Some Effects of Secondary Injection of Gases into a Supersonic Flow Citation Burden, Harvey Worth (1964) Some Effects of Secondary Injection of Gases into a Supersonic Flow. Engineer's thesis, California Institute of Technology. doi:10.7907/DRZK-W405. https://resolver.caltech.edu/CaltechETD:etd-09102002-141125 Abstract An experimental investigation was conducted in order to determine some of the effects of injection of a secondary stream of gas into a supersonic primary airstream. The flow fields behind an orifice producing essential two-dimensional flow and behind that producing full three-dimensional flow were studied. The resulting shock patterns, wall static pressure profiles, and flow field characteristics are described,and use is made of a theoretical injectant penetration height to non-dimensionalize the results as much as possible. It has been possible to draw some conclusions concerning the nature of the flow field and pressure field disturbances caused by secondary injection. Item Type: Thesis (Engineer's thesis) Subject Keywords: (Aeronautical Engineering) Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Aeronautics Thesis Availability: Public (worldwide access) Research Advisor(s): Zukoski, Edward E. Group: GALCIT Thesis Committee: Unknown, Unknown Defense Date: 18 May 1964 Record Number: CaltechETD:etd-09102002-141125 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-09102002-141125 DOI: 10.7907/DRZK-W405 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 3422 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 11 Sep 2002 Last Modified: 18 Jan 2024 23:09 Thesis Files Preview PDF (Burden_hw_1964.pdf) - Final Version See Usage Policy. 4MB Repository Staff Only: item control page

SOME EFFECTS OF SECONDARY INJECTION OF GASES INTO A SUPERSONIC FLOW Thesis by Harvey W. Burden Lieutenant, U. S. Navy In Partial Fulfillment of the Requirements For the Degree of Aeronautical Engineer California Institute of Technology Pasadena, California 1964 (Submitted May 18, 1964) -ii- ACKNOWLEDGMENTS The author wishes to express his deepest appreciation to Dr. Edward E, Zukoski for his many valuable suggestions and his assist- ance in the conduct of the investigation and the preparation of the manuscript. Mr. Frank W. Spaid, who is completing his research in this same area for the degree of Doctor of Philosophy, provided many hours of fruitful discussion and helpful comments as well as providing experimental data essential to the conduct of the investiga- tion. In addition, a debt of gratitude is acknowledged Ms. Robert A. Duffy for ner typing of the final draft. Finally, to the author's wife, Myra, much is due for her patience, encouragement, and cheerfulness when they were sorely needed, ~\il- ABSTRACT An experimental investigation was conducted in order to de- termine some of the effects of injection of a secondary stream of gas into a supersonic primary airstream. The flow fields behind an ori- fice producing essential two-dimensional flow and behind that pro- ducing full three-dimensional flow were studiec. The resulting shock patterns, wall static pressure profiles, and flow field charac- teristics are described,and use is made of a theoretical injectant pensctration height to non-dimensionalize the results as much as pos- sible. It has been possible to Graw some conclusions concerning the nature of the flow field and pressure field disturbances caused by secondary injection. Part -iv- TABLE OF CONTENTS Title Acknowledgments Abstract Table of Contents List of Symbols INTRODUCTION DESCRIP TION OF EXPERIMENTAL EQUIPMENT Test Scctioen Conditions TWO-DIMENSIONAL EXPERIMENTAL RESULTS Description of Flow Field Discussion of Results Summary THREE-DIMENSIONAL INJECTION EXPERIMENTAL RESULTS Description of Flow Field Bourdary Layer Separation Shock Shape Flow Patterns in Boundary Layer Static Pressures Total Pressure and Velocity Profiles Summary CONCLUDING REMARKS References Figures Appendix A ii ili iv Il 17 18 18 we Vi om LIST OF SYMBOLS a sonic velocity d injector orifice width or diameter g acceleration of gravity, gravitational constant h theoretical penetration height m mean molecular weight 1) pressure Vv velocity x axial distance ¥ lateral, or cross~stream, distance Z vertical distance, from injector plate C, specific heat at constant pressure Gy specific heat at constant volume K injectant concentration M Mach number R universal gas constant, for determination of sonic velocity R radial distance, for shock shapes T temperature 8 poundary layer depth Y ratio of specific hcats 8 angular measure Subscripts oo undisturbed upstream condition o total, or stagnation, condition 1 upstream of normal shock vu. ~vie downstream of normal shock injectant jet shock argon helium I, INTRODUCTION For a number of years, there has been a growing engineering interest in the effects of injecting a fluid into a superscnic stream. For many applications, the injectant fluid is also a gas whichis dif- ferent from the main flow. Practical applications of this procedure include thrust vector control of a rocket motor, attitude control of supersonic or hypersonic aircraft or of re-entry vehicles within the atmosphere, and fuel injection in a supersonic burner. Numerous investigators have studied wall pressure patterns ané shock profiles with a view to obtaining scaling laws for the ratio of resultant side force to primary axial thrust!*7>), In contrast with this macroscopic approach, Zukoski and Spaid, Broadwell, and oth- ers have obtained scale parameters which enable them to reduce or non-dimensionalize wall pressure patterns which result from various combinations of free-~stream Mach number, injection pressure ratio, (4-6) and injectant molecular weight Zukoski and Spaid measured concentration profiles rather extensively and gained some insight :n- to the mixing of the injectant with the free stream'°), Other than these concentration measurements and some very crude total-pres-— sure measurements by Charwat'”), no real attempt appears to have been made to study the flow field downstream of the injection port. Such an investigation could indicate quantitatively the extent and rapidity of mixing and the effects of injection upon the primary stream. If a stream of fluid, gaseous or liquid, be injected intoa -~2— supersonic gas stream in a directicn yeneraliy normal to the main flow, a shock wave system is produced. Attendant to this shock system is an interesting and useful structure of boundary-layer sep- aration and reattachment, wali pressure patterns, velocity, total pressure, and Mach number variations, and mixing of the injectant stream with the main stream. In general, the injectant acts as a tunt body protruding into the supersonic flow; however, it has been shown"? that injecting a fluid is more effective and feasible than using a solid ohject which is of the same genera? shape as the iajece tant plume's forward surface. In this investigation, both the two-dimensional and the three- dimensional pictures are considered, The two-dimensional effects are accomplished with a slit injector across the wind-turnel wall, while the three-dimensional effects are obtained by means of a cir~ cular orifice on the centerline of one wall, The two-dimensional system has possible application to fuel injection in a supersonic burner and attitude control devices for supersonic/hypersonic air- erait or re-entry vehicles. The threc-dimensional system also has application to attitude control and, more important currently, to thrust vector control of rocket motors, either licuid or solid, It is the purpose of the present study to provide as detailed a picture as possible of the fiow fielc in and around the injectant plume and further downstream. In the course of this work, use was made of the concentration measurements reported by Zukoski and Spaid, Pitot total pressures were measured within the flow field and, from these, velocity and totai-pressure profiles were obtained. These -3— then were compared with concentration prociles and other measured features of the flow. In addition, various flow visualization techniques were used to observe the flow pattern on the wall during injection. In this way, the direction of flow and re-attachment of the separated boundary layer could be observed, This report is divided into two main sections. The first de- scribes the two-dimensicnal effects of injection anc the experiment conducted tu determine them. The second is composed of lhe same type of material pertaining to the three-dimensional effects. A sum~ mary of pertinent features is given at the end of each section, anc a general flow~field description and summary is at the conclusion of the main body of text. The various sketches, photographs, and plots, and an appendix containing the general computational devices are included after the text. 4. i, DESCRIPTION OF EXPERIMENTAL EQUIPMENT For this investigation, use was made of the 2" x 2a" super sonic wind tunnel at the California Institute of Technology. Both