Effect of multiple rings on side force over an ogive-cylinder body at subsonic speed

Priyank KUMAR,J.K.PRASAD

Department of Space Engineering&Rocketry,Birla Institute of Technology,Mesra,Ranchi 835215,India

1.Introduction

With the advancement in the aerospace technologies,the aerospace vehicles such as missiles and aircraft are often subjected to flying at large angles of attack either for a long or short duration in different flow regimes.The oncoming flow separates and curls up into a couple of vortices that further lift in the downstream owing to the adverse pressure gradients.The flow becomes highly complex in the case of vehicles having pointed forebody as the flow which leads to the establishment of multiple vortex systems arranged alternately.These vortex systems appear to be asymmetric in different cross planes(Fig.1).It is a well-known fact that pointed nose vehicles flying at lower angles of attack experience a symmetric vortex pattern due to which the pressure distribution at any circumferential location remains symmetric and hence no side load is generated.With the increasing angles of attack,one of the vortices lifts while the other remains closer to the body.This leads to the non-symmetric static pressure distribution circumferentially and hence at high angles of attack the body experiences a side force.These side forces were firstly reported by Allen and Perkins in 1951.1Since then investigations have been made to interpret the underlying flow physics for the onset of side force and several control methods have been employed to lessen the side force at different α.The side force highly depends upon factors like Reynolds number,the geom-etry of forebody,slenderness ratio,nose fineness,roll angles,etc.Lamont et al.2,3did extensive experimental investigations on the ogive-cylinder body and reported the dependence of side force on the angles of attack α,Reynolds number Re,and roll angles.Zilliac et al.4and Dexter and Hunt5conducted the experiments with a very good surface finished model,damping system,and low turbulence wind tunnel;however,the dependency of the side force on the roll angles could not be omitted.Hence,they were forced to conclude that the changes in the side force are more or less dependent upon the micro perturbation of the nose.However,still,there are several questions that remain unanswered such as the lifting of one of the vortices,and ‘bistable state” of side force at α=45°to 55°.The experiments conducted by Keener et al.6indicated that the changes in the side force for different roll angles were highly dependent upon the orientation of the nose tip.Experiments made by Luo et al.7demonstrated the effect of forebody on the side force.Computation to obtain the vortex asymmetry on a pointed nose body at high α has been a difficult task.Degani and Schiff,8Degani and Levy9and Taligoski et al.10obtained the vortex asymmetry by suitably inserting a micro tip perturbation.Computational results by Degani and Levy9showed an excellent agreement with the reported experimental results of Lamont and Hunt.2

Fig.1 Asymmetric vortex pattern on slender body.

To alleviate the lateral forces on the ogive-cylinder at large α,several control methods such as Helical grooves,11circular trip,11nose bluntness,12and dimples on the nose,13have been used in the past.Lim et al.14made the computations with different nose shapes.Recent work carried out by Kumar and Prasad15showed the reasons behind the existence of side force and its dependence on the lift-to-drag ratio.The use of a rectangular cross-section ring placed suitably in the early portion changed the side force direction at higher α,as the ring altered the growth of one of the vortex.A ring height of 0.03 times the local diameter was found to reduce the side force.16However,an appreciable amount of side force was experienced at α=35°to 40°.Use of a pair of rings located at X/D=3.5D and 4.5D reduced the side force considerably;however,the side force was not completely alleviated.17Since some aircraft and missiles may fly at α ranging from 35°to 45°,hence the present work is aimed to alleviate the side force on the ogive-cylinder body completely between α =35°to 45°.It is envisaged that use of the additional rings on the body placed suitably might help in further reduction of the side force.Experimental and computational investigations have been made at a diameter Reynolds number of 29000.It is believed that such studies have not been reported previously.

2.Experimental techniques

Experiments were conducted using a low-speed wind tunnel having a test section of 0.6 m×0.6 m.The turbulence intensity of the wind tunnel was found to be below 0.5%.All the experiments were made at U∞=17 m/s.The ogive-cylinder body was 400 mm long and had a base diameter of 25 mm corresponding to lift to drag ratio L/D=16(Fig.2(a)).The nose of the slender body had a L/D of 3.5.The semi-apex angle of the nose was 16.25°.Circular rings having heights of 3%of the local diameter and breadth of 1.4 mm were made.The three rings were placed at X/D=2.5,3.5 and 4.5(Fig.2(b)).Experiments consisted of the measurement of forces which was carried out using an internal 6-component strain gage balance.It had an accuracy better than 0.2%.A 3 V DC power having a high signal to noise ratio was used for exciting the wheat stone bridges.α for the model was varied using a PC based positioning system.The positioning system had an accuracy of 0.1°.An accelerometer was used to ascertain the angle of attack α.Precautions like streamlining of the model incidence mechanism or any attachment used inside the tunnel were made to minimize the effect of blockage.All the data were acquired and analyzed using a data acquisition card.A signal conditioning unit having a gain of 1 to 1000 was used in the force measurement.A low pass filter having a cutoff frequency of 10 Hz was also used so as to remove the unwanted high frequencies.Experiments were made with the model set at ? =360°(Ref.15).

