des and rans of unsteady free-surface wave induced separation · 2010. 10. 28. · modeling and...

42nd AIAA Aerospace Sciences Meeting and Exhibit5 - 8 January 2004, Reno, Nevada

AIAA 2004-65

Copyright © 2004

AIAA 2004-0065 DES and RANS of Unsteady Free-Surface Wave Induced Separation T. Xing, M. Kandasamy, R. Wilson and F. Stern

42nd Aerospace Sciences Meeting & Exhibit 5-8 January 2004

Reno, Nevada

by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

DES AND RANS OF UNSTEADY FREE-SURFACE WAVE-INDUCED SEPARATION

Tao Xing*, Manivannan Kandasamy†, Robert Wilson‡, and Fred Stern§ IIHR—Hydroscience & Engineering

College of Engineering University of Iowa

ABSTRACT vortex and turbulence interactions. First identified

and studied using a surface-piercing foil mounted on the floor of a hydraulic flume1. This building block geometry facilitates identification of the salient features; since, the foil profile was designed for limited separation for the deep, no-wave, and two-dimensional (2D) condition. Tests were conducted for Froude number ( gcUc /=Fr ) range 0. 2- 0.48 with average Reynolds number ( ν/Re cU c= ) = 7x105 (where Uc=carriage speed, c=chord length, and ν=kinematic viscosity). Wave profile photographs and needlepoint, dye injection flow visualization was used to determine the length and depth of the separation region. Separation was defined by a region of highly disturbed free-surface flow, which initiated just beyond the wave trough and extended to the foil trailing edge for all but the highest Fr ranging from separation starting point x/c=. 7 at small Fr=. 2, to maximum x/c=. 42 at medium Fr=. 25, and x/c=. 6 at Fr=. 37. Beyond the separation starting point, the wave profile was nearly constant. The depth of separation was defined by reversed axial flow and upward cross flow, which was observed close to the foil surface in a wedge shaped region gradually expanding from the separation starting point to a maximum depth near the foil trailing edge with magnitude similar to the wave height. Stratford’s laminar separation criterion showed good agreement with separation starting point data.

A general-purpose unsteady Reynolds-averaged Navier-Stokes (URANS) research code CFDSHIP-IOWA developed for ship hydrodynamics application is extended for detached eddy simulation (DES) capability. CFDSHIP-IOWA uses surface-tracking free-surface model, k-ω turbulence model, and high performance computing. Both 2nd and 3rd order upwind biased scheme for spatial derivatives were applied for URANS while 3rd order upwind biased scheme used for DES. DES extensions are based on the blended k-ω model by modifying the length scale in the k equation and validated with surface piercing NACA 0024 benchmark, including IIHR towing-tank EFD data and concurrent URANS. Domain and grid convergence studies were conducted for 2nd order RANS. 3rd order RANS was also studied on a coarse grid and a 3rd order DES was conducted on both coarse and medium grids. Statistical analysis of the results, including time history, running mean, and FFT of total drag and side forces, mean and RMS of wave elevations and pressure on foil surface, and unsteady 3D separation flow pattern are presented. Results show fairly good agreement EFD validation data for mean, RMS, and FFT frequencies for wave elevations and surface pressure; however, many modeling and numerical issues remain. Seemingly credible flow features of unsteady wave-induced separation have been simulated for the first time, which will be used to guide future PIV measurements.

More recently, [2-4] used a similar geometry (surface-piercing NACA 0024) for complementary towing-tank (3x3x100m) experimental fluid dynamics (EFD) and steady RANS computational fluid dynamics (CFD). Wave profiles, mean far field wave elevations, and mean and RMS near field wave elevations and surface-pressure measurements were made for c=1.2m and deep draft d=1.5m foil and Fr=0.19, 0.37, and 0.55 and Re=(0.822, 1.52, 2.26) x 106. EFD results similar to[1], except differences foil geometry and restricted water and foil bottom effects. Steady RANS solutions show good agreement wave profiles and surface pressure, but only fair agreement wave elevations due to poor resolution short waves for low Fr and separation region for medium Fr. RANS solutions also provide details of separated flow pattern, but data not yet available for validation

1. INTRODUCTION

Free-surface wave-induced separation is caused by interactions of free-surface waves and wall boundary layers, which have relevance to ship and platform hydrodynamics with regard to resistance and propulsion, stability, and signatures. Phenomenon is related to general topic of unsteady three-dimensional, boundary-layer separation, but with unique features due to free-surface deformations and * Postdoctoral Associate † Graduate Research Assistant ‡

