Understanding the Manoeuvring Performance of an X- Plane Submarine in Deep Water and Near the Free Surface Authors Name: P Crossland, N Kimber and N Thompson Affiliations: QinetiQ Ltd, UK Email contact: pcrossland@qinetiq.com 1. INTRODUCTION In the UK, the current submarine capability is heavily targeted towards providing support to a submarine fleet with traditional cruciform stern arrangements; however, it is thought that performance improvements may be achieved with the use of alternative control surface arrangements, such as X-planes. Operationally, the advantages of X-planes, over the more traditional cruciform arrangements typical of UK Royal Navy submarines, are that they may provide greater safety; if an X-plane submarine was to experience a single plane jam then the remaining three planes would be able to not just counteract the effects, but also enable the submarine to remain operational. The disadvantages are that when sizing the X- planes to provide a desired horizontal plane performance this effectively sets the performance in the vertical plane too. This trait can be offset to some extent by having an X-plane design with the planes not set at a 9 degree angle to each other, but at an angle that creates a greater component of lift in the horizontal plane than the vertical plane. However, before such X-plane concepts can be considered as design options for potential future UK submarines, the capability to understand the performance of such configurations during the design process must be developed and validated beforehand. A validated method of predicting the performance of a manoeuvring submarine will provide the ability to understand the merits of alternative stern configurations; and reduce risk during the design and procurement of such submarines. As part of a four year programme of work, a validated means to enable the investigation of the relative merits of a range of aft appendage configurations, including X-plane stern arrangements, was developed by QinetiQ Ltd. This paper describes the experiment techniques used to derive the coefficients from captive model tests and the results from free running model tests in deep water and in close proximity to the free surface and, where applicable, compares the model tests with numerical predictions. 2. X-PLANE DESIGN The aim of the study was to develop an X-plane stern arrangement for an existing design of submarine to allow testing in the Ship Tank and Rotating Arm at QinetiQ Haslar and allow tests using a free running model. Due to the requirement to make early design decisions to enable a complete experimental programme to be undertaken in the desired timescales, it was recognised that the X-plane design would not be optimal for that particular hull form but would represent an arrangement that was suitable for generating validation data. The design space is represented in Figure 1. In addition to the time constraints, there were also design constraints; principally that any X-plane stern should easily interface with the existing physical captive model and had to be configurable to be able to cost-effectively implement the design on to the Submarine Research Model (SRM) developed by QinetiQ Ltd and covered later in this paper. So, as a result of the design constraints, the forward and aft radii of the cone section were fixed to interface with the existing model, the cone angle and stock locations were fixed to ensure configurability with SRM and the X-plane
configuration had to be orthogonal. Furthermore, the span of the planes is effectively fixed since it should be contained in a box defined by the maximum beam of the hull. Once the span had been fixed the decision was made to maintain the same aspect ratio of the upper rudder of the existing submarine design which, in effect, fixed the root and tip chords. Thus, each of the X-plane appendages were geosims of the upper rudder from the existing submarine; the result was an increase of around 33% in total lifting surface in the horizontal plane compared with the original upper and lower rudder combined. C r Stock position S C r /4 β R aft X stock R fwd S C t /4 C r C t C t (a) Stern configuration Figure 1: Design variables for an X-plane 3. COEFFICIENT BASED TECHNIQUES (b) Appendage design There are a number of methods used for predicting the manoeuvring performance of a deeply submerged submarine, see (ITTC, 28) for approaches for surface ships. Generally, in order to predict manoeuvring parameters such as advance, transfer overshoots etc, the fundamental trajectories of the submarine undertaking specific manoeuvres are required. The exceptions to this are the stability and control indices, (Spencer, 1968), given as: ' ' ' ' ' ' M uw( m + Zuq ) N GV = 1, uv ( m Yur ) G 1 ' ' H = + ' ' M Z N Y uq uw The traditional system-based methods require a physical model to be manufactured and tested in a series of captive model experiments to measure directly the hydrodynamic forces and moments acting on the appended submarine as a function of the motion state variables, see (Lewis, 1989) for example. This is based on the assumption that the problem can be regarded as quasi-steady state whereby each component of the force and moment is a function of the instantaneous values of the velocity and acceleration components of the body, and the deflection of the control surfaces. One mathematical approach to determining the quasi steady state forces and moments on a manoeuvring submarine is described by (Gertler and Hagen, 1967). For example the equation for pitch moment is given as: M = M + M w + M v 2 +M δb+ M δs + M w υ +M w + M w υ + M w& + M q + M v p +M v r uu uw vw uuδb uuδs wυ u w wυ w& uq vp vr + M q υ + M q δs + M q& + M p 2 + M r 2 + M r p + M q q m g x B x cosφcosθ m g z B z sinθ + M qυ u qδs q& pp rr rp q q G B G B wave ur uv t M = 3 where the ' represents the non-dimensionalised pitch moment given as: 1 ρu 2 L 2 M
