# CFD Aided Ship Design and Helicopter Operation

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## Abstract

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## 1. Introduction

**Background:**Shipboard helicopters play an important role for commerce and military interests. Because of the nature of bluff-body aerodynamics, ship–helicopter interactions are complex; see Shukla et al. [1] who conducted a comprehensive review in ship–helicopter coupled airwake aerodynamics. The present study attempts to identify and bridge the gaps between the needs of the ship–helicopter industry, where the application and adoption of CFD techniques would provide the greatest benefits for the development of future ships, and the current capabilities of the CFD codes and the infrastructure required to use them. Table 1 lists some related and/or supportive studies.

**Objective:**This paper aims to demonstrate the current capability of applying high-fidelity CFD techniques to industry, defence, ship design, shipboard helicopter operations, and flight simulators. Shipboard operations are among the most challenging of any piloting task for fixed or rotary wing aircraft (Polsky [23,24]; Forrest et al. [10]). The launch and recovery of helicopters are often performed from the landing decks of ships, which are subject to motions in six degrees of freedom. The difficulty is increased given that the landing deck is often immersed in the unsteady ship airwake. Because of the nature of bluff bodies, the separated flow and shedding vortices interact and result in an unsteady airwake with highly turbulent structures which can significantly increase the difficulty associated with helicopter launch and recovery manoeuvres. This work has applications for aircraft flight in complex flow fields beyond the ship airwake and is pertinent to other sectors of the aviation industry.

**Benefits:**This technology developed herein is important for simulation of aircraft operations in complex flow fields created by bluff-body structures such as a ship superstructure or an urban landscape. Simulation provides a capability to test new ship and aircraft designs before building them and has the potential to support the estimation of the operational limits prior to full-scale trials (Polsky and Wilkinson [25]; Forrest and Owen [7]). In commercial-flight applications, a level D aircraft simulator does not need to include complex flow fields because commercial aviation currently focusses on smooth flows and clear air turbulence, but simulators for specialized military applications need this kind of information. A key area that affects simulation fidelity is the modelling of ship airwake flows, which is not a trivial computational task. At-sea and wind-tunnel measurements can be used to provide data from which airwake models can be generated. A major limitation with wind tunnels is that one cannot fully correlate flow fields continuously in three dimensions since measurement techniques are usually point-wise or plane-wise sampling. At-sea flight testing is both labour and equipment intensive, requiring a dedicated ship and potentially multiple aircraft for days or weeks (Hodge et al. [10]). As a result, CFD is increasingly used for modelling ship airwake because the simulations can provide many correlated cloud grid points within the flow field and a number of simulations for different conditions can be performed at the same time to reduce testing time and costs. As unmanned aerial vehicles (UAVs) become more advanced, technology developments surrounding their use in urban environments are increasingly in demand. With increasing movement toward urban air mobility and because an urban wind environment has a lot in common with ship flows, likely CFD development and application will be required.

**Barriers:**The major technical barriers to a wider adoption of CFD for industrial ship design and flight simulations, both for shipboard and urban air applications, are accuracy, reliability, speed, and affordability. The airflow past ships is normally at a low Mach number or nearly incompressible. A significant difficulty of incompressible flow calculations is that the continuity equation is not given in a time evolution form of density. Compressible flow solvers do not generally work well for flow simulation past ships because incompressible solutions converge quite slowly, especially when the grid is refined. As Ferziger and Perić [26] pointed out, at high Mach numbers, the computing time increases almost linearly with the number of grid points as the grid size increases. The exponent is approximately 1.1, compared to approximately 1.8 in the case of incompressible flows, which results in costly and time-consuming simulations for low-Mach-number or incompressible flows.

