Special Issue Article
Entropy-based detached-eddy simulation of the airwake over a simple frigate shape
Advances in Mechanical Engineering 2015, Vol. 7(11) 1–13 Ó The Author(s) 2015 DOI: 10.1177/1687814015616930 aime.sagepub.com
Zhao Rui1, Rong Ji-Li1, Li Hai-Xu2 and Zhao Peng-Cheng2
Abstract The wind past the ship superstructure produces an unsteady turbulent airwake which has a significant effect on aircraft performance and consequently pilot workload during ship landing process. Computational fluid dynamics simulations of a generic simple frigate shape ship airwake have been performed using the entropy-based detached-eddy simulation method. The results were compared with the steady-state Reynolds-averaged Navier–Stokes calculations and the wind tunnel data, indicating the capability of entropy-based detached-eddy simulation to resolve the unsteady large-scale turbulent features. An analysis of the airwake flow topology at headwind condition highlights the vortex pairing process which dominates the flowfield above the deck. Additionally, the influence of hangar-door state (open, closed or halfopen) on the airwake was also investigated in detail. Determination of this complex flow can assist in the definition of safe ship–helicopter operating limits and future ship design. Keywords Computational fluid dynamics, detached-eddy simulation, airwake, frigate
Date received: 5 April 2015; accepted: 15 July 2015 Academic Editor: Chin-Lung Chen
Introduction One of the most demanding of all piloting tasks is to land a helicopter on the flight deck of a moving nonaviation ship, such as the frigate, destroyer, and cruiser. It requires the pilot to accurately land on a tightly defined area without overstressing the undercarriage. The unsteady airwake generated by the ship’s superstructures exacerbates this problem still further and can impact severely on the operational availability of the helicopter. As the helicopter enters the ship airwake, the pilot is forced to compensate for the unsteady flow, initially to the aircraft flight path, and finally to the position over the landing spot. Unexpected turbulent fluctuation may force the aircraft dangerously close to the flight deck and superstructure, or may move the helicopter away from the ship into a position where the pilot loses vital visual references.1 In extreme wind
conditions, the pilot may reach the limits of control authority with insufficient maneuver power to compensate for the airwake disturbance, and then a disaster may occur.2 To reduce the risks, the safe ship– helicopter operating limits (SHOLs) should be developed as the guideline for the ship-board operations.3,4 Because of this, modeling and simulation of the ship– helicopter dynamic interface has been an active research area. As a first step in studying this coupling problem,
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School of Aerospace Engineering, Beijing Institute of Technology, Beijing, China 2 Systems Engineering Research Institute, Beijing, China Corresponding author: Zhao Rui, School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China. Email:
[email protected]
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Figure 1. SFS model in the test section of the wind tunnel.7
the ship airwake can be studied without the rotor or helicopter present. This will give insight into the type of the flow structures and also the capability of the numerical methods nowadays. To this end, a typical and representative case of study of the airwake flow is the simple frigate shape (SFS), which contains the most relevant geometry aspects common to the non-aviation ships in an aerodynamic sense. The SFS is a highly simplified ship geometry, first developed as part of an international collaboration in which Canada, Australia, the United Kingdom, and the United States evaluated the ability of computational fluid dynamics (CFD) codes to simulate complex airwake.1 The National Research Council of Canada (NRC) had performed a series of wind tunnel tests of SFS. Cheney and Zan5,6 studied the mean surface flow topology on a 1:60 scale model of SFS using oil and pressure tappings, while the three-dimensional airwake was examined using smoke visualizations. Recently, Bardera Mora7 further studied the flow features of SFS airwake by various experimental techniques including oil film visualization, particle image velocimetry (PIV), and laser Doppler anemometry (LDA) (Figure 1). Several wind-over-deck (WOD) conditions were investigated. The velocity contours of different cross-planes were presented, along with the distributions of the velocity and turbulent intensity magnitudes. Due to the geometry simplicity