two- dimensional and three-dimensional effects were obtained durirg in- jection of gaseous argon and helium through suitable orifices in the tunnel wall. Tunnel free-stream total pressures of one~half anc one atmosphere were used at a Mach number of 2,60+.02. At one at- mosphere, the Reynolds number ver inch was 2.4 X 16° and the boundary layer in the test section was turbulent. t one-half atmos-= phere, the Reynolds number per inch was 1.2 x 10° and a laminar boundary layer was observed, Experimental data consisted of test section conditions, Schlieren photographs, three-dimensional shock shapes during injec- tion, secondary Zlow pvatterns in the boundary layer, wall static- pressure measurements, pitot total pressures in and near the injec- sant plume, and injectant total pressure. Wall static pressures and pitot total pressures were meas~ ured with a mercury manometer bank. The injectant total pressure was measured either with a mercury manometer (low pressures) or a 1/4 percent accuracy Bourdon-Helix pressure gauge (high pres- sures), Secondary flow patterns in the boundary layer were obtained by spreading a mixture of instrument grease, cutting oil, and flake graphite on the tunnel wall. After a period of injection, the wall section was removed, and the flow pattern investigated. In the three-~dimansional configuration, shock shapes were c om obtainec from Schlieren photographs, Off-centerline shock profiles were found by positioning the total prescure probe in the shock itself. The shock position was determined by noting the dip in pitot total- pressure reading as the probe crossed the shock. The probe was then photographed and measurements taken.from the picturcs, For the two-cimensional work, either gaseous argon or gase- ous helium was injected through a slit orifice. This siit spanned the tunnel wall and was cut normal to the dircction of flow. It was C, 006 inches wide (0.015 cm) and extended to within 1/4 inch of each wall. In Figure 1, some of the details of construction are shown. The in- jectant gas was fed into the plenum by two 1/4-inch tubcs which, in turn, were joined by a "Y" connection +o the 1/4-inch supply line. A third 1/4einch tube was used as a pressure tap in order to record the tolal pressure in the plenum. A verforated baffle was added in order to disperse any directed motion of the gas as it issued from the two supply tubes, so that a uniform flow couid be achieved all along the slit. A typical wall static-pressure tap is also shown} there were a number of these along the centerline of the plate. In addition, there were several taps on off-centerline planes to check the two-dimensionality of the flow. The plate proper was of brass, and the 1/4-inch tubes were constructed of copper; the static pres- sure taps were stainless steel tubes of 0.013-inch (0. 033 cm) inside diameter. Three-dimensional effects were obtained by injecting gaseous argon through a 0, 047-inch (0.119 cm) circular hole on the center- line of one wall. As shown in Figure 2, the injection port was sup- -6- plied with gas directly from the 0. 083-inch injector tube. This tube was of stainless steel and, in turn, was supplied from the 1/4-inch copper supply line. The plate itself again was of brass, while the pressure tap tines were stairless steel. Several typical static pressure taps are shown, There were 65 static pressure taps ar- ranged in various patterns on the plate in order to describe the pressure field as completely as possible. In the two=dimensional case, wail static pressures and pitot total pressures were measured in the vertical centerline plane of the test section. Several off~centarline wall staticepressure profiles were taken by Spaia!), and it was verified that the flow was indeed two dimensional away from the side-wail boundary layers. For the three-dimensional jet, pressures were measured both in this centerline plane and in planes off the centerline. This was done by utilizing three~pronged rake probes with spacings of 1/8 inch amd, for the shock shape determinations, 1/2 inch. Test Section Conditions The general characteristics and operating techniques of the GALCIT supersonic wind tunnel are described in detail by Puckett!®, With the nozzle blocks installed for this experiment and the two in- jector plates used, Mach numbers of 2.58 to 2,61 were observed. The variation was due to slight differences in the plates and re- alignment incident to changing them. Figure 3 is a plot of normalized test-section Mach numbers for the turbulent and laminar boundary layers. It was found (Figure 4) that the boundary layer height along =To the test section length was constant at about 0.5 cm for both turbulent anc laminar boundary layers. Within the main flow, the maximum variation of Mach number was less than 3 per cent, and all such vari-~ ations from the mean occurred quite gradualiy. There were two very weak plane obliaue shocks upstream of the test section caused by the joints between the nozzle blocks and the test section blocks. The variation of total head across them was about 1 - 2 per cent and, as can be seen from the angles, they are almost Mach waves. Thus, they were much weaker than the shocks caused by injection, anc introduced an insignificant error. They can be seer. in Figures 5, 6, and 7, and their position is also inci- cated on the appropriate plots of three-dimensional data. During in- jection, the strong bow shock almost completely overpowers this weak wave. The parameter h, which is used throughout to non-dimen- sionalize distance, is a theoretical injectant penetration height. Its derivation is predicated upon the following model .of the flow. The injectant is assumed to enter the flow as a sonic jet flowing normal to the main stream. This jetis allowed to expand isentropically to the mainstream static pressure within a two-dimensional or three- Cimensional space, as the case may be, from which free-stream air is assumed to be excluded. In the two-dimensional case, the space is bounded upstream by a quarter of a circular cylinder, the axis of which lies along the injection slit, and downstream by a plane tangent to the cylincer directly over the slit and parallel to the tunnei wall in which the slit is lecated, The radius of the circular cyitinderis h. a8u In the three-dimensional case, the space is bounded upstrearm by a quarter sphere whose origin is at the injection port, and downstream by 2 circular cylinder whose axis is along the centerline of the wall in which is situated the injection orifice and which is tangent to the quarter sphere over and cross-stream of the orifice. The radius of the sphere and cylinderis h. In cach case, momentum and force balances are made in determining h. The details of derivation are given by Spaic! 9) tn the Schlieren pictures of the three-dimension- al injection (Figures 6 and 7}, the calculated penetration height of about 0.5 cm corresponds quite well with what appears to be the in- jectant plume's height, In the determinztion of the penetration height for the three- dimensional case, a correction to the observed injectant pressure ratio was required. The pressure drop between the irjectant supply line and the injection port due to fluid friction losses is the reason, In this case, it amounted to a 3 per cent reduction in injection total pressure below the supply line pressure. ~16— order of a degree or two) that the shock is too weak to be observed readily. Whether laminar or turbulent separation occurs, the injec- tant protrudes into the separaiec boundary luyer anc appears as a blurt object to the main stream. Since the angle between the free stream and the forward face of the injectant surface approaches 90°, a detached normal shock is formed in front of the injectant few. The injectant enters the flow normal to the main stream direction and im~ mediately starts expanding in the upstream and downstream directions, It is bent downstream by the mzin flow and assumes the shape indi- - catec in Figures 8 and 9. _ The main flow, in going through this shock system, is deflect- ed upward, away from the slit. Because of the rounded top surface of the injectant plume and the source itself, the area just behind the bow shock behaves approximately as a conical flow regime. The main flow which was initially sent upward and decelerated Dy the bow shock is gradually turned downward and accelerated somewhat. When the low reaches the wall Cownstream of the slit, a second, or recom-~ pression, shock results. This is caused sy the filow's having been deflected toward the wali in the conical flow area behind the bow shock. Just downstream of this second shock, the boundary layer ap- parently re-attaches. As would be expected, the recompressicn shock apparently is very diffuse in the region near the wall and does rot have a well-cefined point of attachment on the walt. A slip line is present in the turbulent boundary layer case (Figure 8), This line originates at the intersection of the bow shock and the separation shock, It