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Research Papers: Flows in Complex Systems

Experimental Investigation of the Submarine Crashback ManeuverPUBLIC ACCESS

[+] Author and Article Information
David H. Bridges

Department of Aerospace Engineering, Mississippi State University, Mississippi State, MI 39762

Martin J. Donnelly, Joel T. Park

Naval Surface Warfare Center, Carderock Division, E. Bethesda, MA 20817

J. Fluids Eng 130(1), 011103 (Jan 16, 2008) (11 pages) doi:10.1115/1.2813123 History: Received October 04, 2006; Revised August 17, 2007; Published January 16, 2008

Abstract

In order to decelerate a forward-moving submarine rapidly, often the propeller of the submarine is placed abruptly into reverse rotation, causing the propeller to generate a thrust force in the direction opposite to the submarine’s motion. This maneuver is known as the “crashback” maneuver. During crashback, the relative flow velocities in the vicinity of the propeller lead to the creation of a ring vortex around the propeller. This vortex has an unsteady asymmetry, which produces off-axis forces and moments on the propeller that are transmitted to the submarine. Tests were conducted in the William B. Morgan Large Cavitation Channel using an existing submarine model and propeller. A range of steady crashback conditions with fixed tunnel and propeller speeds was investigated. The dimensionless force and moment data were found to collapse well when plotted against the parameter η, which is defined as the ratio of the actual propeller speed to the propeller speed required for self-propulsion in forward motion. Unsteady crashback maneuvers were also investigated with two different types of simulations in which propeller and tunnel speeds were allowed to vary. It was noted during these simulations that the peak out-of-plane force and moment coefficient magnitudes in some cases exceeded those observed during the steady crashback measurements. Flow visualization and LDV studies showed that the ring vortex structure varied from an elongated vortex structure centered downstream of the propeller to a more compact structure that was located nearer the propeller as η became more negative, up to $η=−0.8$. For more negative values of η, the vortex core appeared to move out toward the propeller tip.

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Introduction

When a submarine is traveling in the forward direction and a rapid deceleration is required, the propeller of the submarine is put into reverse rotation. For some time the submarine continues to move forward while the propeller, operating in the reverse direction, is acting to decelerate the submarine. This condition of forward body velocity and reverse propeller rotation is referred to as crashback, and the maneuver is referred to as a crashback maneuver. All that is desired during the maneuver is a decrease in the submarine’s forward velocity. No trajectory changes are commanded. However, because of the relative flow velocities in the vicinity of the propeller, a ring vortex develops around the propeller. This condition is illustrated schematically in Fig. 1. The velocities shown in this figure are relative to an observer fixed to the submarine. Because of the forward motion of the submarine, the flow velocities outside the propeller are directed rearward. However, because of the flow induced by the propeller operating in reverse, the velocities on the axis are directed upstream, toward the submarine. This shear between the velocities on the axis and the velocities outside the propeller causes the ring vortex to form. The ring vortex is not axisymmetric, however, and the asymmetry moves around the vortex. This asymmetry in the location and strength of the vortex results in unsteady asymmetric loads on the propeller, which are then transmitted to the submarine itself. These asymmetric forces and moments lead to uncommanded trajectory changes, so that in addition to continued forward motion, the submarine may pitch or yaw in an uncommanded fashion. In the shallow waters of littoral regions, where submarines have begun to operate, pinpoint control is a much larger issue than it was when most submarine actions took place in deep water.

The existence of a ring vortex around a propeller operating in a direction counter to forward motion has been known for some time, and according to Jiang et al. (1) was first reported by Lock (2), based upon observations of the flow past a propeller in a wind tunnel. Glauert (3) presented an estimate of propeller performance in the vortex ring state using a blade element analysis. Glauert (3) pointed out that the standard momentum analysis for propeller performance could not be performed, because a true slipstream did not form.

The determination of propeller performance in crashback is a standard component of so-called “four-quadrant” propeller performance tests. The term four quadrant is a reference to the fact that propeller performance in all four quadrants of the velocity-rotational speed $(V-n)$ plane is measured: forward motion ($V>0$, $n>0$), backing motion ($V<0$, $n<0$), crashback ($V>0$, $n<0$), and crashahead ($V<0$, $n>0$). The reports by Hecker and Remmers (4) and Boswell (5) contain examples of such performance measures. In terms of actual flow physics, however, the work of Jiang et al. (1) appears to be one of the first studies of the fluid dynamic phenomena associated with the crashback maneuver on a submerged marine propeller. Jiang et al. (1) studied the flow past David Taylor Model Basin (DTMB) propeller 4381through the use of flow visualization and force measurements. These were propeller only or open-water studies conducted with the propeller mounted on a drive shaft in the DTMB $24in.$ water tunnel. Jiang et al. (1) noted the unsteadiness of the ring vortex and also its frequent “bursting” and reformation. The force measurements indicated strong out-of-plane forces and moments generated on the propeller by the unsteady asymmetry of the ring vortex.

