Mixing In High-Speed Flows With Thick Boundary Layers

Ron Portz and Corin SegalUniversity of Florida, Gainesville, Florida

The penetration of fuel surrogates transversely injected into a supersonic air stream has been measured over varied conditions of relative boundary layer thickness, molecular weight and air Mach number, to complement existing data bases and models. Penetration is an important prerequisite for efficient mixing, which is closely coupled to heat release in combustion. Air Mach numbers of 1.6 and 2.5 were examined. Boundary layer thickness was measured and injection tests were performed for various injector diameters and dynamic pressure ratios. The test section has a square section of width, L = 25 mm, followed by an 18L long constant area duct. Round orifices, with diameters of 1 mm, 1.5 mm, and 3.2 mm were used. Helium and Argon were used to observe the effect of density on penetration and mixing. Schlieren imaging was used to visualize and measure penetration. This study compares penetration to existing models using dynamic pressure ratio, injectant density and boundary layer thickness as independent variables. Greater dependence of penetration on boundary layer thickness is found than has been previously identified.

Introduction:When a gas is injected transversely into a

supersonic air stream, significant shock and viscous interactions occur. The results of these interactions are not always intuitive, and are strongly affected by the ratio of injectant to air dynamic pressures. The Space Shuttle, X-15 and other vehicles have experienced attitude control system reversals at certain ranges of dynamic pressure because of this interaction1. In most circumstances, the injected plume acts as a solid object, resulting in the generation of a bow shock and a system of alternating vortices spilling off the cylinder. As the ratio of gas to air dynamic pressures decreases, the injectant turns parallel to the air and the vortices’ axis of rotation aligns more nearly with the air stream. The currently accepted fuel injection model shows a characteristic shock pattern and turbulent shear layer forming as illustrated in Figure 1. Mixing is facilitated by the streamwise vortices spilling off of the turned injectant plume. This modelpresumes a boundary layer (BL) thickness less than the injector diameter, so that the gas jet exits the BL, forming a strong bow shock in the supersonic free stream. In the body-integrated scramjet design, considered for many aerospace vehicles, a long inlet ramp, with a continuous, strong, adverse pressure gradient, is likely to result in a thick BL in the combustor. High stagnation temperature, intrinsic to hypersonic flight, does not facilitate bleeding the BL, so this condition must be examined and understood.

Current, empirically derived, models of mixing in supersonic air flows with transverse

fuel injection describe the dimensions of the fuel plume penetration and spreading for hydrogen gas, using a definition for the plume boundary, based variously on injectant mole fraction of 0.005 or equivalence ratio of 0.9, depending on the researcher2, 3. Different researchers also incorporate different independent variables (dynamic pressure ratio and possibly boundary layer thickness) in the curve fits used to model penetration. Both jet penetration and boundary layer thickness are, in general, non-dimensionalized by jet diameter.

To create the strong vortices needed to enhance mixing, the fuel must penetrate strongly through the BL into the high speed core flow. Various methods have been suggested, with pylons and ramp injectors showing promise to deliver the majority of fuel into the free stream, away from the wall and BL4, 5, 6.

In transverse injection, air momentum is transferred to the fuel jet, and the jet is turned downstream. As the jet passes downstream, fuel and air mix throughout the plume. For tests relying on auto-ignition due to temperature increase across the bow shock, it has been observed that cooler air, passing through oblique shocks curving off of the bow shock, will quench the flame in zones where the equivalence ratio is otherwise within flammability limits7. Burning is restricted to a small recirculation kernel in the stagnation zone upstream of the fuel jet and in a thin sheet immediately aft of the bow shock. The majority of the fuel does not react with the air. The purpose of this study is to supplement the existing database of penetration depth when

40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit11 - 14 July 2004, Fort Lauderdale, Florida

AIAA 2004-3655

Copyright © 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

the BL is thick, as expected in supersonic combustion chambers, and evaluate the effect of BL thickness on jet penetration.

