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Experimental investigation of hydrodynamic characteristics of a submersible vehicle model with a non-axisymmetric nose in pitch maneuver
Ocean Engineering 100 (2015) 26–34
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Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng
Experimental investigation of hydrodynamic characteristics of a submersible vehicle model with a non-axisymmetric nose in pitch maneuver A. Saeidinezhad a,1, A.A. Dehghan a,n, M. Dehghan Manshadi b,1 a b
Department of Mechanical Engineering, Yazd University, Yazd, Iran Department of Mechanical Engineering, Malek ashtar University, Esfahan, Iran
art ic l e i nf o
a b s t r a c t
Article history: Received 3 April 2013 Accepted 22 March 2015 Available online 10 April 2015
Experimental investigation is conducted to study the behavior of a submarine model with a nonaxisymmetric nose in pitch maneuver. The submarine model with all its appendages is tested in a wind tunnel at Reynolds number of 6.6 106, based on the model length, and a range of pitch angles 101r α r þ 271. The Reynolds number effects on drag coefficient are investigated for a range of Reynolds numbers between 4.7 106 and 8.0 106. By increasing the pitch angle, a continuous increase in drag and lift coefficients is observed. However, the measured pitching moment approaches to almost an asymptotic constant value when the pitch angle increased beyond þ101. Smoke flow visualization tests are also conducted to explore the details of flow structure around the submarine model for various values of pitch angles. The visualized flow revealed the formation of cross flow vortices and flow separation over the submarine model. These results show that the location of the flow separation for the non-axisymmetric nose shape is closer to the nose tip than the symmetric nose shape at high angle of attack. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Submarine Non-axisymmetric nose Pitch maneuver Wind tunnel Hydrodynamic forces and moments
1. Introduction Appropriate hydrodynamic design of an underwater vehicle is an important criterion in order to reach an acceptable and effective performance. The proper design of the external configuration of an underwater vehicle is also essential for minimizing the amount of energy required to power the vehicle through the water for the desired range and at the required speed. An improper body shape can cause extreme drag, noise, and instability (Paster, 1986). Stability and control of underwater vehicles are issues that generally require close attention. To determine the stability, control, and maneuvering characteristics of a submerged vehicle, it is required to properly predict the imposed hydrodynamic forces and moments. Experimental investigation of the hydrodynamic coefficients of a submersible vehicle helps the understanding of its maneuver characteristics. The captive-model test method includes using of models attached through a multi-component balance system installed inside wind or water tunnels and towing tanks for experimentation. The measured forces and moments are then processed to identify the
n
Corresponding author. Tel.: þ 98 353 1232493; fax: þ 98 353 8212781. E-mail addresses: [email protected] (A. Saeidinezhad), [email protected] (A.A. Dehghan), [email protected] (M. Dehghan Manshadi). 1 Tel.: þ98 353 1232493; fax: þ 98 353 8212781. http://dx.doi.org/10.1016/j.oceaneng.2015.03.010 0029-8018/& 2015 Elsevier Ltd. All rights reserved.
hydrodynamic coefficients and their derivatives which can be used in common motion equations. Then, the various stability analysis or computer simulations can be achieved by employing these equations (Gertler, 1972). There are some differences between these three test apparatus. Wind and water tunnels do not have free surface and therefore only fully submerged conditions can be simulated while in the towing tank, all working conditions can be examined. Two principal dimensionless numbers in these experiments are Reynolds and Froude numbers. As an underwater vehicle usually operates far away from the free surface, the Froude scaling is no longer concerned and the most important similarity parameter for this case is the Reynolds number. Several experimental investigations have been conducted on the axisymmetric underwater vehicle models. Some of these tests have been performed in the deep-water basins (Gertler, 1950; Jagadeesh et al., 2009; Roddy, 1990; Van Randwijck and Feldman, 2000) or wind tunnels (Fidler and Smith, 1978; Jiménez et al., 2010; Mackay, 1988, 1990; Neumann, 1983; Patel and Lee, 1977; Watt et al., 1993; Whitfield, 1999) to find out hydrodynamic coefficients or flow properties around the models. All models considered by these research works have streamlined bodies of revolution with axisymmetric curved noses. Gertler (1950) examined the streamlined bodies of revolution of Series 58 (with parabolic curve nose) to measure the resistance of the vehicles moving in a straight line. Van Randwijck and Feldman (2000)
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Nomenclature b diameter of body hall C averaged appendages chord CD, CL, CS drag, lift, side force coefficient CDref CD at zero pitch angle CLref CL at 101 pitch angle CSref CS at 201 pitch angle CK, CN, CM rolling, yawing, pitching moment coefficient CKref CK at 201 pitch angle CNref CN at 201 pitch angle CMref CM at 101 pitch angle Force coefficient 1Force ρU 2 S 2
investigated the sectional and total forces and moments of Series 58 models in the David Taylor Model Basin. Fidler and Smith (1978) studied the hydrodynamic coefficients of a series of submersible vehicle models with various noses and tail geometries in a wind tunnel to obtain the systematic data over a wide range of pitch angle for Reynolds numbers ranging from 4.0 106 to 8.5 106. They considered ellipsoidal noses with length to diameter ratios of 0.5, 1.0 and 2.0 plus a torpedo-like nose. Roddy (1990) measured all forces and moments imposed on the DARPA SUBOFF model (an axisymmetric body with a rounded nose and blunt after body) at Reynolds number 14 106 in the David Taylor Model Basin. The steady and unsteady forces and moments were measured on the same model with the smaller size by Whitfield (1999) in Virginia Tech Stability Wind Tunnel at two Reynolds numbers of 4.16 106 and 5.7 106 (based on model length) and for various angles of attack and roll positions. Tests were also done by attaching trip strips on the bow and sail sections. The comparison between the results of wind tunnel experiments (Whitfield, 1999) and the towing tank data (Roddy, 1990) revealed a good agreement in spite of the differences Reynolds numbers and test rigs employed. Flow visualization and force measurements were carried out in the national aeronautical establishment (now IAR) low speed wind tunnel with test section of 2 3 m2 over a standard submarine model in hull-alone and hull with sail configurations (Mackay, 1988, 1990). The experiments have been conducted at Reynolds numbers between 4.9 106 and 9.5 106. Oil flow visualization results have demonstrated the separation of the flow over the hull, over the sail and on the sail and hull junction. Watt et al. (1993) performed wind tunnel tests employing the same model. These tests were carried out at Re¼ 23 106 and pitch angle of up to 301. Various test configurations were considered and the overall forces and moments were measured. The previous reviewed works employed models with axisymmetric nose while many submarines have non-axisymmetric nose shape. Experimental investigation of the hydrodynamic performance of a submarine model with non-axisymmetric nose shape is scant and hence requires further attention. The main purpose of the present work is to study the static hydrodynamic characteristics of a submarine model with non-axisymmetric nose in a wind tunnel. The nose of the submarine model considered in the present experimental work has blunt curve in pitch sweep plane and round curves in yaw sweep plane. The Reynolds number effect on the drag coefficient is studied for Reynolds numbers ranging from 4.7 106 to 8.0 106. The influence of pitch angle, (α), on the hydrodynamic coefficients is studied for pitch angles ranging from 101 to þ271 and for Reynolds number of 6.6 106. Smoke flow visualization technique is also used to explore the flow structure on both hull and sail of the model and also to capture the details of the flow pattern around the whole body of the model.
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FD, FL, FS K, M, N L U S X (X/L)t
drag, lift, side force components rolling, pitching and yawing moment model length free stream velocity frontal area longitudinal axis along the model Boundary layer transition location α pitch angle Re model length Reynolds number; ρμUl ReC chord Reynolds number; ρUC μ m dynamic viscosity ρ fluid density Moment coefficient Moment 1ρU 2 Sb 2
2. Experimental procedure 2.1. Force and moment measurements A submarine model with a non-axisymmetric nose curve is considered for conducting force and moment measurements. The forebody of the model is not axisymmetric, while it has a plane of symmetry. The nose curve is blunt in the vertical or pitch plane while having rounded shape in the horizontal or yaw plane. The submarine model is constructed from aluminum and wood and a computer numerical control (CNC) machine is used for obtaining a required shape with an acceptable accuracy. Table 1 shows the dimensions of full-scale and wind tunnel models. The experimental investigation is carried out using an open working section wind tunnel. The wind tunnel has an open-jet test section with height, width and length of 2.8 m, 2.3 m and 4 m, respectively. Fig. 1 shows the schematic of the wind tunnel test section as well as the full shape of the model positioned in the test section. The turbulence intensity of the free stream within the test section is less than 0.13%. The aerodynamic forces and moments are measured with a sting-mounted six-component force balance mechanism which is internally mounted at the hull center as shown in Fig. 2. The uncertainty of the measured force and moments, and Reynolds number are calculated and presented in Table 2. A data acquisition system is employed to collect the measured forces and moments. The data acquisition sampling rate is 200 Hz and the duration of measurement at each pitch angle is 10 s. Then, the average values of force and moment are calculated and used for analysis. The trip strip is proposed to simulate the boundary layer transition on the full-scale vehicle (Barlow et al., 1999). Two methods are used in the current research to predict the trip strip location on the model surface. The first method is based on DeMoss and Simpson (2010) recommendation that the trip strip should not be placed in the adverse pressure gradient regions as it may induce separation. In order to comply with this recommendation, some surface pressure measurements on a submarine model with the same nose shape, which was used in the force and moment tests, were conducted in a closed loop wind tunnel by the present authors. The longitudinal surface pressure distributions were measured with a series of pressure
Table 1 Model and full-scale dimensions.