and abundant experimental data, the SFS model has served as a repeatable benchmark case for validating CFD codes. Both Reddy et al.8 and Wakefield et al.9 have simulated the flow around the SFS, using the steady-state Reynolds-averaged Navier–Stokes (RANS) solvers. Although reasonable qualitative agreement with oil flow visualization was shown, the magnitude and location of the recirculation zone differed from the experiment. Tulin10 suggested that it might be inappropriate to apply a steadystate code to simulate the airwake as the steady-state code does not necessarily represent the time-average of the unsteady flow. Liu and Long11 used non-linear disturbance equations (NLDEs) to obtain inviscid, unsteady result from the mean flowfield, which was still
that of a RANS solution. In support of US Department of Defense Joint Shipboard Helicopter Integration Process (JSHIP) project,12 Polsky13 studied the timeaccurate airwake of the beam (90°) winds past SFS, utilizing monotone integrated large eddy simulation (MILES) methods. Compared with the wind tunnel data, it was found that the grid quality was extremely important when attempting to predict flows with large separated regions. More recently, Syms14 used the lattice-Boltzmann technique to perform time-accurate solution. Good agreement to the experimental data was shown, despite a slight over-prediction of turbulent intensity. Forrest and Owen15 studied the airwake of a SFS-like shape (SFS2) and a Royal navy Type 23 Frigate at several WOD conditions. Their work showed the promising ability of detached-eddy simulation (DES) method (based on shear stress transport (SST) turbulence model for closure, SST-DES16) to capture the large-scale turbulent structures in the airwake. Most of the investigations above focused on the experimental or the CFD techniques themselves. The dominant mechanisms responsible for the generation of large-scale turbulent structures over the flight deck are approximated to that of a backward facing step. In this work, the entropy-based detached-eddy simulation (SDES) method developed by Zhao et al.17,18 is employed to further investigate the airwake past SFS. The predicted airwake is compared with the steadystate RANS calculation and the latest experimental data of Bardera Mora, with the discrepancies discussed in detail. Specially, the coupling vortex shedding mechanisms due to the funnel on the hangar are discussed in detail, and the influences of hangar-door states (open, closed, or half-open) on the airwake topology are also comprehensively analyzed.
SFS model and its modifications SFS is a simplified geometry, but has the most relevant aspects in an aerodynamic sense, as funnel, hangar, and flight deck (Figure 2). Figure 3 shows the dimensions of SFS geometry.7 SFS model was manufactured with a hangar height of 80 mm, a beam B = 2.5H, and a flight deck length L2 = 4.0H. The length precedent to the hangar L1 is 8.5H, height over the floor H1 is 0.75H, and the front height H2 is H + H1. The funnel dimensions BL, BW, and BH were adapted from Reddy et al.,8 and these values relative to the hangar height are the following: BX/H = 4.0, BL/H = 1.0, BW/H = 0.5, and BH/H = 1.0. The hangar-door of the original wind tunnel model is closed. However, SHOLs request the state of the hangar-door as the helicopter approaches the deck. Besides the pilot visibility effect, it is also worth investigating the influence of the hangar-door states on the
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airwake structures. With this purpose, two more SFS models are constructed for CFD calculations (Figure 4). The depth of the hangar is set 3.5H with the other dimensions following the original one.
Computational details Grid generation and boundary conditions The key requirement of the numerical grid is an adequate resolution of all separated flow structures, so the detailed flow characteristics can be calculated. Figure 5 shows the cross section of the calculation domain employed for SFS with the hangar-door closed. The longitudinal length is 50H and the transverse direction is 25H, while the depth is set to approximately 12H. Since the geometry of SFS is relatively simple, the structured multi-block grid is meshed with 23 blocks. Spacing normal to the wall is chosen to give wall unit values of y + ’ O(1) and an expansion ratio of 1.2 is applied. According to Spalart’s ‘‘Focus Region,’’19 the grid upon the deck is specially refined, as far as possible, isotropic to fully utilize the power of SDES method. After grid independence test, the target grid spacing in this region is about Do/H = 2.0 3 1022 (Figure 6) and the cell count is kept at 8 million cells.