Brief Summary of Supersonic Mixing:For combustion to occur, fuel and air must

mix molecularly as described by Fick’s Law:dYAmA” = YA (mA”+mB”) - ρDAB dx

• mA” is the mass flow rate of species A into species B

• mB” is the mass flow rate of species B into species A

• YA is the mass fraction of species A• ρ is the density of species A• DAB, is the diffusion coefficient; a

function of temperature, pressure and species

The first term, YA (mA”+mB”), is the bulk flow of species A into B and does not result directly in molecular mixing. The second term, -ρDAB dYA/ dx, shows that the mass flow rate of species A into B increases with increasing density, diffusion coefficient and species gradient. Since the gradient is maximized, pure fuel diffusing into pure air, the species are known and temperature is governed by combustor inlet conditions, the rate of diffusion is not under the combustor designer’s control. To diffuse sufficient fuel into air to support combustion, high speed flow requires a significant length, with unacceptable drag, for a duct large enough to power a practical vehicle.

Improved bulk transport of fuel into air is the only means of improving combustor mixing. When two fluid streams come into contact, a mixing layer, coincident with the shear layer between the fluids, forms. At Reynolds numbersabove 104 this layer is turbulent, with macroscopic vortex structures moving at the convective velocity, Uc, intermediate between the two free stream velocities.

U2a1 + U1a2Uc ≡a1 + a2

Where Ui and ai are respectively the velocity and speed of sound of each of the fluids. The convective Mach numbers, Mci for two fluids in contact are

U1 - Uc Uc – U2Mc1 ≡a1

Mc2 ≡a2

When a gas is initially injected transversely into air, Mci are maxima both transversely and tangentially. They rapidly decrease in both directions as the injected gas is decelerated in the transverse direction and accelerated in the

tangential direction. The growth rate of the shear layer has been found to be a function of Mc, the ratio of fluid velocities and the ratio of fluid densities. The growth rate decreases with increased Mc and increases with increased density ratio between the two fluids12.

Macroscopic processes, rather thanmicroscopic diffusion, dominate the supersonic mixing process. For example, diffusion increases expected with an increase in fuel stagnation temperature did not appear in purely shear layer mixing tests8. Increasing the fuel stagnation temperature resulted in a fuel velocity increase that reduced the convective Mach number, hence shear forces, between the fuel and air. The reduction in shear force and macroscopic turbulence more than offset any diffusion increase from increased temperature. Other studies3 indicate greater lateral spreading than axial penetration for transverse fuel injection, indicating that the shear forces inherent in the vortices spilling off of the side of the fuel jet are more effective at mixing the fuel and air than the momentum of the fuel is at carrying fuel into the air.

Enhanced mixing schemes have been extensively described9, 10 and result in some of the tangential momentum of the air being transformed to transverse momentum and heat, usually by forcing one fluid stream into shear against another, with turbulent vortices being ubiquitous products. Translating tangential to transverse momentum invariably results in stagnation pressure losses detrimental to engine efficiency. Studies with hydrogen fuel have concluded that significant thrust is produced by the injection of fuel with a tangential velocity component11. The “water rocket” effect is acknowledged, and the specific impulse of the hydrogen may be quite high if it is heated by passage through hot engine parts. However, the thrust addition is minor, because of the small fuel mass involved, ~3% H2 by mass at stoichiometric mixture ratio. It is most likely that minimizing the flow disruption and air stagnation pressure loss is the primary source of additional thrust attributed to tangential injection, rather than the contribution of fuel momentum.

Experimental Facility:Figures 2 and 3 are schematic

representations of the continuous-flow, direct-connect, supersonic-combustion wind tunnel used in these experiments. This tunnel can sustain the delivery of .454 kg (1 pound) per

second of air at combustor Mach numbers from 1.3 to 3.6, with stagnation temperature up to 1,200K (1,700 F) and stagnation pressure from 207 to 827 kPa (30 to 120 psia, respectively). Higher flow rates are subject to limited duration. These conditions correspond to flight enthalpy of up to Mach 4.75.