is caused by the difference in total head -9- Itt, TWO-DIMENSIONAL EXPERIMENTAL RESULTS Description of Flow Field When the injectant is introduced into the main stream through a slit in the wall which is perpendicular to the rain stream, the over-— all effect is essentially two dimensional, since end effects are negli- gible. The entire flow, including the boundary layer, is recuirec to go over the injectant surface where it issues from the slit. The pro- trusion of this injectant surface into the main stream establishes an adverse pressure gradient in the wall boundary layer which is felt upstream since subsonic flow exists near the wali. This causes sep- aration of the boundary layer forward of the slit. The distance up- stream and the nature of the separated profile depend upon whether the voundary layer is laininer or turbulent prior to separation. The dependence oi the flow field geometry on the state of the boundary layer is illustrated in Figures 5, 8, and 9. Figure 5is a Schlieren photograph taken when the free-~stream total pressure was one atmos~ phere and the bourndary layer was turbulent; Figure 8 is a sketch of the flow fielc. The laminar boundary layer separation, at one-hali atmosphere, was not readily observable on the Schlieren photographs; Figure 9 is a sketch of the flow field. The abrupt increase in boundary layer thickness at scparation looxs like a ramp to the remainder of the flow, and an oblique shock results, This, as mentioned above, is observed for the separation of the turbulert boundary layer, but not for the laminar; the angle formed at laminar boundary-layer separation is so smail (of tne ~LJ- between the two flow areas which procced through the bow shock; the flow above the intersection nas full free~stream total head, whereas the flow below the intersection nas had its total head diminished in passing through the separation shock, The slip line results where the two flows of different velocity must meet. Discussion of Results During injection of gaseous argon (and, in one case, gaseous helium) through the two-cimensicnal orifice, wall static pressures and pitot total pressures at various axial and vertical (total pressure) stations were recorded, Spaia!?) has made pressure measurements on off-centerline planes and found that the pressure pattern is indeed two-dimensional in nature, A series of wall static pressures were obtained at each injec- tion condition studied, All of the profiles were quite similar to that shown in Pigure 10, with the cxception of the upstreain portion of the laminar boundary layer case. In the turbulent case illustrated, the the rise in static pressure at x/h = ~10 is due to the separation of the boundary layer and the resulting separation shock. The continued increase in pressure is due to the interaction of the bow shock and the boundary layer. The bottom of the bow shock intersecis the boundary layer at about x/h=-3. Inthe laminar case, the initial increase in pressure occurs much farther upstream, about x/h = ~30, and is considerably smaller in magnitude. There is a gentle rise until the bow shock ~ boundary layer intersection is reachec, and then the characteristic large rise in pressure is seen. The ~1l2~ downstream profiles with a turbulent or a laminar boundary layer are almost identical. The pressure beliind the injector has a minimum value of about 0.3 Poo? and at x/h of about 3 starts to rise to the mainstream value, Poo * The recompression zone covers the region3 £x/h£7. This Cownustream repion described here is quite similar to that found downstream of a rearwaré facing step at Mach number 2.6. That is, the pressure minimum is between 1/4 and 1/3 of Poo and the recom~« pression zone geometry is similar. ne total pressure data were obtained throughout the flow field cownstream of the recompression zone. Since the flow is supersonic, the pitot total pressures muc* be corrected to take into account losses which cccur at the bow shock which exists in front of the probe inlet. The Rayleigh formula (equation 6-3 of reference 10) was employed, Because concentration data had been cbtained by Spaial®, account could be taken of the change in ratio of specific heats due tc varying concentrations of injectant. It was assumed that the static pressure was constant verticaily up to the recompression shock (Figures 5, &, and 9), and equal to that measured along the wall (Figure 10) at the appropriate position. As can be seen from Figure 10, the most for- ward station at which this assumption could be made is about x/h = 6, The stations investigated here correspond to those for which concentration prefiles were available frorn Spaial?), For some of the data (Figure 11), account was taken of the change of static pressure across the recompression shock and, since conical flow seems to exist betweer the shocks, a linear variation of static pressure be- ~13- tween them was assumed, The static pressure behind the bow shock was found from known free-stream conditions and the measurec shock angle. The Mach number and flow direction were not known in front of the recompression shock, but they were known behind it from the Rayleigh supersonic pitot formula solution and the wall boundary condition. By an iterative process involving matching the recompres- sion shock angle from the wall and Mach number just downstream of the shock with vossible Mach number and flow direction combinations just upstrearn of the shock (figures 2-1 and 2~7 of reference 11), the upstream Mach number was found. Thus, the static pressure jump across the shock could be calculated giving the static pressure at the hattam of the canical flaw regime. The flow direction just before the recompressicn shock was found to be 32 + 4° into the wall, This cor- rection was not made in most of the data (Figures 12, 13, 14, and 15), so the computed results above the indicated position of the recom- pression shock could be in error vy as much as 10 percent, The in- jectant concentration, however, is usually close to zero in this area, so the error does not materially affect the results of this investiga- tion. With the static pressure thus determined in the area of inter- eat, the Rayleigh supersonic pitot formula was applied graphically, taking into account the injectant concentration. From the Mach num- ber and the ratio of specific heats, the ratio of total to static temper- ature wes calculated. The total temperature was assumed to be 20 om + constant at room temperature, 530 R. The local speed of sound for the appropriate injectant concentration was calculated and tnen the =~]4. iccal velocity found. In addition, the ratio of total pressure to free~ stream total pressure was calculated. The specific formulae, tables, and curves used are shown in Appendix A, The data treated in this manner are presented in Figures 11 to 15 fer a2 range ol test conditions, Plots of total pressure, concen- tration, and velocity are presented as a function of distance from ihe wall for stations 6, 67, 14,7; and 30.8 h downstream of the injector. For Figure 11, the flow field was measured in considerable detail, This then gives a good basis from which <o study the effects of varying injection pressure ratio (Figures 12 and 13), boundary lay- er condition (Figure 14), and injectant molecular weight (Figure 15) as well as the characteristics of the flow itself. From the data re- lated to Figure 11, a mass continuity check on the argon at the three stations was performec. The foremost and aftmost were within 1.2 per cent, while tae center station was 15.1 pez cent higher than their mean, “his is considered to be a good check of the calculations in spite of the difference at the center station. Mixing of the argon with the air is seer to occur smoothly and fairly quickly. The velocity increases rapidly to mean free-stream “magnitude,and by the aftmost station the well-established boundary layer profile is present. The boundary laye~ thickness here is the same as the free stream value, about 0.6 cm. The total pressure sucfers somewhat in passing through the bow shock and even more through the recompression shack. Ir recovers to almost free stream value at x/h = 30, 8; the deficit is that experienced in going through both shocks in this case. The very low total pressure near the wall ~15— is due to a combination of being in the boundary layer and the larger amounts o= injectant present. Since the argon initially entered the tunnel normal to the strearn, it had no momentum axially, and any it gained was cue mainly to mixing with the free stream. The over- shoot of total pressure ratio at x/h = 6.67 at the higher values of z/h indicates that the assumption of conical flow between the bow and re- compression shocks was not completely justified that close to the slit. Further aft it appears satisfactory. By comparing Figures 12 and 13 with Figure 11, the effects of varying injection pressure ratio, and thus the penetration height, can be deduced. As was noted by Spaia'??, the relative effectiveness