Safety Analysis and Simulation Validation of Hose Whipping Phenomenon in Air Refueling

Aerial refueling makes long-distance flying operations a possibility. It is the process of transferring fuel from one tanker to one or more receivers during flight [1]. During the refueling, the tanker and receiver(s) fly in intensive formations, requiring high accuracy and persistent robustness. The success of aerial refueling hinges on the flight quality, which depends on the meticulous design, precision manufacturing, and timely maintenance of the aircrafts. After all, any small mistake may lead to a string of serious accidents, ranging from equipment damage to aircraft collision. All these accidents could impede mission completion and weaken the combat capability of the air force.

The complex process of aerial refueling involves multiple factors, namely, equipment, personnel, air traffic control, and environment [2]. Most accidents in aerial refueling concentrate in the docking phase. Once connected, the tanker and the receiver fly in an ultra-intensive formation. Then, the hose cone sleeve could be affected by the wake of the tanker, the bow shock of the receiver, and the atmospheric turbulence. This shortens the time for the aircrafts to finish the docking phase, and adds to the difficulty in keeping a stable flight posture [3]. Moreover, if the tanker and receiver fly too fast, hose slack could easily occur in the docking phase, resulting in the hose whipping phenomenon (HWP). Despite the fruitful results on the safety of aerial refueling, there is little report on the HWP, which was discovered in 2002 [4]. Some scholars have analyzed the hose-drogue model, and proposed effective suppression methods [5, 6]. But there is a severe lack of reliable safety analysis for guidance.

The traditional linear casual theories cannot identify all the hidden risk factors of the HWP, not to mention designing suitable countermeasures. Typical models of these theories, such as the reason model [7] and the Domino model [8], handle the accident triggers like human, machine, and environment independently, yet fail to consider an ocean of nonlinear factors, e.g., system cross-linking, human-machine interaction, and air-ground coordination. Similarly, traditional safety analysis methods are not applicable to solve complex systems like the aerial refueling. These methods can neither explain accident triggers efficiently, nor derive complete improvement measures.

Against this backdrop, various new safety analysis methods have emerged based on systems theory. Typical examples include the AcciMaps theory [9], the functional resonance analysis method (FRAM) [10], the system-theoretic accident model and process (STAMP), a.k.a. the system-theoretic process analysis (STPA) [11], the contributory factor interactions model [12], and sensitivity analysis [13, 14]. These novel methods can identify the impacts of traditional component failure, and fully reflect on the nonlinear risk factors (e.g. component interaction). By these methods, a complex system is treated as a complete body, and causal factors are analyzed from all levels, and the relationship between system components are clarified, shedding new lights on the safety analysis of complex systems [15-17]. The results of these methods could be validated by simulation with models like hose-drogue model [5] and auxiliary model [6, 18, 19].

Through the above analysis, this paper introduces the STPA to analyze the HWP in the docking phase of aerial refueling, and puts forward rewarding suggestions on how to prevent relevant accidents or hazards. In addition, a simulation validation environment was created to verify the analysis results on the HWP.

The remainder of this paper is organized as follows:  Section 2 carries out the STPA on the HWP, and proposes the critical safety constraints; Section 3 establishes an HWP simulation model, and verifies the proposed constraints; Section 4 draws several important conclusions.

In the aviation field, safety validation can be realized through test flight or simulation [20]. The test flight is an accurate and reliable validation approach. But its complex processes often bring a high cost of manpower and materials. In addition, the test results might be affected by uncertainties in flight environment, personnel condition, and organizational management. Therefore, this paper chooses to verify the feasibility of the proposed SCs through simulation.

3.1 Constructing simulation environment

To simplify the simulation model and ensure its scientific nature, the following hypotheses were presented for the HWP simulation validation platform [6]:

(1) The effect of earth curvature is negligible, and the entire refueling airspace is at the same level;

(2) The effect of earth rotation is negligible, and horizontal coordinate system is taken as the inertial coordinate system;

(3) The gravitational acceleration is fixed across the refueling airspace;

(4) The elasticity of aircraft deformation is negligible, and the aircraft bodies are ideal rigid mechanisms;

(5) The effect of complex electromagnetic environment is negligible.