For the purpose of measuring jet penetration, this test program used unheated air. Ambient air is filtered, compressed and dried before storage at up to 1,380 kPa (200 psia). The air was accelerated to the desired Mach number through a 2-dimensional, converging-diverging nozzle. An isolator was present to physically distance the nozzle from the fuel injectors and avoid shock interference with the nozzle. The entrance to the test section was 25.4 mm x 25.4 mm (1 inch x 1 inch) in section. The cross-section was constant along its length.

Manually controlled solenoid valves and dome-loaded regulators allow remote application and adjustment of fuel surrogate flows to various portions of the test fixture. Helium or argon were injected transversely to the air flow through 1 mm, 1.5 mm, and 3.2 mm (0.040, 0.060 and 0.126 inches, respectively) orifices to vary the ratio of jet diameter, D, to BL thickness, d.

BL thickness was measured using a probe with a square-cut tip of 0.25 mm outside diameter, and a bore diameter of 0.13 mm. The probe was inserted through any of three holes in the side-wall of the test section (see Figure 2) and was traversed in measured increments while measuring the stagnation pressure.

Flow and fluid mixing are visualized by use of a lens-based Schlieren system as described in Figure 3. Images were collected by an SVHS video camera. To capture average penetration, rather than instantaneous variations, each camera exposure was of the order of 20 ms, which is long compared to transient flow excursions. Depending on the optical magnification, the exposure duration required to freeze the flow varies, but is approximately 0.25 µs for a typical field of view.

The extent of a shear mixing layer corresponds well with the Schlieren image12, but estimating penetration by visual examination is influenced by the indices of refraction of the two fluids. The boundary becomes more distinct as the indices of refraction are more different. The helium/air interface, for example is unambiguous, with air’s index of refraction being 1.0002926 and helium’s being 1.000036 at 586.3 nm. Argon presents some interpretation difficulties, even over a short distance

downstream from the point of injection, since it’s index of refraction, at 1.000281, is very close to air’s. Figure 4 shows that determining the exact point of injection from the image is subject to inaccuracy, because while the lee side of the injected jet’s barrel shock is stationary, the windward side is deformed by the oncoming air.

Boundary Layer (BL) MeasurementThe BL thickness was measured around the

isolator outlet circumference for unheated air at 414 kPa (60 psia) stagnation pressure and nozzle exit Mach number of 1.6. The BL measurement was repeated for 552 kPa (80 psia) stagnation pressure, at both Mach 1.56 and Mach 2.5, on the tunnel wall corresponding to the injection plane. The pitot probe traversed the test sectionin 0.2 mm increments.

The BL was measured at several stations downstream of the nozzle exit, as indicated in Figure 2. Measurements showed a relatively small inviscid core flow. At Mach 1.6, BL growth in the 18L long constant-area test section resulted in choking unless a substantial bleed from the last third of the test section was established. At each station, the BL thickness is taken as the point of 99% velocity, or where the measured pitot pressure is 98% of the maximum value. The BL thickness at the point of gas injection was approximated by linear interpolation between the two stations measured on either side of the port. For 552 kPa stagnation pressure and Mach 1.6 flow, the BL thickness at the injector port was 0.145L. For Mach 2.5 flow the BL thickness was 0.10L.

It is known from measurements taken here and elsewhere13 that rectangular, 2-D nozzles yield boundary layers that are not uniform around the passage circumference. Along the curved nozzle walls, the boundary layer is uniform in thickness and thinner than on the flat walls of the 2-D structure. The flat walls have a non-uniform BL as shown in Figure 2, with substantially greater thickness at the center than at the edges, where BL thickness is similar to the curved walls. At the station 1.75L forward of the point of gas injection, the BL thickness was 0.13L on the curved walls, while the maximum BL thickness on the flat walls was 0.26L. This is due to the stronger favorable pressure gradient at the curved walls made evident by reference to the method of characteristics for a 2-D nozzle.

Fuel Surrogate InjectionArgon and helium gas were transversely

injected into the supersonic flow through circular

orifices of 1.0 mm, 1.5 mm, and 3.2 mm diameter. Schlieren images were recorded for variations of orifice size, dynamic pressure ratio, and injectant density. A sample series of Shlieren images, Figure 4, were taken for argon, with stagnation pressure of 641 kPa exiting the 1.5 mm orifice with air velocity increasing from 0 to Mach 1.6 at 552 kPa p0. Inspection of these images shows that the argon plume is turned and displaced by subsonic air close to the wall. The supersonic free stream is presented not with a normal obstacle, but an oblique one, resulting in an oblique shock wave displaced from the wall. This wave does not completely span the test section, minimizing its visibility.