of injection appears to decrease as the injectant penetration height an- proaches the boundary layer depth. Thatis, as h/& increases (6, the boundary layer depth, being constant), che injectant concentration penetrates to a decreasing z/h height. This can be seen by compar- ing Figure 11 with Figure 12, where the penetration height, a, is decreased, and with Figure 13, where it is increased. The z/h height of, say, the 30 per cent concentration point steadily decreases as h increases. Itis to be noted, however, that the concentration at the wall remains constant. This clearly indicates that h is not the perfect scaling pavamater for these purposes; rather, it should increase alittle less rapidly with injection pressure ratio. Veloci- ties and total pressures follow the same general pattern as the con- centration profiles with the exccption that their valucs above the indi- cated position of the recompression shock are not accurate, This is so, since the jump in static pressure across the shock was not ac- -l6- counted for in computing the velocities and pressures in Figures 12, 13, 14, and 15, whe cependence of injection pattern on the ratio A/é is reasonable. For h<< 6, tke forces acting to turn the injectant flow are generated by the impact of relatively low encrgy flow of bourdary layer gases. However, as h approaches 5, the energy of the vri- mary stream material turning the injectant increases rapidly, and it is to be expected that h will ther. increese more slowly. The effect of having a laminar boundary layer instead of a turbulent one can be seen by a comparison of Figures 11 and 14, There is very little cifference betweer. the respective profiles. The velocities are almost exactly alike. The mixing, indicated by con- centration and total pressure, appear to proceed more at higher lev- els into the flow, but the differences are notlarge. The increase in penctration of argon into the main stream is probably Cue to the weakness of the shock off the boundary layer separation streamline. This means that all the flow entering the bow shock is essentially at free-stream total pressure, so that there is a uniform crop with nc slip line. The less energetic air, relative to that existing in the ture bulent case, close to vhe wall alows the injectant to penctrate further into the stream. In addition, the thickness of the separatec laminar bounéary layer at the injection point is greater than that of the care respending turbulent layer, This effect shoulc also produce an in- rease in the penetratioa height. Comparison of Figures 12 and 15 illustrates the effect of dif- Zerent injectant molecular weights. Here, there is little or no effect ~l7~ upon the velocities or total pressures, but the concentration profiles are markedly different. This is explained by noting that a consider~ ably lower mass flow of helium than argon was required to produce similar physical effects at the same h. Note that the physical flow, velocity, and total pressure, are nearly identical, as are the penetra- tion neights, h. The calculation of h involves the reciprocal of molecular weight, and this verifies the derivation in this respect. Summery The salient features of the effects of this two-dimensional case can be summarized prietly as follows: li. “he entire flow upstream of the injector is required to go over the injectant plume mich as it would over a solid, thin, rectangu- lar plate standing normal to the wall. 2, The wall static pressures produced are quite similar to those produced by such an obstruction, especially downstream. 3, Mixing and diffusion of the injectant with the main stream air proceed smoothly and fairly rapidly. 4. As the ratio of penetration height to boundary layer thick- ness {h/6) increases, the relative effectiveness of injection in pro» ducing useful pressure forces is reduced. 5, The bow shock shape is rather insensitive to the state of the boundary layer upstream of the injection slit. The pressure pat- terns downstream and the recompression shock are almost entirely independent of it. ~15. IV. THREE-DIM=NSIONAL INIFECTION EXPERIMENTAL RESULTS Description of Flow Field The three-dimensional injection effects were investigated es- sentially for one injection ratio and one Mach number. Zukoski and Spaial®) developed the scale parameter, or calculated penetration height, h, which was described previously. They found that h isa very good scaling parameter. For this reason, a complete definition of the flow field in terms of normalized quantities and distances made non-dimensicnal by h for a few test conditions should give a good “description of all similar flow fields. The conditions chosen for in« tensive study here are M-= 2,61 and P, /?, = 7.77. j co To obtain the three-dimensional effects of injection, a point- - dike source, in the form of a circuler orifice, is used. Since there is only a partial blockage of the main stream flow end boundary layer here, the resulting flow field is able to develop in all directions above the wail. The injectant, instead of blocking the boundary layer entire- ly, passes through it and expands in a plume whick remains primarily off the wall and may be above the boundary layey. The surface which it forms in passing through the boundary layer is essentially an in- verted frustrum of a cone, the small end resting on and coinciding with the injection port. The resulting plume is then bent back to a flow direction parallel te the piate by the interaction with the main flow. General pictures or sketches of the flow are shown in Figures 6, 7, 16, and 17. ~19~ The most prominent features of the flow shown here are. the bow shock waves. Near the intersection of this shock and the wall is the complex separation region, Boundery Layer Separation Since the injectant passes through, rather than biocks, the soundary layer, the resulting adverse pressure gradient in the bound- ary layer is a local phenomencu restricted to 4 region just upstream of the injection port. Both turbulent and laminar boundary layer sep- aration are observec, The separated regions can be seen quite easily in Figures 6, 7, 16, and 17, where the difference between separation _of the turbulent and laminar boundary layers is also evident. Whe greater upstream s¢paration distance in the laminar case is the re~- sult of the laminar boundary layer's lower resistance to separation when under the influence of an adverse pressure gradient. The great difference in separation angies is also shown here; the laminar angle is always less than 5°, whereas,in the turbulent case, the angle is as large as 30°. In the turbulent boundary layer case, an oblique shock is set up by tne separation of the boundary layer; in the laminar case, this oblique shock is present, Dut is toc weak to be observed, When the injectant plume reaches the main stream and ex- pands, the detached bow shock is formed which becomes weaker as ‘the distance from the injection port is increased. Note again that the first two oblique shocks which look like separation shocks are causec by slight imperfections in the wall. See page 7. = 20m Suvckh Sliape A three-dimensional picture of the shock shape was obtained in the following manner, At three different injection pressure ratios, and thus at three different values of h, the vertical end horizontal positions of the shock wore measured. This was done by noting the dip in pitot total pressure as a pitot probe passed the shock and then -méasuring the probe position from a photograph, These measure~ ments wers compared with the shock shape determined from a Schlie- ren photograph of the shock at the sams axial (x) station and on the Same photograph. Comparison of these measurements indicated that the shock surface is axisymmetric about a centerline whichis one h _from the wall. Figures 18a and 18b illustrate this. In these figures, (2. -~h) is the height of the shock, measured from the axis line which is one h of the wall, 2s measured from the Schlieren of the shock shape. R is the computed radial distance to the point at which the pitct probes met the shock measured from the same axial line one h of= the wall. Both distances are normalized »y h in these figures. Zhe correspondence is within + 4 per cent except for two points, which are apparently cue to auxiliary cross-flows at that tunnel condi- tion (laminar boundary layer) caused by boundary layer separation on the tunnel side wall, Shock shapes as measured above are also compared with those measured from the Schlieren photozraphs (indicated as reference) in Figure 19. The coordinate x! is the axial distance from the front of the bow shock insteac of the distance from the injection orifice used elsewhere in this report, The correspondence is seen to be excel- ~21 lent. The maximum deviations are due to the above mentioned flow anomalies. In these tests, the boundary layer is about 0.5 cm thick. It is felt that the correlation of the data shown in Figures 18 and 19, with the axis of symmetry located at h off the wall, indicates that h and not the boundary layer thickness is the proper distance for the location of the axis of syrameatry. Use of 6= 0,5 cm instead of h as the offset distance for the axis leads to systematic errors in the correlation of shock coordinates for the two higher values of h. Flow Patterns in Boundary Layer Further indication of the flow pattern was obtained by exami- nation of the secondary ‘low pattern in the boundary layer on the wall. A mixture of instrument grease, cutting oil, and flake graphite was spread on the injector plate,and injection pressure ratios of 7. 