Heat Transfer on a Double Wedge Geometry in Hypervelocity Air and Nitrogen Flows

Heat Transfer on a Double Wedge Geometry in

Hypervelocity Air and Nitrogen Flows

A.B. Swantek

∗

, and J. M. Austin

†

University of Illinois, Urbana, Illinois, 61801

We investigate shock wave/boundary-layer interaction and resulting heat transfer in

hypervelocity double wedge flows. An expansion tube is used to generate air and nitrogen

flows with stagnation enthalpies ranging from 2.1-8.0 MJ/kg and Mach numbers from 4-7.

The range of free stream conditions were selected to investigate the impact of thermo-

chemical effects by i) systematically varying the chemical composition from nitrogen to air

while maintaining constant the stagnation enthalpy or the Mach number, and ii) varying

the stagnation enthalpy. Flow features are visualized with schlieren photography, and heat

transfer is measured using fast response coaxial thermocouples. Data are presented for

both nitrogen and air test conditions with eight cases in total. Current results indicate

significantly different behavior in flows with enthalpies as low as 4 MJ/kg between air and

nitrogen test conditions.

Nomenclature

Distance along model in the freestream direction

Forward wedge angle

Aft wedge angle

Length of forward wedge face

Width of double wedge

Thermocouple diameter

sep

Separation length

Location of separation along model face

Boundary layer thickness at separation

Temperature

Pressure

Specific heat ratio

Dynamic viscosity

Mach number

Subscript

Edge of the boundary layer

Wall

∞

Freestream

Superscript

∗

Reference condition

∗

Graduate Student, Department of Aerospace Engineering, Student Member AIAA

†

Associate Professor, Department of Aerospace Engineering, Associate Fellow AIAA

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I. Introduction

The flow over a double wedge model is a canonical problem in the study of hypersonic shock wave-

boundary layer interactions. Flow field computations are very sensitive to the choice of thermochemical

model,

and thus make the problem ideal for model verification. The flow field contains complex, but

coupled phenomena, including: boundary layer separation, shock and shear layers interaction, and shock

impingement. These are illustrated in Figure 1.

Figure 1. Schematic of separated double wedge flow with regions labeled following Davis and Sturtevant.

Some wave

interactions have been omitted for clarity.

Double wedge and cone configurations have been studied computationally and experimentally by numer-

ous researchers, particularly in nitrogen flows. Olejniczak

et al.

performed simulations and experiments in

nitrogen, and found that aft body heat transfer levels could be matched, but not the peak heating location,

and the fore body separation heating could be matched, but not the separation zone size. A concurrent

paper by Olejniczak

et al.

focused on the different types of shock interactions that occur over the double

wedge. They studied the classical shock interactions characterized by Edney

and identified a new type of

interaction with a regular shock reflection from the triple point to the fore body, rather than the aft body.

Olejniczak

et al.

extended their previous work to investigate the effect of different thermochemical models,

but still found discrepancies in the separation zone size or peak heating location.

Perhaps the most comprehensive work relevant to our study is that of Davis and Sturtevant,

who

investigated separation zone length scaling and heat transfer theoretically, computationally, and numerically

in a hypersonic nitrogen flow. Building on triple deck theory

6–8

they derived a partial scaling for the

separation zone with a new parameter Λ

shown in Equation 1. In a previous work,

we have investigated

the application of this scaling to the flow over a double cone model, as well as the current double wedge

experiments.

sep

∝

(

−

)

(1)

Subscripts indicate regions corresponding to Figure 1. Λ

is a parameter unique to the work of Davis and

Sturtevant which describes the effect of wall to boundary layer edge temperature ratio. It is defined as

(

∗

)(

∗

)(

)

(2)

The above studies considered nitrogen flows to simplify the thermochemical modeling. In air flows,

simulations and experiments show considerable discrepancies at high enthalpies (

5 MJ/kg) with signifi-

cant thermochemical activity, in spite of good agreement at lower enthalpies.

10–12

For example, simulations

predict a decrease in the separation length with increasing freestream enthalpy, but this is not observed ex-

perimentally.

In another study investigating possible freestream effects, Nompelis and Candler

simulated

the spectroscopic measurements of freestream NO concentration performed by Parker

et al

Simulations

overpredict the amount of freestream NO by a factor of three, which is outside the experimental error.

In the present work, we extend these previous studies by utilizing an expansion tube facility to access

a broad range of test conditions. The range of test conditions allows the degree to which thermochemical

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effects influence the flow field to be tuned by changing the freestream chemical composition from nitrogen to

air while keeping other parameters, such as Mach number or stagnation enthalpy constant. The stagnation

enthalpy can be varied from 2.1 to 8.8 MJ/kg The expansion tube is able to produce thermochemically

“clean” flows with minimal freestream dissociation, as the gas is never stagnated and is accelerated by an

unsteady expansion fan, rather than a nozzle. More details on the facility are given below.