Propeller 4381 has been the subject of a number of experimental and numerical studies. Chen and Stern (6) performed a four-quadrant computational study of P4381. This study used the unsteady, three-dimensional, incompressible, Reynolds-averaged Navier–Stokes equations in generalized coordinates and the Baldwin–Lomax turbulence model. Their computed results for thrust and torque were in generally good agreement with measured open-water values for P4381 as reported by Hecker and Remmers (4) and cited by Chen and Stern (6). The results of Chen and Stern related to the crashback maneuver were confined to a comparison of their computed streamline patterns with the flow visualization photographs of Jiang et al. (1) and a comment that both the experiments and the computations indicate that the ring vortex grows in size and moves outboard as the advance ratio $J$ becomes less negative, where $J$ is defined as $J=V∕nD$, with $V$ equal to the velocity of flow, $n$ equal to the rotational velocity of the propeller, and $D$ equal to the propeller diameter.

The results of a considerably more in-depth computational study of the crashback maneuver are included in the report edited by Zierke (7). These results are part of a larger study involving various aspects of submarine maneuvering problems. In these studies, the propellers were modeled as being mounted on the SUBOFF submarine body (see Groves et al. (8) for details of the SUBOFF geometry). The crashback studies in Ref. 7 made use of P4381. The unsteady Reynolds-averaged Navier–Stokes equations for incompressible flow were used, along with an algebraic turbulence model. These studies examined not only the fluid mechanics of the ring vortex around the propeller but also the trajectory of the submarine during the crashback maneuver. The studies showed the existence of a ring vortex around the propeller with an unsteady asymmetry that essentially rotated around the submarine axis. The frequency of this rotation was matched to the frequencies of out-of-plane forces and moments obtained from the computations. The studies also demonstrated some of the behavior of the ring vortex relative to the propeller, such as instances where the ring vortex “touched” a propeller blade and the corresponding pressure signatures on the blade. The submarine trajectories predicted by the computations demonstrated the “wandering” motion caused by the out-of-place forces and moments generated by the asymmetry of the ring vortex. It is precisely these “wanderings” that are the major concern for shallow-water maneuvers. The results of the computational studies did not demonstrate vortex bursting or reformation, however, and the behavior of the ring vortex was generally much more benign than that usually observed in experiments.

The study of crashback to be described in this paper was performed in the U. S. Navy’s William B. Morgan Large Cavitation Channel. Propeller 4381 was attached to a standard axisymmetric submarine hull model (DTMB model 5495-3), which was then suspended in the large cavitation channel (LCC). Forces and moments were measured on both the body and the propeller for steady and unsteady crashback conditions. The unsteady conditions were simulated by allowing the propeller to “windmill” in the forward direction and then engaging the propeller in the reverse direction, with the tunnel velocity held constant. Forces and moments were measured during the change in propeller speed. A further simulation was undertaken whereby the tunnel motor was shut off once the windmilling propeller engaged in reverse rotation, and the tunnel speed was allowed to coast down to zero. Forces and moments were measured during this simulation also. In addition to the force and moment measurements, laser Doppler velocimeter (LDV) measurements of the flow field around the propeller during steady crashback were obtained, in addition to extensive flow visualization studies.

Experimental Apparatus and Procedure

The LCC is part of the Carderock Division of the Naval Surface Warfare Center (NSWCCD) and was first made operational in 1991. The LCC has a test section that is $3.05m$$(10ft)$ high, $3.05m$$(10ft)$ wide, and $12.2m$$(40ft)$ long. The maximum test section speed is approximately $18m∕s$$(35kts)$, and the pressurization range for the test section extends from $3.5kPa$ ($0.05psi$ (absolute)) to $415kPa$ ($60psi$ (absolute)). The freestream turbulence level is less than 0.5%. Details of the design, construction, and operation of this facility may be found in Etter and Wilson (9-10). More recently, Park et al. (11) have done an extensive study of the performance characteristics of the LCC and have documented in detail the flow temporal and spatial uniformity and the turbulence levels in the facility, as well as the data acquisition equipment and procedures for velocity measurements in the LCC test section. According to Ref. 11, the temporal stability of the LCC test section flow speed is $±0.15%$ for test section velocities between $0.5m∕s$ and $18m∕s$. The test section velocity is spatially uniform to within $±0.60%$ for velocities between $3m∕s$ and $16m∕s$. The turbulence level in the facility is between 0.2% and 0.5% for test section velocities from $0.5m∕sto15m∕s$, with no harmonics appearing in the power spectra of the velocity signals. For all of the tests conducted during the current study, the tunnel pressure was set at $50psi(gauge)$ at the test section top.