3.Computations

Fig.2 Details of ogive-cylinder body and rings.

The present computations have been made using the commercial software Fluent.The unsteady,segregated and implicit schemes were used in the present computations.Secondorder discretization was utilized for time,space and turbulence equations.For the case without ring,computational studies were made using laminar-turbulent flow assumptions.The flow was assumed to be laminar up to X/D=3.25.16The computation made adopting this assumption indicated better agreement of the local and overall side force obtained using experiments and computations.16For the case with the ring,computation made with the laminar flow assumption only did not produce satisfactory results.Moreover,the convergence history was also unsatisfactory.This is likely due to the fact that the presence of a ring on the slender body is expected to make the flow turbulent11in the downstream.Hence,computations with rings have been made using different turbulence models like Spalart-Allamaras(S-A)turbulence model,Menter’s k-ω Shear Stress Transport(SST),standard k-ω,standard k-ε,etc.The overall side force obtained using the turbulence models indicated that the S-A turbulence model showed much better agreement in comparison to the other turbulence models15for the case of a single ring.However,with an increase in the number of rings S-A turbulence was not able to predict results closer to the experiments.Better agreement of the computational and experimental overall side force was obtained for different rings with the use of k-ω SST turbulence model with curvature correction.Similar models used with complex flows showed the improved agreement of the computational and experimental results.18–20Results of grid independence tests and convergence are reported in Refs.15,16.

A spherical domain(Fig.3)consisting of around 1.8 million grids was adopted for the present computation.The computational domain was kept at 40D from the center of the model.Based on the observation of Levy and Degani,9a micro tip disturbance having a length,height and width of 0.04D,0.004D and 0.004D(as shown in Fig.4)respectively was kept at X/D=0.08 and ? =90°in order to produce the asymmetry of the vortices.The first mesh cell height was kept as 4×10-5D.This yielded y+＜5 near the body surface.Grid clustering was ensured at the nose tip and around the ring so as to capture the flow properly.At the inlet,a free stream velocity U∞=17 m/s was enforced.Out flow boundary condition was kept at the exit boundary where the velocity and pressures were extrapolated from the interior.

Fig.3 Overall computational domain.

Fig.4 Nose tip perturbation at ? =90°.

4.Results and discussion

Variation in the side force with respect to the angle of attack is presented in Fig.5,CYis the side force coefficient.It indicates the increase in the side force with increasing angle of attack α.The key reason behind the increase in the side force with the increasing α is due to the increasing vortex asymmetry along the body length.More details of the asymmetric flow and side force on the pointed nose body at higher α is reported in Ref.15.The use of a circular ring at a given axial location helped in the drastic reduction of the lateral loads on the slender body at higher α.The side force at angles of attack beyond 40°was observed to change its direction.This was mainly because at high α,the use of a ring(5%)at an axial location of 3.5D restricted the growth of one of the vortices which led to the change in the local side force,and therefore the overall side force was altered.A reasonable agreement between the measured and the reported values of side force was observed in Fig.5.The differences observed could mainly due to the micromachining imperfections of the two models or due to the differences in the wind tunnel(Kumar and Prasad15).Based on this observation,experimental and computational investigations were conducted to arrive at a suitable height of the ring so that the side force reduces at all the angles of attack without changing its direction.Use of a single ring of 3%height of the local diameter located at X/D=3.5 showed a decrease in the side force at all the angles of attack.However,appreciable side force was observed at α =30°to 40°.It was observed that the side force was highly dependent on the location and size of the ring(Refs.16,17).Hence investigations were performed with an additional ring of height 3%placed at typical axial distances.

Fig.6 shows the experiments performed by Kumar and Prasad17on the slender body by placing two rings at typical axial distances of X/D=2.5 and 3.5 and X/D=3.5 and 4.5.In both cases,use of a pair of ring decreased the side force in α range of 30°to 40°;however,the side force reversed for the case of rings located at X/D=2.5 and 3.5 at angles of attack beyond 45°.Such reversal of the side force was not observed in the case of rings placed at X/D=3.5 and 4.5.