Research Engineer § Professor Mechanical Engineering and Research Engineer

American Institute of Aeronautics and Astronautics Paper

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and verification difficult due to difficulties in obtaining steady flow solutions. Restricted water and foil bottom effects were also studied for shallow draft d=0.75m and Fr=0.37 (EFD) and Fr=0.19 and 0.37 (CFD). More details of these studies will be presented below. Ref. [5] also investigated free-surface wave-induced separation as part of their towing tank (1.52x3x43 m) study on the flow structure around a surface-piercing 33% thickness strut (c=. 9 m, d=1.37 m). PIV for three orientations of the laser sheet and above and below free-surface video and high-speed film measurements were made for 0.051 Fr 0.51 and 1.4x105 Re 1.4x106; however, most of the data is for Fr=0.255 and one orientation and carriage run. Breaking and splashing occur just beyond the wave trough (i.e., tow of shoulder wave) at x/c=0.41 for all Fr 0.15. For Fr=0.255 a downstream shoulder wave crest is evident, but for Fr=0.36 there is no distinct shoulder wave crest all the way to the trailing edge. The flow is increasingly more unsteady and violent for increasing Fr. For Fr 0.255, the shoulder wave and the separation region that forms behind it are dissipative such that the free-surface is constant in the separation region with Kelvin waves only evident away from the model, but with a phase shift that starts in the bow wave trough. Authors point out that phenomena is similar[2], but at different Fr which is attributed to differences in body shape. For Fr=0. 255, the forward face of bow wave resembles a spilling breaking wave, including capillary waves emanating from the toe, and underlying “necklace” vortex. In the separated region the total head is 50-60%, whereas for larger y/c the level is 70-80%. The wave breaking occurs only very close to the model (up to y/c<. 2). At x/c=0. 64 boundary-layer separations begin at the intersection of the model and the free-surface. The separated region grows, but never extends far from the free-surface. The separation process originates from secondary flows associated with impingement and breaking at the root of the mid-body wave, which generates a series of pairs of longitudinal counter-rotating vortices. At Fr=0.255 there is no reverse flow in the separation region, but at Fr>0.3, flow reversal does occur. Authors point out necklace vortex and gross features of separation region are similar to [2], but structures within the separated region differ greatly, which is attributed to deficiencies of RANS/Baldwin-Lomax model in accounting for wave breaking and associated massive energy dissipation.

≤ ≤≤ ≤

≥

≥

Ref. [6] performed turbulent flow CFD for a surface-piercing NACA 0012 foil for study of incipient turbulent wave breaking. An Euler explicit time-

stepping, third-order upwind convection, second-order central viscous, iterative relaxation solution Poisson pressure equation, and k-ε turbulence model CFD code was used. A surface tracking method is used, including a third derivative term of the wave elevation and a high frequency disturbance used to trigger wave breaking. Fr=0.22, 0.25, 0.3, and 0.4 with Re ranging from 5x104 to 2x106. An infinite foil depth, large outer boundary, and half solution domain was used. Solutions were obtained on 4 grids with 307,200 points for the finest grid. The solutions were oscillatory with very large oscillations for the larger Fr. The bow flow is complicated, including a “necklace” vortex. Also of relevance are studies for surface-piercing circular cylinders, although in this case deep flow is unsteady 2D separation. Ref. [7] performed LES studies for Fr=0.2, 0.5, and 0.8 and Re=2.7x104, including comparisons with available EFD data. A second-order, finite volume, fractional-step, surface-tracking method is used. Results show fairly good agreement with data for mean and RMS wave elevations and mean stream-wise velocity. The vortex shedding is attenuated within one diameter of the free-surface, which is attributed to the inclination of the shear layers outward due to generation of surface waves. By now, all CFD studies for free-surface flows used either RANS or LES. For high Reynolds number flows, RANS is efficient inside the boundary layer but predicts very excessive diffusions in the separated regions. Large Eddy Simulation (LES) is accurate in the separated regions but is unaffordable for resolving the thin near-wall turbulent boundary layers. To combine the most favorable features of RANS and LES, [8] proposed the detached eddy simulation (DES), which is a hybrid technique, i.e. use URANS inside the attached boundary layer and LES in the separated regions. Typical related works on DES can be found by [8], who first established DES formulation and preliminarily tested the 2D flows with DES, [9], who for the first time, successfully use DES to study a true, 3D, turbulent flows around NACA0012 with high angles of attack, and [10], who used DES to study the flow around a circular cylinder. Their results have proven DES to be a promising tool to study massively separated flows, and therefore the motivation to use DES to study wave-induced separation flows. The objectives of the present study are to extend the previous steady RANS of [4] for the surface-piercing

American Institute of Aeronautics and Astronautics

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NACA 0024 for unsteady RANS and DES simulations. Of particular interest is analysis of the separation region for Fr=0.37, as guidance for planned PIV validation experiments.