The model used in these experiments was a standard axisymmetric hull with a sail and four standard cruciform stern appendages (DTMB model 5495-3). The hull length $L$ was $6.92m$$(272.36in.)$ and the diameter $Dh$ was $0.623m$$(24.54in.)$. The hull outline is shown in Fig. 2. The model was suspended using the standard LCC strut. A fairing that essentially duplicated the sail was initially wrapped around the strut, but during preliminary tests it was decided that the fairing was not necessary and so it was removed before the actual testing began. The placement of the stern appendages is illustrated in Fig. 3. The fin cross sections were NACA 0012 airfoil sections. When it had been determined that the propeller dynamometer results were consistent with the body dynamometer results, a stabilization strut was added to the rear of the model, connecting one of the stern fins to the LCC test section wall. This strut was added to secure the model against possible damage caused by large-amplitude oscillations at higher tunnel and propeller speeds. When this strut was in place, only propeller dynamometer readings could be obtained.

The propeller used in this test was DTMB Propeller No. 4381 (hereinafter referred to as P4381). This propeller was originally designed and built as part of a study of the effects of skew on marine propellers (5). P4381 was the unskewed propeller in this series. Interestingly, this study was funded by several commercial shipping companies, and so the propeller design itself and the results of the study were unclassified. The fact that P4381 has an unclassified geometry and that the actual model propeller still exists has resulted in a number of both experimental and computational studies being performed on it, including the current study. P4381 may be seen in Fig. 3. P4381 is a five-bladed propeller with a diameter of $1ft$, an expanded area ratio of 0.725, a NACA $a=0.8$ section meanline, and an NACA 66 section thickness distribution with NSRDC modifications to the nose and tail thicknesses. The design advance coefficient $J$ was 0.889, and the design thrust loading coefficient $Cth$ was 0.534 (Ref. 5).

The forces on the model were measured using a AMTI six-component dynamometer. This device is an internal force balance that was attached between the strut and the model. It was set up to measure forces in all three directions and moments about all three axes. The MicroCraft six-component propeller dynamometer was a multicomponent cylindrical assembly that attached to the propeller on its upstream face. It was used to measure three orthogonal forces and three moments. An absolute position digital encoder, Model 25HN from Sequential Information Systems Inc., was used to monitor the angular location of the propeller and dynamometer. The encoder had a resolution of $211$ resulting in an angular position accuracy of $0.18deg$. The output of the encoder was passed through a frequency-to-voltage converter so that the speed of the propeller could be recorded along with the force and moment and other data acquired by the computer.

Measurements of the velocity field were obtained using the LCC’s Dantec LDV system. This system is described in great detail in the report by Park et al. (11). The system consists of four Dantec BSA 57N11 signal processors, three fiber optic probes, two Spectra Physics $6W$ argon-ion lasers, a Dantec 3D traverse, and Dantec flow software. The LDV system was calibrated using a rotating disk. The resulting uncertainty in the calibration is reported in Ref. 11 to be less than $0.018m∕s$ at a disk speed corresponding to a tunnel speed of $15m∕s$.

Data were collected from 16 channels: 3 propeller force components, 3 propeller moment components, 3 body force components, 3 body moment components, the tunnel pressure, the venturi velocity, the propeller speed, and the tunnel temperature. These were usually sampled at a rate of $200Hz$ and the number of samples taken per channel was usually 48,000, yielding a total of 768,000 measurements for each test. The coordinate system used was the standard body-fixed coordinate system. Positive $x$ was taken to be forward, in the direction of forward motion. The coordinate $y$ was taken to be positive to starboard, and $z$ was positive down through the keel, completing the right-handed coordinate system. Body forces in the $x$, $y$, and $z$ directions are denoted as $Fx$, $Fy$, and $Fz$ forces, respectively, and body moments about the $x$, $y$, and $z$ axes are denoted as $Mx$, $My$, and $Mz$. Propeller forces in the $x$, $y$, and $z$ directions are denoted as $fx$, $fy$, and $fz$, respectively, and propeller moments about the $x$, $y$, and $z$ axes are denoted as $mx$, $my$, and $mz$. Note that an upper case $F$ or $M$ is used to indicate a body force or moment, and a lower case $f$ or $m$ is used to indicate a propeller force or moment.