Full scale Wind tunnel model
L (m)
D (m)
44 2
5.03 0.23
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Fig. 1. Schematic of test section setup.
Fig. 2. Schematic of the submarine model and the internal balance equipment.
Table 2 The uncertainty of the measured parameters.
Table 3 Transition position at full scale Reynolds number.
Parameter
Relative uncertainty (%)
Curve plane
(X/L)t
(X/L)t%
Reynolds number
uRe Re ¼ 1:04 uFD;L;S FD;L;S ¼ 2:5 uMM;N;l
Vertical (pitch) plane Horizontal (yaw) plane
0.025 0.067
2.5 6.7
Hydrodynamic forces Hydrodynamic moments Hydrodynamic force coefficient Hydrodynamic moment coefficient
MM;N;l ¼ 2 uCD;L;S CD;L;S ¼ 3:5 uCM;N;l CM;N;l
¼4
taps along the nose surface. The surface pressure results revealed that the position X/L¼0.03 is a good choice to place the trip strip. The second method employed for predicting the proper location of the trip strip was based on using the XFOIL program (Drela, 2001) in order to find out the transition location on the full-scale vehicle surface. The panel points based on the submarine profile in both vertical and horizontal planes are imported into the XFOIL program and the boundary layer is simulated for full-scale Reynolds and Mach numbers at zero pitch and yaw angles. The resulting locations of transition, (X/L)t, in both vertical (pitch) and horizontal (yaw) planes are presented in Table 3. From the data presented in Table 3, it is seen that on the average, location of X/L¼0.03 is a proper choice for trip strip position and this conclusion is in agreement with the finding of the first method employed. In addition, a thorough literature survey (Huang and Liu, 1994; Huggins and Packwood, 1995; Jiménez et al., 2010; Watt et al.,
1993) shows that in the most of submarine model tests, trip strip was placed in the range of 0.03 r(X/L) r0.05. According to the aforementioned justification, a band of grit acting as a transition tripping is attached on the model at 3% of the length of the model, measured on the surface from the nose tip. The width of this trip strip was 1 cm. Three different sizes of grit are used for trip strip and their specifications are listed in Table 4. Initially, the force and moment measurements are conducted for Reynolds number ranging from 4.7 106 to 8.0 106 to explore the variation of drag coefficient with Reynolds number. Then the other tests are performed for pitch angles of 101r α r271 and for uniform wind velocity corresponding to Reynolds numbers of 6.6 106. Mach number is calculated for all the free stream velocities and is found to be lower than 0.3 at all Reynolds numbers and hence, the flow is assumed to be incompressible. Additional tests have been conducted to study the influence of the trip strips attached on the bow of the model. The blockage ratio of the model in force and moment experiments is calculated and is found to be less than 5% at 271 pitch angle which is acceptable for tests in an open test section wind tunnel as recommended by Barlow et al. (1999).
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2.2. Flow visualization setup The flow visualizations have been performed in a low speed smoke tunnel to determine the flow pattern around the model for various pitch angle values. Because of the smaller size of the smoke wind tunnel, the models used for the flow visualizations are smaller than the models used for hydrodynamic force and moment measurements, although the geometric similarity between the two models is preserved. A wire as trip strip with a diameter of 0.2 mm was used to stimulate turbulent boundary layer flow around the small model. The trip strip is placed at 5% of the length of the model, measured on the surface from the nose tip. As discussed in Section 2.1, suitable locations for trip strip positioning are suggested to be in the range of 0.03r (X/L)r0.05. For the flow visualization test model, X/L¼0.05 is selected for trip strip location as it is commensurate with the size of the model selected. Two flash bulbs are used to illuminate the smoke path lines and flow structures around the model. They aligned normal to the Table 4 The size of grit for trip strip. Trip strip no.
Grit number
Nominal grit size (mm)
1 2 3
80 90 120
0.21 0.18 0.15
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direction of the smoke filament plane. The movement of the smoke-lines is captured with a high-speed camera at a rate of 2500 frames/s. A schematic view of the flow visualization test rig is shown in Fig. 3a. Laser light sheet illumination technique is also used to capture cross flow characteristics. A 50 mW pointer laser is used to achieve this particular aim. The laser sheet is obtained by using a simple cylindrical lens. The cylindrical lens is mounted in such a way to have its focal line positioned very close to the laser output mirror. The laser sheet creates an illuminated plane normal to the model axis and hence, the camera is aligned normal to the plane of laser sheet as shown in Fig. 3b. The blockage ratios for the smoke flow visualization experiments are less than 6% at 201 pitch angle which is acceptable for wind tunnel flow visualization tests as recommended by West and Apelt (1982).
3. Results and discussion The first part of the experimental result focuses on the drag coefficient variation with flow Reynolds number. Furthermore, the effects of the pitch angle (α) on the force and moment coefficients are presented and discussed. In-plane forces and moment which include drag, lift and pitch moment coefficients are studied and discussed by presenting the out-of-plane force and moments including side force, yaw and roll moment coefficients. Fig. 4 shows definitions of pitch angle, flow direction and the force and moment components.
Fig. 3. Schematic of the visualization setup: (a) illumination with two flash bulbs; (b) illumination with laser source.
Fig. 4. Wind tunnel fixed coordinate system and force and moment components.
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3.1. Influence of Reynolds number on the drag coefficient The type of laminar or turbulent flow separation and transition location on a streamlined body surface is influenced by the flow Reynolds number. Beyond a certain value of Reynolds number, which is called critical Reynolds number, the separation type and its location are independent of the flow Reynolds number (Hosder and Simpson, 2001). Thus, the knowledge of relationship between the hydrodynamic coefficients and Reynolds number is important. Fig. 5 shows the variation of the drag coefficient with flow Reynolds numbers for zero pitch angle, α ¼01. It should be noted that all the measured drag coefficients are scaled over the corresponding value for Re¼ 4.72 106. It is seen from Fig. 5 that the drag coefficient increases with increasing Reynolds number until around Re ¼ 5.9 106 and remains nearly constant afterward. This behavior of drag coefficient with Reynolds number in the range of 106–107 for streamlined bodies has been also observed in the previous works (Beheshti et al., 2009; Huggins and Packwood, 1995). Hoerner (1992) showed that by increasing Reynolds number, drag coefficient of streamlined bodies initially decreases until Re ¼106. Through the transition to turbulent flow (Re ¼106–107), an increase in CD is observed. A local minimum of the drag coefficient, CD, is observed in the region of laminar-to-turbulent transition. Full turbulent boundary layer covers the entire length of the model for Reynolds number of 107 and the variation of the drag coefficient is negligible by further increasing the flow Reynolds numbers. A number of submarine model experimental investigations (Bridges et al., 2003; Feldman, 1995; Roddy, 1990) have reported the critical Reynolds number for their submarine model occurring in the range of 107–1.5 107. Based on the results presented in Fig. 5, the boundary layer of the flow around the present model is in the region of transition to turbulent for Re¼4.7 106–5.9 106. Hence, it is deduced that the critical Reynolds number for the present model is 5.9 106, which is lower than the amount reported by other investigators. The lower value of the critical Reynolds number obtained through the present study is attributed to the nose shape of the present model. The blunt nose causes the boundary layer around the model becomes fully turbulent at lower Reynolds number. Therefore, the drag coefficient also remains constant for full-scale model in the high Reynolds number flows. In order to study the effects of Reynolds number on the hydrodynamic behavior of the submarine model under various pitch angle maneuver, the drag coefficients are measured for various pitch angles (101r α r291) and for three Reynolds number values of 5.4, 6.6 and 7.9 106. In order to compare the model behavior with respect to a reference condition, the measured drag coefficients are scaled
Fig. 5. Drag coefficient variation with Reynolds number.