Gases injected into a Mach 1.6 air stream donot penetrate far beyond the boundary layer. The classic picture of the bow shock is no longer accurate when the boundary layer is significantly thicker than the injector diameter. As shown in figure 4, the outer edge of the plume is identified on the Schlieren image by a band where light has been refracted diffusively away, leaving a smoky outline of the plume edge. The depth of argon and helium penetration at various dynamic pressure ratios, as a multiple of injector diameters, versus downstream position, is presented in Table 1 and Figures 5 and 6.

When the air Mach number was increased to 2.5 at constant stagnation pressure, the BL decreased to 0.1L at the injector and the air dynamic pressure decreased from 235 kPa to 143 kPa, since air’s density decreased faster than the square of velocity increased. Injected gas penetrated equally into the air, as shown in Figure 8, for the same conditions of injectant orifice size and reduced pressure. This assessment is qualitative only, since the injectant/air plume is not clearly enough visible for measurement at Mach 2.5. For Mach 2.5 flow, a distinct bow shock is visible and the interaction of the bow shock with the boundary layer is clear. Note that the air’s temperature has no effect on its dynamic pressure, since the higher velocity, squared, is exactly counteracted by reduced density.

Results and Discussion:Gas penetration was calculated in terms of

P/D, defined as the penetration, P, divided by the jet diameter, D. The data in Table 1 and Figures 5 and 6, show that in general, decreasing the relative BL thickness - increasing jet diameter in this case - results in lower P/D, since the average air velocity the jet must traverse is higher when the BL is thin in relation to the jet diameter.

Despite increased penetration from the wallwhen the BL is thick, the penetration out of the BL and into the free stream is decreased. The strong, nearly normal, bow shock is absent. The supersonic freestream interacts with the deflected plume by forming a weaker oblique shock. With the weakened virtual obstruction of the injectant jet in the freestream, the vortex generation essential to effective bulk mixing processes is weakened. The resulting flow approaches the case of tangential, rather than transverse injection.

The injectant is turned from the transverse to the tangential direction quickly after injection, and is dispersed by the vortex pairs flanking the jet and the turbulent shear layer between the air and injectant. Freestream momentum is transferred to the injectant, decreasing freestream kinetic energy through shock wave formation and viscous dissipation.

The magnitude of gas penetration can be estimated by an empirically fit curve, as presented in previous studies2. Figure 7a presents new data with data from reference 2, in the same format as reference 2 for ease of comparison, and shows gas penetration into supersonic flows for varied gas densities, injector diameters and dynamic pressure ratios. The straight line curves fit to the data are modifications of the curve from reference 2:

P/D = α ((X/D)[(qj/qa)2.1][(d/D)0.4])ξ

α ξHydrogen 3.87 0.143Helium 1.89 0.25Argon 1.05 0.35

Careful inspection of Figure 7a shows that helium penetration is decreased more by decreased BL thickness than was previously predicted, for hydrogen. The evidence for this result is ambiguous for argon. To better account for the effect of a thick boundary layer, helium data was replotted in Figure 7b with the exponent applied to the BL thickness ratio changed from 0.4 to 1.3. This indicates that the thickness of the boundary layer is more significant than previously proposed. Further research is suggested to determine if this is an effect of the low Mach number used for this study, gas density or other factors.

The penetration pattern for the heavier gases is immediately apparent. The high initial velocity of light gases injected via sonic orifice results in deeper initial penetration, however, the

visible shear layer growth is noticeably slower for lighter gases like hydrogen and helium than for argon. Reduced shear layer growth is associated with the lighter gases’ higher convective Mach number12. This trend is evident in the fact that even though argon initially penetrates less than helium, its penetration is equal after passing 30 jet diameters downstream from the injector.