2. UNSTEADY RANS AND DES METHODS 2.1. CFDSHIP-IOWA The CFD code is CFDSHIP-IOWA, which is a general-purpose unsteady Reynolds-averaged Navier-Stokes (RANS) research CFD code[11]. Modeling includes prescribed and predicted 6DOF motions; incident waves; blended k-ω turbulent model; free-surface tracking method through solution of the exact nonlinear kinematic and approximate dynamic conditions; and inertial and non-inertial coordinate systems. Numerical methods include structured, higher-order finite-difference discretization; advanced iterative solvers (PETSC toolkit); inner iterations for fully implicit coupling of free-surface, velocity-pressure, and ship motions. It permits multi-block and high performance computing (parallel), which includes portable, multi-level parallelism for both static and dynamic load balance using message-passing interface (MPI) and OpenMP standards. The simulations in this paper were run on NCSA IBM690 with 8 processors, corresponding to 8 blocks (see section 5 for details). Overall solution algorithm follows PISO[12] with pressure Poisson equation. The fluid forces and moments acting on the system are obtained by integration of the normal and tangential stresses over all no-slip. The blended k-ω model[13] was applied for all the RANS simulations in this study. CFDSHIP-IOWA has interface with existing 3rd-party software for grid generation and boundary condition specification (GRIDGEN) and post-processing and visualization (TECPLOT).

2.2. DES model Most of previous DES models were based on the Spalart-Allmaras (S-A) turbulence model. In order to improve the accuracy of predictions of separation, [14] developed a DES model based on the two-equation Menter’s SST model[13], and his methodology was applied in this study. The BKW model used for unsteady RANS calculation was extended to DES model on top of CFDSHIP-IOWA v.303. The modification is to

modify the dissipative term of the k-transport equation:

(1)* 3 2

3 2

/kRANS k

kDES

D k k l

kDl

ωρβ ω ρ

ρ

−= =

=

(2)The length scale was defined as:

(3)

1 2 *( )

min( , )k

k DESl l Cω

ω

β ω−

−

=l k

= ∆ (4)

Where CDES is the DES constant and was set to 0.65, following the typical value for homogeneous turbulence. Initial DES extensions are for 2D NACA 0012, as motivated by the work[9], whose study showed DES significantly improves the accuracy of the calculations of the lift and drag coefficients than the URANS does for high angle of attack airfoil with massively separated flows. Present URANS results using CFDSHIP-IOWA show good agreement with the previous URANS and EFD data. Present DES results show same features as previous DES results, such as smaller-scale vortices comparing to unsteady RANS, three-dimensional flow patterns, but larger reductions for both lift and drag coefficients. Most of previous DES studies applied the 5th order upwind biased scheme for the convective terms of momentum equation [9,10,14], while others applied relative lower numerical scheme, such as [7] using 2nd order QUICK scheme for LES of free-surface flows, [15] used a second-order accurate finite volume scheme for DES past a circular cylinder, and [16] used 3rd order Roe scheme for DES of supersonic flow over cavity. In the 2D foil study, we attribute the reduction in lift and drag coefficients using DES to the order of accuracy of numerical scheme (2nd order upwind). In this study, 3rd order upwind biased scheme was used for DES for all spatial derivatives in the governing equations, but 5th order scheme is under developing, as will address in the future work.

3. SURFACE PIERCING NACA 0024 FOIL The surface-piecing NACA 0024 foil for Fr=0.37 is shown in Fig. 1. The bow wave breaking is relatively steady with features similar to spilling breakers, including capillary waves in front of the toe. Wave-induced separation initiates just beyond the shoulder wave trough: wedge shaped region with relatively constant wave elevations and intense free-surface turbulence and underlying vortical flow. Splashing and bubbles are most intense at the toe of the separation region. Wide wake region also disturbed with relatively constant wave elevations. Outside the separation and wake region the usual Kelvin


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diverging and transverse waves are evident. For Fr=0.19, there is no separation and Kelvin wave system is observed, but with large bow wave and wide wake due to relatively blunt bow and large beam and draft compared usual ship. For Fr=0.55, the bow wave is similar to Fr=0.37; region of wave-induced separation is reduced and shifted towards the trailing edge with increased splashing and bubbles; and Kelvin waves are no longer distinguishable due to increased free-surface turbulence. 4. SUMMARY OF EFD VALIDATION DATA AND UNCERTAINTY ASSESSMENT The NACA 0024 foil is constructed of fiber-reinforced Plexiglas and epoxy resin. 183, 1mm diameter pressure taps were drilled in the starboard side covering the region 0 and (Cartesian coordinates non-dimensional using c with origin at intersection leading edge, calm water-plane, and center-plane), based on CFD solutions of [2]. 9 were drilled on the port side for checking symmetry. 4mm height, 3.6mm diameter cylindrical studs with 2cm spacing were fixed to the model at x=0.042 for turbulence stimulation. Horizontal and vertical grid lines were painted on the starboard side of the model. Model accuracy was checked using rulers and plumb. The trailing edge was blunted starting at x=0.998.