with the drag coefficient obtained at zero pitch angle (CDref) at Re¼6.6 106. Fig. 6 presents the variation of the drag coefficient for various pitch angles at three flow Reynolds number values. It is seen that at small pitch angles, drag coefficient variation with Reynolds number is marginal while for larger pitch angles, the influence of Reynolds number on the drag coefficient is noticeable. Moreover, for large values of pitch angle, the measured drag coefficients slightly diverged from each other especially at high Reynolds number. Consequently, Reynolds number effect becomes significant in large angle of attack (α Z181). Lamont (1982) also reported similar Reynolds number effects on the hydrodynamic coefficients in high pitch angles between 301 and 901 for an ogive cylinder without appendage. The difference between the present results at high pitch angles (α Z181), which the Reynolds number effect becomes noticeable, and the findings of Lamont (1982) is due to the different model shape and the presence of appendages in our test model. The rudder and elevator are small wings that placed in afterbody part of the submarine model. The effect of elevator on the hydrodynamic forces and moments become important when the pitch angle of the submarine model increases. In the present work, the chord Reynolds number of these appendages is lower than appendages critical chord Reynolds number, ReC ¼106 (Mackay, 2003) and hence, the boundary layer transition location on the appendages depends on the Reynolds number. Therefore, at high angles of attack α Z 181 where the appendages performance is important, Reynolds number effects on the appendages is more pronounced. In the next step, several experimental tests have been conducted by utilizing three transition trip strips with various sizes to ensure that the boundary layer around the model is turbulent. A comparison of the drag measurements for three trip strip sizes at Reynolds number of 6.6 106 and for various values of pitch angle is shown in Fig. 7. The results obtained for models equipped with the trip strips are compared with the test results of the clean model i.e., model without trip strip. It is seen that drag coefficients obtained for both the clean model case and model equipped with various trip strip sizes are almost collapsed on each other and no appreciable changes on the drag coefficients are observed. Similar trends are observed for all pitch angel experiments. As it was noticed in Fig. 5, the drag coefficient is not depending on the Reynolds number for Re45.9 106. One can conclude that boundary layer on the entire surface of the model is already turbulent for Reynolds number of 6.6 106 which the present test are conducted. Therefore, the presence of the trip strips has no noticeable effect on the measured drag coefficients and hence, the entire test runs, except the one with the data presented in Fig. 7, are conducted without trip strip on the model surface.
Fig. 6. Variation of drag coefficient with pitch angles for various Reynolds numbers.
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Fig. 7. Effect of trip strip on drag coefficient of the model for various pitch angles at Re ¼6.6 106.
3.2. Influence of pitch angle on in-plane force and moment coefficients The measured in-plane forces and moment including drag and lift forces and pitch moment in pitch maneuver at Re ¼6.6 106 are presented in this section. In addition, flow visualization experiments are conducted to determine the physical observation of flow structures such as boundary layer separation and vortical flows around the model for various pitch angle values. Fig. 8 shows the drag coefficient versus pitch angle for four repeated test runs under the same operating conditions. The average values of the four similar test runs are also presented in this figure. The measured drag coefficients presented in Fig. 8 are scaled over the drag coefficient of zero pitch angle. It is observed that drag value rises with increasing pitch angle. This is due to formation of large separation region on the leeward of the model which results in increasing the pressure drag. The drag coefficient shows a parabolic trend with a relatively high slope such that at 301, 201 and 101 pitch angles the measured drag coefficients are approximately five, four and three times larger than the drag coefficient value at zero angle respectively. This is attributed to the nose shape of the model selected. The nose has blunt curve in the pitch sweep plane which causes flow spouted for high pitch angles. There is not symmetry between the measured values at positive and negative pitch angles. This is due to the sail effect of the submarine model. The results obtained during the four similar test runs are almost collapsed in a single curve, indicating the accuracy and repeatability of the experimental work presented. Fig. 9 shows the visualized flow pattern around the model subjected to various pitch angles. At zero pitch angle, the boundary layer is almost fully attached to the entire body surface. When the pitch angle increases, the flow separation occurs near to the afterbody of the model. As shown in Fig. 9b (α ¼ 61), the separation region is small and located downstream of the sail. The separation region combines with the cross flow and creates a counter rotating vortex pair at the leeward of the main flow. As the pitch angle increases, the separation line moves both forward (towards the nose of the model) and windward, and the separation region extends almost over the entire length of the model (α ¼181). The flow around the model with axisymmetric elliptical nose at pitch angle of α ¼181 is also presented in Fig. 9e for comparison. By comparing Fig. 9d and e, it may be seen that for the blunt nose shape, the location of the flow separation is closer to the nose than the elliptical nose type. Cross flow vortex becomes stronger and dominates the flow field at the leeside of the model for higher pitch angles. The flow visualization results confirm that the separation starts to appear at small pitch angles and almost extents over the whole body of the model as pitch angle increases.
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Fig. 8. Drag coefficient versus pitch angle at Re¼ 6.6 106.
In Fig. 10 the measured lift coefficient is plotted versus pitch angle for Re¼ 6.6 106. This figure shows a continuous increases in the lift coefficient as pitch angle is increased. A symmetry between the results is seen for both positive and negative pitch angles. The trend of the lift coefficient curve obtained in the present study is similar to the data presented by Whitfield (1999). Again, the data obtained from the four test runs are collapsed to a single curve, especially for pitch angle range of 101 to þ 201and all the data from all four test runs pass through the origin at zero pitch angle. The authors in their recent work, Saeidinezhad et al. (2014), studied the separation and formation of cross-flow vortex over two axisymmetric body of revolution at various incidence angles. Their results show that as the pitch angle is increased, the longitudinal and cross-flow separation region moves to the forward and also to the windward side of the model. The longitudinal separation along the model causes an uplift force that is imposed on the body at pitch angle. In addition, as the pitch angle increases, the circumferential (cross-flow) separation causes the excess lift force which coupled with lift force due to the longitudinal separation and increases the overall normal force acting on the body. This is the main source for a large increase in CL value at higher pitch angles. Fig. 11 shows the pitching moment coefficient versus the pitch angle at Re¼6.6 106. The variation of the pitching moment in the range of 101 to þ101 pitch angle is almost linear and symmetric. By increasing the pitch angle beyond 101, the slope decreases and finally the pitching moment approaches to an asymptotic value. This is due to the fact that at high pitch angle ( þ101 to þ291), appendages especially elevators (horizontal control plane appendages) creates negative pitching moment due to the combination of both drag and lift forces imposed upon them. This negative pitching moment partially compensates the increasing positive pitching moment created by the combination of both drag and lift forces imposing on the main body. Hence, the net combinations of these effects causes a reduction in the slope of the positive pitching moment and approaching to an asymptotic value as pitch angle increased beyond 101. Again, the measured values for the four test runs under similar operating conditions are close to each other, indicating the repeatability of the experiments. 3.3. Influence of pitch angle on out-of-plane force and moment coefficients The out-of-plane force and moments include side force and yawing and rolling moments in pitch maneuvers. The variation of the side force coefficient at Re ¼6.6 106 is shown in Fig. 12. The side force has a relatively negligible value for α o141 however, it starts increasing when the pitch angles increases beyond 141. Yawing and rolling moments are presented in Figs. 13 and 14. The behaviors of both moments are quite similar to the side force as
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Fig. 9. Visualized flow pattern around the model in various pitch angles: (a) α ¼ 01; (b) α¼ 61; (c) α ¼121; (d) α ¼181; (e) α ¼181 (standard nose).
these moments are strongly related to the side force in the pitch maneuvers. While the shape of the model has symmetry between the left and right sides, one of the sources of the lateral force and yawing moment is the possible asymmetry of the flow field around the model. Visualization results have revealed that the cross-flow vortices are formed in the leeside of the model from α Z61 (See Fig. 9). Fig. 15 presents the visualized cross-flow vortex in the leeward of the model at various longitudinal positions (X/L) ranging from 0.3 to 0.8 and for maneuver pitch angle of 151. The cross flow vortices are captured by creating a laser illuminated sheet at the prescribed positions. It is seen that the cross-vortex grows in size as it moves along the model. In addition, formation
of a secondary vortex is shown in this figure. Other researchers have indicated that cross-flow vortex becomes asymmetric and is partially responsible for inducing side force for a certain range of pitch angles. Ericsson and Reding (1986) characterized four distinct regions in the flow around a slender body when the model subjected to a flow with angle of attack in the range of 0–901. At small angles of attack, the flow is attached to the model and the axial flow field dominates. The variation of the lift force and pitching moment are linear with pitch angle. At intermediate angles, formation of the cross-flow creates pressure gradient across the model and the boundary layer is separated, leading to a formation of symmetric vortex pair on the leeside of the model. However, no out-of-plane force and moments
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Fig. 10. Lift coefficient versus pitch angle at Re¼ 6.6 106.