Traditionally, the dimensionless parameter associated with propeller performance data has been the advance ratio $J$, defined by $J=V∕nD$, where $V$ is the forward velocity of the vehicle, $n$ is the propeller rotational speed (usually in rev/s), and $D$ is the diameter of the propeller. However, recent studies have shown that the data may also be collapsed well by using the similarity parameter η, defined as $η=n∕nsp$, where $n$ is the actual propeller speed and $nsp$ is the propeller speed required for self-propulsion; that is, the propeller speed at a given forward velocity $V$ at which the thrust produced by the propeller is equal to the drag of the vehicle. As will be seen later in this report, the data do collapse well when plotted versus η. However, the use of η requires the determination of $nsp$, which must be determined experimentally and usually during the test itself, since the thrust of the propeller and the drag of the vehicle will depend on such things as the propeller mount, the interaction between the propeller and the vehicle body, the manner in which the vehicle is mounted in the water tunnel, and so forth. The values of $nsp$ were determined in the following manner. The propeller motor in the model was set for forward rotation. The tunnel speed $V$ was set at a particular speed. Then the propeller speed was varied until the net thrust force as measured by the body force balance was nominally zero. Since it was usually not possible to get a reading of exactly zero, points were obtained on either side of zero and then a linear interpolation was performed to obtain the actual value of $nsp$. These points were obtained at tunnel set speeds of $2.5kts$, $5kts$, $7.5kts$, and $10kts$ ($1.29m∕s$, $2.57m∕s$, $3.86m∕s$, and $5.14m∕s$, respectively). The variation of $nsp$ with tunnel speed $V$ turned out to be very close to a straight line, and so a linear regression was performed to obtain a relation between $nsp$ and $V$. The resulting regression wasDisplay Formula

$nsprpm=102.04Vventurikts+19.831$
(1)
Ideally the intercept would be zero, since the propeller speed required for self-propulsion at zero forward velocity is zero. However, adding the intercept increased the accuracy of the linear regression so that the standard $R2$ value for the regression was greater than 0.99995. The speed $Vventuri$ was the test section speed obtained by a calibration of the pressure drop across the tunnel contraction.

In addition to using two different dimensionless representations of the propeller speed, it is also possible to normalize the resulting force and moment data in two different ways, depending on the quantities of interest. One is to use the dynamic pressure and model length scale as the normalizing values, so force and moment coefficients are calculated as follows:Display Formula

$CF=Fq∞L2CM=Mq∞L3q∞=12ρ∞V∞2$
(2)
In these formulas, $F$ and $M$ are arbitrary forces and moments, $CF$ and $CM$ are the corresponding force and moment coefficients, $q∞$ is the freestream dynamic pressure based on the freestream density and velocity, and $L$ is a body length scale. The other way in which the forces and moments may be normalized is through the use of propulsive quantities, as follows:Display Formula
$CF=Fρ∞n2D4CM=Mρ∞n2D5$
(3)
Here, $n$ is the propeller speed in rev/s, and $D$ is the propeller diameter. Both of these definitions were used in reducing the data as necessary, and, in particular, they were used to normalize the rms values of the forces and moments. Both definitions were found to collapse the data well.

Estimating the uncertainties in the force and moment coefficients presented something of a challenge, because twice the standard deviation $(2σ)$ is usually used as the measure of the random uncertainty of the measurement, for a sufficiently large number of samples. However, in these tests, the quantities of interest were the standard deviations or rms values of the forces and moments, represented as dimensionless coefficients. It was the variations of these quantities, used as a measurement of the unsteadiness of the flow, that were being tracked as a function of the parameter η. A procedure was developed for determining the uncertainty in the rms values using essentially a rms value of the rms value. For details of this procedure, see the report by Bridges (12). The total uncertainties were estimated using standard techniques, as outlined in Coleman and Steele (13). The results indicated an uncertainty of approximately 6% in the value of the yawing moment coefficient obtained using the rms values at a value of η where the magnitude of the yawing moment coefficient tended to reach its peak. Since the yawing moment coefficient demonstrated the greatest variations, this value should be representative of the uncertainties in the other force and moment coefficients. The uncertainty in η itself ranged from approximately 18% at low propeller speeds to 2.4% at the highest propeller speeds (see Ref. 12 for the details of this analysis). The data themselves demonstrated a strong repeatability with η, so it is believed that the relatively large uncertainty at low values of the propeller speed was overestimated for reasons that are not clear.