8613.00613. ≤≤ x1175.09304.0 ≤≤− z

Wave profiles (all three Fr) were measured using markers and video camera. Data was reduced for mean and maximum and minimum values. Far-field wave elevations (all three Fr) were measured using an array of 3 capacitance wires mounted to a boom with a one-dimensional automated traverse affixed to the towing tank wall for 36 longitudinal cuts covering the region − and

. A photoelectric switch also affixed to the towing tank wall initiates data acquisition. The capacitance wires were statically calibrated using an automated vertical traverse. For each longitudinal cut, data is acquired at 100 Hz for 15 seconds. Data was reduced for mean values and contour plots. Near-field wave elevations (Fr=0.19 and 0.37) were measured using 2 servo-mechanism wave probes (10 and 30 cm needles with 700 and 1200 mm/s response speeds, respectively) mounted to a two-dimensional automated traverse affixed to the towing tank carriage for 976 locations covering the region and

0.30.2 ≤≤ x

5.1≤

01.1135.0 ≤≤ y

5.0 ≤− x 1.0≤∆5 4.0≥x

yy

for and for (where 4.0<x ≤∆y .0 ∆ is

measured from the center-plane or foil surface). The servo-mechanism wave probes were statically calibrated using an automated vertical traverse. For

each location, data is acquired at 100 Hz for 20 (Fr=0.19) and 15 (Fr=0.37) seconds. Data was reduced for mean, RMS, and FFT values and contour plots. Surface pressures were measured using an upstream mounted static Pitot tube for reference pressure connected via a manifold to ten differential pressure transducers with 0.32psi (2500 Hz) range. Overall system frequency response is estimated at 40 Hz due to tubing response limitations. The differential pressure transducers were statically calibrated using an automated vertical traverse with stationary and movable water baths. For each pressure tap, data is acquired at 91 Hz for 15 seconds. 1Hz and 1 KHz low pass filters were used for average and unsteady data, respectively. Data was reduced for mean, RMS, and FFT values and contour plots. EFD uncertainty analysis procedures followed [17,18] standard procedures. Wave profile Fr average Uζ=2.0%ζmax; bias limits include accuracy of measuring marked model and precision limit based on three repeat tests for each Fr. Far-field wave elevations Fr average UζFF=2.6%ζmax; bias limits include positioning and calibration and precision limit based on four and six repeat tests for low and medium/high Fr, respectively. Near-field wave elevations Fr average UζNF=0.7%ζmax; bias limits include positioning and calibration and precision limit based eleven repeat tests at two locations (x, y)=(0.0, 0.135) and (1.0, 0.135) for both Fr. Surface pressure Fr average UCp=2.0% maxpC ; bias limits

include location, calibration, and carriage speed and precision limit based on ten repeat tests for two depths z =(0.0, -0.5) and all three Fr. Uncertainty intervals for all measurements are reasonable in comparison other geometries for same and other towing tank facilities[19].

5. COMPUTATIONAL DOMAIN, BOUNDARY

CONDITIONS , FLOW CONDITIONS AND GRIDS

Present computations are for Fr=0.37 with large foil draft without towing-tank walls and bottom condition. The towing tank conditions are w/c=2.5 and h/d =2 (where w=width of tow tank, h=depth of tow tank). In the real flow, there is also flow beneath the foil, which changes the flow near the foil bottom[3]. For the simulations though, Instead of modeling the exact tow tank conditions, we model the foil with extended foil draft (2 x t) where the foil reaches all way down to the bottom boundary with no flow beneath foil (Fig .2). The foil draft was extended so that restricted water effects due to the bottom don’t affect the free-surface solutions. Also the tow


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tank walls are ignored. So restricted water and bottom effects are lacking in comparison EFD. Previous studies [3,4] established relatively small dependence of the free-surface separation pattern to the wall, foil bottom (whose effects were confined only to the lower regions of the foil) and the tow-tank floor effects. C-grid used with far-field boundary replacing the tow tank-wall boundary. The C-grid is a body-fitted grid whose far-field boundary is a semicircle of radius R encircling the foil with the trailing edge as its focal point. From the trailing edge to the exit we have a rectangular grid of length Le and half-width R. The grid is clustered near the foil surface and also near the free-surface. The grids were generated using commercial code GRIDGEN. Referring to Fig. 2, the boundary condition on each boundary is: on the foil surface (no slip), (U, V, W)= ∂P/∂n =0 (where n is normal to the body); on the exit plane, axial diffusion and pressure gradient are assumed negligible, i.e., ∂2(U, V, W)/ ∂X2 = ∂P/∂X=0, on the bottom deep boundary, an impenetrable slip condition is used, i.e. ∂ (U, V, P)/ ∂Z=W=0 and on the outer boundary the far-field boundary condition, U=Uc, V=W=P= 0. In order to make the solutions independent of domain size three simulations were performed on a fine grid with 8 blocks. The small domain has 194,670 grid points. Medium and large domains were got by extending the farfield boundary in the foil-normal direction by adding one extra j-plane, and also extending the exit boundary by adding one extra i-plane in flow direction to the previous domain, thus increasing the grid points to 199,962 for medium domain and 205,296 for large domain. The depth was kept constant (2xt) for all three domains. Values for R/c= 5, 7, 10 and Le/c = 5.5, 6.6, 8.1 for the three domains. The solutions show convergence for both the mean and the FFT. For the mean the convergence ratio is 0.6, and the percent change for the largest two grids is 0.15 %. The dominant frequency for the small, medium, large domains are 1.39, 1.41, 1.4 Hz respectively, showing an oscillation of 0.7 %. The convergence ratio for the magnitude of the dominant frequency (1.4 Hz) is 0.55, and the percent change for the largest two grids is 10%. The largest domain was then picked for grid studies and all other simulations. Three grids were generated with refinement ratio 1.19, Coarse Grid (71,280) Medium Grid (126,720) and Fine Grid (205,296). Computations were carried out using unsteady RANS with 2nd order spatial discritization (called URANS2