Fig. 13. Yawing moment coefficient versus pitch angle at Re¼6.6 106.
Fig. 11. Pitching moment coefficient versus pitch angle at Re¼ 6.6 106.
Fig. 14. Rolling moment coefficient versus pitch angle at Re¼ 6.6 106.
Fig. 12. Side force coefficient versus pitch angle at Re¼ 6.6 106.
Fig. 15. Cross-flow vortex in the lee-side of the model at α ¼ 151 in various longitudinal positions (X/L ¼ 0.3–0.8).
are present. Further increasing the incidence angles, the cross-flow vortices become asymmetric and induce side force and yawing moment. Finally, at very high angles, the flow pattern becomes similar to the flow across a cylinder. It is important that the onset angle of asymmetric vortex formation is a function of the flow Reynolds number, and hull geometric parameters including the nose shape, surface finishing and fineness ratio (Watson et al., 1993). The presence of the side force is also reported in the works conducted by Allen and Perkins (1951), Dexter and Hunt (1981), Levy et al. (1996) and Zilliac et al. (1991) on the flow around symmetric bodies at high pitch angles. The measured side force and consequently its induced yawing and rolling moments which are presented in Figs. 12–14 were seen in all
test runs. The presence of the side force acting on the axisymmetric ogive models in pure pitch maneuver was also reported by other researchers in aerodynamics testing in wind tunnels. This phenomenon was first discovered by Allen and Perkins (1951) in the early 1950s; and since then, a great number of studies in this subject has been carried out (Bridges, 2006). In some of these studies, it is noted that the magnitude and direction of side force varies irregularly when the nose of an axisymmetric body is rolled at high angle of attack. Some research works (Bridges and Hornung, 1994; Levy et al., 1996; Xuerui et al., 2002) have reported that the side force might be originated due to the vortex asymmetry primarily arising from imperfections on the nose-tip of a body.
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From the above discussions and observations reported on the literature, the presence of the side force and its strange behavior at high pitch angles (α Z121), might be attributed to the imperfections in model preparation especially its nose, its strut which is responsible for pitching the model, test rig vibration, appendages installation and other unidentified sources. Close look at the drag, lift and pitching moment variations presented in Figs. 8, 10 and 11 reveals that these data are not much affected by the aforementioned sources as no noticeable scattering in drag, lift and pitching moment data are seen at high pitch angles. However, it should be stated that the submarine vehicles do not experience the pitch angles beyond 151 in their normal missions and hence, the side force effects are not important for low angles of attacks. 4. Conclusions In order to explore the influence of the Reynolds number on the drag coefficient of a submarine model, a model with a non-axisymmetric nose is examined in a wind tunnel for various Reynolds numbers ranging from 4.7 106 to 8.0 106. Furthermore, to investigate the hydrodynamic characteristics of the model under various pitch maneuver, the experiments are also conducted for various values of pitch angle at Re¼6.6 106. The closed loop wind tunnel employed has an open-jet test section with height, width and length of 2.8 m, 2.3 m and 4 m, respectively. It is noticed that the drag coefficient increases by increasing the Reynolds number up to 5.9 106 (critical Reynolds number) after which it approaches to an asymptotic value. Hence, it can be concluded that the same drag coefficient can be deduced for a full scale model with a similar geometry. The critical Reynolds number for the present model with non-axisymmetric nose is lower than the corresponding value estimated by the previous research works on the models with symmetric nose shape. Furthermore, extensive flow visualization experiments were conducted to capture the details of the flow structure around the model under investigation for various pitch maneuvers. Visualized flow revealed that flow separation occurs on the afterbody of the model at small pitch angles (α ¼61). As pitch angle increases, separation region moves towards forebody and vortical field dominates the leeside of the model. Finally, the separated flow covers almost the entire length of the model (α ¼ 181). Therefore, pitch angle has significant effects on the hydrodynamic coefficients. It was observed that the measured drag and lift forces increase with increasing pitch angle. Pitching moment shows the same behavior in a range of pitch angle 101r α r þ101 but approaches an asymptotic value by increasing pitch angle beyond 101. It was observed that the out-of-plane forces and moments have relatively negligible values for pitch maneuver in the range of 101o α o141 while they increase with increasing the pitch angle. This might be attributed to the asymmetric nature of the cross flow vortices, imperfections in model preparation especially its nose, its strut which is responsible for pitching the model, test rig vibration, appendages installation and other unidentified sources. References Allen, H.J., Perkins, E.W., 1951. Characteristics of Flow Over Inclined Bodies of Revolution. Research Memorandum RM A50L07, National Advisory Committee on Aeronautics (NACA). Barlow, J.B., Rae, W.H., Pope, A., 1999. Low-Speed Wind Tunnel Testing, 3th edition. Wiley. Beheshti, B.H., Wittmer, F., Abhari, R.S., 2009. Flow visualization study of an airship model using a water towing tank. Aerosp. Sci. Technol. 13 (8), 450–458. Bridges, D.H., 2006. The asymmetric vortex wake problem-asking the right question. In: Proceedings of the 36th AIAA Fluid Dynamics Conference and Exhibit, San Francisco, California.
Bridges, D.H., Blanton, J.N., Brewer, W.H., Park, J.T., 2003. Experimental investigation of the flow past a submarine at angle of drift. AIAA J. 41 (1), 71–81. Bridges, D.H., Hornung, H.G., 1994. Elliptic tip effects on the vortex wake of an axisymmetric body at incidence. AIAA J. 32 (7), 1437–1445. DeMoss, J.A., Simpson, R.L., 2010. Measurements of the steady skin friction and cross-flow separation location on an ellipsoidal model in yaw or pitch over a range of roll angles. In: Proceedings of the 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, Florida, January. Dexter, P., Hunt, B., 1981. The effect of roll angle on the flow over a slender body of revolution at high angles of attack. In: Proceedings of the 19th Aerospace Sciences Meeting. St. Louis, MO, U.S.A. Drela, M., 2001. XFOIL 6.9 User Primer, MIT Aero & Astro, 〈http://web.mit.edu/ aeroutil_v1.0/xfoil_doc.txt〉. Ericsson LE. and Reding JP, 1986. Asymmetric vortex shedding from bodies of revolution. In: Tactical Missile Aerodynamics, 104, pp. 243–296. Feldman, J.P., 1995. Method of performing captive-model experiments to predict the stability and control characteristics of submarines. CRDKNSWC-HD 039325, June. Fidler, J.E., Smith, C.A., 1978. Methods for predicting submersible hydrodynamic characteristics. NCSC/TM 238-78, July. Gertler, M., 1950. Resistance experiments on a systematic series of streamlined bodies of revolution-for application to the design of high-speed submarines. DTRC Report: C-849, April. Gertler, M., 1972. some recent advances in dynamic stability and control of submerged vehicles. J. Mech. Eng. Sci. 14 (7), 14–19. Sighard, F. Hoerner, 1992. Fluid-dynamic drag: practical information on aerodynamic drag and hydrodynamic resistance. In: Hoerner Fluid Dynamics. Hosder, S., Simpson, R.L., 2001. Unsteady skin-friction measurements on a maneuvering darpa2 suboff mode. Virginia Polytechnic Institute and State University, VPI-AOE-272, June. Huang, T., Liu, H., 1994. Measurements of flows over an axisymmetric body with various appendages in a wind tunnel: the DARPA SUBOFF experimental program. In: Proceedings of the 19th Symposium on Naval Hydrodynamics. Seoul, Korea. Huggins, A., Packwood, A., 1995. Wind tunnel experiments on a fully appended laminar flow submersible for oceanographic survey. Ocean Eng. 22 (2), 207–221. Jagadeesh, P., Murali, K., Idichandy, V., 2009. Experimental investigation of hydrodynamic force coefficients over AUV hull form. Ocean Eng. 36 (1), 113–118. Jiménez, J.M., Hultmark, M., Smits, A.J., 2010. The intermediate wake of a body of revolution at high Reynolds numbers. J. Fluid Mech. 659, 516–539. Lamont, P., 1982. Pressures around an inclined ogive cylinder with laminar, transitional, or turbulent separation. AIAA J. 20 (11), 1492–1499. Levy, Y., Hesselnik, L., Degani, D., 1996. Systematic study of the correlation between geometrical disturbances and flow asymmetries. AIAA J. 34 (4), 772–777. Mackay, M., 1988. Flow visualization experiments with submarine models in a wind tunnel. DRDC TM 88/204, February. Mackay, M., 1990. Static pressure measurement with surface-mounted disc probes. Exp. Fluids 9 (1), 105–107. Mackay, M., 2003. Wind tunnel experiments with a submarine afterbody model. DRDC TM 2002-194, March. Neumann, B.J., 1983. Optimum forebody shaping for axisymmetric submersibles with turbulent boundary layers and blc (boundary layer control) afterbodies. DTNSRDC-83/055, July. Paster, D., 1986. Importance of hydrodynamic considerations for underwater vehicle design. In: Proceedings of the OCEANS'86. IEEE, Washington, DC, USA. Patel, V.C., Lee, Y., 1977. Thick axisymmetric turbulent boundary layer and near wake of a low-drag body of revolution. IIHR Report no. 210, December. Roddy, R.F., 1990. Investigation of the stability and control characteristics of several configurations of the DARPA SUBOFF model (DTRC Model 5470) from captivemodel experiments. DTRC-SHD 1298-08, September. Saeidinezhad, A., Dehghan, A.A., Dehghan Manshadi, M., 