INTRODUCTION In recent years a great deal of effort has been spent on developing numerical techniques to solve the Navier-Stokes equations of fluid motion.
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From page 418... ...
The authors use computational fluid dynamics (CFD) methods to calculate the fluid velocity in the propeller disc to deduce the Taylor wake fraction and the associated radial and circumferential distributions of wake.
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From page 419... ...
The eddy viscosity is calculated from the standard twoequation k-e model with convective transport equations for the turbulence kinetic energy and dissipation rate. All of the equations are written in dimensionless form, using a partial transformation, where only the independent coordinate variables are transformed from the physical domain to a logical computational domain.
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From page 420... ...
The method represents a major extension of ideas and techniques for twodimensional flows reported by Baliga and Patankar [83. Features held in common with method 1 include the application of the three dimensional RANS equations subject to the assumptions of steady, incompressible flow, and the eddy viscosity concept calculated from the convective transport equations for k and e.
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From page 421... ...
The particular attributes chosen for the investigation were: a. Turbulence Model The k-e model was used with three different values of C,, (the constant of proportionality relating the eddy viscosity to the computed ratio k2/~.
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From page 422... ...
the Taylor wake fraction, w, at the radius of the propeller disc, and at half the radius: w~r,§)
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From page 423... ...
, which strays significantly from the experiment data, the Taylor wake fraction at the edge of the propeller disc (Figure 1) is predicted reasonably accurately.
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From page 424... ...
It must be emphasised that the only change to the datum run was the application of a set of no-slip conditions to those nodes closest to the wire; the grid and all other features remained the same. Finally, the volumetric mean wake fraction, w2, is listed in Table 6 for all the runs performed.
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From page 425... ...
. Although the crude approach adopted led to worse quantitative predictions of the nominal wake, it dramatically improved the qualitative prediction of the axial velocity contours.
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From page 426... ...
12. Chen, Y.-S and Kim, S.-W, "Computation of Turbulent Flows Using an Extended k-e Turbulence Closure Model," NASA October 1987.
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From page 427... ...
Table 3 - Verification Runs for Method 2 r switch # turbulence grid alignment wire 1 yes yes no yes 2 yes no no 3 yes no no 4 no 5 ~~ no ~ Table 4 - Verification Runs for Method 3 . switch # turbulence grid alignment wire 1 no no yes no 2 no yes yes 3 no no yes .
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From page 428... ...
Table 6 - Description of Run Numbers . Run # MethodSwitchw2 Settings 1 l 1datum #0 |0.46 l 2 | 1turbulence #3 |0.48 3 1grid #30.46 4 ~1grid #4 ~0.50 5 | 2datum#O |0.38 6 ~2turbulence #1 ~0.40 7 ~2turbulence #2 ~0.43 2turbulence #3 ~0.41 9 ~2 wire #1 ~0.21 10 1 2 wire #1, 1 0.23 turbulence #3 11 ~2 grid #1 ~0.41 12 ~2 wire#l, ~0.33 grid #1 13 1 datum #0 | 0 44 14 3 alignment #1 0.33/0 15 ~3 alignment #2 ~0.31 16 ~3 alignment #3 ~0.21 17 ~3 grid #2 ~0.40 18 ~4 datum#O T 045 19 ~4 grid #5 ~0.46 20 ~5 see text ~0.78 428
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From page 429... ...
_1 _ ~ O . O o o , _ _ ° o O ~ ~ ~ 11 lo v a_% 'N`o '\ `\ ~ 0.3{ 0 .2( 0.1t ~ V O.00 ~I~.·I·I··I···1~····I~··I····I ~I -2.0-1.5 -1.0 -0.5 0.0 0.5 t.0 1.5 2.0 Figure 1 Taylor wake fraction at r=R (comparison of methods)
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From page 430... ...
a 0.3C 0.2C 0.10 ~, 0.00 ................ -2 .0 -1 .5 -1 .0 -0 .5 '/ ~ ~ - ~ ~ ~°°°°°Oo /~o~_ oOO -- ~ oOo ~ I ~ ~ · · I · · · · I ~ · t- · t ~I o.o 0.5 1.0 1.5 2.0 Figure 7 Taylor wake fraction at r=R/2 (effect of misalignment)
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From page 431... ...
0.8 O.8 7) / / Method S _~0.9 Figure 6 Axial velocity contours (comparison of methods)
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From page 432... ...
· . t 0.0 0.5 1.0 1.5 2.0 ~ Figure 9 Taylor wake fraction at r=R (effect of cell density)
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From page 433... ...
~ . 1 ~ ~ 1 -2.0 -1.5 -l.D -0.5 O.0 0.5 1.0 l.S 2.0 Figure 13 Taylor wake fraction at r=R/2 (effect of wire - run 9)
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From page 434... ...
. 1 · ~ ~ ~ I ' ' ' ' I ' ' l.' I 0.0 2.5 5.0 7.5 1 0.0 1 2.5 1 5.0 3 - r/L Figure 14 Average circumferential wake fraction (effect of wire - run 9)
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From page 435... ...
Figure 17 Axial velocity contours showing effect of support wire 435 experiment l 1 :~0.8 ~ 0.9
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From page 436... ...
To simulate the influence of the support wire on the experimental measurements you stated you adjusted the computed velocity. Another way the authors might consider simulating the support wire numerically would be to use the drag force of the wire (which can be estimated rather accurately)
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From page 437... ...
, using hybrid turbulence model and Deng et al., EDeng et al., 19931 (Figure 18) , with an unconventional localized change of the eddy viscosity otherwise obtained by the standard k-~-model.