henceforth) for all three grids and with 3rd order unsteady RANS (URANS3) for just the coarse grid and 3rd order DES (DES3) for the coarse and medium grids. Most of the results presented here for the RANS simulations are for the cases runs with URANS2, and preliminary results are presented for URANS3. Though the overall flow pattern predicted by the two cases are the same, there are certain prominent differences in the solutions that will also be mentioned.

6. VERIFICATION AND VALDIATION The V&V procedure is based on the approach of [20]. Verification is the process of assessing simulation numerical uncertainty USN. Validation is defined as a process for assessing simulation modeling uncertainty by using benchmark experimental data. Validation is achieved if the comparison error (difference between data and simulation values) is less than the root sum square of USN and UD. Iterative convergence of the unsteady solutions was established by statistical convergence of the running average on the time histories of the total drag (CTx). All three grids show iterative convergence (Fig. 3) for CTx for URANS2. Grid studies with a refinement ratio of 1.19 were conducted for frictional drag (CFx), pressure drag (CPx) and CTx for URANS2. CTx and CPx show monotonic convergence and CFx exhibits oscillatory convergence. Fig 3 shows the grid convergence for CTx. The FFT on CTx shows monotonic convergence for the dominant frequency and oscillatory convergence for the magnitude of the dominant frequency. The results and uncertainties are tabulated in table 1 and 2. The results are relatively reasonable considering the complexity of the flow. URANS3 and DES3 both show statistically stationary solutions for CTx and side force(CTy) (Fig. 3,4). Statistical convergence is the fastest for URANS2 and the longest for URANS3, with DES3 being intermediate. Grid studies have not yet been conducted for URANS3 and DES3. Time step studies are also yet to be done for all the cases. Quantitative validations of flow field with the experiments are underway. Experimental uncertainty UD is already available and corresponding USN will be available for CFD soon. So far we have qualitative validation of the flow field with the EFD data.


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7. RESULTS

7.1. Time histories and FFT The time history, running mean and FFT of CTx was shown in Fig. 3. If defining one flow time as c/UC, it takes about 20 flow times for the URANS2, 80 flow times for DES3 and 340 flow times for URANS3 to reach statistically steady state. The mean values for CTx increased by 28% from URANS2 to URANS3, while increased 51% from URANS2 to DES3. The RMS values for CTx can be seen from Table 3: very small for URANS2 and DES3 has two times of RMS predicted by URANS3. DES3 on medium grid did not change the RMS much on the coarse grid. The percentages of RMS of the mean values are: 4% for URANS3, 7.7% for DES3 on coarse grid and 8.6% for DES3 on medium grid. The dominant frequency of 1.4 Hz for CTx from the URANS2 is exhibited. However, both URANS3 and DES3 have a broader range of frequencies, ranging from 0.1 to 2.0. CTy for URANS2 is almost zero as the flow is symmetric. The RMS values for CTy are much higher than that for CTx for URANS3, but DES3 predicted even higher values, as presented in table 4. For the dominant frequency for CTy, DES3 has a much lower value than URANS3 has. The corresponding Strouhal number based on the foil chord length is 0.1 for DES3 and 1.5 for URANS3. Almost all of the frequencies extracted arise from the unsteadiness in the separation region. The physical mechanisms causing the frequencies will be discussed later on in the section for the flow patterns using URANS2. 7.2 Comparison with EFD EFD wave profile (Fig. 5) shows large bow wave crest and shoulder wave trough. There is a sharp rise in elevation at the toe of the separation region x=0.425 (just beyond shoulder wave trough x=0.375) and gradual rise towards trailing edge. The closest near field wave elevation (along center-plane upstream and down stream of foil and ∆y=0.025 off foil surface) from Metcalf (2001) shows similar trends as the wave profile. The URANS2 solutions accurately predict the location of the toe a gradual rise of wave elevation right after the toe. Both URANS3 and DES3 predict a sharp rise in elevation at the toe of the separation region, followed by a gradual rise toward trailing edge, similar to EFD. However, the depth of the toe point was less accurately captured and the separation point is moved