77 and and 30.2 were used to gain a physical picture of the flow patterns on the plate. Bigure 20 is a sketch of the flow pattern at Po. [Py = 7.77; and Figure 21 is a photograph of the plate itself after the ‘van w was made. In the sketch, Figure 20, typical streamlines are shown. The first heavy line is the locus of points at which non~axial flow first oc- curred; it is thought that this boundary represents the line along which boundary layer separation starts. The second heavy line is the locus of points along which a second abrupt change in flow direction occurs. It is judged to be the line at which the wall static pressure is a maxi- mum and hence is the intersection of the bow shock with the separated boundary layer. If the axisymmetric shock shape were drawn on this sketch, it would fall abcut one boundary-layer depth cutside this ~22— shock - boundary layer intersection curve. Thus, it falls in region l. It is felt that when the bow shock hits the top of the boundary layer, it creates a lambda structure, as seen from the side, with one leg bending toward the orifice and the other away. After the secondary flow passes through the bow shock and is turned, it exhibits a definite and strong flow toward the axis. Near the orifice and behind it,there is a back flow which was visible during the run by its effect upon the grease mixture. The grease could be seen being swept forward and piled up in a small mound directly be- hind the orifice at the vertex of the V-shaped region, region 3, This mound of grease was blown downstream by the collapsing flow when the tunnel was stopped, and hence does not appear in Figure 21. After crossing the V-shaped curve, bounding region 3, the flow pro- ceeds essentially axially. The angle formed at the vertex is about 15°, At the far aft end of the plate, the flow appears to be turned in- to the centerline by about 7°, The most obvious interpretation of the V-shaped boundary is that it is a wake shock caused by the impinge- ment of the two flows which have gone around the sides of the plume. However, near the body, or around x/h= 2, the flow picture is con- fused and the boundary may only be an indication oi the recirculation paitern, This same technique was used at a pressure ratio of 30. 2 and alaminar boundary layer. The same general pa-tern was seen except that boundary layer separation took vlace at or upstream of the front edge of the plate. Consequently, only one curve, the bow shock - houndary layer interaction, was seen around the orifice. The same = 236 V-shaped region was present downstream, and the flow pattern, from the lines in the grease, was qualitatively similar. The flow pattern in region 2 suggests that two vortices are shed from the obstacle formed by the injection process. Their pres- ence is indicated here by the strong inflow suggested by the stream- lines of secondary flow in this region. Tn addition ta this data, ex-~ amination of concentration data obtained by Zukoski and Spaia! 9) also indicate that vortices are attached to either side of the injectant plume, They arc apparcntly arranged in such a manner that air from the free stream is swept from outside the plume into and under it, These induced flows meet on the centerline and produce an upward motion there. As observed from upstream, the right vortex rotates clockwise, and the left vortex counterclockwise. The effects of this can be seen quite clearly in the concentration and total pressure pro files to be discussed later. Static Pressures Typical variation of static pressure with distance from the in- jector is shown in Figure 22, Upstream of the injector, the wail pressure rises rapidly due to separation and the bow shock; dowr- stream, the pressure is very low and gradually rises to the free stream value at about 4h. These data are for the centerline of the flow; off the centerline, static pressures rise more slowly and do not reach the free-stream value until about 8h. The low-pressure region downstream of the injector is ap- parently a region of flow separation, and the gradual rise in pressure suggests that the flow becomes reattached to the wall in this region, that is, 24xfhZz4. An attempt was made to find the re~attachment point of the flow by a direct meothed, <A sitot probe was advanced along the wall while the measured pitot total pressure was compared with corre- sponding wall static pressure from the static-pressure taps. When the two were just equal, re-attachment would be indicated. This was attempted at injection pressure ratios of 7.77, about 10, and about 15, The results were not very precise, but it appeared that re- attachment starts at about x/h=2. This corresponds fairly well with conclusions drawn from wall static pressure plots '° 9), The off- axis pressure data also suggest that the re-attachment region is con- - nected with the weak shock bounding region 3, Comparison of the secondary flow patterns. Figure 20, and static pressure measurements such as those shown in Figure 22 con» firm the general features of the flow discussed in connection with Figure 20. This agreement is shown in more detail by the pressure contour map of Figure 23, Here, the contours have been drawn through all the static pressure data which were available along cuts at y/h= 0, 1,2, 2,2, and at x/h= 1.2 and 2.3, Although consider- able imagination was used in certain areas, the map is in good quali- tative agreement with the observations. The map shows the pressure rise along the boundary of region 3 and suggests again that downstream of x/h = 2 this boundary is a shock wave which straightens out the vortex-like Slow which is converging on the centerline from either side of the injector. In addition, the adverse pressure gradient in the separated region, region 1, and the pressure peak along the boundary 2 Bm between regions 1 and 2 are clearly shown. The pressure peak at 3 £x/h £4 is apparently due to the interaction of the weak recom- pression shock, which bounds region 3, and the flow in the wake. Thus, this region is similar to the neck and wake shock found in super- sonic flow behind two-dimensional blunt bodies, held normal to the flow. Total Pressure and Velocity Profiles In general, the same technique was used to obtain the total pressure and velocity profiles as was used in the two-dimensional case. Again, the wall static-pressure data were used to determine the velocity. I: was found (Figure 23) that the static wall pressure ap- proached the undisturbed flow values by sflu= 4 along the centerline but not until x/h= 8 at off-axis stations since the outboard probe was at y/h=1.22. Thus, the station x/h = 8 was the most forward one at which the static pressure could be assumed constant vertically into the flow at all positions off axis. This pressure was required in order to ap-~ ply the Rayleigh supersonic pitot formula. Pitot static pressures were measured at various axial atati ans downstream of x/h=8 and vertically into the flow. A three~pronged rake probs was used so tha: centerline and two off-axis pressure readings were <aken at cach ' probe position. These pitot total pressures, the respective static pressures, and concentration profiles taken by Spaia!?) were applied to a graphical solution of the Rayleigh supersonic pitot formula. The ~Z20~ same technique was used here as was used in the two-dimensional cal- culations discussed earlier. Since concentration data were available at slightly different acsial positions from those used here (5.77 and 11. 81), interpolated ~-rofiles were used. The results of these calcu- lations are plotted in Figures 24, 25, 26, and 27, where the inter- polated concentration profiles are also shown. | The Mach numbers are shown only in Fignre 24, since they have the same relationship to V/V 5 in all cases. The undisturbed boundary-layer profile is plotted in Figure. 