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From page 438... ...
Suzuki, H., Toda, Y., and Suzuki, T., "Computation of Viscous Flow Around a Rudder Behind a Propeller - Laminar Flow Around a Flat Plate Rudder in Propeller Slipstream," Sixth International Conference on Numerical Ship Hydrodynamics, Iowa City, Iowa, 1993, Proceedings 6. Tanaka, I., "Three-Dimensional S hip Boundary Layer and Wake," Advances in Applied Mechanics, Vol.
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From page 439... ...
NOMENCLATURE Ci contour of cylinder N°i distance between the centers of the two circular cylinders a radius of one circular cylinder p mass density of the fluid U amplitude of the ambient harmonic oscillatory flow velocity or the ambient steady flow velocity 1; characteristic length of one body (L = 2a) T period of the oscillatory ambient flow velocity kinematic viscosity coefficient fo frequency of vortex shedding At time step 439 Re Reynolds number (Re = Ups)
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From page 440... ...
Extension to Multi-body Configurations The modelling of viscous flows around multiple cylinders has been investigated for the past decade. The validation has been essentially done by comparisons with experimental data for two identical circular cylinders of radius a spaced with a distance ~ between the centers.
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From page 441... ...
Thus, two sub-problems are successively solved in the physical plane. Mapping of two cylinders into an annulus The exterior domain of two arbitrary cylinders Cat and C2 may be mapped into an annular domain bounded by two concentric circular cylinders.
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From page 442... ...
This causes an approximately constant distance between mesh points along the line joining the centers of the two bodies in the physical plane. SOLUTION OF THE BOUNDARY VALUE PROBLEM Due to the linearity of the Poisson equation, the stream function can be decomposed into the following three components: tThc Jacobi of the transformation between the physical and transformed planes (respectively z and ()
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From page 443... ...
The BVPs in the physical plane In order to represent accurately the boundary layer which is formed around each solid contour, the Poisson equation is solved in an annular domain around each body.
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From page 444... ...
;=~,2 are chosen so that the two outer boundaries (EiJi=~,: do not intersect, but they may touch In one point. The two BVPs are solved successively and separately in the physical plane.
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From page 445... ...
For steady incident flows, the cirag coefficient (CD) is calculated in the direction on the ambient flow, and the lift coefficient (C~ is calculated in the transverse direction.
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From page 446... ...
Two Tandem Cylinders in a Steady Incident Flow For the tandem arrangement its steady incident flow, (21) reported that there exists a critical spacing ~ the subcritical and laminar flow regimes.
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From page 447... ...
) tbe vortex shedding ~ cbaracte~zed by "n~ow _ ^ wakes whicb are fb~rned beldod twolden11csJ pipes1 respectively]
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From page 448... ...
The numerical results are validated by studying two identical cylinders in tandem and side-by-side arrangements. The force coefficients are calculated for both steady and oscillating ambient flows and compared with experimental data.
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From page 449... ...
: Tandem cylinders in osciBating ambient flow with the gap width d/a = 4; variation of the numerically calculated force coefficients of the cylinder N°1 with the Keulegan Carpenter number KC at ,6 = 534; CDf: drag coefficient due to skin friction; CDP: drag coefficient due to pressure; CM: mass coefficient; a: standard deviation of each coefficient through a total of NC cycles of oscillation.
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From page 450... ...
| ~C,,, 0.5 10 0.97 0.04 2.63 0.11 2.07 0.02 1.0 10 0.49 0.02 1.34 0.07 2.06 0.01 1.5 10 0.33 0.01 0.98 0.05 2.0S -0-.02 2.0 10 0.25 0.01 0.83 0.03 2.04 0.02 2.5 10 0.20 ~ 0.01 0.89 0.05 1.99 0.01 3.0 10 0.16 0.00 0.98 0.11 1.94 0.02 3.5 10 0.14 0.01 1.11 0.16 1.92 0.03 4.0 10 0.12 0.01 1.14 0.21 1.94 0.06 4.5 10 0.~! 0.00 1.13 0.11 1.94 0.04 5.0 9 0.09 0.00 1.17 0.10 1.94 0.09 5.5 -~-i 0.09 0.01 1.18 0.11 1.84 0.08 6.0 7 0.08 0.00 1.18 0.11 1.87 0.08 6.5 7 0.07 0.00 1.12 0.13 1.86 0.08 7.0 6 0.07 0.00 -- 1.14 0.20 1.87 0.14 7.5 -IF- 0.06 0.00 1.10 0.19 1.95 0.23 8.0 _ 0.06 0.00 1.08 0.26 1.92 0.18 Table (4~: Tandem cylinders in oscillating ambient flow with the gap width d/a = 8 variation of the numerically calculated force coefficients of the cylinder N°2 with the Keulegan Carpenter number KC at ,6 = 534 CDj: drag coefficient due to skin friction; CDP: drag coefficient clue to pressure; Cay: mass coefficient; a: standard deviation of each coefficient through a total of Nc cycles of oscillation.
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From page 451... ...
! Figure 3: Force coefficients of two tandem circles at ,8 = 534 with the gap width d/a = 4; drag and mass coefficients respectively in figure (a)
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From page 452... ...
ItC 'I is o. r Figure 4: Force coefficients of two tandem circles at ~ = 534 with the gap width d/a = 8; drag and mass coefficients respectively in figure (a)
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From page 453... ...
1 7~ v v v ~ ~ I) , v o Figure 8: Drag coefficients of two side-by-side cylinders in a steady incident flow at Re = 200; Add: upper cylinder (present numerical results)
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