2014. Nose shape effect on the visualized flow field around an axisymmetric body of revolution at incidence. J. Vis. 18 (1), 83–93. http://dx.doi.org/10.1007/s12650-014-0226-1. Van Randwijck, E.F., Feldman, J.P., 2000. Results of experiments with a segmented model to investigate the distribution of the hydrodynamic forces and moments on a streamlined body of revolution at an angle of attack or with a pitching angular velocity. NSWCCD-50-TR-2000/008, February. Watson, K., Webster, J., Crane, J., Smith, N., 1993. Prediction of submersible maneuvering performance at high incidence angles, In: Proceedings of the OCEANS'93. Engineering in Harmony with Ocean. Victoria, BC. Watt, G., Nguyen, V., Cooper, K., Tanguay, B., 1993. Wind tunnel investigations of submarine hydrodynamics. The development of the DREA static test rig and some results. Can. Aeronaut. Space J. 39 (3), 119–126. West, G., Apelt, C., 1982. The effects of tunnel blockage and aspect ratio on the mean flow past a circular cylinder with Reynolds numbers between 104 and 105. J. Fluid Mech. 114, 361–377. Whitfield, C.C., 1999. Steady and unsteady force and moment data on a DARPA2 submarine MS Thesis. Virginia Polytechnic Institute and State University. Xuerui, C., Xueying, D., Yankui, W., Peiqing, L., Zhifu, G., 2002. Influence of nose perturbations on behaviors of asymmetric vortices over slender body. Acta Mech. Sin. 18 (6), 581–593. Zilliac, G., Degani, D., Tobak, M., 1991. Asymmetric vortices on a slender body of revolution. AIAA J. 29 (5), 667–675.
Contents lists available at ScienceDirect
Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng
Experimental investigation of hydrodynamic characteristics of a submersible vehicle model with a non-axisymmetric nose in pitch maneuver A. Saeidinezhad a,1, A.A. Dehghan a,n, M. Dehghan Manshadi b,1 a b
Department of Mechanical Engineering, Yazd University, Yazd, Iran Department of Mechanical Engineering, Malek ashtar University, Esfahan, Iran
art ic l e i nf o
a b s t r a c t
Article history: Received 3 April 2013 Accepted 22 March 2015 Available online 10 April 2015
Experimental investigation is conducted to study the behavior of a submarine model with a nonaxisymmetric nose in pitch maneuver. The submarine model with all its appendages is tested in a wind tunnel at Reynolds number of 6.6 106, based on the model length, and a range of pitch angles 101r α r þ 271. The Reynolds number effects on drag coefficient are investigated for a range of Reynolds numbers between 4.7 106 and 8.0 106. By increasing the pitch angle, a continuous increase in drag and lift coefficients is observed. However, the measured pitching moment approaches to almost an asymptotic constant value when the pitch angle increased beyond þ101. Smoke flow visualization tests are also conducted to explore the details of flow structure around the submarine model for various values of pitch angles. The visualized flow revealed the formation of cross flow vortices and flow separation over the submarine model. These results show that the location of the flow separation for the non-axisymmetric nose shape is closer to the nose tip than the symmetric nose shape at high angle of attack. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Submarine Non-axisymmetric nose Pitch maneuver Wind tunnel Hydrodynamic forces and moments
1. Introduction Appropriate hydrodynamic design of an underwater vehicle is an important criterion in order to reach an acceptable and effective performance. The proper design of the external configuration of an underwater vehicle is also essential for minimizing the amount of energy required to power the vehicle through the water for the desired range and at the required speed. An improper body shape can cause extreme drag, noise, and instability (Paster, 1986). Stability and control of underwater vehicles are issues that generally require close attention. To determine the stability, control, and maneuvering characteristics of a submerged vehicle, it is required to properly predict the imposed hydrodynamic forces and moments. Experimental investigation of the hydrodynamic coefficients of a submersible vehicle helps the understanding of its maneuver characteristics. The captive-model test method includes using of models attached through a multi-component balance system installed inside wind or water tunnels and towing tanks for experimentation. The measured forces and moments are then processed to identify the
n
Corresponding author. Tel.: þ 98 353 1232493; fax: þ 98 353 8212781. E-mail addresses: [email protected] (A. Saeidinezhad), [email protected] (A.A. Dehghan), [email protected] (M. Dehghan Manshadi). 1 Tel.: þ98 353 1232493; fax: þ 98 353 8212781. http://dx.doi.org/10.1016/j.oceaneng.2015.03.010 0029-8018/& 2015 Elsevier Ltd. All rights reserved.
hydrodynamic coefficients and their derivatives which can be used in common motion equations. Then, the various stability analysis or computer simulations can be achieved by employing these equations (Gertler, 1972). There are some differences between these three test apparatus. Wind and water tunnels do not have free surface and therefore only fully submerged conditions can be simulated while in the towing tank, all working conditions can be examined. Two principal dimensionless numbers in these experiments are Reynolds and Froude numbers. As an underwater vehicle usually operates far away from the free surface, the Froude scaling is no longer concerned and the most important similarity parameter for this case is the Reynolds number. Several experimental investigations have been conducted on the axisymmetric underwater vehicle models. Some of these tests have been performed in the deep-water basins (Gertler, 1950; Jagadeesh et al., 2009; Roddy, 1990; Van Randwijck and Feldman, 2000) or wind tunnels (Fidler and Smith, 1978; Jiménez et al., 2010; Mackay, 1988, 1990; Neumann, 1983; Patel and Lee, 1977; Watt et al., 1993; Whitfield, 1999) to find out hydrodynamic coefficients or flow properties around the models. All models considered by these research works have streamlined bodies of revolution with axisymmetric curved noses. Gertler (1950) examined the streamlined bodies of revolution of Series 58 (with parabolic curve nose) to measure the resistance of the vehicles moving in a straight line. Van Randwijck and Feldman (2000)
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Nomenclature b diameter of body hall C averaged appendages chord CD, CL, CS drag, lift, side force coefficient CDref CD at zero pitch angle CLref CL at 101 pitch angle CSref CS at 201 pitch angle CK, CN, CM rolling, yawing, pitching moment coefficient CKref CK at 201 pitch angle CNref CN at 201 pitch angle CMref CM at 101 pitch angle Force coefficient 1Force ρU 2 S 2
investigated the sectional and total forces and moments of Series 58 models in the David Taylor Model Basin. Fidler and Smith (1978) studied the hydrodynamic coefficients of a series of submersible vehicle models with various noses and tail geometries in a wind tunnel to obtain the systematic data over a wide range of pitch angle for Reynolds numbers ranging from 4.0 106 to 8.5 106. They considered ellipsoidal noses with length to diameter ratios of 0.5, 1.0 and 2.0 plus a torpedo-like nose. Roddy (1990) measured all forces and moments imposed on the DARPA SUBOFF model (an axisymmetric body with a rounded nose and blunt after body) at Reynolds number 14 106 in the David Taylor Model Basin. The steady and unsteady forces and moments were measured on the same model with the smaller size by Whitfield (1999) in Virginia Tech Stability Wind Tunnel at two Reynolds numbers of 4.16 106 and 5.7 106 (based on model length) and for various angles of attack and roll positions. Tests were also done by attaching trip strips on the bow and sail sections. The comparison between the results of wind tunnel experiments (Whitfield, 1999) and the towing tank data (Roddy, 1990) revealed a good agreement in spite of the differences Reynolds numbers and test rigs employed. Flow visualization and force measurements were carried out in the national aeronautical establishment (now IAR) low speed wind tunnel with test section of 2 3 m2 over a standard submarine model in hull-alone and hull with sail configurations (Mackay, 1988, 1990). The experiments have been conducted at Reynolds numbers between 4.9 106 and 9.5 106. Oil flow visualization results have demonstrated the separation of the flow over the hull, over the sail and on the sail and hull junction. Watt et al. (1993) performed wind tunnel tests employing the same model. These tests were carried out at Re¼ 23 106 and pitch angle of up to 301. Various test configurations were considered and the overall forces and moments were measured. The previous reviewed works employed models with axisymmetric nose while many submarines have non-axisymmetric nose shape. Experimental investigation of the hydrodynamic performance of a submarine model with non-axisymmetric nose shape is scant and hence requires further attention. The main purpose of the present work is to study the static hydrodynamic characteristics of a submarine model with non-axisymmetric nose in a wind tunnel. The nose of the submarine model considered in the present experimental work has blunt curve in pitch sweep plane and round curves in yaw sweep plane. The Reynolds number effect on the drag coefficient is studied for Reynolds numbers ranging from 4.7 106 to 8.0 106. The influence of pitch angle, (α), on the hydrodynamic coefficients is studied for pitch angles ranging from 101 to þ271 and for Reynolds number of 6.6 106. Smoke flow visualization technique is also used to explore the flow structure on both hull and sail of the model and also to capture the details of the flow pattern around the whole body of the model.