26 to illustrate the effects of injection. The indi- cated shock positions arc those of the shock from the crack between the nozzle block and the injector block, They are not the bow shock; in no case was it reached by the probe, The concentration profiles (Figures 24, 25, 26, and 27), when compared at centerline and off-centerlinas stations, ‘illustrate the ef- fect of the two vortices in lifting the plume in the center. This is il- lustrated even rm.ore clearly in Figure 28, discussed below. Itis_ seen that as the plume proceeds downstrearn it remains within about the same vertical boundary, diffusing upward only slightly. Its cross- stream extent remains fairly constant. Near the centerline, the vertical position of maximum concentration also increases somewhat, while cross~stream, it decreases, This again indicates the vortex motion. Consider Figure 24. At the centerline station, y/h=0, the total pressure, velocity, and Mach number near the wall have been reduced considerably below free-stream conditions because of the shock system and the obstruction of the injectant plume itself. The peaks near the wall and at the outer edge of the boundary layer are ~Z{~ due to the fresh, energetic air swept in by the vortex motion. Note that the boundary layer height here is only about one~half of the un- disturbed value. Above the boundary layer, the total head decreases to a mini- mum and then starts increasing toward near free~stream values. The decrease and very low value of total head at the minimum are due to several factors. First, if the free stream had suffered a simvle normal or near-normal shock, the total pressure would only have been decreased to about one-half of its former value. With the injectant entering ata total head ratio of abont 8, it would be expected that, if ‘anything, it would produce a slight increase upon the reduced (to about one-half) total pressure profile, even with the right-angle turn the in- jectant makes, Since the ratio of injectant mass flow to main ectream mass flow is of the order of several per cent, this increase, albeit a localized effect, would not be extremely great, but it would at least be an increase. However, the ivasurements show a decrease in this same area, The other factor which must be considered here, and which explains the drop in total head, is the aspiration effect of the in- jectant jet upon the boundary layer. Just as an eductor, the jet car- ries the adjacent boundary-layer air up with it. Since the boundary layer is separated downstream, a considerable backflow up to and up with the jet results. This flow was observed in the grease experi- ment. This very low energy boundary~layer air mixes with and de-~- grades the energy of the injectant. Instead of the simple, normal shock system upstream, there is a rather complex shock structure which tends ‘to decrease the total head even more. The sum effect is -28- the dip in total pressure which is observed. In addition, the back flow due to the aspiration effect tends to feed and maintain the vor- tices. Note that the minimum points of total pressure, velocity, and Mach number approximately coincide with the peak of the concentra- tion profile. This correspondence is a result of the above described mixing of the injectant jet and the separated boundary layer. Beyond the area of maximum injectant concentration, the to- tal head steadily increases toward the free-stream valuss. Above the plume, the flow has passed through the upper part of the bow shock. This upper part is seen to have a more acute angle than the lower portion and is not so strong; hence, the totel pressure ap- proaches more closely the upstream value. In the cross-stream direction, the effect of boundary layer entrainment is seen to persist practically undiminished out to y/h = 0.6, but the boundary layer itself has not been affected rearly so strongly by the jet. At y/h= 1.2, the flow has not been seriously affected by injection, and the extreme limit is probably about y/h = 165. The boundary layer at y/h = 1.2 is close to the undisturbed profile (Figure 26 emphasizes this); thus, it can be seen that the plume itself possesses somewhat of the axisymmetric shape, one h off the wall, which the bow shock was shown to have, with the excep- tion of the dip to the plate near the centerline plane (much as a stand or support). As the flow proceeds downstream (Figures 25, 26, and 27), the boundary layer is seen to redevelop until it reaches its former -29- level of about 0.5 cm near the x/h = 12 station. The effects of the jet's mixing are seen to diminish as the flow progresses; however, the containment of the injectant by the vortices along the centerline plane appears to persist rather strongly. At best, it can be said that there is a very complex flow field within and around the injectant plume. The complex nature of the flow field apparently does not sim- plify itself very rapidly; even at x/h = 12 or 15, itis far from uni- form except above the plume. Figure 28 is a comparison plot of argon concentration profiles and total pressure-ratio profiles at x/hw12. The concentration pro-~ files are from reference 9. In this plot, the very direct relationship between injectant concentration and total pressure within the plume is seen. Note that the area of minimum total head corresponds almost exactly with that of maximum argon concentration. Conversely, the total head increases toward free~stream values ou: ide the plume when concentrations approach zero. The effect of the two vortices in sweeping fresh, high total head air under and into the plume can be observed above the boundazy layer. The boundary layer is seen to have recovered its former, un- disturbed height of about one hj; at the upstream stations it was as low as one-half h. The contour of total head in the boundary layer is the normal one expected except on the centerline plane where the lift- ing effects of the two impinging vortex flows is evident. The low total head near z/h=2 is a combination of the low-energy boundary-layer air which is swept up and contained by the vortices and the injectant itself, which lost a considerable amount of its energy in being turned ~30- so abruptly through a right angle. Note that the disturbed region is roughly circular in cross section, with a center at about 1.7h and a diameter of about 2.6 h. At x/h of about 1.6, concentration data (Spaid!°?) show that the diameter is about 2h and the center is about h above the wall, Hence, it is evident that the spreading rate of the disturbed region is very slow. At this axial station (x/h a 12), the axisymmetric shock has a radius of 7.94 h with the origin at zf/fh=1 from the wall. The areas of significant injectant concentration and reduction of total pressure are well within the shock envelope. In addition.to the measurements described above, pitot total pressures were measured ai three axial positions between the orifice and the x/h= & station. Since, in this areca, there are quite large static-pressure gradients both in the axial and “he cross~strearn di- rections, the assumption of constant static pressure vertically could not be made. Nevertheless, these pitot total pressures follow the same general pattern as those which were reduced. This can be seen in Figure 29, where they are plotted along with the corresponding pitot total pressures from station x/a = 8, whichis the most forward station for which computations were made. Particularly at x/h=2., there is some doubt that the complete pivot total pressure was indi-~ cated, since it is knowa that the injectant issuing from the orifice causes widely varying flow directions within the plume near its origin, The fact that the pitot total pressures very close behind the in- jection orifice (0.9 cm) were of the same pattern as those discussed above is interesting, It indicates that the general oattern of the flow ~ 31 field is established very quickly after the injectant enters the stream. As pointed out previously, this pattern persists beyond the limits of measurement in these experiments, or x/h=15. The very low val- ues of pitot total pressures near the wall close to the orifice indicate the separated and reverse flow which was actually observed in the grease film experiment described carlier. The increase of pressure through the boundary layer and then the dip close to the vortices is of the same pattern as further down- stream. Particularly at x/h= 1.75, the rapid rise in total pressure as the probe moved through the injectant jet (which at this point is still quite energetic) is apparent. Summary The most important cffocts of threc-dimensional injection ac investigated herein can be summarized as follows. 1. The injectant plume penetrates through the boundary layer and into the main stream, essentially allowing the boundary layer to flow under and around it. 2. The bow shock standing upstream of and above the plume is axisyrametric in shape. Its axis is a straight line lying in the centerline plane and parallel to the tunnel wall at a height of one h. 3. Twovortices are shed from the top front area of the plume. These vortices are associated with considerable back flow along the wall behind the injection port. 4, The above-mentioned vortices and back flow aid in mixing of the injectant at the boundaries of the plume, but somewhat contain -32- it also. Mixing progresses less rapidly than in the two-dimensional CASA. 5. The parameter h appears to be a good scaling parameter for shock shapes as well as for wall pressure profiles, This is in spite of the complex nature of the shock systems and flow field. 