**Capabilities and limitations:**The airwake flow over the flight deck or in a cityscape is massively separated and unsteady. The simulations must be time-accurate, which is time consuming and costly. Since military ships are large in size when compared to aircraft, the Reynolds number is of the order of 10

^{8}. It is not feasible to resolve the flow past the ship using direct numerical simulations (DNS); however, it is unacceptable to perform the CFD simulations using an inviscid Euler solver for separated flows. Moreover, the superstructures of ships contain multiple bluff-body structures. The flows past and around the multi-bluff body structures interact and often cause numerical instabilities. Furthermore, ship motion increases the difficulties in handling the grid motion in time-accurate CFD simulations. Because the ship airwake flow separation is mainly inertia-driven and the separation points are fixed by the model sharp edges rather than caused by boundary layer separation, detached-eddy simulation (DES) is suitable for this kind of bluff-body aerodynamic flow. Although the urban landscape does not experience motions like ships caused by the water waves, the geometry is more complex than a navy ship and therefore the challenges in the application of CFD to urban air mobility are similar.

**Dependable and affordable high-fidelity CFD:**In this study, sufficient accuracy and reliability were obtained through a rigorous validation process by combining the results from in-house computational, wind-tunnel, and sea-trial tests. To speed up the computations, parallel computing was employed using as many CPU cores as possible. The open-source software OpenFOAM was applied in this study, meaning that there was no restriction or costs to adding CPU power to the problem, which is a significant cost barrier when using commercial CFD codes for larger industrial and defence problems where additional license costs escalate with the number of CPU cores used.

**Approaches to improve the fidelity of flight simulation:**For commercial and defence simulator applications, the physics-based approach calculates the forces on the simulated aircraft by consulting a look-up table of the flow information based on the CFD simulations. In parallel, we are developing engineering models to simplify the determination of the forces on the aircraft.

## 2. CFD Method and Validation Using SFS2

## 3. Challenges and Lessons Learned

#### 3.1. Complexity of Ship Geometry

_{∞}was set to 20 m/s in the computations, which is in the mid-range wind speed for helicopter operations. The freestream turbulence intensity was set to 10% for the CFD simulations, which is close to the 9% measured in wind-tunnel tests of the CPF model. In this study, computations were carried out for a headwind and a Red 20° wind condition (red winds are relative winds coming from the port side, green winds from the starboard side). Because of the multiple complex bluff-body structures, numerical instabilities were encountered in the computations when using the second-order central differencing scheme that was employed for the SFS2 geometry. Instead, a linear-upwind stabilized transport (LUST) scheme was used for the no-mast case and a linear-upwind scheme for the with-masts case. The computations were started from a uniform flow set as the freestream. A timestep of 1 × 10

^{−3}s was used in the current CFD work, which resulted in a non-dimensional timestep CFL

_{max}~4 (detected at the masts rather than in the ship airwake). The computations were performed for 60 s of physical time, resulting in nine units of flow-through time (l

_{s}/U

_{∞}), with the last 50 s used for sampling. The computed results were compared with the available wind-tunnel data of a 1:50-scale CPF model. In the experiment, three points in the airwake (located starboard, port, and at mid-deck in the CPF airwake, at a height and longitudinal location close to the rotor disc in high hover), were set up for velocity measurements using Cobra probes (Yuan et al. [14]).

#### 3.2. Transient Time Period and Time Integration

_{∞}) is used to help decide how to truncate the transient process, where c is a chord length of a representative airfoil. In the DNS performed by Shan et al. [33] for a 2D NACA 0012 airfoil at an angle of attack of four degrees, the amplitude of the velocity oscillations stayed at a certain level without significant change in time after the flow was established at t = 10c/U

_{∞}. In a large eddy simulation (LES) of flow around an airfoil near stall (Mary and Sagaut [34]), around six time units were necessary to get a well-established unsteady solution from the initial steady Reynolds-averaged Navier–Stokes (RANS) solution, while the application of LES using a coarser mesh as an initial solution limited the initial transient to 1.5 time units. For computing mean quantities, the averaging procedure was performed in the homogeneous spanwise direction and in time over a period of 2.4c/U

_{∞}in the work of Mary and Sagaut [34].