The obstruction created by the injected plume reduces the effective flow area of the air and may result in choking the flow. At an inlet Mach number of 1.6, the area reduction required to isentropically decelerate flow to subsonic speed is low - 0.18. For a narrow injectant plume at high stagnation pressure – hence high penetration, the area blocked is fortunately smaller yet. Figure 9 shows that flow is not choked, but the Mach number does decrease from 1.6 to 1.1 near the point of injection, with the formation of an oblique shock wave. An oblique shock wave in Mach 1.6 flow is approximated as isentropic deceleration in Figure 9. The possibility of choking the flow is of concern, particularly during transition from subsonic to supersonic combustion, where small area ratio changes can result in choking.Variable inlet or combustor geometry may be essential to successful transition from ramjet to scramjet operation.

There are several possible remedies for the problems caused by a thick BL. The first is to employ fuel injector orifices with diameters similar to, or larger than, the BL thickness, so that the fuel will punch through the boundary layer normally, restoring the model of Figure 1. The disadvantage of this method is a large volume of fuel that is more difficult to diffuse into the air and which results in locally strong shock waves and significant stagnation pressure

losses in the free stream. Another option is to place a pylon ahead of the injector port. Pylons have shown the capacity to help a transverse jet penetrate more deeply into a supersonic stream4. A third option is to insert a parallel injector plate into the free stream clear of the boundary layer. Finally, some investigators, in yet-to-be-published work, are pursuing bleeding a hypersonic boundary layer.

Conclusions:This study has evaluated the penetration of

fuel surrogates into supersonic flows with thick boundary layers. The following conclusions can be drawn from results of this study:• Boundary layer thickness is more significant

to jet penetration than previous studies have indicated. Increased BL thickness increases absolute penetration, but decreases penetration into the free stream.

• A thick boundary layer impairs fuel-air mixing in the free stream. Most mixing is restricted to the boundary layer when the boundary layer is thick.

• The density of the injected gas has a significant effect on penetration. At the same conditions of air Mach number, gas stagnation pressure and orifice size, lighter gases initially penetrate further into the free stream. Heavier gases exhibit faster shear layer growth, however.

• Ramjet to scramjet transition probably requires a variable geometry combustor.

Acknowledgements:This work has been performed with support from NASA grant NCC3-994 with Claudia Meyer as the Program Manager.

References:1. Glass, C. E., “A Parametric Study of Jet

Interactions with Rarefied Flow” 21st

International Symposium on Rarefied Gas Dynamics

2. McClinton, C. R., “Effect of Wall Boundary-Layer Thickness to Jet Diameter on Mixing of a Normal Hydrogen Jet in a Supersonic Stream”, NASA TM X-3030, June 1974

3. Torrence, M. G., “Efffect of Injectant Molecular Weight on Mixing of a Normal Jet in a Mach 4 Airstream”, NASA TN D-6061, January 1971

4. Owens, M.; Tehranian, S.; Segal, C. and Vinogradov, V.; "Flame-Holding Configurations for Kerosene Combustion in a Mach 1.8 Airflow", Journal of Propulsion and Power, Vol 14, No. 4, July-August 1998

5. Gallimore, S.; Jabobsen, L.; O’Brien, W. and Schetz, J.; “Operational Sensitivities of an Integrated Scramjet Ignition/Fuel Injection System”; Journal of Propulsion and Power, Vol. 19, March –April 2003

6. Parent, B. and Sislian, J.; "Effect of Geometrical Parameters on the Mixing Performance of Cantilevered Ramp Injectors", AIAA Journal, Volume 41, No. 3

7. Ben-Yakar, A. and Hanson, R.; “Cavity Flameholders for Ignition and Flame

Stabilization in Scramjets: Review and Experimental Study”

8. Wendt, M.; Stalker, R. and Jacobs, P.; “Fuel Stagnation Temperature Effects on Mixing with Supersonic Combustion Flows”, Journal of Propulsion and Power, Vol 13, No. 2