From the functional control structure in Figure 1, it is easy to derive the key objects of simulation validation: hose cone dynamic model, the reel mechanism control model, the tanker vortex field model, and the atmospheric turbulence model. Drawing on the relevant literature [6, 18, 19], the hose cone dynamic model adopts the multi-rigid body dynamic model based on the centralized parameter principle [6]; the reel mechanism control model considers the driving mechanism of the constant force spring; the tanker vortex field model employs the Hallock-Burnham model [19]; the atmospheric turbulence model uses the Dryden model [18]. On this basis, a 24-section hose cone was adopted. Each section can be employed as a hinge. Figure 2 shows the HWP model of the k-th section hose. The HWP model of every other section is the same as that of the k-th section. They are connected by the distance vector from hinge k-1 to hinge k(p_k), derivative of p_k (p_k-dot) of each section relative to the drag point system, air resistance (D_k) of each section, and pull of (t_k) each section.

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Figure 2. The HWP model of the k-th section hose

The spatial position vector r_k, speed v_k, and acceleration a_k of the k-th hinge can be respectively described as:

${{r}_{k}}={{r}_{k-1}}+{{p}_{k}}$     (1)

${{v}_{k}}={{v}_{k-1}}+{{p}_{k}}\_dot$     (2)

${{a}_{k}}={\left( {{Q}_{k}}+{{t}_{k}}-{{t}_{k+1}} \right)}/{{{m}_{k}}}\;={\left( {{Q}_{k}}+{{t}_{k}}-{{t}_{k+1}} \right)}/{{{l}_{k}}\mu }\;$     (3)

where, l_k is the length of the k-th hinge; μ is the mass per unit length of hose; t_k is the internal force of the system that cannot be obtained directly, but solved under additional constraints；

${{p}_{k}}\cdot {{p}_{k}}=l_{k}^{2}$     (4)

Q_k is the external force on the k-th hinge, including hose gravity, bending recovery torque R_k, and air resistance D_k of the hose:

${{Q}_{k}}=mg+{{R}_{k}}+{\left( {{D}_{k-1}}+{{D}_{k}} \right)}/{2}\;$     (5)

${{R}_{k}}={8EI\gamma }/{{{l}^{2}}}\;$     (6)

where, I is the moment of inertia; E is the elastic modulus of the hose; γ is the angle between the k -th and the k-1-th hinges; l is the length of the hinge.

$\begin{align}  & {{D}_{k}}=\left\{ -0.5{{p}_{\infty }}{{\left[ {{V}_{{k}/{air}\;}}\cdot {{n}_{k}} \right]}^{2}}\pi {{d}_{0}}l{{c}_{t,k}} \right\}{{n}_{k}} \\ & +\left\{ -0.5{{p}_{\infty }}\left. \left\| {{V}_{{k}/{air}\;}}- \right.\left( {{V}_{{k}/{air}\;}}\cdot {{n}_{k}} \right){{n}_{k}} \right\|\pi {{d}_{0}}l{{c}_{n,k}} \right\}{{n}_{k}} \\ & \times \left[ {{V}_{{k}/{air}\;}}-\left( {{V}_{{k}/{air}\;}}\cdot {{n}_{k}} \right){{n}_{k}} \right] \\\end{align}$     (7)

${{V}_{{k}/{air}\;}}={{v}_{k}}-{{u}_{k}}$     (8)

where, V_k/air is the speed of the k-th hinge under the environment influence; u_k is the vector sum of steady flow, tanker wake, and atmospheric turbulence at the k-th hinge; p_∞is the air density; d₀ is the outer diameter of the hose; c_t,k is tangential dynamic drag coefficient; c_n,k  is the normal aerodynamic drag coefficient; l is the hinge length.

3.2 Validation of HWP

As mentioned in Section 2, CA-3 mainly establishes the interaction between pilots, and ensures the realization of CA-1 and CA-2. The UACs related to CA-1 (SC-6, SC-7, SC-8, SC-9, SC-10, SC-11, SC-12) are mainly caused by the speed difference between the two aircrafts during docking. The SCs related to CA-2 (SC-13, SC-14, SC-15, SC-16) are mainly triggered by the tension control of the hose through expansion and contraction. In actual control, the main strategy is to control the hose length and tension by the reel mechanism. Therefore, the following validation will focus on the speed difference during docking, the tension control by the reel mechanism, and the hose length.

