Comparison of Jet Plume Shape Predictions and Plume Influence on Sonic Boom Siganture

An Euler shocktting marching code yields good agreement with semiempirically determined plume shapes, although the agreement decreases somewhat with increasing nozzle angle and the attendant increase in the nonisentropic nature of the ow. Some calculations for a low-boom con guration with a sample engine indicated that, for ight at altitudes above 60 000 ft, the plume e ect is dominant. This negates the advantages of a low-boom design. At lower altitudes, plume e ects are signi cant but of the order that can be incorporated into the low-boom design process. Introduction The plume that results from an underexpanded jet is a signi cant factor in assessing the feasibility of potential supersonic commercial aircraft because of its in uence on the sonic boom signature and on aerodynamic performance. Consequently, reliable procedures for computing both the plume shape and the e ects of the plume on the sonic boom signature are required. This report presents a comparison of plume shapes computed by several methods, together with an examination of the kinds of sonic boom e ects the plume introduces. The primary reference in the current literature on plume shapes and plume sonic boom e ects is reference 1. This reference describes a combined experimental-computational study to determine empirically the shapes of jet equivalent solid bodies, that is, an e ective discrete jet free-stream slip line. These shapes were compared with plume shapes predicted by two computational methods. Reference 1 also includes some sample calculations to illustrate the plume sonic boom e ect. The present report describes calculations that yield a closer correlation with the semiempirically determined shapes than the methods described in reference 1. Also included is a study of the in uence of ight altitude and con guration geometry on the problem of plume sonic boom e ects with some illustrative examples. Symbols A(x) equivalent area distribution D external nozzle exit diameter, d + Lip thickness d internal nozzle diameter at jet exit, 2h F value of Whitham F -function h internal nozzle radius at jet exit L airplane reference length M Mach number p static pressure p = p po r radial coordinate t time t = 0 time at which a pulse, traveling at ambient sound speed, arrives at ground x coordinate in direction of nozzle axis nozzle expansion angle nozzle boattail angle dummy integration variable Subscripts: j jet o undisturbed condition 1 free stream Plume Calculations The plume shapes were computed with the Euler shocktting marching code described in reference 2. Calculations were made for some, but not all, of the nozzle shapes and conditions included in the investigation described in reference 1. Calculations were not made for the boattailed shapes because the plume code could not treat this case without modi cation. The type of nozzle that was tested is depicted in gure 1. The nozzle divergence angles for the nonboattailed shapes were 7:28 , 9:06 , and 11:50 . The measurements of reference 1 indicated that, for the two larger divergence angles, an internal shock was generated inside the nozzle. This shock is apparently associated with the curvature discontinuity that occurs where the circular-arc throat section meets the conical nozzle section. The experimental results indicated that this shock was relatively weak and its presence was not considered in the direct calculation of the plume shape or in the calculation of the exit Mach number. Figure 2 shows a set of calculations for plumes emitted from the nozzle with = 11:5 . In this gure, the solid line indicates the semiempirically determined jet equivalent plume shape. It was obtained by measuring the ow conditions along a line outside the plume and parallel to the nozzle axis. Then, with these initial conditions, a characteristic net was computed inward, taking the streamline that matches the nozzle lip as the jet equivalent solid body. The dash lines in gure 2 denote calculations, reported in reference 1, by a linearized technique described in reference 3. The long-dash{short-dash lines, also from reference 1, denote calculations by a method of characteristics assuming straight shock lines and conical nozzle ow. The circles denote calculations by the Euler method of reference 2. All these calculations predict plume shapes larger than