6. The shock shapes and downstream pressure patterns, in- deed the total pressure paiterns, are quite insensitive to the state of the boundary layer upstream of the injection port. ~33— V. CONCLUDING REMARKS The flow field which is produced by secondary injection has the following general features. When the secondary flow is introduced, it appears to the main stream of gus as a blunt object. A shock wave is produced with the forward portion being anormal or near-normal detached shock and the upper portion an oblique shock of gradually decreasing strength, The main flow which passes through the upper part of the oblique shock is little affected by it; however, that part traversing the lower part is greatly decelerated and deflected. This decelerated flow is then required to make its way through and around the injectant plume; this results in rather rapid mixing and diffusion of the injectant gas into the main gas flow. The presence of the injectant jet and the interaction of the bow snock with the boundary layer cause an adverse pressure ‘gradient in the boundary layer, which, in turn, cause separation. In both types of boundary layers (turbulent or laminar), the separation forms an ef- fective ramp, anda shock results forward of the bow shock at the point of separation. Since the turbulent separation occurs later and forms alarger effective ramp angle, the separation shock in this case is considerably stronger and more readily observable than in the laminar case. The separated boundary layer re-attaches within a moderate distance downstream of the injection orifice, and it quickly re-establishes its former depth and profile. The state of the boundary layer upstream oz injection has little effect upon the flow field down- stream except in the severity of oblique separation shock which the rnain flow traverses prior to meeting the bow shock. =~3 46 in the case of an injectant line source across the direction of main flow, the flow field is essentially two-dimensional in nature. The entire flow, after passing through the bow shock, !s required to go over the injectant plume in one direction (the vertical) as well as partially through it, This ensures rather rapid mixing of the twa streams, especially at the top of the plume. The flow, in being lifted over the plume, is accelerated and deflected back toward the injector plate, tending to hold the plume close to it. An oblique recompres- sion shock results in turning the flow parallel with the plate once more, The separated boundary layer, which must also go over the plume, becomes mixed with tae main flow and injectant. There is a small region of back flow just downstream of the injection orifice fol- lowed by re-attachraent and growth of the boundary layer. As can be expected, the separated flow consists largely of injectant gas. Mixing near the plate, in and hear the boundary layer, is much slower than at the top of the plume. At lower injection »ressures, the injectant plume is enatirely within the boundary layer and looks somewhat like an aggravated sur- face roughness. As the pressure is increased and the plume heighi, or penetration height, approaches the boundary layer depth, the rela- tive effectiveness of injection in producing disturbances in the main f.ow per amount of injectant employed decreases. In the limit of very large pressure, the injectant acts merely as the exhaust of a converg- ent nozzle, and the jet reaction effect overrides the flow disturbance effects. 356 When the injectant enters the main stream throngh a peintelike orifice, the resulting flow field is three-dimensional in character. The jet forces its way through the boundary layer and almost entirely remains above ite It expands into a vlume which is semi-axisymmet- ric with the horizontal plane of symmetry, above which the plume re- mains, being above the boundary layer. Since, in this case, the plume has flaite dimensions in all directions, the flow can go around it as well as over and through. As a result, the mixing of the injec- tant gas with the main stream gas is not quite so rapid as previously. As the injectant goes through the boundary layer, it drags much of the low-energy air with it, particularly from the area behind the jet. This aspiration effect, along with the result of the flow's going around the plume on each side and the top, creates a pair of vortices much iike wing-tip vortices in reverse, These vortices tend to contain the plume on top, but help to mix main strearn gas into it from the sides and bottom. The effect is a somewhat mushroom-shaped cross sec- tion. Because the.boundary layar is able to go around and under the jet plurne in this case, the separated flow behind the jet is largely main flow gas. Re-attachment of the boundary layer occurs fairly close behind the jet and it quickly reaches its forces depth. Qe 10, ll. 12, “~36— REFERENCES Newton, J.F., Jv.and Soaid, F.W., "Interaction of Secondary Injectanits and Rocket Exhaust for Thrust Vector Control, "' fRS Journal, Volume 32, No. 8 (August 1952), pp. 1203-121, Walker, R.E., Stone, ALR., and Snandor, M., "Secondary Gas Injection in a Conical Rocket Nozzle,’ ALAA Journel, Vol. 1, No. 2 (February 1963), op. 334-338, Green, C.J. and McCulloigh, F.,Jr., "Liquid Injection Thrust Vector Control,'!' AIAA Journal, Vol. 1, No. 3 (March 1963), po. 573-578, Broadwell, J.E., "Analysis of the Fluid Mechanics of Second- ary Injection for Thrust Vactor Control, '' ATAA Journal, Vol- ume l, No. 5 (May 1963), pp. 1067-1075. Cubbison, R.W., Ardersoa, B.H.., and Ward, J.J.,. “Surface Pressure Distributions with 2 Sonic Jet Normal to Adjacent lat Surfaces at Mach 2.92 to 6.4,"' NASA TN D-580, Wash- ington, D.C. (1951). Zukoski, E.E. and fpaid, F.W., "Secondary Injection of Gases into a Supersonic Flow," Jat Propulsion Center, Cali- fornia Institute of Technology, Pasadena (1963), Charwat, A., paper to be published in the AIA Journal. Puckett, A.E,, "Final Report, Model Supersonic Wind Tunnel Project, ' GCALCIT Repoxt No. 43, California Institute of Tech- nology (1943). Spaid, F.W., “A Study of Secondary Injection of Gases inio a Supersonic Fiow,!' Ph.D. Thesis, California Institute of Tech nology, Pasadena (1964). , Liepmann, H.W. and Roshko, A., Elements of Gasdynamics, John Wiley and Sons, Inc., New York (1957). Dailey, C.L. and Wocd, L.C., Computation Curves for Com- pressible #luid Problems, John Wiley and tons, Inc., New York (1949). Ames Research Center Staff, "Equations, Tables, and Charts for Compressible Flow, '' NACA Report 1135, Washington, D.C. (1953), Parkhurst, R.C., and Holder, D.W., Wind~Tvrnel Techniques, Sir Isaac Pitman and Sons, Lid., London (1952), 14, on Heyser, A. and Maurer, F., "Experimental Investigation on Solid Spoilers and Jet Spoilers at Mach Numbers of 0.6 to 2.8," Astronautics Information Translation No. 227, Jet Proe pulsion Laboratory, Pasadena, California (Feb. 21, 1954). ~384 -,- TUBE FOR INJECTION E PRESSURE MEASUREMENT < TYP:CAL STATIC | TWO 0.25 in. TUBES FOR PRESSURE TAP | LC INJECTANT SUPPLY, | ‘ SPACED 0.476 in. APART N PERFORATED BAFFLE Locsin. | PLENUM CHAMBER SLOT DETAIL Fig. 1. Construction of Injector Used in Two-Dimensional Injection Experiment. -39- yuourltedx” uopyoaluyz TeuotsUeUlTq-selyy, UL pes ro.oefuy to uotyonijysuoy ¢°7 "STT ‘ VIVA NOILOSS IS3L 180d NOILOSPNI YALSANVIC “Yl 27000 ~~ OWN o) L NSN ene 7 pms aie Sete : ONIGNL G'O ‘UlIe0°O SVL SYASSIYd OLLVLS WOdAL SdNL YOLOSPNI £80°0 UNDISTURBED FLOW GALCIT WT Oy Mo & 2.6 : PAN Laminar 5.1L. | (cm) O6- = APo = Latm. = | Turbulen? 8.L. 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JAYM NOLWYTd3S ~A7~ rose ATepuno g yWoTAqiny, 2 Wp uopyooefuy Tewotsucutgq-omy, duranqg sernssorg D17e1g Trem TeotdAy, (rene meee ee meee ‘OL *R1T aon OZ Ol O Ol- a Oe fo? i f _ tr ny ie Oo” . f wf o / ‘BH UID 61 =Md woeslro=y glog) = dy 'd BH WO Ppp sPod g7g¢ =u “0'2 NOLLOAPN] G-2 NOOUY roan SHUNSSAMd OWLS T1IVM os Ol >roAeT Axcepunog ywoTnqiny TeIxy ool, ye seTtyord uolyesyusesouoy = AG we NS re 0) Ol co “9OLG°S = OW @ UWIM uosay fo uoT}Iefuy Teuotstounq OM], TOF suotyeyg pue ‘ouey ernssotg TejOL foyey AQTOOTOA "TT 7*8ta GyworseLs "4 2 pi= i 8 g v a 0 i : MOCHS 9d 4unaingunaL Vug Suwa ee. =" 3 Pog 194 oas/w zeg=™ Prn7NO ne) 9109 l= oa)! wo ssilrOs4 J zoo2t x l ] _t. "rakeT ATepunog qwornqsny, e& YI wodry Jo uoyoofuy Teuotsuswuiq- QO 9°% = AJ, LOF suotwyeig Ww Tet<y CoAT, 7@ soTorg woyeryuoouoD pue ‘oney sanssorg Teo, ‘omey AoA “ZTE Sta O71 8 iS) 7 a Oo Ol om gy v0 a Qo Ol 8 9g v 3 O i t i ~T T 1 “i i _ T T T i fe) or MIOHS i fp a4 JSoL 4, , CG fe) 1 é i — 4 a 4 = / A¢ f ‘ é = _ = ~ / AD Ul HOOHS ’ | | i Al 1 i a) de 4 ' J / 7 i ! i I — 4 = . cA ya & _ p H “yg LNaINgUNL 9 bHeree= Ud xy a _l . tf. a ! pels [ee] I «eyo 0, ‘ Sara a 4 Hwa s8ed=~ I Bw be= Yd 98S/u! 29g=™A & fy Mo Ig Mo fo ny A te) a 225280: ‘d/ d 4oL besv0s “d/d 4 - seseO= ‘d/"d wossso0=y dg 20¢=4 bO'ple GP'9 a) xX x x | cal i I | I | I i | 8 foe) "972 = UW sredery Arepunog JUo[Nqingy, & ypay Uoswy fo uoTJOOfUT TeuolsUSeWTG-OM], TOF