27
FD, FL, FS K, M, N L U S X (X/L)t
drag, lift, side force components rolling, pitching and yawing moment model length free stream velocity frontal area longitudinal axis along the model Boundary layer transition location α pitch angle Re model length Reynolds number; ρμUl ReC chord Reynolds number; ρUC μ m dynamic viscosity ρ fluid density Moment coefficient Moment 1ρU 2 Sb 2
2. Experimental procedure 2.1. Force and moment measurements A submarine model with a non-axisymmetric nose curve is considered for conducting force and moment measurements. The forebody of the model is not axisymmetric, while it has a plane of symmetry. The nose curve is blunt in the vertical or pitch plane while having rounded shape in the horizontal or yaw plane. The submarine model is constructed from aluminum and wood and a computer numerical control (CNC) machine is used for obtaining a required shape with an acceptable accuracy. Table 1 shows the dimensions of full-scale and wind tunnel models. The experimental investigation is carried out using an open working section wind tunnel. The wind tunnel has an open-jet test section with height, width and length of 2.8 m, 2.3 m and 4 m, respectively. Fig. 1 shows the schematic of the wind tunnel test section as well as the full shape of the model positioned in the test section. The turbulence intensity of the free stream within the test section is less than 0.13%. The aerodynamic forces and moments are measured with a sting-mounted six-component force balance mechanism which is internally mounted at the hull center as shown in Fig. 2. The uncertainty of the measured force and moments, and Reynolds number are calculated and presented in Table 2. A data acquisition system is employed to collect the measured forces and moments. The data acquisition sampling rate is 200 Hz and the duration of measurement at each pitch angle is 10 s. Then, the average values of force and moment are calculated and used for analysis. The trip strip is proposed to simulate the boundary layer transition on the full-scale vehicle (Barlow et al., 1999). Two methods are used in the current research to predict the trip strip location on the model surface. The first method is based on DeMoss and Simpson (2010) recommendation that the trip strip should not be placed in the adverse pressure gradient regions as it may induce separation. In order to comply with this recommendation, some surface pressure measurements on a submarine model with the same nose shape, which was used in the force and moment tests, were conducted in a closed loop wind tunnel by the present authors. The longitudinal surface pressure distributions were measured with a series of pressure
Table 1 Model and full-scale dimensions.
Full scale Wind tunnel model
L (m)
D (m)
44 2
5.03 0.23
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Fig. 1. Schematic of test section setup.
Fig. 2. Schematic of the submarine model and the internal balance equipment.
Table 2 The uncertainty of the measured parameters.
Table 3 Transition position at full scale Reynolds number.
Parameter
Relative uncertainty (%)
Curve plane
(X/L)t
(X/L)t%
Reynolds number
uRe Re ¼ 1:04 uFD;L;S FD;L;S ¼ 2:5 uMM;N;l
Vertical (pitch) plane Horizontal (yaw) plane
0.025 0.067
2.5 6.7
Hydrodynamic forces Hydrodynamic moments Hydrodynamic force coefficient Hydrodynamic moment coefficient
MM;N;l ¼ 2 uCD;L;S CD;L;S ¼ 3:5 uCM;N;l CM;N;l
¼4
taps along the nose surface. The surface pressure results revealed that the position X/L¼0.03 is a good choice to place the trip strip. The second method employed for predicting the proper location of the trip strip was based on using the XFOIL program (Drela, 2001) in order to find out the transition location on the full-scale vehicle surface. The panel points based on the submarine profile in both vertical and horizontal planes are imported into the XFOIL program and the boundary layer is simulated for full-scale Reynolds and Mach numbers at zero pitch and yaw angles. The resulting locations of transition, (X/L)t, in both vertical (pitch) and horizontal (yaw) planes are presented in Table 3. From the data presented in Table 3, it is seen that on the average, location of X/L¼0.03 is a proper choice for trip strip position and this conclusion is in agreement with the finding of the first method employed. In addition, a thorough literature survey (Huang and Liu, 1994; Huggins and Packwood, 1995; Jiménez et al., 2010; Watt et al.,
1993) shows that in the most of submarine model tests, trip strip was placed in the range of 0.03 r(X/L) r0.05. According to the aforementioned justification, a band of grit acting as a transition tripping is attached on the model at 3% of the length of the model, measured on the surface from the nose tip. The width of this trip strip was 1 cm. Three different sizes of grit are used for trip strip and their specifications are listed in Table 4. Initially, the force and moment measurements are conducted for Reynolds number ranging from 4.7 106 to 8.0 106 to explore the variation of drag coefficient with Reynolds number. Then the other tests are performed for pitch angles of 101r α r271 and for uniform wind velocity corresponding to Reynolds numbers of 6.6 106. Mach number is calculated for all the free stream velocities and is found to be lower than 0.3 at all Reynolds numbers and hence, the flow is assumed to be incompressible. Additional tests have been conducted to study the influence of the trip strips attached on the bow of the model. The blockage ratio of the model in force and moment experiments is calculated and is found to be less than 5% at 271 pitch angle which is acceptable for tests in an open test section wind tunnel as recommended by Barlow et al. (1999).
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2.2. Flow visualization setup The flow visualizations have been performed in a low speed smoke tunnel to determine the flow pattern around the model for various pitch angle values. Because of the smaller size of the smoke wind tunnel, the models used for the flow visualizations are smaller than the models used for hydrodynamic force and moment measurements, although the geometric similarity between the two models is preserved. A wire as trip strip with a diameter of 0.2 mm was used to stimulate turbulent boundary layer flow around the small model. The trip strip is placed at 5% of the length of the model, measured on the surface from the nose tip. As discussed in Section 2.1, suitable locations for trip strip positioning are suggested to be in the range of 0.03r (X/L)r0.05. For the flow visualization test model, X/L¼0.05 is selected for trip strip location as it is commensurate with the size of the model selected. Two flash bulbs are used to illuminate the smoke path lines and flow structures around the model. They aligned normal to the Table 4 The size of grit for trip strip. Trip strip no.
Grit number
Nominal grit size (mm)
1 2 3
80 90 120
0.21 0.18 0.15
29
direction of the smoke filament plane. The movement of the smoke-lines is captured with a high-speed camera at a rate of 2500 frames/s. A schematic view of the flow visualization test rig is shown in Fig. 3a. Laser light sheet illumination technique is also used to capture cross flow characteristics. A 50 mW pointer laser is used to achieve this particular aim. The laser sheet is obtained by using a simple cylindrical lens. The cylindrical lens is mounted in such a way to have its focal line positioned very close to the laser output mirror. The laser sheet creates an illuminated plane normal to the model axis and hence, the camera is aligned normal to the plane of laser sheet as shown in Fig. 3b. The blockage ratios for the smoke flow visualization experiments are less than 6% at 201 pitch angle which is acceptable for wind tunnel flow visualization tests as recommended by West and Apelt (1982).