The mesh strategy is the same for the other two models (hangar-door open and half-open) besides one more block in the hangar. The outer and upper boundary is specified as pressure far-field, while the lower surfaces are set as walls with zero shear stress and the ship surface is modeled as a wall with a non-slip boundary condition imposed. The inflow Mach number is kept 0.2 and the Reynolds number based on the hangar height is 1.1 3 105. The relative wind angles considered here are 0°and 20°.
Numerical method The governing equations describing the mean flowfield are the time-dependent, compressible RANS equations. Other restrictions on the equations include the constant specific heats and the Sutherland viscosity law. To get rid of the numerical dissipation as far as possible, the fifth-order WENO scheme20 for the inviscid terms combined with fourth-order central differencing21 for the viscous terms is employed. Second-order accuracy is obtained in the temporal discretization via dual-time stepping with sub-iterative procedure. Two levels of turbulence closure strategies are adopted and compared in the study of SFS airwake. Spalart–Allmaras model. The one-equation model of Spalart–Allmaras (SA)22 is chosen to achieve the steady state of the airwake flow, which also serves as the base for the construction of SDES. The transport equation for a variable n^ related to the eddy viscosity reads
Figure 2. SFS with the hangar-door closed.
∂^ n ∂^ n + uj = Cb1 ½1 ft2 O^ n ∂t ∂xj 2 1 n^ + Cb1 ½(1 ft2 )fv2 + ft2 2 Cw1 fw k d~ 1 ∂ ∂^ n Cb2 ∂2 n^ n^ + (n + (1 + Cb2 )^ n) s ∂x2j s ∂xj ∂xj
Figure 3. SFS dimensions.7
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ð1Þ
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Figure 6. Grid distributions on the deck.
The SDES method relies on a new length scale d~ in replacement of dw given by e d = dw fs max (0, dw CDES D)
Figure 4. Modified SFS geometries: (a) hangar-door open and (b) hangar-door half-open.
ð2Þ
where CDES is a calibrated constant equal to 0.65 and D is the grid spacing defined by D = max(Dx, Dy, Dz). The shielding function fs for SDES method is recently reformulated as svis fs = 1:0 tanh 3 ls
ð3Þ
to confine the predicted turbulent boundary-layer near the wall, in which svis = ls =
Dsvis Ds F = 3 Dsmax Dsmax F + ac
Cs f (a1 , a2 )d=CDES D, d=CDES D,
svis .0:05 otherwise
ð4Þ ð5Þ
A detailed description of SDES can be found in Zhao et al.18
Figure 5. Cross-sectional view of grid.
where the length scale d~ = dw is actually the nearest distance to the wall. Definitions for the remaining variables can be found in the previously cited reference. The first term on the right-hand side is the turbulence production term, the second one is the destruction term, and the rest are the diffusion terms.
SDES. A new version of hybrid strategy, named SDES, was proposed from the consideration of energy dissipation.17,18 This method employs the entropy concept to discern the local boundary-layer region and then partly suppresses the modeled stress depletion (MSD) phenomenon inherent in DES97.23,24
Solution strategy As the code employed in this work is a density-based code, the Mach number scaling method is adopted to avoid potential numerical problems associated with applying a density-based CFD code to a flow which is essentially incompressible. The calculated inflow Mach number is set as 0.2, which is much larger than the experimental Mach number of 0.06. This approach has been validated in Polsky and Bruner12,25 with good results. For the time-accurate calculation, the time step is 1.0 3 1025 s per iteration. By removing the transient 1200 iterations, flow statistics were in general compiled over the next 6500 iterations to reach full convergence.