For an X-plane configuration, the terms involving the movement of the stern plane, δs, are more complex since the use of independently actuated planes means there are potentially individual contributions from each appendage. Hence, for an X-plane arrangement there will be a separate set of hydroplane coefficients derived for each individual control surface (Xi), as shown in Table 1. Furthermore, the experimental design is fundamentally a function of the coefficients that are to be derived; that is, the experiment must be designed so that the state variables can be controlled as independent variables. Cruciform Rudder Sternplane Xuuδrδr' Xuuδsδs' Yuuδr' Zuuδs' Kuuδr' Muuδs' Nuuδr' - X-plane XuuδXδXi' YuuδXi' ZuuδXi' KuuδXi' MuuδXi' NuuδXi' Table 1: Comparison of cruciform and X-plane appendage coefficients 4. CAPTIVE MODEL TESTS A 5m Glass Reinforced Plastic (GRP) model of the existing submarine design was modified such that the standard cruciform appendage configuration was replaced with the orthogonal X-plane configuration. For the experiment, the model had a balance fitted that measured the forces and moments acting on the model during both steady state and dynamic load conditions. (a) Ship Tank (b) Rotating Arm Figure 2: Captive model experiments The model was towed in the Ship Tank to provide the relationship between the forces, moments and velocities and the various state variables such as body angles of attack and plane angles of attack. During these runs the four X-plane appendages were moved individually, as adjacent dual planes, opposing dual planes, and all four planes together, over their operational range to help understand any interference effects. The experimental runs on the Rotating Arm were designed to measure relationships between the forces, moments and velocities and the various state variables for non-zero pitch and yaw rate. Figure 2 shows the captive model mounted on the Ship Tank carriage and the Rotating Arm; in total approximately 2,7 runs were undertaken in order to capture the full effects of the X-plane design. One particular area of extensive investigation was whether there were any significant interference effects due to the all moving X-planes. That is, can the effect of each X-plane be simply added together to get the effect of any combination of planes moving together? Figure 3 shows the resulting heave force and pitch moment
associated with moving all four planes (as stern planes) and comparing with the summation of the heave forces and pitch moments associated with moving the planes individually. This appears to show that except at the largest angles of attack the interference effects are negligible. (a) Heave force (b) Pitch moment Figure 3: Comparison between forces due to moving all planes and moving planes individually 5. CFD TECHNIQUES Determining the unsteady forces and moments on a manoeuvring submarine using computational methods represents a challenging problem and perhaps these methods are not sufficiently mature for use as a design tool; the alternative to determining these forces and moments directly is to assume that the hydrodynamic forces and moments acting on the appended submarine can be represented as a function of the motion state variables in the same way as that assumed for experiments. QinetiQ Ltd has used the commercially available CFD code ANSYS CFX5 with some success in capturing the steady state forces and moments on a submarine at angles of attack. In parallel to the extensive experimental programme, a series of CFD calculations were undertaken using the same X-plane geometry (propulsor not shown), Figure 4. Figure 4: Hull with X-plane A (Baseline) Reynolds Stress model of turbulence was used in all the calculations which included an Automatic Wall Function capable of resolving the turbulent boundary layer near solid boundaries down to the viscous sub-layer. Transition effects were not modelled and the flow was assumed to be fully turbulent over the whole domain. Propulsor effects were modelled by applying a uniform momentum source distribution over the volume occupied by the propulsor. In cases of non-zero pitch and yaw rate, the calculations were carried out in a rotating frame of reference. The entire computational domain was assumed to be rotating at a constant angular velocity about a fixed centre of rotation, giving a quasi-