The first set of tests conducted studied cases of steady crashback, which means that both propeller speed and tunnel speed were held constant and data were collected over a period of time. Data were collected from the body and propeller force balances for a set of crashback conditions and when it was ascertained that the propeller force balance was producing results in line with the body force balance, the restraint strut was added and further measurements were made. Two different types of unsteady crashback studies were conducted. Because of the way the power was connected to the propeller motor, the motor was “hard wired” for either forward or reverse rotation in a given test. The only way to reverse propeller direction was to manually reverse the motor leads. This meant that the propeller could not be started in the forward direction, stopped, and then placed in reverse rotation. However, it was noted that with the propeller motor off and the tunnel speed set at some value, the propeller would “windmill” in forward rotation at some speed. The propeller motor could then be engaged in reverse rotation. Once engaged, it would slow its forward rotation to zero and then begin rotating in reverse, reaching its commanded reverse speed in a fairly short time. This behavior was used to simulate the initiation of the crashback maneuver. The fact that the fluctuating force and moment component amplitudes were now functions of time required a modification to the data reduction procedure. The rms values of the forces and moments were obtained for 200-sample subsets of the complete record. The time associated with each rms value thus obtained was taken as the time midpoint of the 200-sample subset. The second unsteady crashback study simulated the actual deceleration of the submarine. In these studies, the tunnel speed was set at a particular value (usually $7.5kts$) and the propeller was allowed to windmill in forward rotation. The propeller motor was then engaged. As soon as the personnel observing the test noted the propeller speed beginning to change, the tunnel operator sets the tunnel speed to zero. This would cause the tunnel speed to gradually coast down to zero. The same procedure for using 200-sample subsets to compute rms values was implemented.

When the force and moment measurements were completed for the steady crashback studies, detailed LDV surveys of the propeller flowfield were conducted at flow conditions of interest noted in the steady crashback results. Flow visualization studies using a laser sheet, fluorescent dye, and bubbles were also conducted at these flow conditions of interest.

Results

Figure 4 shows the variation of the coefficient of body rms yawing moment with η for the different tunnel speeds tested. It was observed throughout the results that the data at $6.25kts$ tended to be somewhat noisier than the rest of the data and hence had higher rms values. These are the data points that are separated from the others in Fig. 4. The data show good repeatability and all of the curves demonstrate a local maximum around $η=−0.8$. Figure 5 shows the results for the coefficient of propeller rms side force with η. These data exhibit a high degree of repeatability and produce what appears to be a very characteristic response curve. The local maxima again occur around $η=−0.8$. The propeller side force is the $y$ component of the force on the propeller measured in a reference frame attached to the propeller. Figure 6 shows the variation of the coefficient of propeller rms resultant force with η. The rms resultant force is simply the resultant of the propeller rms $y$ and $z$ (i.e., off axis) forces that act perpendicular to the axis of the propeller. Again the high degree of repeatability, the local maximum around $η=−0.8$, and the characteristic response are all exhibited. Figures  456 are representative of the results for all of the out-of-plane body and propeller rms forces and moments.

There had been some concern that the addition of the restraint strut would interfere with the flow to the point of invalidating the forces and moments measured with the propeller dynamometer. Figure 7 compares the results obtained for the propeller horizontal force (propeller $y$ and $z$ forces resolved into a component perpendicular to the wall of the tunnel) for restrained and unrestrained model conditions. As can be seen in this figure, the results track each other very well, indicating that the restraint strut did not unduly interfere with the flow or the force and moment measurements.

As was noted in the Introduction, the ring vortex asymmetry rotates around the propeller, creating the unsteady out-of-plane forces and moments for which the rms values have just been presented. The frequencies of these rotations were also determined by performing a Fourier spectral analysis of the propeller side force data records. The frequency at which each record had a maximum amplitude, denoted here by $f$, was recorded. A reduced frequency $ω$ was computed from $ω=2π(f−n)D∕V$, where $n$ is the propeller rotation speed, $D$ is the propeller diameter, and $V$ is the free stream velocity. The variation of $σ$ with η is shown in Fig. 8. These data demonstrate the repeatability exhibited by the force data. For low magnitudes of η, $ω$ begins with a negative value, indicating that the peak amplitude frequency is less than the propeller rotational speed. This actually means that seen in the reference frame of the rotating propeller, the asymmetry is rotating in the same direction as the propeller rotation. As η becomes more negative, $ω$ changes sign rapidly around $η=−0.5$ and becomes positive, indicating that the peak amplitude frequency is now higher than the rotational speed. Now the asymmetry is rotating in the opposite direction as the propeller, as seen in the propeller reference frame. The value of $σ$ then reduces gradually as η becomes more negative, changing sign again around $η=−1.7$. The data become rather noisy around these values of η, since it becomes difficult to distinguish the peak in the force signal arising from the rotation of the vortex asymmetry and the peak arising from the propeller rotation itself in this range of η.