Fig.5 Effect of single ring on measured side force.

Fig.6 Effect of two ring combination on measured side force.17

Use of a pair of ring reduced the side force significantly.However,the side force was not completely reduced in the angle of attack range of 35°to 45°,which is practically very important,as most of the tactical missiles and aircraft often encounter these angles of attack.Hence,in the present study more focus was given in the angle of attack ranging from 35°to 45°.Based on the investigations made earlier(Kumar and Prasad17),the use of two rings of 3%height of the local diameter at axial locations of 3.5 and 4.5 showed better reductions.Therefore,it was decided to add one more ring(3%)at an axial location of X/D=2.5.It is expected that disturbances,if induced in the initial portion as well,will definitely alter the flow that might further reduce the side force.Surprisingly,the inclusion of an additional ring at the locations of 2.5D showed a drastic decrease in the side force at α =30°to 45°(Fig.7).The maximum side force measured was around 0.1 at an angle of attack of 35°.The results clearly indicate that the use of 3 rings completely alleviates the side force up to α=45°for the given flow conditions.

In order to obtain more details about the decrease in the side force because of the rings,computations were made for the case with and without rings using Fluent at α=35°,40°,and 45°.The comparison of the side force obtained from the present experiments and computations(Fig.8)shows reasonable agreement.Although a significantdifferenceis observed in the computed and measured side force at α=40°,the acquired results will be useful in understanding the decrease in the side force at α =40°.The better agreement could be obtained with more grids and better turbulence models.Since the experimental results indicated appreciable side force at an angle of attack of 40°for the case of single and two rings,in the present paper more emphasis has been given to understand the alleviation in the side force with three rings at α =40°.

Fig.7 Effect of three ring combination on measured side force.

Fig.8 Comparison of measured and computed side force.

Fig.9 presents the computed static pressure distributions at different axial locations of X/D=2,4,6 and 8 at α =40°for different rings.Fig.9(a)shows the circumferential pressure distribution obtained at X/D=2 for different rings.The circumferential pressures indicated no major change in the pressure distribution from ? =290°to 70°with the increase in the number of the rings.However,changes in the pressures were observed from ? =70°to 290°with the rings.Fig.9(b)shows the circumferential pressure distribution at X/D=4.It is observed that for the case of single and two rings,the pressure distribution at X/D=4 behaved almost in a similar way.It is quite clear that the use of single and two rings affects the vortex formation in the right side(view from the tip towards the downstream).The inclusion of one additional ring alters the pressure in the windward region as well.At X/D=6,increase in the number of rings increased the magnitude of the negative pressure from ? ≈ 20°to 160°while the pressure remained almost the same from ? ≈ 216°to 0°.This clearly indicates that the flow is affected in the leeward as well as windward side due to the increased number of rings.Further at X/D=8,the pressure distribution for the case without and with single and two rings indicated no significant change in the pressures.However,an appreciable change in the pressure was obtained at X/D=8 with the use of three rings.This clearly proves that use of three rings affects the flow to a larger region in the downstream.

Fig.10 shows the changes in the local side force downstream CYxof the body at α =40°for increasing number of rings.For the case without ring,a wavy variation of the local side force was obtained,which is mainly because of the establishment of a multi-vortex system arranged alternately in the wake of the body.Changes in the local side force were observed with the use of single ring at X/D=3.5.It is observed that the use of a single ring not only affects the flow in the downstream but also influences the flow upstream of the ring.Due to these,changes in the local side force are also observed in front of the ring.The local side force decreased in the X/D range of 0 to 6 and increased in the range of X/D=6 to 9 in the negative direction,which resulted in the decrease of the side force using one ring.Similar observations were also made for the case of two rings at α=40°.Interestingly,the behavior of the local side force along the length of the body for the case of three rings was much different in comparison to the other cases.Reduction in the local side force was observed from X/D=0 to 5.However,at X/D=5 to 9,the local side force was almost similar being in the negative direction.Further beyond X/D≈10,it started to oscillate.To have a more meaningful interpretation of the forces along the body,the local side forces were integrated in the axial direction.

Fig.9 Computed static pressure distributions at different axial locations of X/D=2,4,6 and 8 at α =40°for different rings.

Fig.10 Computed local side force distribution at α =40°.

Fig.11 Integrated local side force distribution at α =40°.