_{s}/U

_{∞}) to remove transients before unsteady sampling began, and the flow statistics were then averaged over the next 9 units of flow-through time. Analysing the data published by Yuan et al. [14], Figure 3a,b illustrate the time histories of the velocities at two locations in the SFS2 airwake, namely at a probe location at the middle over the flight deck and at a location that is 15 cm (at full scale) away from the coordinate origin located on the centreline of the flight deck at the intersection of the flight deck surface and the aft face of the hangar. As can be seen in the figures, flow in the ship airwake reached a statistically stationary state after two units of flow-through time at the probe location. However, near the coordinate origin, the statistically dead flow did not reach a statistically stationary state until 15 flow-through time units. As a result, the statistical analysis was conducted by removing 16 time units. An alternative to evaluate if the simulation reached the statistically steady state is to check the maximum CFL number outputted by OpenFOAM. Figure 3c illustrates the time history of the maximum CFL number of the CPF, which indicates that the CPF simulation reached a steady state after ~3 flow-through time units; however, this is configuration dependent. As shown in Figure 3d, the time history of the maximum CFL number of the CFD simulations conducted for an undisclosed Canadian ship (Canadian ship A in this study) reached a steady state after ~9 flow-through time units, which is a long time period resulting in high CPU cost for the complex geometry. Since truncation of the transient period is configuration dependent, one has to check it case by case. Parallel computing is a practical mechanism to overcome the challenge of speeding up the computational time.

#### 3.3. Ship Motion

## 4. Application of CFD Data to Piloted Flight Simulators

#### 4.1. Flight Simulator Look-Up Table

#### 4.2. Airwake Load Modelling for Flight Simulation

## 5. Conclusions

**Accuracy:**As discussed in the introduction, it is infeasible to resolve the flow past the ship using DNS; however, it is reasonable to perform CFD simulations using an inviscid Euler solver for separated flows. Because the ship airwake flow separation is mainly inertia-driven and the separation points are fixed around the model’s sharp edges rather than caused by boundary layer separation, DES is suitable for this kind of bluff-body aerodynamic flow. The grid spacing should prevail over the focus region (here airwake). Spalart [32] advocated very similar grid spacing in the three directions or cubic grid cells since the flow field is filtered with a length scale proportional to the grid spacing in DES. Therefore, a structured block over the flight deck was used for all simulations in this study. A 30 cm (one-foot) grid spacing at full scale is recommended in the airwake region over the flight deck, which provides a good balance between accuracy and affordability. The accuracy was confirmed by the CFD practice used for the SFS2. This value of the grid spacing in the wake region is comparable to the 35 cm used in Forrest and Owen’s [7] work after their grid refinement study. Considering that the superstructure geometry of real-world ships is more complex, a 25 cm spacing was used for all Canadian ships in this study.

**Reliability:**In this study, sufficient accuracy and reliability were obtained through a rigorous validation process by combining the Canadian in-house computational simulations, wind-tunnel measurements, and sea-trial tests. In particular, aggressive simplification of configuration or improper time truncation may affect the simulation reliability.

- (1)
- Geometry of the ship superstructure affects the airwake aerodynamics. However, the complexity of small structures, on the other hand, may influence the numerical instability of the computations. Exclusion of non-critical small structures may improve the numerical stability and thus allow the use of higher-order or more accurate numerical schemes, which would increase results accuracy and simulation reliability. However, omitting small geometric features is configuration dependent, and it should be verified by combined numerical and experimental investigations.
- (2)
- In terms of time truncation and integration, the current practice showed that three to nine units of flow-through time are required for removing transient periods before sampling begins. The values are higher than the 2.4 units used for the SFS2 by Forrest and Owen [7]. Appropriateness of the compromise between reliability and affordability can be cross-checked using the available experimental data.

**Speed:**To speed up the computations, parallel computing was employed using as many CPU cores as possible, thanks to the use of the open-source software OpenFOAM with no restriction caused by a software license. However, the speed-up efficiency is dependent on the computational facilities and ship configurations. Low speed-up efficiency may mean inefficient use of computational resources. According to our current practises, 240 processors are the best start for a good balance between computational speed and CPU cost.