9. Billig, F. S., “Research on Supersonic Combustion”, Journal of Propulsion and Power, Vol. 9, No. 4, July-August 1993

10. Seiner, J.; Dash, S. and Kenzakowski, D.; “Historical Survey on Enhanced Mixing in Scramjet Engines”, Journal of Propulsion and Power, Volume 17, No. 6, November-December 2001

11. McClinton, C. R., “The Effect of Injection Angle on the Interaction Between Sonic Secondary Jets and a Supersonic Free Stream”, NASA TN D-6669, February 1972

12. Dimotakis, P. E., “Turbulent Free Shear Layer Mixing and Combustion”, AIAA 1991

13. Gaffney, R. L. Jr., Korte, J.; “Analysis and Design of Rectangular Cross-Section Nozzles For Scramjet Engine Testing”; 42nd

AIAA Aerospace Science Meeting and Exhibit, 5-8 January 2004, AIAA 2004-1137

14. Clayton, R. R., “A Study of the Mixing of Hydrogen Injected Normal to a Supersonic Airstream”, NASA TN S-6114, 1971

NozzleIsolator

Test Section

127 mm 76 mm

25 mmWindows146 mm L = 25 mm

Figure 2. Schematic of Boundary Layer Measurement. The BL was measured at locations bounding the injector port to estimate the BL at the injector assuming linear growth.

Fuel Injector

Air from stagnation chamber

0.13L 0.26L

0.145L

0.15L

114 mm38

mm

Boundary layer growth at Mach 1.56 and 414 kPa air stagnation pressure.

Velocity Profile

Concentration Profiles

Spilled Vortex, same on both sides

Bow ShockOuter limit of turbulent shear

layer/penetration

Potential Core

Figure 1. Model of Transverse, Underexpanded Injection into a Supersonic Airstream.

NozzleIsolator

Collar

Test Section

Bleed

127 mm

25 mm Windows146 mm L = 25 mm

Figure 3. Schematic of Scramjet Wind Tunnel and Schlieren Optics

Fuel Injector

Precision Pinhole

150 mm, f4 lens

150 mm, f2.5 lens

Video Camera

Air from stagnation chamber

Precision Pinhole, Band-Pass Filter and Ground Glass Located at Second Focus of Ellipsoid

Lamp at focus of ellipsoidal reflector

76 mm

Table 1. Penetration Depth at Various Injection ConditionsAir Mach Number 1.56, Air Stagnation Pressure – 80 psia, Stagnation Temperatures – 300 K for air and Injectant. Shaded entries were not used in subsequent analysis due to scarcity of comparative data or suspicion of anomaly.

Injectant Stagnation Pressure (kPa)

Dynamic Pressure Ratio, qj/qair

Orifice Diameter (mm)

Ar, x/D =7

Ar, x/D =15

Ar, x/D =30

He, x/D =7

He, x/D =15

He, x/D =30

1.0 2.82 4.10 5.90 3.46 4.56 5.901.5 3.03 3.83 3.05 3.88 4.22

641 1.11

3.2 2.541.0 3.33 4.49 6.36 3.92 4.74 5.821.5 3.50 4.33 4.38

807 1.39

3.2 3.021.0 3.59 5.05 6.74 4.18 5.13 6.101.5 3.83 3.75 4.58 5.42

965 1.67

3.2 3.611.0 3.72 4.36 5.33 6.411,124 1.951.5 4.25 3.93 5.00 5.881.0 3.85 5.08 4.95 5.82 6.741,289 2.231.5 4.33

0.060”

Boundary Layer Thickness,

approximately 0.140”

Figure 4. Schlieren Video Stills of an Argon Jet at P0 = 90 psia , as Free Stream Velocity Increases from 0 at left to Mach 1.56, at air stagnation pressure of 414 kPa in the right-hand photograph.

