Entropy-based detached-eddy simulation of the airwake over a simple frigate shape

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 half-open) 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.

Introduction

One of the most demanding of all piloting tasks is to land a helicopter on the flight deck of a moving non-aviation 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, 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 Zan^5,6 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 Mora ⁷ 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.

Figure 1.

SFS model in the test section of the wind tunnel. ⁷

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. Tulin ¹⁰ suggested that it might be inappropriate to apply a steady-state code to simulate the airwake as the steady-state code does not necessarily represent the time-average of the unsteady flow. Liu and Long ¹¹ 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 Polsky ¹³ studied the time-accurate 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, Syms ¹⁴ 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 Owen ¹⁵ 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-DES ¹⁶ ) 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 steady-state 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 L ₂ = 4.0H. The length precedent to the hangar L ₁ is 8.5H, height over the floor H ₁ is 0.75H, and the front height H ₂ is H + H ₁. 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.

Figure 2.

SFS with the hangar-door closed.

Figure 3.

SFS dimensions. ⁷

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 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.

Figure 4.

Modified SFS geometries: (a) hangar-door open and (b) hangar-door half-open.

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 Δ_o/H = 2.0 × 10⁻² (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.

Figure 5.

Cross-sectional view of grid.

Figure 6.

Grid distributions on the deck.

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 × 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 scheme ²⁰ for the inviscid terms combined with fourth-order central differencing ²¹ 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 $\hat{\nu }$ related to the eddy viscosity reads

$$\begin{array}{c}\multicolumn{1}{c}{\frac{\partial \hat{\nu }}{\partial t}+u_j\frac{\partial \hat{\nu }}{\partial x_j}=C_{b1}[1-f_{t2}]\Omega \hat{\nu }}\\ \multicolumn{1}{c}{+\{C_{b1}[(1-f_{t2})f_{v2}+f_{t2}]\frac{1}{{\kappa }^2}-C_{w1}{f}_w\}{\left(\frac{\hat{\nu }}{\tilde{d}}\right)}^2}\\ \multicolumn{1}{c}{+\frac{1}{\sigma }\frac{\partial }{\partial x_j}[(\nu +(1+C_{b2})\hat{\nu })\frac{\partial \hat{\nu }}{\partial x_j}]-\frac{C_{b2}}{\sigma }\hat{\nu }\frac{{\partial }^2\hat{\nu }}{\partial x_j^2}}\end{array}$$

(1)

where the length scale $\tilde{d}=d_w$ 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

The SDES method relies on a new length scale $\tilde{d}$ in replacement of d_w given by

$$\tilde{d}=d_w-f_{\mathrm{s}}max(0,d_w-C_{\mathrm{DES}}\Delta )$$

(2)

where C _DES is a calibrated constant equal to 0.65 and Δ is the grid spacing defined by Δ = max(Δx, Δy, Δz).

The shielding function f _s for SDES method is recently reformulated as

$$f_{\mathrm{s}}=1.0-\tanh \left(\frac{{\overline{s}}_{\mathrm{vis}}}{l_{\mathrm{s}}^3}\right)$$

(3)

to confine the predicted turbulent boundary-layer near the wall, in which

$${\overline{s}}_{\mathrm{vis}}=\frac{\Delta {\overline{s}}_{\mathrm{vis}}}{\Delta s_{max}}=\frac{\overline{\Phi }}{\overline{\Phi }+\alpha \overline{\psi }}\times \frac{\Delta \overline{s}}{\Delta s_{max}}$$

(4)

$$l_{\mathrm{s}}=\{\begin{array}{c}\hfill C_{\mathrm{s}}f(a_1,a_2)d/C_{\mathrm{DES}}\Delta ,{\overline{s}}_{\mathrm{vis}}>0.05\hfill \\ \multicolumn{1}{c}{d/C_{\mathrm{DES}}\Delta ,\mathrm{otherwise}}\end{array}$$

(5)

A detailed description of SDES can be found in Zhao et al. ¹⁸

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 Bruner^12,25 with good results. For the time-accurate calculation, the time step is 1.0 × 10⁻⁵ s per iteration. By removing the transient 1200 iterations, flow statistics were in general compiled over the next 6500 iterations to reach full convergence.

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. ²⁶ Figure 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.

Figure 7.

Airwake above the deck at relative wind angle of 0° (time-averaged result of SDES).

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, steady-state 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 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 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.

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.

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.

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

$$I_i=\frac{{\sigma }_i}{U_{\infty }}$$

(6)

where I_i and σ_i represent the turbulence intensity and standard deviation of the i-direction velocity component, respectively, and U _∞ 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 I_u at relative wind angle of 0° and component I_v 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.

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.

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 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 I_w 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 I_w 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.

Figure 12.

Contours of the time-averaged non-dimensional z-direction turbulent intensity: (a) SFS model without funnel and (b) SFS model.

Figure 13.

Time-averaged non-dimensional z-direction turbulent intensity along the lines normal to the flight deck.

Three-dimensional vortex structures can be underlined by plotting an isosurface of the Q-criterion, which is defined as follows ²⁷

$$Q=-\frac{1}{2}(S_{\mathrm{ij}}{S}_{\mathrm{ij}}-{\Omega }_{\mathrm{ij}}{\Omega }_{\mathrm{ij}})$$

(7)

where S and Ω denote, respectively, the rate of strain and rotation tensors. This quantity is useful to highlight the vortical turbulent structures. An isosurface of $Q=U_{\infty }^2/2H^2$ 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.

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.

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 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 I_w 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, 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 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.

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 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 hangar-door is half-open, which may be the reason why the magnitude of downwash turbulence in the airwake is the smallest.

Figure 17.

Isosurface of $Q=U_{\infty }^2/2H^2$ with velocity w contours: (a) hangar-door open and (b) hangar-door half-open.

Conclusion

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 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, large-scale coherent turbulent structures are shed and interact with the vortices generated at the edge of the hangar-roof. 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 half-open 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 flow of the rotor is added to the simulation, which is left for further research.