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5 longitudinal direction (x-direction). Meanwhile, the shape of the horseshoe vortex structure is more regular and symmetry at relative wind angle of 0° (Figure 9A). When the flow is coming with an incident angle of 20°, the recirculation bubble is asymmetric and displaced. One obvious eye of the vortex is visualized in both the experimental data and SDES result (Figure 9B (a) and (b)), although the locations are slightly different. Figure 10 shows the velocity and turbulent intensity profiles along the line normal to the center of the flight deck. The turbulent intensity is defined as follows Ii =
Figure 7. Airwake above the deck at relative wind angle of 0° (time-averaged result of SDES).
Results and discussion Validation and comparison The flow past SFS configuration has been experimentally studied using oil film visualization, PIV, and LDA, respectively.7 Flight deck is located downstream the hangar and dedicated to the helicopter operations as a helideck. A typical ship structure resembles the back-facing step, which has a massive separated region in its wake at Reynolds number ranges of order of 104 and greater.26Figure 7 shows the flow pattern on the deck of SFS at relative wind angle of 0°. A large recirculation region behind the hangar is produced by the flow incoming to the flight deck from the sides of the ship and causing counter-rotating vortices on each side of the recirculation region. The result is an unsteady horseshoe vortex structure. The unsteadiness of the flow causes this turbulent structure to grow, dissipate, and move spatially in an unpredictable manner. Figures 8–10 compare the time-averaged result of SDES with those of steady-state SA and the experimental data at relative wind angles of 0°and 20°. Note that all the CFD results are scaled to experimental inflow condition for the Mach number independence.12,25 It has been argued that even if a flow contains some unsteady features, a converged, steadystate CFD solution should result in a time-averaged solution of the actual flowfield; however, that is not the case for this flow. Figures 8 and 9 present the calculated velocity magnitude contours of different sections on the flight deck. As these figures demonstrate, the steady-state solutions do not compare nearly as well to the experiment as the time-averaged SDES results. In general, the range of the recirculation zone predicted by SA model is much larger and the freestream velocity is recovered more slowly along the
si U‘
ð6Þ
where Ii and si represent the turbulence intensity and standard deviation of the i-direction velocity component, respectively, and UN is the inflow velocity. The deviation of the capabilities of SDES and SA in simulating the unsteady airwake flow is more obvious in Figure 10. The longitudinal velocity predicted by the steady-state SA model shows discrepancy, although the trend exhibits the same with the wind tunnel data and SDES result. The distributions of turbulent intensity predicted by SDES are also compared well with the wind tunnel data at most locations, with the largest discrepancy occurring at 0.75H for component Iu at relative wind angle of 0° and component Iv at relative wind angle of 20°. From the comparisons above, we can safely draw a conclusion that the accuracy of SDES used in this study is sufficient for investigating the SFS airwake flow.
Flow mechanism analysis To identify the mechanisms for the formation of turbulent vortex structures in the airwake, the funnel on the hangar of SFS is removed for CFD simulation. Figure 11 shows the instantaneous downwash flows (z-direction velocity) over SFS and SFS without funnel at headwind condition. This velocity component is expected to impact on the helicopter–ship operations mostly. At this relative wind angle, the flow separates from the head of SFS. High levels of unsteady shear layers are generated with turbulent vortex structures shedding downstream. These vortical structures appear to be dissipated toward the flight deck where the dominant flow features are still the vortex sheet formed at the sharp edge of hangar-roof (Figure 11(a)). However, the strength of the vortical structures seems enforced as they encounter the funnel, with powerful vortexes shedding from the edges of the rectangular funnel and interacting with the ones formed at the edge of hangar-roof (Figure 11(b)). Due to this interaction, larger and more
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Figure 8. Comparisons of the velocity magnitude contours in the vertical plane of symmetry of the SFS flight deck at relative wind angle of 0°: (a) PIV result,7 (b) time-averaged SDES result, and (c) steady-state SA result.