steady flow solution. Figure 5 shows an example of the quality of the predictions when compared with the experiments. In this particular case, CFD predictions were undertaken and compared with the conditions from the experiments. These data were taken from the Ship Tank experiments but similar quality of predictions was observed for the Rotating Arm experiments for non-zero pitch and yaw rate. Z' 15 1 5-2 -1 1 2-5 -1-15 Pitch (degrees) (a) Heave force Expts CFD (b)pitch moment Figure 5: Predicted and measured forces and moments The coefficients relating to the acceleration terms in the force and moments equation were derived using the Submarine Component Added Mass program (SCAM) which is based on the approach developed by (Watt, 1988) and is used to estimate the added mass coefficients. In SCAM, each component of the submarine is approximated by an equivalent ellipsoid. SCAM, thus, takes account of the added mass contributions from the appendages as well as the hull. 6. IMPLEMENTATION OF MATHEMATICAL MODEL As mentioned earlier, the basis for the hydrodynamic coefficient set which populates the simulation model comes from the constrained model experiments. The next step in the design evaluation process was to incorporate this coefficient set into a format suitable for use in simulation. Until free-running model experiments have been conducted, there are no validation data available for simulations using this mathematical model. However, the initial simulation model can be used in the analysis of submarine stability and design of control algorithms that are usually based on simplified linear models of the submarine dynamics, or so called linear derivatives. Having obtained the values for the derivatives for the X-plane design, the vertical and horizontal stability indices were calculated as G v =.11 and G h =. 4. The accepted stability criteria are that Gv and G h should be positive to indicate vertical and horizontal stability respectively, suggesting that this particular X-plane would not meet the design criteria for both the horizontal and vertical plane. Experience shows that submarines with negative Gv and G h are not typical; indeed, this was not the case for the original cruciform design which has flapped stern planes with stabilisers. So, the result of adding an X-plane, with all four appendages moving, has imparted some dynamic stability issues on this design. The key question is how this instability would manifest itself in any free running model with this configuration, which will be demonstrated later in this paper. 7. AUTOPILOT DESIGN. -2-1 -.5 1 2-2. Pitch (degrees) One key aspect of the design using X-planes is the design of the control algorithms that accompany them; the design is different to that for a cruciform arrangement. A conventional cruciform dive command, which would just be applied to the stern planes, would be applied to all four X-plane control surfaces, as shown in Figure 6(a). (The view is M' Expts CFD 2.5 2. 1.5 1..5-1. -1.5
from aft looking forward.) Similarly, when a conventional cruciform initiates a turn, this would just be applied to the rudder, which for the X-plane would be applied to all the control surfaces as shown in Figure 6(b). (a) Acting as a stern plane (b) Acting as a rudder (c) Combination of depth and heading control Figure 6: Cruciform to X-plane transformation When simultaneous depth and heading demands are made, the demanded control surfaces are simply summed. Figure 6(c) shows an example of a combined dive on the planes and a starboard rudder. The upper starboard and lower port control surfaces sum their deflections, while the upper port and lower starboard demands cancel out. During the development of the coefficient set and implementation in simulation, it was found that the lower pair of X-plane control surfaces was slightly more effective than the upper pair, despite being geometrically identical, see Table 2. This is reflected in the pertinent coefficients, where the lower pair values are around 8% greater than the upper pair values. This is possibly due to the presence of the bridge fin creating vortices that are transported downstream and impact on the upper pair of control surfaces. The table also shows the relative power (as a magnitude of the X-plane coefficient divided by the pertinent coefficient from the cruciform) of the X-plane relative to the cruciform; this table demonstrates the increase in control authority that is attained from the four all moving appendages. Indeed there is around 9% increase in control authority in the vertical plane which is not particularly the plane in which agility is a desired feature. Coefficient Cruciform (baseline) X-plane upper pair X-plane lower pair X-plane combined Zds 1.91.98 1.89 Mds 1.92.98 1.9 Ydr 1.67.71 1.38 Ndr 1.69.76 1.45 Table 2: Relative power of the X-plane The approach to the design of the course and depth autopilots was to treat them separately, with the demands summed at the output to the control surfaces themselves as illustrated in the above example. The course control (and similarly depth control) was divided into two modes, course-keeping and course-changing (or depth-keeping and depth-changing for the vertical plane). The controllers themselves take the form of a high order state-space system; embedded in the autopilot is a procedure for switching between the different