Figure 9 shows the results of one of the unsteady crashback simulations in which the tunnel speed was held constant and the propeller was engaged in reverse rotation, having been allowed to windmill in forward rotation at a speed of $+330rpm$. This figure shows the development of the dimensional propeller side force fluctuations with time. The variable $t0$ is the time at which the propeller first began to decelerate, as indicated by the values for propeller speed in the data record. This figure shows that the propeller side force develops extremely rapidly then oscillates about some mean, nonzero value. It is the rms of this value that was examined in previous figures. Figure 1 illustrates the development of the propeller side force and body pitching and yawing moments for the same type of unsteady crashback simulation. This figure includes the time history of the propeller speed and the instantaneous value of η, obtained from instantaneous values of the propeller and tunnel speeds. In this figure, all of the values have been normalized by the maximum value for each variable (with the exception of η) so that they could all be displayed on the same figure. The time axis has been renormalized as a dimensionless variable $x∕L$, where $L$ is the total length of the model. The position variable $x$ was obtained by integrating numerically in time the tunnel free stream velocity. This figure essentially shows that the propeller completes its transition from positive to negative rotation in approximately 13 model lengths and that the propeller side force and the body moments develop in less than 2 model lengths.

Figure 1 shows the results of some of the unsteady crashback simulations in which the propeller speed was allowed to vary as described in the previous paragraph, but the tunnel speed was set to zero when the propeller was observed to engage in reverse rotation and the tunnel was allowed to coast down to zero speed. This figure again shows the rapid buildup of the propeller side force but then its gradual decay as the tunnel velocity decreased, presumably due to the decreased shear between the free stream flow and the reversed flow induced by the propeller and the corresponding weakening of the ring vortex. This explanation is reinforced by Fig. 1, which shows the development of the propeller horizontal force and the body yawing moment, along with the propeller speed, tunnel speed, and η (all normalized by their maximum values). The abscissa is again a dimensionless length that represents the number of model lengths over which the phenomena occur, and again is obtained by integrating numerically in time the tunnel free stream velocity. These curves show the rapid development of the out-of-plane force and moment but then their gradual reduction as the tunnel speed decreases. The propeller horizontal force tracks the tunnel speed fairly closely, but the body yawing moment tends to damp out a little more quickly. The value of η in this figure would in theory approach minus infinity since the propeller speed is fixed but the tunnel speed and hence the self-propulsion propeller speed are approaching zero. Figures  1314 compare some of the steady and unsteady crashback simulation results. The instantaneous values of the free stream speed $V$ and propeller speed $n$ recorded during the unsteady crashback simulations just discussed were used to calculate instantaneous values of η at each instant in the data record. For each value of 0 so obtained, the minimum and maximum values of the coefficients of propeller side force and body yawing moment were determined. These were plotted in Figs.  1314 along with the corresponding values from the steady crashback studies. The propeller side force data are shown in Fig. 1 and the body yawing moment data are shown in Fig. 1. These figures show that the magnitudes of the coefficients in the unsteady crashback studies exceeded those obtained in the steady crashback studies in some instances.

Figure 1 shows the LDV data obtained at $η=−0.801$. In each figure, the variable being plotted (mean and fluctuating streamwise velocities and mean and fluctuating transverse velocities) are overlaid with the mean velocity vectors. Similar data sets were obtained at values of η of $−0.380$, $−0.570$, and $−1.1$. The surveys at $η=−0.380$ indicated that the ring vortex was somewhat elongated in the streamwise direction. As η became more negative, the apparent position of the vortex core moved upstream and radially outward, in agreement with flow visualization results obtained by Jiang et al. (1) for a propeller in an “open-water” test. This vortex core “migration” is shown in Fig. 1. These core positions were obtained by examining the LDV surveys and determining the survey point at which the magnitude of the mean velocity was a minimum. Figure 1 shows some further results of the LDV measurements. This figure shows the mean and fluctuating streamwise and transverse velocity components measured at the LDV grid location closest to the propeller for which a full transverse survey was obtained (i.e., the $x$ location at the right edge of the “notches” in Fig. 1). The velocities at this streamwise location are representative of the inflow velocities for the propeller. These profiles were examined at each of the values of η listed above. One feature, in particular, exhibited by these profiles was the movement of the peak in the fluctuating velocity components radially outward as η became more negative. This movement would tend to increase the magnitude of the out-of-plane forces and moments acting on the propeller, since the changes in the forces on the blades caused by the fluctuating velocities would act through larger moment arms thus magnifying the forces and moments exerted on the propeller shaft and thereby transmitted to the submarine body.