to the upstream, more like the EFD data by Metcalf. The URANS2 solutions being very dissipative shows a much smaller RMS band than the other solutions. URANS3 predicts a broader RMS band (10% wave height). DES3 has even a larger RSM band, especially at the toe point (20% wave height). RMS of URANS3 and DES3 agree better with EFD. EFD mean wave elevations (Fig. 6) are consistent with observations (e.g., Fig. 1) showing blunt bow wave, wide separation region with relatively flat wave elevation, and displaced Kelvin waves. We see some improvement in the separation region prediction for the URANS3 and DES3 compared to URANS2, such as flat separation region like EFD, and higher elevation regions moved away from the foil surface near trailing edge. But all CFD cases fail to capture the propagation angle of the Kelvin waves as observed in EFD due to the insufficient grid points in that region. EFD RMS is also consistent with observations with largest amplitudes in separation region, especially near the toe. URANS2 predicts very small region of unsteadiness, while URANS3 and DES3 agree with the EFD data better. DES3 shows highest values for the RMS. The region where the flow separates at the foil surface (x=0.49) shows the region of highest RMS amplitude (0.023). The foil surface pressure contours shown in Fig. 7 display bow wave crest high-pressure rise, shoulder wave trough and separation region low pressure. A large pressure gradient is evident in the free-surface right after the shoulder wave trough, which is the primary cause of the “wave-induced” separation. The same features of the EFD are captured in all three simulation cases with some differences. The URANS2 predicts faster pressure recovery after the shoulder wave trough and hence smaller separation. URANS3 shows a better match with EFD in the separation region. DES3 shows a delayed pressure recovery. The minimum pressure region size was under-predicted by both URANS3 and DES3. We attribute this to the premature prediction of separation. The EFD RMS show largest values in the separation region, which initiates at the toe of the separation region x=0.425 with penetration depth enlarging towards the trailing edge to a depth of the order of the wave height. Maximum amplitudes occur near x=0.65 and z=-0.175. The CFD simulations predict similar features. As with the free-surface RMS, DES3 gives the highest values for foil surface RMS, much higher than EFD. URANS3 RMS values are also higher than EFD, but not as high as DES3, and URANS2 magnitudes are a little lower than EFD. The region of highest RMS for the CFD at


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the toe corresponds to the region of the body vortex inception, which will be discussed in section 7.3. Fig. 8 and Fig. 9 show the EFD frequency for the maximum amplitude distribution on the free-surface and foil surface. The dominant frequency near the leading edge region is 7 Hz and 2 Hz in the separation region. That is consistent with the findings using URANS2, whose FFT of the CTx exhibit dominant non-dimensional frequency around 1.4 Hz, which corresponds to a real time frequency of 1.4xUc/c = 1.5Hz. This frequency is linked to the vortex shedding and free-surface shoulder wave oscillation in the separation region, which will be discussed in the following section. 7.3 Separated flow pattern The unsteady flow pattern in the separation region is complicated, making detailed investigation hard. One way to analyze the flow is by extracting vortex structures in the flow. Vortex cores in the separation region were extracted using CFD-ANALYZER, a TECPLOT add-in feature, where velocity gradient eigenmodes are used for core detection. The analysis method requires fine grid solutions that are not yet available for URANS3 and DES3. As of now, detailed analysis of the flow pattern has been completed for URANS2 for the frequency corresponding to the EFD in the separation region, namely 2 Hz.

Prominent points along a period (last period from Fig. 3) were picked and the analysis revealed a very interesting phenomenon of a body vortex inception, merging with the free-surface vortex and subsequent vortex-breakdown. Fig. 10a shows the separation region picked for close up scrutiny. Fig. 10b shows the close-up of strength of the vortex core, Fig. 10c shows swirl and Fig. 10d shows corresponding CTx along the time period. At t/T =0.03 (where t=instantaneous time and T=time period-0.71 sec) we see the inception of a strong body vortex at the time of peak CTx, at the toe region just ahead of separation region at x/c=0.49. There is also a free-surface vortex, which is relatively weaker extending downward into the separated region. At time t/T=0.2 we see the body vortex has propagated downstream increasing in strength and stretching out toward the free-surface vortex. The free-surface vortex core reaches downward and upstream toward the body vortex increasing in strength. Further along the period at t/T=0.4 the body vortex and the free-surface vortex merge and there is a single vortex core with ends attached to the free-surface and the body-