modes in the horizontal and vertical plane. All the controllers were run in parallel to ensure instabilities between plane angle demands were avoided during the switching process. 8. FREE RUNNING MODEL TESTS Once the autopilot algorithm had been developed it was implemented into a real time operating system for use in the free running model, the QinetiQ Submarine Research Model (SRM). The model is capable of replicating most of the manoeuvres that would be pertinent on a full scale submarine and in some areas more; one primary area is that of exploring extreme manoeuvres such as hydroplane jams and the subsequent recovery strategies. The SRM was configured as a geosim, Figure 7, of the model used in the constrained experiments. Figure 7: Profile view of SRM clad as an X-plane The experiments fall into two distinct parts: manoeuvres in the Ocean Basin and manoeuvres at the deep-water reservoir. In general, the Ocean Basin manoeuvres were limited to the slow and moderate speed runs and some limited depth changes to investigate turning circles, zig-zags and autopilot performance. The bulk of the programme was conducted at the reservoir where the available space allowed for the higher speed manoeuvres to be conducted as well as those which required larger depth changes, such as jam scenarios. On directional instability, during a turn at 8 knots where a pull-out manoeuvre was initiated, the yaw rate actually persisted beyond setting the rudder amidships. The yaw rate does decay, but settles on a non-zero value, i.e. the submarine keeps turning. Further experiments demonstrated that whilst in the vertical plane there was some transient instability, the design can be controlled by the planes without incurring excessive plane activity. Figure 8 shows an example of the data from the free running model tests; Figure 8(a) shows how the tactical diameter varies with rudder angle for a range of speeds tested. These turning circles were conducted using all four control surfaces as rudders, with additive depth control applied as required. Because of the requirement for depth control, some of the 3 rudder turns did not quite achieve this angle. The data show a consistent variation in the tactical diameter with rudder angle and are largely independent of speed. There is a distinct flattening off at the higher rudder angles with no improvement in diameter at 3 rudder over 25 rudder, possibly as a result of the planes stalling. A series of tests included the application of a single hydroplane jam following a steady period of straight and level running. All other control surfaces remained under autopilot authority, and the initial response was to do nothing, i.e. allow the autopilot to simply carry on with the current ordered depth and heading. An example of an 8 knot jam to rise is shown in Figure 8(b). Generally, for modest jam angles of say 1 and 2, any pitch, depth and yaw excursions were minimal. However, for the higher 3 jam to rise on the upper port plane, the excursions were more considerable, and yaw became uncontrolled. The initial response of the course keeping and depth keeping controllers is to control yaw and pitch equally; however, both failed in this scenario. When the heading error reached
1, the autopilot switched to the course-changing controller which had no integral action. As such the demands of the heading control then become swamped by the depth control so the submarine is no longer controlled in yaw. As a result the control of depth and pitch are regained at the expense of increasing the yaw rate. (a) Tactical diameter (b) Single stern plane jam Figure 8: Free running model data In general, single hydroplane jams at moderate angles were comfortably dealt with by the autopilot without any further action, with depth and heading successfully maintained. However, single hydroplane jams at the maximum deflection were not successfully controlled by the do nothing strategy. An alternative strategy of slowing down and allowing heading changes meant that depth and pitch were better maintained. 9. SUBMARINES NEAR THE FREE SURFACE There are times when a submarine is required to operate close to the sea surface when using the periscope or, in the case of a diesel-electric boat, when snorting during the period of recharging the batteries, the submarine can experience complex oscillatory motion [Musker et al, 1988] that can present problems in that the submarine may broach the surface, increasing the possibility of detection, or in the event of a temporary loss of the suction force the submarine may sink below depths that periscope and snorting operations can be undertaken. This issue creates a design challenge associated with the development of submarine autopilots controlling depth, (Burcher and Rydill, 1995), which manifests itself as two technical problems one of size and actuation of lifting surfaces such as hydroplanes and the other of capacity of any onboard trim and ballast system. The main concern to the designer is how to accommodate the effects of the second order suction force, which could mean that if the planes and trim systems are poorly designed they could become saturated in certain wave conditions. The non-linear behaviour of the submarine means that it is susceptible to the effects of wave grouping. Groups of large waves can be passing over the submarine for a period of time, whereby the suction force is temporarily increased, which must be counteracted in order to prevent the submarine from broaching (Burcher and Rydill, 1995). One method of quantifying wave groups is by the Smoothed Instantaneous Wave Energy (SIWEH) function, introduced by (Funke and Mansard,198), which is computed by squaring the wave surface elevation and applying a low pass filter (based on the spectrum peak period).