3. Results and discussion The first part of the experimental result focuses on the drag coefficient variation with flow Reynolds number. Furthermore, the effects of the pitch angle (α) on the force and moment coefficients are presented and discussed. In-plane forces and moment which include drag, lift and pitch moment coefficients are studied and discussed by presenting the out-of-plane force and moments including side force, yaw and roll moment coefficients. Fig. 4 shows definitions of pitch angle, flow direction and the force and moment components.
Fig. 3. Schematic of the visualization setup: (a) illumination with two flash bulbs; (b) illumination with laser source.
Fig. 4. Wind tunnel fixed coordinate system and force and moment components.
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3.1. Influence of Reynolds number on the drag coefficient The type of laminar or turbulent flow separation and transition location on a streamlined body surface is influenced by the flow Reynolds number. Beyond a certain value of Reynolds number, which is called critical Reynolds number, the separation type and its location are independent of the flow Reynolds number (Hosder and Simpson, 2001). Thus, the knowledge of relationship between the hydrodynamic coefficients and Reynolds number is important. Fig. 5 shows the variation of the drag coefficient with flow Reynolds numbers for zero pitch angle, α ¼01. It should be noted that all the measured drag coefficients are scaled over the corresponding value for Re¼ 4.72 106. It is seen from Fig. 5 that the drag coefficient increases with increasing Reynolds number until around Re ¼ 5.9 106 and remains nearly constant afterward. This behavior of drag coefficient with Reynolds number in the range of 106–107 for streamlined bodies has been also observed in the previous works (Beheshti et al., 2009; Huggins and Packwood, 1995). Hoerner (1992) showed that by increasing Reynolds number, drag coefficient of streamlined bodies initially decreases until Re ¼106. Through the transition to turbulent flow (Re ¼106–107), an increase in CD is observed. A local minimum of the drag coefficient, CD, is observed in the region of laminar-to-turbulent transition. Full turbulent boundary layer covers the entire length of the model for Reynolds number of 107 and the variation of the drag coefficient is negligible by further increasing the flow Reynolds numbers. A number of submarine model experimental investigations (Bridges et al., 2003; Feldman, 1995; Roddy, 1990) have reported the critical Reynolds number for their submarine model occurring in the range of 107–1.5 107. Based on the results presented in Fig. 5, the boundary layer of the flow around the present model is in the region of transition to turbulent for Re¼4.7 106–5.9 106. Hence, it is deduced that the critical Reynolds number for the present model is 5.9 106, which is lower than the amount reported by other investigators. The lower value of the critical Reynolds number obtained through the present study is attributed to the nose shape of the present model. The blunt nose causes the boundary layer around the model becomes fully turbulent at lower Reynolds number. Therefore, the drag coefficient also remains constant for full-scale model in the high Reynolds number flows. In order to study the effects of Reynolds number on the hydrodynamic behavior of the submarine model under various pitch angle maneuver, the drag coefficients are measured for various pitch angles (101r α r291) and for three Reynolds number values of 5.4, 6.6 and 7.9 106. In order to compare the model behavior with respect to a reference condition, the measured drag coefficients are scaled
Fig. 5. Drag coefficient variation with Reynolds number.
with the drag coefficient obtained at zero pitch angle (CDref) at Re¼6.6 106. Fig. 6 presents the variation of the drag coefficient for various pitch angles at three flow Reynolds number values. It is seen that at small pitch angles, drag coefficient variation with Reynolds number is marginal while for larger pitch angles, the influence of Reynolds number on the drag coefficient is noticeable. Moreover, for large values of pitch angle, the measured drag coefficients slightly diverged from each other especially at high Reynolds number. Consequently, Reynolds number effect becomes significant in large angle of attack (α Z181). Lamont (1982) also reported similar Reynolds number effects on the hydrodynamic coefficients in high pitch angles between 301 and 901 for an ogive cylinder without appendage. The difference between the present results at high pitch angles (α Z181), which the Reynolds number effect becomes noticeable, and the findings of Lamont (1982) is due to the different model shape and the presence of appendages in our test model. The rudder and elevator are small wings that placed in afterbody part of the submarine model. The effect of elevator on the hydrodynamic forces and moments become important when the pitch angle of the submarine model increases. In the present work, the chord Reynolds number of these appendages is lower than appendages critical chord Reynolds number, ReC ¼106 (Mackay, 2003) and hence, the boundary layer transition location on the appendages depends on the Reynolds number. Therefore, at high angles of attack α Z 181 where the appendages performance is important, Reynolds number effects on the appendages is more pronounced. In the next step, several experimental tests have been conducted by utilizing three transition trip strips with various sizes to ensure that the boundary layer around the model is turbulent. A comparison of the drag measurements for three trip strip sizes at Reynolds number of 6.6 106 and for various values of pitch angle is shown in Fig. 7. The results obtained for models equipped with the trip strips are compared with the test results of the clean model i.e., model without trip strip. It is seen that drag coefficients obtained for both the clean model case and model equipped with various trip strip sizes are almost collapsed on each other and no appreciable changes on the drag coefficients are observed. Similar trends are observed for all pitch angel experiments. As it was noticed in Fig. 5, the drag coefficient is not depending on the Reynolds number for Re45.9 106. One can conclude that boundary layer on the entire surface of the model is already turbulent for Reynolds number of 6.6 106 which the present test are conducted. Therefore, the presence of the trip strips has no noticeable effect on the measured drag coefficients and hence, the entire test runs, except the one with the data presented in Fig. 7, are conducted without trip strip on the model surface.
Fig. 6. Variation of drag coefficient with pitch angles for various Reynolds numbers.
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Fig. 7. Effect of trip strip on drag coefficient of the model for various pitch angles at Re ¼6.6 106.
3.2. Influence of pitch angle on in-plane force and moment coefficients The measured in-plane forces and moment including drag and lift forces and pitch moment in pitch maneuver at Re ¼6.6 106 are presented in this section. In addition, flow visualization experiments are conducted to determine the physical observation of flow structures such as boundary layer separation and vortical flows around the model for various pitch angle values. Fig. 8 shows the drag coefficient versus pitch angle for four repeated test runs under the same operating conditions. The average values of the four similar test runs are also presented in this figure. The measured drag coefficients presented in Fig. 8 are scaled over the drag coefficient of zero pitch angle. It is observed that drag value rises with increasing pitch angle. This is due to formation of large separation region on the leeward of the model which results in increasing the pressure drag. The drag coefficient shows a parabolic trend with a relatively high slope such that at 301, 201 and 101 pitch angles the measured drag coefficients are approximately five, four and three times larger than the drag coefficient value at zero angle respectively. This is attributed to the nose shape of the model selected. The nose has blunt curve in the pitch sweep plane which causes flow spouted for high pitch angles. There is not symmetry between the measured values at positive and negative pitch angles. This is due to the sail effect of the submarine model. The results obtained during the four similar test runs are almost collapsed in a single curve, indicating the accuracy and repeatability of the experimental work presented. Fig. 9 shows the visualized flow pattern around the model subjected to various pitch angles. At zero pitch angle, the boundary layer is almost fully attached to the entire body surface. When the pitch angle increases, the flow separation occurs near to the afterbody of the model. As shown in Fig. 9b (α ¼ 61), the separation region is small and located downstream of the sail. The separation region combines with the cross flow and creates a counter rotating vortex pair at the leeward of the main flow. As the pitch angle increases, the separation line moves both forward (towards the nose of the model) and windward, and the separation region extends almost over the entire length of the model (α ¼181). The flow around the model with axisymmetric elliptical nose at pitch angle of α ¼181 is also presented in Fig. 9e for comparison. By comparing Fig. 9d and e, it may be seen that for the blunt nose shape, the location of the flow separation is closer to the nose than the elliptical nose type. Cross flow vortex becomes stronger and dominates the flow field at the leeside of the model for higher pitch angles. The flow visualization results confirm that the separation starts to appear at small pitch angles and almost extents over the whole body of the model as pitch angle increases.
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Fig. 8. Drag coefficient versus pitch angle at Re¼ 6.6 106.