Air Flow Direction

Figure 5. Helium Penetration vs Distance from Injector, Mach 1.56 Air Flow

0

1

2

3

4

5

6

7

8

0 5 10 15 20 25 30 35

Distance from Injector, in Jet Diameters

Jet

Pen

etra

tio

n,

in J

et

Dia

met

ers

qj/qa = 1.11, D = 1.0 mm qj/qa = 1.11, D = 1.5 mmqj/qa = 1.39, D = 1.0 mm qj/qa = 1.39, D = 1.5 mmqj/qa = 1.67, D = 1.0 mm qj/qa = 1.67, D = 1.5 mmqj/qa = 1.95, D = 1.0 mm qj/qa = 1.95, D = 1.5 mmqj/qa = 2.23, D = 1.0 mm

Figure 6. Argon Penetration vs. Distance from Injector. Mach 1.56 Air Flow

0

1

2

3

4

5

6

7

8

0 5 10 15 20 25 30 35

Distance from Injector, in Jet Diameters

Pen

etra

tion,

in J

et

Dia

met

ers

qj/qa = 1.11, D = 1.0 mm qj/qa = 1.11, D = 1.5 mm qj/qa = 1.11, D = 3.2 mm

qj/qa = 1.39, D = 1.0 mm qj/qa = 1.39, D = 3.2 mm qj/qa = 1.67, D = 1.0 mm

qj/qa = 1.67, D = 1.5 mm qj/qa = 1.67, D = 3.2 mm qj/qa = 1.95, D = 1.0 mm

qj/qa = 1.95, D = 1.5 mm qj/qa = 2.23, D = 1.0 mm qj/qa = 2.23, D = 1.0 mm

Figures 5 and 6, Helium and Argon Penetration. These graphs show that at the same conditions of dynamic pressure ratio and boundary layer thickness, the lighter gas, helium, initially penetrated significantly more into the free stream than argon, but that by 30 jet diameters downstream, penetration is equal.

Jet Penetration

1

10

100

1 10 100 1000

(x/D)(qj/qa)2.1(d/D).4

P/D

H2 P/D

H2 Curve Fit (d/D = 2.51)

He P/D (d/D = 3.72)

He Curve Fit (d/D = 3.72)

He P/D (d/D = 2.42)

He Curve Fit (d/D = 2.42)

Ar P/D (d/D = 3.72)

Ar Curve Fit (d/D = 3.72)

Ar P/D (d/D = 2.42)

Ar Curve Fit (d/D = 2.42)

Figure 7a. Jet P/D, Penetration Divided by Jet Diameter, versus a linearizing function empirically drived in reference 2. General agreement in trends are accurately followed for helium and argon, with modifications to the linearizing functions shown.

Helium Jet Penetration

1

10

10 100 1000

(x/D)(qj/qa)^2.1(d/D)^1.3

P/D

He P/D (d/D = 3.72) He P/D (d/D = 2.42) He Curve Fit

Figure 7b. For helium, a curve fit, that better takes into account the effect of boundary layer thickness is proposed. The effect of the boundary layer is more pronounced.

Mach 2.5 Mach 1.6

Figure 8. Argon injection from 1.5 mm orifices, with air stagnation pressure of 552 kPa in both cases. Compare argon penetration at Mach 2.48 and p0 of 883 kPa on left, and penetration at Mach 1.58 and p0 of 965 kPa on right. Penetration at 7 jet diameters is essentially equal, despite lower stagnation pressure in Mach 2.5 flow. Note the clearly defined bow shock and boundary layer interactions in Mach 2.5 flow.

Figure 9. Injection of helium at X = 1.2, indicated by arrow, presents the supersonic air stream with a virtual obstruction that causes shock formation, with expected increase in static pressure and decrease in Mach number upstream of the point of injection. The “shadow” of the jet can be seen following the injector. The pressure reduction in a jet’s shadow leads to the reversal of attitude control force experienced in several aerospace vehicles.

S ta tic P ressu re an d M ach N u m b er b y Lo cation a t M ach 1 .56 an d 552 kP a In le t F lo w

50

100

150

200

250

300

-10 .00 -5 .00 0 .00 5 .00 10 .00 15 .00

X L o catio n (in tu n n el w id th s , L )

Sta

tic

Pre

ssu

re (

kPa)

0 .00

0 .20

0 .40

0 .60

0 .80

1 .00

1 .20

1 .40

1 .60

1 .80

2 .00

S ta tic P ressure(kP a)Isen trop ic M achN um ber

M ach N u m be r