Fig.11 presents the integrated local sidefor a different number of rings at α =40°.It is evident from Fig.11 that the use of the ring in the initial portion of the body drastically reduces the side force of the body.The use of single ring located at 3.5D decreased the side force substantially.The inclusion of one more ring at X/D=4.5 did not induce any major variation in the side force at α =40°.However,three rings placed at X/D=2.5,3.5 and 4.5 largely reduced the side force in the frontal portion of the body.The side force reached negligible values at X/D=11.Further increase in the length of the body raised the side force by a small amount.

In order to have more details of the flow due to the rings at α =40°,vorticity magnitude contours are presented in Fig.12.The growth,movement of the vortices and its lifting are well observed for the case of a slender body with no ring.With the addition of one ring at X/D=3.5,the flow in the downstream was disturbed up to X/D=8.This led to the reduction in the local side force and changed the overall side force.The addition of one more ring at X/D=4.5 along with the ring at X/D=3.5 did not show any major change in the flow in comparison to the case of one ring.Hence,rings placed at X/D=3.5 and 4.5 did not help in reducing the side force at α =40°(Fig.6).However,placing one more ring at X/D=2.5 in addition to the two rings placed at X/D=3.5 and 4.5 disturbed the local flow in the downstream and made the vortical structures appear symmetric at X/D=8.This is the possible reason for the reduction of side force at α =40°with three rings.Similar flow features were also captured from the velocity vectors(Fig.13).The overall vorticity magnitude contours(Fig.14)clearly show the effect of rings on the body.It is observed that,with the use of three rings,the asymmetric nature of the vortices is suppressed significantly in the downstream.Moreover,the alternate arrangement of the multi-vortex system also gets disturbed,which may decrease the lift and drag of the body.Fig.14 clearly shows the delayed vortex lift in the downstream for the case of three rings in comparison to others.

Fig.12 Vorticity magnitude contours at α =40°.

Fig.13 Velocity vectors at α =40°.

Fig.14 Vorticity magnitude contours at α =40°on overall body.

Based on the computational studies,it becomes imperative to observe the effect of the rings on the lift and drag of the body as well.Hence,measurements were also made so as to obtain the lift and drag.Fig.15 shows the variation in the lift coefficient CLat different angles of attack for the case with and without rings.It is observed that the lift of the body decreases due to the presence of the rings.With the increase in α,further reduction in the lift was observed due to the rings.A decrease in the drag coefficient CDof the body was also observed with increasing α(Fig.16).It is mainly due to the increased number of rings which alters the flow field along the axial direction of the body(Fig.14).

Fig.15 Variation of lift coefficient with angle of attack for case with and without rings.

The present study was mostly focused at α =40°.The computations performed indicated a quasi-steady flow which can be observed from the convergence history of the side force shown in Fig.17,t is the flow time.On the other hand,the computations made at α =4°showed large oscillations in the overall side force with time.The time-averaged side force was almost negligible at α =45°,see Fig.18.The vorticity magnitude contours observed from Fig.19 clearly indicate the changes in the flow pattern at two different flow time t.Such computational results with rings clearly call for the investigations of the unsteady flow field using good experiments.The results obtained will be highly useful in the design of modern tactical missiles.

Fig.16 Variation of drag coefficient with angle of attack for case with and without rings.

Fig.17 Convergence history of overall side force at α =40°.

Fig.18 Convergence history of overall side force at α =45°.

Fig.19 Vorticity contour at α =45°for different flow time.

5.Conclusions

Experimental and computational investigations were made on an ogive nose slender body having a semi-apex angle of 16.25°and L/D ratio of 16 at a Reynolds number of 29000 based on the base diameter.The side force on the body(without a ring)was found to increase with the increasing α,which is mainly due to the difference in the counter-rotating vortices with increasing α.Based on the reported literature,complete alleviation of the side force at different angles of attack remains a challenging task especially in the angle of attack range of 35°to 45°.In the present study,an effort has been made to fully reduce the side loads by using three rectangular crosssectioned rings(3%height of the local diameter)located at different locations of X/D=2.5,3.5 and 4.5.Results obtained indicated that these rings altered the growth of the initial vortex system and hence symmetric circumferential pressure distributions were observed at different axial locations due to which the side force was reduced.However,the use of these rings also reduced the lift and drag of the body considerably.Based on these observations,it can be concluded that using three circumferential rings placed at X/D=2.5,3.5 and 4.5 reduces the side force to negligible values for the present flow conditions.

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