**Affordability:**When using commercial CFD codes for larger industrial and defence problems, additional license costs escalate with the number of CPU cores used, which is a significant cost barrier. The successful application of open-source tools minimized the restrictions or costs when adding CPU power to the problem. The open-source software also provides an opportunity to improve numerical accuracy and expand the CFD capability by developing additional individual libraries when needed, which reduces costs in code development by focusing on the priority techniques.

**Capabilities and limitations:**With the current capabilities, it is possible to generate CFD results within a few days for airwake behind static ships. However, ship motions make CFD simulations more difficult from both accuracy and affordability points of view. In addition, the data collection within the extraction box to be used for flight simulators may possess another technical issue in real-world engineering applications. Current data were collected based on the ship body-axis coordinates. Some flight simulators may require the data allocated in the stationary global coordinate frame. This requires searching for new control cells and updating the new locations of the sampling points on the moving grid. This searching and interpolation process may result in huge CPU costs for large-sized extraction boxes. New techniques need to be developed either to accelerate the point-searching process in the CFD code or to convert the data from ship coordinates to the stationary global coordinate system.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Computed results for the SFS 2 model at headwind condition (Yuan et al. [14]). (

**a**) Pressure distribution on ship surface. (

**b**) Pressure distribution on the mid-plane. (

**c**) Mean velocity. (

**d**) Power spectra of the streamwise velocity.

**Figure 2.**CPF models used in the present CFD study. (

**a**) Surface meshes. (

**b**) Masts. (

**c**) With-masts model. (

**d**) No-mast model.

**Figure 3.**Time histories of velocity. (

**a**) SFS2, longitudinal and lateral velocity components u and v at a middle location over flight deck at a headwind condition. (

**b**) SFS2, longitudinal and lateral velocity components u and v near intersection of the flight deck and hangar aft face. (

**c**) CPF, max. CFL number at Green 30°. (

**d**) Canadian ship A, max. CFL at Green 30°.

**Figure 4.**Combined experimental and computational investigation of the CPF in motion. (

**a**) Setup of the oscillating CPF model in the wind tunnel. (

**b**) Corresponding anemometer support masts on flight deck at sea trial. (

**c**) Mean velocity vector and standard deviation in the CPF flight deck wake for roll conditions; red—wind tunnel, blue—CFD, black—sea trial.

**Figure 5.**Effect of ship motion on airwakes—spectra of a probe in the airwake middle at the height of the rotor plane in helicopter high hover, adopted from Yuan et al. [15].

**Figure 8.**CPF airwake data on x-z planes at constant y-coordinates, longitudinal mean flow, headwind, flow from right to left, and dimensions in meters, and the coordinate origin is located on the centreline of the flight deck at the intersection of the flight deck surface and the aft face of the hangar as shown in Figure 2c,d.

**Figure 9.**Relationship between unsteady loads and computed turbulence on rotor disc planes; each line represents a wind speed, line type for different rotor positions, and line colour for directions.

Year | Researchers | Models | Approaches |
---|---|---|---|

1998 | Wilkinson et al. [2] | Simple frigate shape (SFS) | Overview (conceptual design) |

1998 | Zan et al. [3] | Canadian patrol frigate (CPF) | Wind tunnel + steady CFD-RANS |

2005 | Zan [4] | Simple frigate shape 2 (SFS2) | Overview |

2008 | Polsky and Ghee [5] | Generic antenna mast | Wind tunnel + CFD-LES |

2008 | Syms [6] | SFS2 | CFD-RANS |

2010 | Forrest and Owen [7] | SFS2 and Type 23 frigate | CFD-DDES |

2011 | Zhang and Su [8] | SFS2 with Bell 412 helicopter | CFD-Euler |

2012 | Forrest et al. [9] | SFS2, Type 23 frigate, and Wave class AO | Piloted flight simulation |

2012 | Hodge et al. [10] | Type 23 frigate with SH-60B helicopter model | Ship–helicopter dynamic interface |

2015 | Rajmohan et al. [11] | SFS2 | Reduced order model |

2016 | Forrest et al. [12] | Ship superstructure | CFD + flight simulation |

2017 | Oruc et al. [13] | Simplified shedding wake | Ship–helicopter dynamic interface |