the semiempirically determined shapes. The discrepancy is signi cantly smaller for the Euler calculation. Figure 3 shows a similar comparison of computed and semiempirically determined shapes for a nozzle with = 9:06 . For this nozzle, the points calculated by the Euler method represent a close approximation to the empirical shape, although it is still slightly overpredicted. The nozzle with = 7:28 was tested at only one pressure ratio. For this case, shown in gure 4, the Euler method yields an excellent representation of the empirically determined shape. Thus these results indicate that as the nozzle expansion angle increases, the correlation of the Euler calculations and the empirical results tends to deteriorate. As the nozzle angle increases, the observation was made that an internal shock forms. If this shock signi cantly reduces the Mach number at the nozzle lip, this e ect would account for at least part of the disagreement, since the exit Mach number is computed in reference 1 with the assumption of isentropic nozzle ow. However, a number of other factors could be involved. These factors include viscous e ects, the e ect of the bluntness of the nozzle lip, and assumptions involved in initializing the Euler plume code. Some attempts were made to determine the precise nozzle exit ow by computing the internal nozzle ow eld by time-relaxation Euler codes, but these attempts failed to yield the type of shock structure observed in the experimental results. No further attempt was made to investigate the various sources of error. The accuracy of the computed shapes is probably consistent with the accuracy of the approximate procedures that are used to obtain the e ective area distributions that are required for sonic boom calculations (ref. 4). For the purpose of comparing computed shapes with the semiempirical shapes of reference 1, a simple adjustment formula could be applied, since the discrepancy increases with nozzle divergence angle in a systematic manner. Sonic Boom Considerations Once the jet plumes have been modelled as equivalent solid bodies their sonic boom e ects can readily be determined. The equivalent solid body is simply treated as an extension of the engine nacelle. Then an equivalent area distribution obtained from projected Mach slice cuts through the con guration is generated. This area distribution is added to an equivalent area distribution due to lift to obtain a total area distribution A(x). This area distribution is related to the sonic boom wave shape through the \F -function" which is de ned by the formula F (x) = 1 2 Z x 0 A00(x ) d px The wave shape is determined directly from the F -function, and the ground level signature is determined by a propagation and shocktting code. These concepts are explained in greater detail in the standard sonic boom literature. (See, for example, ref. 5.) In view of the wide variety of approaches to con guration geometry and aircraft cruise conditions that are being considered for civil supersonic aircraft, it would not be practical at this point to attempt to compute plume e ects for each case. However, a few calculations in addition to those already reported in reference 1 may serve to indicate the types and orders of magnitude of the e ects to be expected. Some factors involved are the ight Mach number and altitude, the con guration geometry, and the manner in which the engine nacelles are integrated into the geometry. Con gurations that are designed for diminished sonic boom levels are usually laid out in such a way that the lift is distributed longitudinally to the greatest possible extent. The result is a planform somewhat like that shown schematically in gure 5(a). This geometry may be compared with that of a conventional supersonic ghter-type design with a more concentrated lift distribution ( g. 5(b)) or with a conventional civil transport con guration 2 without highly distributed lift but with an exten-sively notched arrow wing ( g. 5(c)).For a relatively high ight altitude, the ambientpressure is so low that the nozzle ow is greatly un-derexpanded and consequently large plume e ectsare realized. For example, gure 6 shows the plumeshape computed for a high performance afterburn-ing engine with assumed ambient pressure equiva-lent to that at 60 000 ft M1 = 3:0; pj=p1 = 8:86 .Flow parameters for this engine were computed bythe method of reference 6. The pluming is signi -cant, and consequently, the plumes for the four en-gines would contribute a signi cant equivalent area.The actual e ect on the F -function and ground levelsignature is shown in gure 7 for a low-boom con-guration of the type shown in gure 5(a). Fig-ure 7(a) represents the F -function and signature witha cylindrical afterbody (no pluming) assumed, andgure 7(b) shows the corresponding results with theplume of gure 6. The plume has a dominant e ecton the sonic boom signature for this case. The com-pression associated with the plume causes a shock ofsuch magnitude that it moves forward and overridesthe nose shock. The ground level overpressure is in-creased from a level slightly under 1 psf ( g. 7(a)) toabout 2.2 psf ( g. 7(b)). It would not be feasible toattempt to tailor the con guration to allow for theadditional area associated with this plume, since thisarea is so large.However, the problem is mitigated at lower alti-tudes where the ambient pressure is higher and theplume is consequently smaller. Figure 8 shows theplume shape (with the same engine) for ight at55 000 ft and M1 = 2:1. This plume is considerablysmaller than that shown in gure 6, but it still hasa signi cant e ect on the F -function and signature.Figure 9(a) gives these results for the con gurationwith no plume, and gure 9(b) gives the correspond-ing results with the plume e ect included. In thiscase the plume compression signi cantly alters theF -function and the signature, but the e ect is muchsmaller than in the previous case.A cursory e ort was made to reduce the plumee ect further by staggering the engine nacelles a dis-tance of 10 ft and making modest changes (about20-percent local variation) in the fuselage area dis-tribution. The result, shown in gure 10, is somereduction of the plume e ect. The maximum over-pressure is reduced from 1.8 to 1.6 psf. Further re-duction could probably be realized through a moresystematic design approach (ref. 7), which might in-corporate techniques such as those of references 8and 9.Reducing the ight altitude from 65 000 to55 000 ft is so e ective in reducing the plume e ectthat it would appear that, by extrapolation, a furtherreduction in cruise altitude, say to 45 000 ft, wouldrender the plume e ect negligible. However, suchan extrapolation cannot be made. The high perfor-mance afterburning engines are not appropriate forthe lower altitude ight, which would be associatedwith a lower Mach number.Consequently, a sample case was computed forM = 1:6 ight at M1 = 1:6 and 45 000 ft with con-ventional turbo engines having an internal nozzle ex-pansion of about 58 percent. The results are shownin gures 11 and 12. Figure 11 shows the plumeshape. Figure 12(a) shows the F -function and signa-ture with the assumption of a cylindrical plume, andgure 12(b) gives the corresponding results with theplume shape of gure 11. Again, a slight reductionin the plume e ect can be realized by staggering theengines and tailoring the fuselage ( g. 13). This tai-loring is substantial, about a 40-percent variation incross-sectional area, as is shown in gure 14.The results given in gures 9 and 11 may be com-pared with some calculations shown in gure 20 ofreference 1. Those calculations demonstrate that, forcon gurations like the ones depicted in gures 5(b)and 5(c), relatively small jet plumes actually have afavorable e ect on the sonic boom signature. Theexplanation for this di erence involves both the am-plitude of the aft expansion region of the F -functionand the location of the plume e ect relative to thisexpansion region. Low-boom con gurations have arelatively gradual, low amplitude expansion (as illus-trated in gs. 7(a), 9(a), and 12(a)), which resultsin a ground level amplitude of about 1.0 to 1.5 psf.When the compressive e ect of the plume is imposedon the expanding ow, it is only partially cancelledby the expansion and leaves a secondary compres-sion. On the other hand, a conventional con gura-tion design, like that of gure 5(b) or (c), has a moresudden and larger amplitude expansion region in theF -function; this leads to a ground level amplitude onthe order of 2.5 psf (ref. 1). In this case, the plumecompression can be completely submersed in thisexpansion.Figure 5(b) also illustrates another means thatcan be e ective in controlling the location of theplume. Engine nacelles mounted on the fuselage canbe situated in the optimum longitudinal position.It should