energetic vortex structures are generated, which fill the whole landing area above the flight deck. Figure 12 compares the time-averaged downwash turbulent intensity distributions on the middle plane. The separated flows from the head of SFS generate very energetic turbulence, which is dissipated and has little effect on the airwake above the flight deck (Figure 12(a)). With the funnel standing on the hangar, the downwash turbulence is obviously enforced in the airwake, as can be seen in Figure 12(b). Quantitative profiles of Iw at different locations (Figure 12(b)) are extracted and presented in Figure 13. These locations were chosen as they represent the region closest to where a helicopter would be hovering during a deck landing. In the recirculation region, the profiles are nearly consistent with each other. With the vortexes traveling downstream, the influence of the funnel on the airwake gradually emerges (x/H . 1.875). The magnitude of Iw is larger than that of the SFS model without funnel, with the maximum discrepancy up to 33% at the location x/H = 2.5. For both models, the peaks
of the downwash turbulence occur at about half hangar height where x . 1.875. Three-dimensional vortex structures can be underlined by plotting an isosurface of the Q-criterion, which is defined as follows27 1 Q = (Sij Sij Oij Oij ) 2
ð7Þ
where S and O denote, respectively, the rate of strain and rotation tensors. This quantity is useful to highlight the vortical turbulent structures. An isosurface of Q = U‘2 =2H 2 is represented in Figure 14 to further illustrate the evolution of the airwake. When the large coherent structures shedding from the funnel pass above the flight deck, the vortexes generated at the edge of hangar-roof seem to be attracted and roll upward. New pairing vortexes are found in the airwake, which appear instable and easily broken up into small turbulent eddies, resulting in a dangerous area for the helicopter when approaching the ship from the stern.
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Figure 9. Comparisons of the velocity magnitude contours in the horizontal plane of the SFS flight deck (z/H = 0.5) at relative wind angles of 0° and 20°. (A) relative wind angle = 0°: (a) PIV result,7 (b) time-averaged SDES result, and (c) steady-state SA result. (B) Relative wind angle = 20°: (a) PIV result,7 (b) time-averaged SDES result, and (c) steady-state SA result.
Effect of hangar-door state In the development of SHOLs, it is required to denote the conditions of hangar-door. For this reason, the
effect of the hangar-door state on the airwake at relative wind angle of 0° is investigated in this part. As we can see in Figure 15, the ranges of the recirculation
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Figure 10. Comparisons of velocity and turbulent intensity distributions along the line normal to the center of the SFS flight deck at relative wind angles of 0°and 20°. (A) Relative wind angle = 0° and (B) relative wind angle = 20°: (a) non-dimensional x-direction velocity, (b) x-direction turbulent intensity, and (c) y-direction turbulent intensity.
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Figure 11. Contours of the instantaneous downwash flow, plotted on the middle plane along the y-direction: (a) SFS model without funnel and (b) SFS model.
Figure 12. Contours of the time-averaged non-dimensional z-direction turbulent intensity: (a) SFS model without funnel and (b) SFS model.
zones for the three conditions are almost the same. However, as part of the flow enters the hangar, the core of the recirculation bubble moves closer to the door (Figure 15(b)). Meanwhile, the strength of downwash turbulence in the airwake is also diminished (compared with Figure 15(a)). From the comparisons of the
profiles of Iw at different locations on the flight deck (Figure 16), the values are lower than those of the original SFS, except the profile which is closer to the hangar-door (x/H = 1.25). It is also interesting to find that the downwash turbulence is reduced mostly when the hangar-door is half-open. For all the three models,
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Advances in Mechanical Engineering because the absolute gradient of the low-speed recirculated flow is very small. The coherent structures shedding from the funnel get paired with the vortexes generated at the edge of the hangar-roof, as denoted in section ‘‘Flow mechanism analysis.’’ However, the vortices seem not as rich as the others when the hangardoor is half-open, which may be the reason why the magnitude of downwash turbulence in the airwake is the smallest.