surface. The core strength at the free-surface is still lower than the rest of the vortex. The merger occurs in region of highest negative swirl. The time of merger corresponds to lowest CTx. The body-attached end of the vortex continues to move down stream stretching the vortex core and starts decreasing in strength. The CTx starts increasing and at t/T=0.66 the vortex breaks down. In contrast to the merger the breakdown occurs in region of highest positive swirl. The body vortex then gets swept away into the wake and the free-surface vortex still remains attached to the free-surface with reduced strength. This pattern repeats over and over again with real time frequency 1.5 Hz. On the whole, the free-surface vortex remains fixed in locality whereas the body surface vortex incepts at toe, then propagates downstream merging with free-surface vortex, breaks down and gets swept away into the wake. We can also see from the free-surface wave profile at contact line (Fig 10c) that the free-surface shoulder wave frequency is the same as the vortex shedding frequency (1.5 Hz). The breakdown follows [21] criteria for vortex breakdown, which states for breakdown to occur the helix angle of velocity should exceed that of vorticity along some stream surface (necessary not sufficient condition). i.e If, δ=tan-1 (ν/w)- tan-1 (η/ζ), where the ratios (ν/w) and (η/ζ) are of the azimuthal and axial components of velocity and vorticity respectively, then δ has to be positive in order for breakdown to occur. Contours of δ along the vortex core is shown in Fig. 11 and the criteria is shown to be satisfied with the breakdown occurring at maximum positive δ(0.4) on the core. Fig. 11 also shows the diverging streamlines and stagnation in the vortex core at the breakdown point with flow converging from the top and bottom. .

8. CONCLUSIONS AND FUTURE WORK

Simulations of unsteady free-surface induced separation have been conducted using both unsteady RANS (URANS2, URANS3) and DES (DES3) methods. Results show fairly good agreement EFD validation data for mean, RMS, and FFT frequencies for wave elevations and surface pressure; however, more analysis is required and many modeling and numerical issues remain. Seemingly credible flow features of unsteady wave-induced separation have been simulated for the first time, which support previous steady simulations [2, 4] in terms of gross separation features, but better in terms of comparison with EFD. The results from the CFD will be used to guide PIV measurements in the tow tank.


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ACKNOWLEDGEMENTS 10. Travin, A., Shur, M., Strelets, M., and Spalart, P., “Detached-Eddy Simulations Past a Circular Cylinder”, Flow, Turbulence and Combustion, Vol. 63, 1999, pp. 293-313.

Sponsored by the Office of Naval Research under Grant N00014-01-1-0073, under the administration of Dr. Patrick Purtell. 11. Paterson, E., Wilson, R., and Stern, F.,

“General Purpose Parallel Unsteady RANS Ship Hydrodynamics Code: CFDSHIP-IOWA,” IIHR Report No. 432, 2003.

REFERENCES

1. Chow, S. K., “Free-surface Effects on Boundary Layer Separation on Vertical Strus,” Ph.D. Thesis, The University of Iowa, Iowa City, IA, 1967.

12. Issa, R. I., “Solution of the Implicitly Discretised Fluid Flow Equations by Operator-Splitting”, Journal of Computational Physics, Vol. 62, 1985, pp. 40-65.

2. Zhang, Z. and Stern, F., "Free-Surface Wave-Induced Separation," ASME J. Fluids Eng., Vol. 118, September 1996, pp. 546-554.

13. Menter, F. R., “Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications”, AIAA Journal, Vol. 32, No. 8, August 1994, pp. 1598-1605.

3. Metcalf, B., Longo, J., and Stern, F., “Experimental Investigation of Wave-Induced Separation Around a Surface-Piercing Hydrofoil, Proceedings 26th ATTC, 23-24 July, 2001, Web Institute, Glen Cove, NY.

14. Travin, A, Shur, M. and Strelets, M., “ Physical and Numerical Upgrades in the Detached-Eddy Simulation of Complex Turbulent Flows”, R. Friedrich and W. Rodi (eds.). Advances in LES of Complex Flows, 239-254, 2002.

4. Kandasamy, K., Wilson, R., Stern, F., “Unsteady RANS Simulation Free-Surface Wave-Induced Separation,” Proceedings 26th ATTC, 23-24 July, 2001, Web Institute, Glen Cove, NY.

15. Vatsa, V. N., and Singer B. A., “Evaluation of a Second-Order Accurate Navier-Stokes Code for Detached Eddy Simulation Past a Circular Cylinder”, AIAA 2003-4085. 5. Pogozelski, E. M., Katz, J., and Huang, T.

T., “The Flow Structure Around a Surface Piercing Strut,” Physics of Fluids, Vol. 9, No. 5 May 1997, pp. 1387-1399.

16. Hamed, A., Basu, D., and Das, K., “Detached Eddy Simulation of Supersonic Flow Over Cavity”, AIAA 2003-0549.

17. AIAA Standard, “Assessment Experimental Uncertainty With Application Wind Tunnel Testing,” AIAA S-017A, Washington DC, 1999.