2018 | Yuan et al. [14] | SFS2 and CPF | Combined CFD and wind tunnels |

2018 | Yuan et al. [15] | SFS2 and CPF in motion | Combined CFD and wind tunnels |

2020 | Owen et al. [16] | Generic destroyer (GD) | Conceptual design |

2020 | Lu et al. [17] | Wasp-class amphibious assault ship + Robin helicopter | CFD-RANS |

2020 | Watson et al. [18] | Queen Elizabeth class aircraft carrier | Flight simulation |

2021 | Nisham et al. [19] | SFS2 with underwater hull in waves | CFD-DDES |

2021 | Linton & Thornber [20] | SFS | CFD-DDES + uncertainty analysis |

2022 | Wall et al. [21] | GD and CPF in motion | Combined wind tunnel and sea trials |

2022 | Setiawan et al. [22] | SFS2 and GD | Wind tunnel–PIV |

Current | Yuan et al. | SFS2, CPF, and a undisclosed Canadian ship | Combined CFD, wind tunnel, sea trials, and flight simulator |

**Table 2.**Mean velocity magnitude (U/U

_{∞}), pitch θ [°], and yaw ψ [°] in CPF airwake with red 20° wind.

Approaches | 1 (Starboard) | 2 (Port) | 3 (Mid) | ||||||
---|---|---|---|---|---|---|---|---|---|

$\mathit{U}\mathbf{/}{\mathit{U}}_{\mathbf{\infty}}$ | $\mathit{\theta}\mathbf{[}{}^{\mathbf{\xb0}}\mathbf{]}$ | $\mathit{\psi}\mathbf{[}{}^{\mathbf{\xb0}}\mathbf{]}$ | $\mathit{U}\mathbf{/}{\mathit{U}}_{\mathbf{\infty}}$ | $\mathit{\theta}\mathbf{[}{}^{\mathit{\xb0}}\mathbf{]}$ | $\mathit{\psi}\mathbf{[}{}^{\mathbf{\xb0}}\mathbf{]}$ | $\mathit{U}\mathbf{/}{\mathit{U}}_{\mathbf{\infty}}$ | $\mathit{\theta}\mathbf{[}{}^{\mathbf{\xb0}}\mathbf{]}$ | $\mathit{\psi}\mathbf{[}{}^{\mathbf{\xb0}}\mathbf{]}$ | |

Experimental | 0.56 | −16.93 | 6.70 | 0.87 | 9.67 | 35.55 | 0.74 | −4.02 | 33.35 |

Linear-upwind (with masts) | 0.62 | −11.27 | 7.43 | 0.69 | 6.21 | 26.19 | 0.93 | 2.65 | 27.48 |

Linear-upwind (no masts) | 0.70 | −13.00 | 14.09 | 0.66 | 7.96 | 26.79 | 1.02 | 1.83 | 25.71 |

LUST (no masts) | 0.49 | −14.16 | −4.65 | 0.69 | 3.23 | 26.04 | 0.73 | 2.98 | 27.27 |

**Table 3.**Efficiency of OpenFOAM parallelization for a test case of the CPF at headwind condition with 28.5 million cells.

Processors | 64 | 96 | 128 | 256 |
---|---|---|---|---|

Physical time | 0.2 s | 0.2 s | 0.2 s | 0.2 s |

Clock time | 491 m | 346 m | 341 m | 571 m |

Speed-up | 1 | 1.42 | 1.44 | 0.86 |

Efficiency | 100% | 95% | 72% | 21% |

**Table 4.**Efficiency of OpenFOAM parallelization for a test case of the Canadian ship A at headwind with 43.4 million cells.

Processors | 64 | 96 | 128 | 160 |
---|---|---|---|---|

Physical time | 4 s | 4 s | 4 s | 4 s |

Clock time | 288,393 s | 197,266 s | 152,428 s | 124,340 s |

Speed-up | 1 | 1.46 | 1.89 | 2.32 |

Efficiency | 100% | 97.5% | 94.6% | 92.8% |

**Table 5.**Efficiency of OpenFOAM parallelization for a test case of the Canadian ship A at R15° wind with 43.4 million cells.