In Fig. 10 the measured lift coefficient is plotted versus pitch angle for Re¼ 6.6 106. This figure shows a continuous increases in the lift coefficient as pitch angle is increased. A symmetry between the results is seen for both positive and negative pitch angles. The trend of the lift coefficient curve obtained in the present study is similar to the data presented by Whitfield (1999). Again, the data obtained from the four test runs are collapsed to a single curve, especially for pitch angle range of 101 to þ 201and all the data from all four test runs pass through the origin at zero pitch angle. The authors in their recent work, Saeidinezhad et al. (2014), studied the separation and formation of cross-flow vortex over two axisymmetric body of revolution at various incidence angles. Their results show that as the pitch angle is increased, the longitudinal and cross-flow separation region moves to the forward and also to the windward side of the model. The longitudinal separation along the model causes an uplift force that is imposed on the body at pitch angle. In addition, as the pitch angle increases, the circumferential (cross-flow) separation causes the excess lift force which coupled with lift force due to the longitudinal separation and increases the overall normal force acting on the body. This is the main source for a large increase in CL value at higher pitch angles. Fig. 11 shows the pitching moment coefficient versus the pitch angle at Re¼6.6 106. The variation of the pitching moment in the range of 101 to þ101 pitch angle is almost linear and symmetric. By increasing the pitch angle beyond 101, the slope decreases and finally the pitching moment approaches to an asymptotic value. This is due to the fact that at high pitch angle ( þ101 to þ291), appendages especially elevators (horizontal control plane appendages) creates negative pitching moment due to the combination of both drag and lift forces imposed upon them. This negative pitching moment partially compensates the increasing positive pitching moment created by the combination of both drag and lift forces imposing on the main body. Hence, the net combinations of these effects causes a reduction in the slope of the positive pitching moment and approaching to an asymptotic value as pitch angle increased beyond 101. Again, the measured values for the four test runs under similar operating conditions are close to each other, indicating the repeatability of the experiments. 3.3. Influence of pitch angle on out-of-plane force and moment coefficients The out-of-plane force and moments include side force and yawing and rolling moments in pitch maneuvers. The variation of the side force coefficient at Re ¼6.6 106 is shown in Fig. 12. The side force has a relatively negligible value for α o141 however, it starts increasing when the pitch angles increases beyond 141. Yawing and rolling moments are presented in Figs. 13 and 14. The behaviors of both moments are quite similar to the side force as
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Fig. 9. Visualized flow pattern around the model in various pitch angles: (a) α ¼ 01; (b) α¼ 61; (c) α ¼121; (d) α ¼181; (e) α ¼181 (standard nose).
these moments are strongly related to the side force in the pitch maneuvers. While the shape of the model has symmetry between the left and right sides, one of the sources of the lateral force and yawing moment is the possible asymmetry of the flow field around the model. Visualization results have revealed that the cross-flow vortices are formed in the leeside of the model from α Z61 (See Fig. 9). Fig. 15 presents the visualized cross-flow vortex in the leeward of the model at various longitudinal positions (X/L) ranging from 0.3 to 0.8 and for maneuver pitch angle of 151. The cross flow vortices are captured by creating a laser illuminated sheet at the prescribed positions. It is seen that the cross-vortex grows in size as it moves along the model. In addition, formation
of a secondary vortex is shown in this figure. Other researchers have indicated that cross-flow vortex becomes asymmetric and is partially responsible for inducing side force for a certain range of pitch angles. Ericsson and Reding (1986) characterized four distinct regions in the flow around a slender body when the model subjected to a flow with angle of attack in the range of 0–901. At small angles of attack, the flow is attached to the model and the axial flow field dominates. The variation of the lift force and pitching moment are linear with pitch angle. At intermediate angles, formation of the cross-flow creates pressure gradient across the model and the boundary layer is separated, leading to a formation of symmetric vortex pair on the leeside of the model. However, no out-of-plane force and moments
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Fig. 10. Lift coefficient versus pitch angle at Re¼ 6.6 106.
Fig. 13. Yawing moment coefficient versus pitch angle at Re¼6.6 106.
Fig. 11. Pitching moment coefficient versus pitch angle at Re¼ 6.6 106.
Fig. 14. Rolling moment coefficient versus pitch angle at Re¼ 6.6 106.
Fig. 12. Side force coefficient versus pitch angle at Re¼ 6.6 106.
Fig. 15. Cross-flow vortex in the lee-side of the model at α ¼ 151 in various longitudinal positions (X/L ¼ 0.3–0.8).
are present. Further increasing the incidence angles, the cross-flow vortices become asymmetric and induce side force and yawing moment. Finally, at very high angles, the flow pattern becomes similar to the flow across a cylinder. It is important that the onset angle of asymmetric vortex formation is a function of the flow Reynolds number, and hull geometric parameters including the nose shape, surface finishing and fineness ratio (Watson et al., 1993). The presence of the side force is also reported in the works conducted by Allen and Perkins (1951), Dexter and Hunt (1981), Levy et al. (1996) and Zilliac et al. (1991) on the flow around symmetric bodies at high pitch angles. The measured side force and consequently its induced yawing and rolling moments which are presented in Figs. 12–14 were seen in all
test runs. The presence of the side force acting on the axisymmetric ogive models in pure pitch maneuver was also reported by other researchers in aerodynamics testing in wind tunnels. This phenomenon was first discovered by Allen and Perkins (1951) in the early 1950s; and since then, a great number of studies in this subject has been carried out (Bridges, 2006). In some of these studies, it is noted that the magnitude and direction of side force varies irregularly when the nose of an axisymmetric body is rolled at high angle of attack. Some research works (Bridges and Hornung, 1994; Levy et al., 1996; Xuerui et al., 2002) have reported that the side force might be originated due to the vortex asymmetry primarily arising from imperfections on the nose-tip of a body.
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From the above discussions and observations reported on the literature, the presence of the side force and its strange behavior at high pitch angles (α Z121), might be attributed to the imperfections in model preparation especially its nose, its strut which is responsible for pitching the model, test rig vibration, appendages installation and other unidentified sources. Close look at the drag, lift and pitching moment variations presented in Figs. 8, 10 and 11 reveals that these data are not much affected by the aforementioned sources as no noticeable scattering in drag, lift and pitching moment data are seen at high pitch angles. However, it should be stated that the submarine vehicles do not experience the pitch angles beyond 151 in their normal missions and hence, the side force effects are not important for low angles of attacks. 4. Conclusions In order to explore the influence of the Reynolds number on the drag coefficient of a submarine model, a model with a non-axisymmetric nose is examined in a wind tunnel for various Reynolds numbers ranging from 4.7 106 to 8.0 106. Furthermore, to investigate the hydrodynamic characteristics of the model under various pitch maneuver, the experiments are also conducted for various values of pitch angle at Re¼6.6 106. The closed loop wind tunnel employed has an open-jet test section with height, width and length of 2.8 m, 2.3 m and 4 m, respectively. It is noticed that the drag coefficient increases by increasing the Reynolds number up to 5.9 106 (critical Reynolds number) after which it approaches to an asymptotic value. Hence, it can be concluded that the same drag coefficient can be deduced for a full scale model with a similar geometry. The critical Reynolds number for the present model with non-axisymmetric nose is lower than the corresponding value estimated by the previous research works on the models with symmetric nose shape. Furthermore, extensive flow visualization experiments were conducted to capture the details of the flow structure around the model under investigation for various pitch maneuvers. Visualized flow revealed that flow separation occurs on the afterbody of the model at small pitch angles (α ¼61). As pitch angle increases, separation region moves towards forebody and vortical field dominates the leeside of the model. Finally, the separated flow covers almost the entire length of the model (α ¼ 181). Therefore, pitch angle has significant effects on the hydrodynamic coefficients. It was observed that the measured drag and lift forces increase with increasing pitch angle. Pitching moment shows the same behavior in a range of pitch angle 101r α r þ101 but approaches an asymptotic value by increasing pitch angle beyond 101. It was observed that the out-of-plane forces and moments have relatively negligible values for pitch maneuver in the range of 101o α o141 while they increase with increasing the pitch angle. This might be attributed to the asymmetric nature of the cross flow vortices, imperfections in model preparation especially its nose, its strut which is responsible for pitching the model, test rig vibration, appendages installation and other unidentified sources. References Allen, H.J., Perkins, E.W., 1951. Characteristics of Flow Over Inclined Bodies of Revolution. Research Memorandum RM A50L07, National Advisory Committee on Aeronautics (NACA). Barlow, J.B., Rae, W.H., Pope, A., 1999. Low-Speed Wind Tunnel Testing, 3th edition. Wiley. Beheshti, B.H., Wittmer, F., Abhari, R.S., 2009. Flow visualization study of an airship model using a water towing tank. Aerosp. Sci. Technol. 13 (8), 450–458. Bridges, D.H., 2006. The asymmetric vortex wake problem-asking the right question. In: Proceedings of the 36th AIAA Fluid Dynamics Conference and Exhibit, San Francisco, California.
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