6. Lungu, A., “Modeling of the Incipient Turbulent Wave Breaking,” Ocean Engineering International, Vol. 5, No. 1, 2000, pp. 1-15. 18. ITTC Quality Manual, Proceedings 23rd

International Towing Tank Conference, Venice, IT, 2002.

7. Kawamura, T., Mayer, S., Garapon, A., and Sorensen, L., “Large Eddy Simulation of a Flow Past a Free-surface Piercing Circular Cylinder, ASME Journal Fluids Engineering,” Vol. 124, March 2002, pp. 91-101.

19. Longo, J. and Stern, F., “Resistance, Sinkage and Trim, Wave Profile, and Nominal Wake and Uncertainty Assessment for DTMB Model 5512,” Proc. 25th ATTC, Iowa City, IA, 24-25 September, 1998. 8. Spalart, P. R., Jou, W. H., streets, M. and

Allmaras, S. R., “Comments on the Feasibility of LES for Wings, and on a Hybrid RANS/LES Approach”, presented at the First AFOSR International Conference on DNS/LES, Rouston, Louisiana, 1997.

20. Stern, F., Wilson, R. V., Coleman, H., and Paterson, E., “Comprehensive Approach to Verification and Validation of CFD Simulations—Part 1: Methodology and Procedures,” ASME Journal of Fluids Engineering, Vol. 123, Issue 4, December 2001, pp. 793-802

9. Shur, M., Spalart, P. R., Strelets, M., and Travin, A., “Detached-eddy Simulation of an airfoil at high angle of attack”, In: Rodi, W., and Laurence, D. (eds.) 4th Int. Symp. Eng. Turb. Modeling and Measurements, pp. 669-678. May 24-24, 1999, Corsica, Elsevier, Amsterdam.

21. Brown G. L., and Lopez, J. M., “Axisymmetric Vortex Breakdown: Part 2. Physical Mechanisms”, Vol. 221, pp. 553-576, 1990.


8

Table 2. Verification of CTx, CPx, and CFx for URANS2

Table 1. Grid Convergence of CTx, CPx, and CFx for URANS2

Coarse

Grid (71,280)

Medium Grid

(126,720)

Fine Grid

(205,296)CTx

ε 0.01315

0.01295 -1.6%

0.01284 -0.8%

CPx ε

0.009575

0.00942 -1.7%

0.009286 -1.4%

CFx ε

0.00401

0.003985 -0.62%

0.004054 1.7%

RG PG CG UG %S

UGC %Sc

CTx

0.522 3.7 2.21 6.9 2.44

CPx

0.86 0.84 0.37 7.8 2.16

CFx

-2.76 - - 1.5 -

Table 3. Mean and RMS for CTx Case CTx CTx (RMS) Grid

URANS2 0.01284 6e-05 Fine URANS3 0.0165 0.0007 Coarse

DES3 0.0194 0.0015 Coarse DES3 0.0187 0.0016 Medium

Table 4. RMS for CTy

Case CTy (RMS) Grid URANS2 8e-06 Coarse, Medium, Fine URANS3 0.008 Coarse

DES3 0.0387 Coarse DES3 0.0294 Medium

e

d

e

Fig. 1 Surface-piercing NACA 0024 foil for Fr=0.37.

American Institute of Aeronautics and Astro

9

Exit

nautics

Free surfac

Far-fiel

No-slip
Fig. 2. Computational domain, boundaryconditions and fine grid
R
L

TX

CTX

3 3

CTY

URANS3

CTX

Fig. 3. Time history, running mean and FFT of CTx

3 3
URANS3
Fig. 4. T

Fi

American

URANS3

URANS3

CTY

ime history, running

g. 5. Mean and RMS

Institute of Aeronaut

10

DES

mean and FFT of C

of wave profile

ics and Astronautics

DES
DES
Ty

DES

3
URANS3 DES URANS2
URANS2

C

EFD

URANS2

URANS3

DES3

Fig. 6. Free-Surface elevation - Mean and RMS


11

CP

RMS

EFD

URANS2

URANS3

DES3

Fig. 7. Foil-surface pressure - Mean and RMS


12


13

Fig. 8 EFD free-surface Frequency (Hz)

Fig. 9 EFD frequency on foil surface (Hz)

)

1

Contact line

) ) Fig. 10. Unsteady wave-induced separation flow pattern: (a) separation

contours of vortex strength on vortex cores (c) contours of swirl on vortecorresponding t/T.

American Institute of Aeronautics and Astronautic

14

T=0.7

t/T=0.03

t

t/T=0.2

t

t/T=0.4

t

t/T=0.66

t

t/T=0.75

t )
(b (d (c
(a

region relative to foil (b) x cores (d) CTx with dot for

s


15

Fig. 11. Contour plots of δ at breakdown (t/T=0.66).

des and rans of unsteady free-surface wave induced separation · 2010. 10. 28. · modeling and...

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