The migration of the apparent vortex core position is shown by the flow visualization photographs contained in Fig. 1. The vortex in these figures demonstrates the behaviors inferred from the LDV measurements as discussed in the previous paragraph. These figures are similar to those obtained by Jiang et al. (1). However, it should be noted that the flows observed by Jiang et al.  apparently were more steady than the flows in the current experiments, based on the comments by Jiang et al.  They noted occasional disturbances in which the vortex would apparently disappear altogether in a random burst of bubbles and then reform, but on the whole would tend to oscillate about a more or less fixed position. In the current experiments, two different types of large-scale disturbances were noted in the flow visualization images. The first was a large-scale disruption similar to that reported by Jiang et al. (1). The second was a vortex shedding event in which the vortex would apparently detach from the propeller and move off downstream, and a new vortex would form on the propeller. Figure 1 illustrates a vortex shedding event, in which the shed vortex is just about to move out of the laser sheet, and a new vortex is forming near the propeller tip. Figure 1 is an example of a large-scale disruption.

The vortex shedding events and the large-scale disruptions of the flow did not appear to be quite periodic but did occur on a fairly frequent basis for the appropriate values of η. The “frequency” of these events seemed to be dictated more by the free stream flow speed than by the propeller speed. The sheddings and disruptions occurred more frequently at higher tunnel set speeds. Generally speaking, the large-scale disturbances were separated by intervals during which the formed vortex structure was present. These intervals tended to decrease as the magnitude of η increased. Recall from the earlier discussion that the peak values of the dimensionless out-of-plane force and moment coefficients occurred in the vicinity of $η=−0.8$. The flow visualization studies showed that the ring vortex seemed to have its most organized structure at this value of η. There were some large disturbances. At $η=−0.8$, these large disturbances, mostly vortex shedding events, exhibited their most periodic behavior. The ring vortex would form and shed in almost equal intervals of time. The resulting wake behind the propeller appeared to swirl about the propeller and acquired a corkscrewlike appearance downstream. In the two-dimensional view provided by the laser sheet, the flow most closely resembled that of vortex shedding behind a circular cylinder. Recall the earlier discussion, which said that the large disturbance aspect of the flow seemed to be influenced more by the free stream speed than the propeller speed. In the author’s opinion, the best way to describe what is happening in the flow in the vicinity of $η=−0.8$, as illustrated by these flow visualization images, is that the apparently free stream dominated phenomenon that is causing the large disturbances is coupling with the vortex ring flow, creating a periodic large disturbance that in turn is producing the peak in the dimensionless out-of-plane force and moment coefficients.

Conclusions

The LDV measurements revealed a variation in the vortex structure and core location as η varied, with the propulsion parameter η defined as the ratio of the propeller rotational speed to the propeller speed required for self-propulsion. At the smaller magnitudes of η, the vortex structure appeared to be elongated somewhat in the streamwise direction. As the magnitude of η increased, the vortex structure became tighter and the vortex core appeared to move upstream and radially outward toward the propeller tip. Profiles of the fluctuating velocity components at the LDV streamwise measurement position closest to the propeller showed that the spatial peaks in the fluctuations moved radially outward as η became more negative.

The flow visualization results confirmed the movements of the vortex core indicated by the LDV measurements and also showed that at very large negative values of η, the ring vortex could actually be located upstream of the propeller. The flow visualization experiments also revealed that the ring vortex could experience large-scale disturbances, either through apparent “vortex-shedding” events or through large-scale disruptions where the ring vortex essentially disappeared for brief periods of time. These large-scale disturbances did not appear to be periodic, except in the vicinity of $η=−0.8$, where the large-scale disturbances and the inherent unsteadiness in the ring vortex appeared to couple and produce a very large periodic disturbance to the wake, resulting in large periodic forces on the propeller and the submarine. Both the LDV measurements and the flow visualizations seemed to suggest that the vortex structure was the most organized in the vicinity of $η=−0.8$.

The out-of-plane force and moment coefficient values obtained from both the propeller and body dynamometers for the steady crashback simulations were correlated well with η. The coefficients demonstrated a relative maximum for values of η near $−0.8$ for both the propeller and body data. It was near this value of $η$ that the LDV and flow visualization measurements indicated the most-organized vortex structure. Spectral analyses of the propeller data indicated a reversal in the direction of the ring vortex asymmetry rotation relative to the propeller as the magnitude of η was increased past its lowest value. The magnitude of this relative rotation frequency then decreased in magnitude as the magnitude of η was increased further (i.e., as 0 became more negative).

The unsteady crashback simulations revealed that the magnitudes of the out-of-plane force and moment coefficients could exceed those obtained during the steady crashback measurements. The data from the ramped propeller and tunnel speed tests also indicated that the magnitudes of the coefficients tracked the tunnel speed fairly closely, suggesting that the strength of the ring vortex decreased as the relative shear between the free stream flow and the propeller-induced flow decreased.