3.2.1 Docking speed

Assuming that the reel mechanism is not working and the hose length is 22m, the receiver was docked with two speed control methods at time T=35s. The control results are illustrated in Figure 3, and the changes in hose shape at two control modes are manifested in Figure 4, where X_n, Y_w, and Z_w are the distances of the current hose position relative to the x, y, and z axes, respectively. In addition, the changes in hose tension at two control modes are displayed in Figure 5. The simulation results indicate that the HWP is more obvious when the receiver is docked under the mode of speed control-2.

3.png

Figure 3. The control results

3.2.2 Reel control

The reel mechanism takes the tanker outlet tension as a feedback to control the pulling force on the hose within a certain range. Our simulation aims to disclose how the reel mechanism affects the hose state during the docking. The main technical parameters were configured as: the total mass M of the reel and hose, 68.08kg; the initial hose length L₀: 14m; the controllable spring length L₁: 3m; the binding force coefficient κ: 10,000N/m. To obtain more obvious control effect, the speed control-2 was adopted for the reel control simulation. The change in hose shape during docking is illustrated in Figure 6.

4.png

Figure 4. The changes in hose shape at two control modes

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Figure 5. The changes in hose tension at two control modes

6.png

Figure 6. The change in hose shape during docking

3.2.3 Hose length

During the docking, the hose is fully towed. Hence, its dynamic performance hinges on its length. Suppose the reel mechanism is not working, the hose length is 14m, and the receiver is docked at speed control-2. Then, the changes in hose shape and hose tension are recorded in Figures 7 and 8, respectively.

7.png

Figure 7. The changes in hose shape at speed control-2

8.png

Figure 8. The changes in hose tension at speed control-2

3.3 Discussion

(1) Validation results on speed control

Figure 4 shows that, in speed control-1, the forward distance of the receiver and the forward movement of the cone sleeve became shorter, and the hose had a low degree of slackness, along with the slow and limited speed changes. On the contrary, in speed control-2, the hose shape changed significantly, along with the fast and significant speed changes. The contrast suggests that the speed should be controlled to smoothen the change and minimize the amplitude of hose shape, thereby reducing the HWP during the docking.

Figure 5 shows that the hose tension plunged during docking under the two speed control modes. After docking, the tension gradually increased along the hose. Comparatively, speed control-2 brought a larger changing amplitude than speed control-1. Under speed control-2, the tension was not restored for a long time, indicating that the hose is relaxed; the oscillation of the tension means the hose slightly flutters. At this time, a strong incoming airflow will blow the loose hose towards the cone sleeve, leading to HWP hazard and causing serious accidents (L-1, L-2, L-3).

The above results demonstrate the necessity of speed control (CA-1) during docking. In this phase, SC-6, SC-9, SC-10, and SC-12 must be observed to control the speed, and prevent excessive hose slack from forming HWP.

(2) Validation results on reel control

As shown in Figure 6, the hose could be rewound quickly, and the swing amplitude was clearly reduced under reel control. It can be concluded that the reel mechanism can significantly suppress the large swing of the hose and mitigate the HWP. Hence, it is highly necessary to check the reel mechanism, and maintain its ideal working condition (SC-34).

(3) Validation results on hose length

Comparing Figure 7 with Figure 4(b), it can be seen that the hose swing was intensified during docking, as the hose length was reduced to 14m. This is because a short hose has a light weight and stays close to the tanker vortex. Consequently, the hose is easily affected by the wake field, and thus shakes more vibrantly.

As shown in Figure 8, after the hose length was shortened from 22m to 14m, the hose tension of the 24^th section was out of control 4s after docking, entering the state of fierce swing. This increases the probability of system-level losses (L-1, L-2, L-3). Therefore, properly increasing the hose length can effectively enhance the safety of aerial refueling (SC-32).

To sum up, the HWP of aerial refueling is mainly controlled by three factors: the docking speed, the hose tension controlled by the reel mechanism, and the hose length. The proposed SCs were proved effective and accurate through simulation validation.