Conclusion Figure 13. Time-averaged non-dimensional z-direction turbulent intensity along the lines normal to the flight deck.
the maximum of the profiles occurs at about half hangar height (x/H . 1.875), whereas the curves are flatter when the hangar-door is open and half-open. Figure 17(a) and (b) shows the turbulent structures visualized by the isosurface of Q-criterion, respectively. For both models, the vortices are few inside the hangar
The flows past the SFS configurations were numerically simulated to investigate the complex airwake above the flight deck. Time-accurate unsteady simulations were performed using SDES for turbulent closure. This method was proven to be suitable for such flows to resolve the large-scale turbulent structures shedding from ship superstructures. A comprehensive validation exercise, comparing SDES results to wind tunnel data, has been described at relative wind angles of 0° and 20°. The mean velocity and turbulence data were also compared using contours and line plots, showing that
Figure 14. Visualization of time-accurate evolution of vortex in the airwake (flooded by the magnitude of downwash flow): (a) T = 0 s, (b) T = 0.0022 s, (c) T = 0.0044 s, and (d) T = 0.0066 s.
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Figure 15. Contours of the time-averaged non-dimensional z-direction turbulent intensity: (a) SFS with hangar-door open and (b) SFS with hangar-door half-open.
Figure 16. Time-averaged non-dimensional z-direction turbulent intensity along the lines normal to the flight deck.
SDES could accurately predict levels of turbulence in the airwake. This is essential if CFD-generated airwake data are to be used for SHOL development.
As the flow approaches the rectangular funnel, largescale coherent turbulent structures are shed and interact with the vortices generated at the edge of the hangarroof. This interaction may bear new pairing vortexes, which fulfill the landing region above the deck. The strength of the turbulence in the airwake is enforced, greatly affecting the handling qualities of helicopters. This coupling mechanism for turbulence generation should be drawn attention in the ship design phase. The influences of the hangar-door states, open and half-open, on the airwake were also investigated. The ranges of the recirculation zones behind the hangars are almost the same, while the downwash turbulence in the airwake is suppressed when the door is open or half-open. From the analysis of the three-dimensional vortex visualization, SFS with the hangar-door halfopen contains fewer turbulent structures, which maybe the reason why the strength of downwash turbulence is the weakest among the three models. The state of the hangar-door may take more effect when the downwash
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Figure 17. Isosurface of Q = U2‘ =2H2 with velocity w contours: (a) hangar-door open and (b) hangar-door half-open.
flow of the rotor is added to the simulation, which is left for further research. 6.
Declaration of conflicting interests
7.
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
8.
Funding
9.
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (grant no. 11402024), Excellent Young Scholars Research Fund of Beijing Institute of Technology.
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11.
References 1. Wilkinson CH, Zan SJ, Gilbert NE, et al. Modelling and simulation of ship air wakes for helicopter operations—a collaborative venture. In: Proceedings of RTO AVT symposium on ‘‘Fluid Dynamics Problems of Vehicles Operation near or in the Air-Sea Interface,’’ Amsterdam, 5–8 October, 1998, paper no. RTO-MP-15, pp.8.1–8.12. Hull: Canada Communication Croup, Inc. 2. Youtube Website. Sea king helicopter Crash accident on carrier. www.youtube.com/watch? v=MlVx96D19pI (2008, accessed 2 November 2015). 3. Carico GD, Fang R, Finch RS, et al. Helicopter/ship qualification testing. Report no. RTO-AG-300-V22, 2003, https://www.cso.nato.int/pubs/rdp.asp?RDP=RTOAG-300-V22 4. Bardera Mora R. An experimental helicopter wind envelope for ship operations. Eng Technol 2012; 68: 1362–1369. 5. Cheney BT and Zan SJ. CFD code validation data and flow topology for the technical co-operation program AER-TP2 simple frigate shape. Report no. LTR-A-035,
12.