Acknowledgements

This work was performed under an Office of Naval Research Defense Experimental Program to Stimulate Competitive Research (DEPSCoR) Grant No. N00014-97-1-1069. The program monitor was L. Patrick Purtell of the ONR. Part of the funding for this project was in the form of matching funds provided by the principal investigator’s department, the Department of Aerospace Engineering at Mississippi State University.

Nomenclature

$CF$

generic force coefficient

$Cfh$

coefficient of rms propeller horizontal force

$Cfr$

coefficient of rms propeller resultant force

$Cfy$

coefficient of rms propeller side force

$CM$

generic moment coefficient

$CMz$

coefficient of rms body yawing moment

$Cth$

$D$

propeller diameter

$Dh$

model hull diameter

$F$

generic force component

$Fx$

force component on body in $x$ direction

$Fy$

force component on body in $y$ direction

$Fz$

force component on body in $z$ direction

$f$

hydrodynamic frequency

$fx$

force component on propeller in $x$ direction

$fy$

force component on propeller in $y$ direction

$fz$

force component on propeller in $z$ direction

$J$

advance ratio, $J=V∕nD$

$L$

model hull length

$M$

generic moment component

$Mx$

moment component on body in $x$ direction

$My$

moment component on body in $y$ direction

$Mz$

moment component on body in $z$ direction

$mx$

moment component on propeller in $x$ direction

$my$

moment component on propeller in $y$ direction

$mz$

moment component on propeller in $z$ direction

$n$

propeller rotational speed

$nsp$

propeller rotational speed at self-propulsion point

$q$

dynamic pressure

$Rprop$

$r$

$t$

time

$t0$

time of propeller direction reversal

$U$, $V$, $V4$

free stream velocity

$u$

mean streamwise velocity component

$u′$

fluctuating streamwise velocity component

$v$

$v′$

$x$

coordinate direction parallel to body axis, positive forward

$y$

coordinate direction perpendicular to body axis, positive starboard

$z$

coordinate direction perpendicular to body axis, positive down through keel

$η$

ratio of actual propeller rotational speed to speed required for self-propulsion, $η=n∕nsp$

$ρ∞$

fluid density

$σ$

standard deviation

$ω$

reduced hydrodynamic frequency

$ωp,FFT$

reduced hydrodynamic frequency at peak fast Fourier transform (FFT) amplitude of propeller side force

References

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Figures

Figure 1

Schematic of flow (velocities in reference frame of submarine in forward motion)

Figure 7

Comparison of propeller rms horizontal force coefficient values with and without restraint strut

Figure 2

Submarine hull contour; sail not used in experiments but indicates location of strut

Figure 3

Illustration of propeller, stern appendage placement, and stabilization strut

Figure 4

Body rms yawing moment coefficient (based on propulsive scaling)

Figure 5

Propeller rms side force coefficient (based on propulsive scaling)

Figure 6

Propeller rms resultant force coefficient (based on propulsive scaling)

Figure 17

Velocity components at complete survey position nearest propeller for η=−0.80

Figure 19

Examples of large-scale disturbances to vortex flow for η=−0.780: (a) vortex shedding event and (b) large-scale disruption

Figure 8

Dimensionless frequency of peak propeller y force amplitude (u∕r—restraint strut off /on)

Figure 9

rms propeller side force development for ramped propeller speed simulation of unsteady crashback

Figure 10

Development of rms propeller y force and rms body pitching and yawing moments during constant tunnel velocity, ramped propeller speed simulation of unsteady crashback maneuver (values normalized by maximum data value in each set)

Figure 11

Development of rms propeller y force during ramped tunnel velocity, ramped propeller speed simulation of unsteady crashback maneuver

Figure 12

Development of rms propeller horizontal force and rms body yawing moment during unsteady crashback maneuver simulation

Figure 13

Comparison of coefficients of rms propeller y force between unsteady crashback conditions and the minimum and maximum values of the three ramped tunnel velocity, ramped propeller speed simulations of the unsteady crashback maneuver

Figure 14

Comparison of coefficients of rms body yawing moment between steady crashback conditions and the minimum and maximum values of the three ramped tunnel velocity, ramped propeller speed simulations of the unsteady crashback maneuver

Figure 15

Summary of LDV velocity field surveys for η=−0.801 (in coordinates shown, propeller tip would be located at x=809.2mm, z=152.4mm)

Figure 16

Vortex center positions estimated from LDV measurements (downstream direction is to the right in this figure)

Figure 18

Comparison of “formed vortex” positions at different values of η: (a) η=−0.387, (b) η=−0.580, (c) η=−0.725, (d) η=−0.825, (e) η=−1.09, and (f) η=−1.52

Errata

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