Processors | 160 | 192 | 208 | 240 |
---|---|---|---|---|

Physical time | 1 s | 1 s | 1 s | 1 s |

Clock time | 23,939 s | 23,720 s | 22,115 s | 19,862 s |

Speed-up | 1 | 1.01 | 1.08 | 1.2 |

Efficiency | 100% | 84% | 83% | 80% |

**Table 6.**Mean velocity and fluctuations of velocity in the airwake over the flight deck behind the CPF in motion, at location C5 in Figure 4b—the highest elevation (z = 9.5 m) of the centre probe (x = 14 m).

Condition | Motion | $\mathit{U}\mathbf{/}{\mathit{U}}_{\mathbf{\infty}}$ | $\mathit{\theta}\mathbf{[}{}^{\mathbf{\xb0}}\mathbf{]}$ | $\mathit{\psi}\mathbf{[}{}^{\mathbf{\xb0}}\mathbf{]}$ | ${\mathit{U}}^{\mathbf{\prime}}\mathbf{/}{\mathit{U}}_{\mathbf{\infty}}$ | ${\mathit{\theta}}^{\mathbf{\prime}}\mathbf{[}{}^{\mathbf{\xb0}}\mathbf{]}$ | ${\mathit{\psi}}^{\mathbf{\prime}}\mathbf{[}{}^{\mathbf{\xb0}}\mathbf{]}$ | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

CFD | Exp | CFD | Exp | CFD | Exp | CFD | Exp | CFD | Exp | CFD | Exp | ||

Headwind | Static | 0.76 | 0.76 | −9.01 | −8.66 | 0.41 | −3.44 | 0.09 | 0.16 | 5.41 | 9.09 | 7.41 | 12.15 |

Headwind | Heave | 0.77 | 0.76 | −9.45 | −8.66 | 0.26 | −2.73 | 0.10 | 0.16 | 5.54 | 9.03 | 6.77 | 12.21 |

Headwind | Pitch | 0.63 | 0.76 | −11.07 | −8.85 | 1.86 | −2.61 | 0.23 | 0.17 | 10.61 | 9.08 | 12.93 | 12.06 |

Headwind | Roll | 0.78 | 0.76 | −9.83 | −8.53 | 0.44 | −2.41 | 0.09 | 0.15 | 4.75 | 8.86 | 8.01 | 12.00 |

Red 15° | Heave | 0.79 | 0.84 | 1.88 | −1.32 | 22.41 | 21.23 | 0.18 | 0.21 | 11.53 | 11.01 | 13.72 | 13.24 |

Headwind | Heave–Pitch | 0.72 | 0.76 | −9.77 | −8.51 | 0.72 | −2.78 | 0.15 | 0.16 | 6.38 | 9.16 | 8.31 | 12.24 |

Headwind | Heave–Roll | 0.76 | 0.76 | −9.29 | −8.67 | 0.39 | −3.32 | 0.11 | 0.16 | 5.99 | 9.23 | 7.76 | 12.36 |

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## Share and Cite

**MDPI and ACS Style**

Yuan, W.; Wall, A.; Thornhill, E.; Sideroff, C.; Mamou, M.; Lee, R.
CFD Aided Ship Design and Helicopter Operation. *J. Mar. Sci. Eng.* **2022**, *10*, 1304.
https://doi.org/10.3390/jmse10091304

**AMA Style**

Yuan W, Wall A, Thornhill E, Sideroff C, Mamou M, Lee R.
CFD Aided Ship Design and Helicopter Operation. *Journal of Marine Science and Engineering*. 2022; 10(9):1304.
https://doi.org/10.3390/jmse10091304

**Chicago/Turabian Style**

Yuan, Weixing, Alanna Wall, Eric Thornhill, Chris Sideroff, Mahmoud Mamou, and Richard Lee.
2022. "CFD Aided Ship Design and Helicopter Operation" *Journal of Marine Science and Engineering* 10, no. 9: 1304.
https://doi.org/10.3390/jmse10091304