13.
14.
15.
16. 17.
April 1999. Ottawa, ON, Canada: National Research Council Canada, Institute for Aerospace Research, 1999 Zan SJ. Surface flow topology for a simple frigate shape. Can Aero Space J 2001; 47(1): 33–43. Bardera Mora R. Experimental investigation of the flow on a simple frigate shape (SFS). Sci World J 2014; 2014: 818132. Reddy K, Toffoletto R and Jones K. Numerical simulation of ship airwake. Comput Fluids 2000; 29: 451–465. Wakefield N, Newman S and Wilson P. Helicopter flight around a ship’s superstructure. Proc IMechE, Part G: J Aerospace Engineering 2002; 216: 13–28. Tulin M. Technical evaluation report. In: Proceedings of the RTO AVT symposium ‘‘Fluid Dynamics Problems of Vehicles Operation near or in the Air-Sea Interface,’’ Amsterdam, 5–8 October 1998, paper no. RTO-MP-1, pp.1.1–1.10. Hull: Canada Communication Group, Inc. Liu J and Long LN. Higher order accurate ship airwake predictions for the helicopter/ship interface problem. In: 54th annual forum proceedings—American helicopter society, Washington, DC, 20–22 May 1998, pp.58–70. Alexandra, VA: American Helicopter Society International. Polsky SA and Bruner CW. Time-accurate computational simulations of an LHA ship airwake. AIAA paper 20004126, 2000. Polsky SA. CFD prediction of airwake flowfields for ships experiencing beam winds. AIAA paper 2003-3657, 2003. Syms GF. Simulation of simplified-frigate airwakes using a Lattice-Boltzmann method. J Wind Eng Ind Aerod 2008; 96: 1197–1120. Forrest JS and Owen L. An investigation of ship airwakes using Detached-Eddy Simulation. Comput Fluids 2010; 39: 656–673. Strelets M. Detached eddy simulation of massively separated flows. AIAA paper 2001-0879, 2001. Zhao R, Yan C, Li XL, et al. Towards an entropy-based detached-eddy simulation. Sci China G 2013; 56: 1970–1980.
Downloaded from ade.sagepub.com by guest on January 6, 2016
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18. Zhao R, Rong JL and Li XL. Entropy and its application in turbulence modeling. Chin Sci Bull 2014; 59: 4137–4141. 19. Spalart PR. Young-person’s guide to detached-eddy simulation grids. Report no. NASA/CR-2001-211032, 2001, http://ntrs.nasa.gov/search.jsp?R=20010080473 20. Nichols RH, Tramel RW and Bunning PG. Evaluation of two high-order weighted essentially nonoscillatory schemes. AIAA J 2008; 46: 3090–3102. 21. Shen YQ, Zha GC and Chen XY. High order conservative differencing for viscous terms and the application to vortex-induced vibration flows. AIAA paper 2008-4059, 2008. 22. Spalart PR and Allmaras SR. A one-equation turbulence model for aerodynamic flows. AIAA paper 92-0439, 1992.
23. Spalart PR, Jou WH and Allmaras SR. Comments on the feasibility of LES for wings, and on a hybrid RANS/ LES approach. In: Proceedings of the 1st AFSOR international conference on DNS/LES (ed Liu CQ and Liu ZN), Columbus, OH, 4–8 August 1997, pp.137–147. Columbus, OH: Greyden Press. 24. Spalart PR. Detached-eddy simulation. Annu Rev Fluid Mech 2009; 41: 181–202. 25. Polsky SA and Bruner CWS. A computational study of unsteady ship airwake. AIAA paper 2002-1022, 2002. 26. Platt JR. Wind detection in a microcosm: ship/aircraft environment sensors. IEEE Aero El Sys Mag 1998; 13: 26–33. 27. Jeong J and Hussain F. On the identification of a vortex. J Fluid Mech 1995; 285: 69–94.
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