The logic behind this approach is to enable a method of predicting the dynamic response of a floating structure which responds only to low frequency drift excitation; this is not dissimilar to the phenomenon creating the second order effects on a submarine at periscope depth. For a surface elevation η with spectral peak period of T p the SIWEH is: 1 2 E( t) = η ( t + τ ). Q( τ ) dτ Tp where Q(τ) is a smoothing function given as τ 1 for T p τ T Q(τ ) = T p elsewhere Figure 9 gives an example of the spectral responses in a scaled sea state 3 (with an ITTC spectrum) in head seas with the speed of the model equivalent to around 8 knots. There are clear first order responses at frequencies contained in the wave spectrum; there are also higher order responses at frequencies much lower than any contained in the wave spectrum. p 6 x 1-4 5 wave 5 4 3 2 1.5 1 1.5 2 2.5 3 3.5 4 bowplanes 4 3 2 1.5 1 1.5 2 2.5 3 3.5 4 depth 1.2 x 1-3 1.8.6.4.2.1.5 1 1.5 2 2.5 3 3.5 4 stern planes 7 6 5 4 3 2 1.5 1 1.5 2 2.5 3 3.5 4 Frequency (Hz).8.6 pitch.4.2.5 1 1.5 2 2.5 3 3.5 4 Frequency (Hz) Figure 9: Response spectra in a sea state 3 The first order depth response (heave) has been practically removed, which is as a result of the autopilot in the model responding to depth error; the autopilot is aimed at maintaining depth and thus induces small angles of pitch in the model to achieve this. Again, as a result of the autopilot, the planes are responding to both the first and higher order responses; with the bow planes (or fore planes) correcting for most of the low frequency components. Figure 1 shows the spectral analysis of the SIWEH function (of the wave) compared with the pitch and depth response, for the same run conditions illustrated in Figure 9. The results show that the frequency content of the SIWEH function is very similar to that of the depth and pitch response, in contrast to the encounter wave spectrum. The spectral ordinates have been normalised by the maximum spectral ordinate for each response to enable the plots to be compared more easily. For the pitch response, there are frequency components that are contained in the wave spectrum but clearly lower frequency components that are not present in the waves. There are frequencies that coincide with the frequency content of the SIWEH function suggesting that pitch response is related to the group structure; there are however, intermediate frequencies where there is no clear forcing function. For the depth response, there is very little response at the wave frequencies
(likely due to the effect of the autopilot) but there is a significant response at frequencies close to those contained in the SIWEH function, again suggesting the possible relationship between depth response and group structure. Normalised spectral ordinate 1.9.8.7.6.5.4.3.2.1 SIWH Waves Pitch.5 1 1.5 2 2.5 3 3.5 4 Frequency (Hz) (a) Pitch Normalised spectral ordinate 1.8.6.4.2 (b) Depth Depth SIWEH Waves.5 1 1.5 2 2.5 3 3.5 4 Frequency (Hz) 1. CONCLUSIONS Figure 1: Normalised response spectra for pitch and depth This paper has described the principal elements of a four year research programme undertaken by QinetiQ Ltd to develop the numerical and experimental capability to assess the performance of an X-plane submarine design. The paper has brought together the development of a design toolset and an extensive experimental programme of captive and free running model tests to provide the capability to evaluate novel stern plane configurations and provide safe operator guidance. 11. ACKNOWLEDGEMENTS The authors acknowledge the UK MoD for supporting this research programme and acknowledge the efforts of the QinetiQ Hydrodynamics Team for their support in undertaking the work described here. 12. REFERENCES 25 th International Towing Tank Conference (ITTC), The Manoeuvring Committee report. Proceedings, Vol I, Fukuoka, Japan, 28. Burcher, RK., Rydill, L. Concepts in submarine design, Cambridge University Press, 1994. ISBN 521 41681 7. Funke ER., Mansard EPD., On the synthesis of realistic sea states. Proceedings of the 17 th International conference on Coastal Engineering, 198, pp167-168. Gertler, M., Hagen, GR., Standard equations of motion for submarine simulation Naval Ship Research and Development Centre, Report No. 251, USA, 1967. Lewis, EV., Principles of Naval Architecture, Vol III, Motions in waves and controllability, SNAME, 1989. Musker, AJ., Loader, PR., Butcher, MC., Simulation of a submarine under waves. International Shipbuilding Progress, 35, No. 44, 1998, pp 389-41. Spencer, JB., Stability and control of submarines Parts I-IV, Journal of the Royal Navy Scientific Service. Vol 23, No. 3, May 1968. Watt, G.D., Estimates for the Added Mass of a Multi-Component, Deeply Submerged Vehicle, RINA WARSHIP Conventional Naval Submarines, UK, 1988.