uoOTTEIg Texy euO ye eTljorg wowerjymecoucyg pue “oyey oanssorg feroy, *orey APIOOTIAA 7ST est oy oe 9 ye a 0) \ =5O0— Om, = ae L S = ‘Va LNZINguNL = —-|9 Vy =v a 5H wo 2E pL 00% OrnAsA 20 , ‘oas/ Ui 29g a wagleZ’O =U "5. fo | oolre a7 '0d 90°61 = a de co “9°2 = IW oO 8 9g 2 oo 8 98 ¥ Fz 0 T T t ! ‘ : 4 Ff i a a / “Va UVNINGT b Yig U 1+ oF bywoteze=°% Pogda 7 99S/W Z8G=% 0% 700 na: @0, , {0 i JooL Iss9le G/U woesiosy 4 ane 4 ‘pie 60k == évlese 4 i I t t it . *toAery Arepunog reujureq ve yy uosay jo uotoefuy Teuotsteurtq-omy, LOF STONES TRixy OAL ye soTtford uolperprasouog pue ‘foley ormnssotg yeloy, *otpexy AytoopTo, O om, ¥ T “al LT Ss "7 = WOT}? co W “soXeryT Arepunog UejAqany, & YA WNIT] fo uoToofuy TevotsuseuitC-OMy, LOF 1G TexXy OMY, Fe soltyorg uotverjus0u0Dg pue folyey eansserg [eqoy, O Ol 80 90 vO 20 05 BW OWPL= @ GIZ8'O = | vOEy T WT 9 Ore eee AOVIBH “TE INF INEYNL BL WI 092 Poy HOOHS 99S/W 28G=% Hug fee) 1 °a/%d0 cy Or 7NO | iia Sarre ae 04 sf GIEBO= “d/'%d WW) SYGO'O=Y we 4H Ovi =X i ! { NS meek U) foryey ALPDOTSA GT “Sta ‘rekeT Arepunog wwe NqIny, B pwe woyjoofuy Secrest UTIL PTET AOTA Fo yo.eNg F 1 “oT °S1g SAAV TT AUWONNO NaWSeOL — J pena ne ween LPOG _ ak LLL, Ly / LLLLLLL 4 LLLLL he % ey CSC AN VAL LASLELSALLEL LL Le LL LL, Go DOG RD OG Oy Trey Gong ID GF OBA GO OC wun” NN MOOHS NOLWAYWdas 1 ioe) a po NOLWsvVdasS 7 CA sresery Axepunog reurwrey e pue uotjoefuy TEUOlsUSWIq eet, YA pTety MoT Jo jwo.oxy YEAWT AUVONNOG UVNIAVT ht Sta LLL LLLLLL LLLLI LA heh Sa = 5 eon Se EEE 3 WWE JLLLEDLLLL LLL LE. LNW Os PNI NOLLY aN das f° SOHS MOG oTIOGKSsOLIg swuinyty jue} ~doluy Uy UOTTSOg FO suoTpoUNT s¥ VOT MNd Ly Wioay stotsueulig 3OOYS PoeZTTeUlION FO Ciyey Fo OTA FeO OT9°z = MIN cUoOHoefuy TeuOTsuSUITC “sory, ULI yooyg Fo:AcjpourutAsizy Zutmoyg sodeyg yooyg fo suofsueutic "aT “stay poZziTeUlLoN Jo uostaedwieg Teouly l 5 4 9 GS Pv g. A | "gl “Sta Ons ~556 ie) LO1 V a 610 1 ISO O (usoyy rr | | I | | “oP ~ u Xx £ co “BLA "019°Z = OW =f (eoueteyey) SotnzoTg Woerepyog woxy pesznseoyp sedeyg yooyg oupprequeD Wy sped Yooyg ouppreywegrj7O Fo uostreduroy "6T Uy 3 | Ol g 9 y 2 | | _s Og, | | | ; DOTY TC Oks p= VY ] :*) i “d / et — WO GL Os 2 Slae— A ~ te) I hme wi boom f A @ - Og a ava iJ woegozu feels p= O SD ot O- SJONSYASAS a ~ pore 7 O- a “ TAI PLIQ 1! a (1 SaaWViIS OOOH - 1e8) is “3 ite pr P ¢ 02 hE ae OT a ee me eens ee a —e, Comet emt een, - ee ore cements men — Sow pene my See pa ™ Sone ee et eee may ae — NN ™ or ee / we rome eee mene eg ct ~~ , , a ~ ~ ~~ eS woe ~ ~ ~~ oe ~ ~ we Lf wa - a a. go ne ee cern eeneme Po “ a“ oA -58= f quat—nqiny & pue yp‘, = co Oa) { ‘“OI9°Z = ON *rofeT Arepunog Og ye uot oeful Teuotsuswig-se14y Buyang sanyxyy astern uodn mo,q raXey Arepunog jo j.eassq Fupmoys o3eTqG t01Defuy yo yYderZo0j,04g ‘Iz ‘Sta ~59- WALL STATIC PRESSURES ARGON 3-D INJECTION — Meo= 2.610 Pog= 73.69 cmHg. Poj “Pog = 7.77 h= 0.520 cm Po 3.63 cm Hg ! 2 0 2 4 6 8 10 h Fig. 22. Typical Wall Static Pressure During Three-Dimensional Injection with a Turbulent Boundary Layer. fee) c . OO . “OT9"S = OW PUR AL = Og) 9d 32 pereduioy CORPZTTENSTA MOTT toAerT ALepunog pue sanoquog ( d/d) ovey ornsserg oneig "oz °Styq ~60~ “O19 "Z = © Ww *rakery Arcepunog queTaqiny, © YH uoToefuy feuotsusuliq-seryy, 1OF g = Y/X 7e suOTIeIg TeLeTET veTYT, 32 SoTTjoig woljerjusouoy pue ‘foyjey rtoquiny yoryy ‘foley ernsserg Teloy ‘foney To TeA pz “Staz O'l 2 0 0 Ol bHuo6ge2 =” Y ry olg'z= W 99S/w SaG=™ tuo Z0zS'O=y O= a> G=y Vy , °Ww%dO ®y/Wwo On re) ‘O19 °*Z = ON ‘roker'y Arepunog jus[nqiny, & YIM uoTOOfuy TeuotsuswWIIg-serIU, tOF OL = y/x ye suotyeys Teroyery 9otyqy, ye soTtfoid uotyerjus0Uuey pue OTFEYU AYLIO TIA "GZ "St Ol e 9° v re O Ol 8 9° v Co Oo Ol 8 9 v Co T I T gr T i] = A ~o 1 4 4 2222, oq Vy — 490HS—— . 93S/WSBS=PA DAsrpA GS + “joo. 4 wd 202S'0=y ot y 4 y Zee lea 190 = ot —l. t A f I i i A ] L i j A a } N[s ‘O19 °e = co Ww ‘rake ATepunog juetnqiny, & YIM voy oOfuy TevotsusUTIq-90I4y, 1OF ZT = U/X Je suotzeyg Tetoyey] sory, ye seTtjord wowexrjusouo0y pie foey einssorg Telos, ‘omey Aytooje, srakeq-drepunog paqinisipuy *opyey AyrooTaA «°92 «STL SST 0 41 42 LLL = PO 7'od Vy—\ 4 eu BHU PEEL Fg Pd /Pd Q Z —— ¥90HS —— “Va Q3GYN.LSIGNN Paz b 29as/wWGaG= A PrsrnO Tk "WD 20250 =Y Zi: ¢ tc 4 o-d =4 22227 90-7 OFF { i \ 4 f it A 1 } 9 ‘019 °*Z = On ‘rokeq Arepunog jyuernqiny, & yyim uooefuy Teuofsusurtq-se1yy LOF GT = U/X Ye suotyejg TeroqzeyT ory, ye soplorg uopyearjusoueg puv oey AipooTeA "Lz *8tz Ol 8. 9g v of 0 oc 0 Ol 8 g v A f 4 4 pens ds Vy —_— 4 4 dessW seg =7A nt VEO) wo ZOz2S'0= Y SIs + a OF ~65— os aN 0 _| 1.0 0.5 0 0.5 1.0 Fig. 28. Comparison of Total Pressure Ratio and Concentration Contours at x/hx 12, M_ 2.6, Pp «74cm Hg, Po [Po = 7.77, and h= w. 52 cm. co . j =o 5 roe) “0OT9 “2 = OW (Hj wo)! on srokeryT Axepunog yuoTNqany, & YIM uotpoefuy Teuolsueuliq~oeacyy, sUlING suotjeig TeIxXy SNOLIPA je Soinssatg Teo] JOU, Ov Of ol ae j Pa Ap? | _ oo a O, vA OO, = ves Ort comme OE 0 O0OO8FR ¥ a ou se OGE Gey V — i aki ed 1 by ae ca af . u ~ ay 4 eM [2 % Ji OOO'SIl=% 8 82Ovey 9 ao , Gr ¥ 9 ° = once » (e ae Oy eK Y CODOl=y O BGAiley oO Cc} 4 Ss Ol 22-25 Mog /[0%q Bi WO vd) ws 20g Nw | Wd ZOZG‘O= Y | "67 Sta 8] to) U ~67= APPENDIX A Formulae: l. y= E,mCwi z meCvs 2 2, Rayleigh Supersonic Pitot Formula a Pa (EME) ?. 2Y. Me. ¥-1\F7 (FA Mr - oo i} 3. Fay = Kyl 39974) + C1 - KN 28.97) Ty, > Ky, (4.00) + (1- Ky X28.97) $ ae SVG ET = Lie lnb VE 5 To 2 F50'R Te P- 22 /4+ BM fo Pe , 7 9. Po eo rZ) Pa ) pant known 10, For continuity of argon check in twoedimensional case: d i n TABLE A-l ~69~ Specific Heats and Ratio of Specific Heats as a Function of Injectant Concentration K (%) = mp: mle, xv 0 7.00 5, 00 1, 400 1 6. 98 4,98 1. 402 2 6. 96 4, 96 1. 403 3 6.94 4.94 1. 405 4 6.92 4.92 1. 406 5 6. 90 4.90 1. 408 6 6. 88 4, 88 1. 410 7 6. 86 4, 86 1. 412 8 6.84 4.84 1. 413 9 6. 82 4. 82 1. 415 10 6. 80 4,80 1. 417 11 6. 78 4.78 1.418 12 6,76 4.76 1,420 13 6.74 4.74 1, 422 14 6. 72 4.72 1, 424 15 6. 70 A. 70 1. 426 16 6. 68 4, 68 1. 427 17 6. 66 4,66 1, 429 18 6.64 4,64 1. 431 19 6.62 4.62 1, 433 20 6. 60 4, 60 1, 435 21 6.58 4. 58 1, 437 22 6. 56 4.56 1. 439 23 6. 34 4, 54 lL. 441 24 6.52 4,52 1. 442 25 6. 50 4, 50 1. 444 26 6.48. 4,48 1, 446 K(%) SmCp S meCu: ra 27 6, 46 4.46 1. 448 28 6. 44 4,44 1, 450 29 6. 42 4. 42 1, 452 30 6, 40 4, 40 1. 455 31 6, 38 4, 38 1. 457 32 6. 36 4.36 1. 459 33 6.34 4,34 1. 461 34 6. 32 4,32 1. 463 35 6. 30 4, 30 1. 465 36 6. 28 4. 28 1. 467 37 6. 26 4. 26 1. 469 38 6.24 4.24 1. 472 39 6. 22 4.22 1, 474 40 6, 20 4. 20 1. 476 4] 6.18 4.18 1. 478 A2 6. 16 4.16 1, 481 43 6.14 414 1,483 44 6.12 4,12 1,485 45 6. 10 4.10 1, 488 46 6, 08 4. 08 1. 490 47 6. 06 4. 06 1. 493 48 6.04 4,04 1. 495 49 6. 02 4,02 1. 498 50 6. 00 4, 00 1. 500 5l 5. 98 3.98 1, 503 52 5. 96 3.96 1, 505 53 5.94 3.94 1. 508 K(%) Srln Sma 7 5A 5.92 3.92 1,510 55 5.90 3.90 1,513 56 5.88 3.88 1.575 57 5.86 3.86 1,518 58 5. 84 3.84 1. 521 59 5.82 3.82 1.524 60 5.80 3.80 1,526 61 5.78 3.78 1,529 62 5. 76 3,76 1,532 63 5.74 3.74 1.535 64 5.72 3.72 1,538 65 5.70 3.70 41,541 66 5.68 3.68 1,543 67 5.66. 3.66 1.546 68 5.64 3.64 1,549 69 5.62 3.62 1.552 70 5.60 3.60 1,556 71 5.58 3.58 1,559 72 5.56 3,56 1,562 73 5.54 3.54 1,565 74 5.52 3.52 1,568 75 5.50 3,50 1.571 76 5.48 3.48 1,575 77 5.46 3.46 1.578 78 5.44 3.44 1,581 79 5.42 3.42 1,585 80 5.40 3.40 1,588 81 5.38 3.38 1,592 82 5.36 ©6336-1595 83 5. 34 3. 34 1.599 84 5.32 3.32 1,602 =~70—- K(%e) Ble Bymele 7 85 5.30 3.30 1.606 86 5. 28 3. 28 1. 610 87 5. 26 3, 26 1. 613 88 5.24 3.24 1.617 89 5. 22 3, 22 1.621 90 5. 20 3. 20 1, 625 91 5,18 3,18 1.629 92 5.16 3. 16 1. 633 93 5, 14 3, 14 L. 637 94 5.12, 3,12 1. 641 95 5,10 3,10 1. 645 96 5. 08 3.08 1. 649 97 5. 06 3. 06 1. 654 98 5.04 3.04 1, 658 99 5.02 3. 02 1. 662 100 5. 00 3. 00 1. 667 -71-# TABLE A-II Mean Molecular Weights of Argon and Air and Helium and Air Mixtures as Functions of Concentrations K(%) Mae nie 7 te +Aig 28.97 28.97 5 29. 52 27.72 10 30. 07 26. 47 15 30. 62 25, 22 20 31.16 23.98 25 31.71 (22.73 30 32.26 21. 48 35 32.81 20. 23 40 33.36 (18.98 45 33.91 17. 73 50 34. 46 16, 48 55 35.00 15. 24 60 35.52 13.99 65 36.10 | 12.74 70 36. 65 11. 49 75 37. 20 10. 24 80 37.75 8.99 85 38. 29 7.75 90 38, 84 6. 50 95 39, 39 5.25 100 39.94 4,00 =7 2m PLOT OF RAYLEIGH PITOT FORMULA FOR VARIOUS SPECIFIC HEAT RATIOS { 2.0 3.0 4.0 5.0 on /P, Figure A«1, 28 2.7 2.6 z.5 2.4 2.3 2.2 2.4 2,0 ~736 PLOT OF RAYLEIGH PITOT FORMULA FOR VARIOUS SPECIFIC HEAT RATIOS —_L 1 | { 8 3 ~ 10 rT Pon 7 Py Figure A-2, 4.8 4.4 4.0 3.8 3.6 3.4 3.2 3.0 2.8 PLOT OF RAYLEIGH PITOT FORMULA FOR VARIOUS SPECIFIC HEAT RATIOS Po, /P, Figure A«3, 38 ~T5= 2¢al (%) Vy 7 001 06 os OL o9 QS Ov oe [ers ol (6) T T T T 1 T T T a NOSHY @ uly 4O SBUNLXIN 7 GNNOS 40 ALIOOT3A Y¥oOES = osoi oso! ozo! ogo! 0601 ool OM (988 743) °p Figure A~=4, do( ft/sec) 2800 2600 2400 2200 2000 1800 1600 1400 1200 =T6— | i HELIUM = —R fe J 7 Kye 9 i (Kye) Vs. Kite on a/ T G5 3; To =530°R VELOCITY OF SOUND “MIXTURES OF AIR AND HELIUM | 4 | ___| 7 20 40 — 60 80 Se Figure A«5, KHe a 100