be emphasized that the con gurations ofgures 5(b) and (c) are not low-boom designs. Evenwith some reduction of the tail wave strength, theconcentrated lift distributions associated with such3 designs generally yield unacceptably high compres-sive overpressures.Concluding RemarksAn Euler shocktting marching code yielded rel-atively good agreement with semiempirically deter-mined plume shapes, although the agreement de-creased somewhat with increasing nozzle expansionangle. Some evidence indicates that the discrepancymay be attributable to nonisentropic internal noz-zle ow which is not accounted for in initializing theplume calculation.Some calculations were carried out to obtain ageneral assessment of the nature and orders of mag-nitudes of the plume e ects on the sonic boomsignature. The calculations were for a low-boomcon guration with a high performance engine. Theresults indicated that, for ight at altitudes above60 000 ft, the plume e ects were dominant; but for al-titudes below 55 000 ft, they were signi cant but notdominant.Some factors associated with incorporating theplume shape into the con guration design were alsodiscussed.NASA Langley Research CenterHampton, VA 23665-5225January 24, 1992References1. Putnam, Lawrence E.; and Capone, Francis J.: Experi-mental Determination of Equivalent Solid Bodies To Rep-resent Jets Exhausting Into a Mach 2.20 External Stream.NASA TN D-5553, 1969.2. Salas, Manuel D.: The Numerical Calculation of InviscidPlume Flow Fields. AIAA Paper No. 74-523, June 1974.3. Englert, Gerald W.: Operational Method of DeterminingInitial Contour of and Pressure Field About a SupersonicJet. NASA TN D-279, 1960.4. Middleton, W. D.; Lundry, J. L.; and Coleman, R. G.:A System for Aerodynamic Design and Analysis of Super-sonic Aircraft. Part 2|User's Manual. NASA CR-3352,1980.5. Hayes, Wallace D.; Haefeli, Rudolph C.; and Kulsrud,H. E.: Sonic Boom Propagation in a Strati ed Atmo-sphere, With Computer Program. NASA CR-1299, 1969.6. Geiselhart, Karl A.; Caddy, Michael J.; and Morris,Shelby J., Jr.: Computer Program for Estimating Per-formance of Air-Breathing Aircraft Engines. NASA TM-4254, 1991.7. Darden, Christine M.: Sonic-Boom Minimization WithNose-Bluntness Relaxation. NASA TP-1348, 1979.8. Barger, Raymond L.; and Adams, Mary S.: Fuselage De-sign for a Speci ed Mach-Sliced Area Distribution. NASATP-2975, 1990.9. Mack, Robert J.; and Needleman, Kathy E.: A Semiem-pirical Method for Obtaining Fuselage Normal Areas FromFuselage Mach Sliced Areas. NASA TM-4228, 1991.4 Figure 1. Nozzle geometry.Figure 2. Semiempirical and computed plume shapes for nozzle with = 11:50 . M1 = 2:2; Mj = 2:523.Figure 3. Semiempirical and computed plume shapes for nozzle with = 9:06 . M1 = 2:2; Mj = 2:267.Figure 4. Semiempirical and computed plume shapes for nozzle with = 7:28 . M1 = 2:2; Mj = 2:272.(a) Low-boom design.(b) Fighter con guration with nacelles mounted from fuselage.(c) Commercial transport with notched wings.Figure 5. Three types of supersonic con gurations.Figure 6. Computed plume shape for ight at M1 = 3:0 and altitude of 60 000 ft.(a) Cylindrical jet.Figure 7. F -functions and ground level signatures for low-boom con guration with cylindrical jet and computedplume of gure 6 at M1 = 3:0 and altitude of 60 000 ft.(b) Computed plume of gure 6.Figure 7. Concluded.Figure 8. Computed plume shape for ight at M1 = 2:1 and altitude of 55 000 ft.(a) Cylindrical jet.Figure 9. F -functions and ground level signatures for low-boom con guration with cylindrical jet and computedplume of gure 6 at M1 = 2:1 and altitude of 55 000 ft.(b) Computed plume of gure 6.Figure 9. Concluded.Figure 10. F -function and ground level signature for low-boom con guration with the computed plume ofgure 6 at M1 = 2:1 and altitude of 55 000 ft with modi ed fuselage and staggered engines.Figure 11. Computed plume shape for ight at M1 = 1:6 and altitude of 45000 ft with turbo engine.(a) Cylindrical jet.Figure 12. F -functions and ground level signatures for low-boom con guration with cylindrical plume andcomputed plume of gure 11 at M1 = 1:6 and altitude of 45 000 ft with turbo engine.(b) Computed plume of gure 11.Figure 12. Concluded.1 Figure 13. F -function and signature for con guration with computed plume of gure 11 at M1 = 1:6 andaltitude of 45 000 ft with fuselage modi ed and engines staggered.Figure 14. Fuselage modi cation required for results of gure 13.2