II. Experimental

Experiments are performed in the Hypervelocity Expansion Tube (HET) at the University of Illinois.

The HET is a 9.14m long expansion tube facility, consisting of a driver, driven, and accelerator section

all with an internal diameter of 150mm. Facility capabilities include: operating at Mach numbers of 3.5-

7.5 and achieving stagnation enthalpies of 2.1-8.8 MJ/kg. Further details of facility instrumentation and

operation can be found in Dufrene

et al

Four test conditions at various enthalpies are utilized for this

study; parameters are caclulated using 1-D unsteady gas dynamics, Table 1. Test conditions are identified

by the Mach number and stagnation enthalpy. Each of the four test conditions shown can be achieved using

both air and nitrogen, resulting in eight different test cases in total. Changes in freestream parameters are

less than 0.5% between nitrogen and air.

Table 1. Theoretical parameters for HET test conditions.

Freestream Parameters

3.6

Mach Number

5.12

7.11

7.14

4.01

Static temperature,

676

191

710

853

Static pressure,

kPa

8.13

0.391

0.78

18.3

Velocity,

m/s

2664

1972

3812

2340

Density,

kg/m

0.042

0.0071

0.0038

0.0747

Test Time,

μs

361

327

242

562

Unit Reynolds Number, 10

3.42

1.10

0.435

4.64

Stagnation Enthalpy,

MJ/kg

4.1

2.1

8.0

3.6

A double wedge model (

= 30

◦

= 25

◦

= 50.8 mm, and

= 101.6 mm) is machined from A2 tool steel.

The model is dimensioned according the criteria summarized by Davis and Sturtevant,

and is designed as a

one half scale version of theirs. The minimum

value is

∼

125, which exceeds the recommended minimum

of 85. A PCO1600 digital camera with a Nikon zoom lens (

= 70-300 mm) in a Z-type schlieren system

is used for visualization. Illumination is provided by a Xenon spark gap with a pulse width time of 20 ns,

effectively freezing the flow features. The model is instrumented with nineteen, 1

s response time, coaxial

thermocouples

(

= 2.4 mm) for heat transfer measurements at sixteen different streamwise locations.

Three of the stream wise locations have two gauges to asses any spanwise variation. The spacing of gauges

varies along the model and gauges are clustered around areas of interest (boundary layer separation, shock

boundary layer interaction, etc...). The instrumented model is shown in Figure 2. Error bars on the heat

transfer data due to gauge uncertainties are 8 %.

III. Results

III.A. Schlieren Images

Sample schlieren images of flow over the double wedge are shown in Figures 3(a)-(d) for four test conditions:

4 in nitrogen and air, and M7

8 in nitrogen and air. Both of the M7

8 experiments appear to show

generally laminar flow, while the M5

4 images appear to have large regions of fluctuating flow. This is

consistent with the fact that the unit Reynolds number of the the M5

4 test condition is nearly an order

of magnitude larger that that of the M7

8 conditions, Table 1. Both sets of images show at least one

distinct triple point with a shear layer and transverse wave. The wave interaction observed in the M5

test conditions appear more complex than in the M7

8 conditions with a possible secondary triple point

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Figure 2. The experimental double wedge model used in the current study. The coaxial thermocouple gauges can be

seen along the center of the model. Note: Some gauges are staggered to increase spatial resolution.

appearing. The shear layer turns upward to align with the flow above the second wedge, and in the case of

the higher Reynolds number condition, it is still visible some distance after the compression. It appears that

the intersection of the reattachment shock with the shear layer is the mechanism for turning the shear layer

upwards along the aft wedge.

The effects of thermochemistry are very apparent in the images. A distinct region with natural flow

luminescence indicating a region of relatively hot gas in behind the bow shock can be observed in Figure 3(c).

This is in contrast to the region on the other side of the shear layer which contains relatively cold, high

speed flow. Both sets of test conditions exhibit bow shocks which reduced shock standoff distance for the

air conditions in comparison to nitrogen. This agrees with normal shock equilibrium calculations using the

SD Toolbox

and

Cantera

which predict higher post-shock densities for the air conditions. In the M5

nitrogen flow, Figure 3(a), we do not observe a wave emanating near the corner to turn the flow up the

aft portion of the model, as is evident in images for the air flow, Figure 3(b). The departure from laminar

behavior is observed further upstream in the case of the nitrogen, when compared to the air. Lastly, the

regions of largest flow luminescence in these images both appear to occur between gauges

and

. For

the case of the the M7

8 air condition, the shock impingement on the aft wedge and region of largest flow

luminescence are seen to move noticeably downstream, compared to the nitrogen. This behavior is most

likely coupled with the corresponding shift in the triple point location.

Polar calculations of the triple point structure and wave interactions in the different conditions have been

performed, building on our previous studies.

19,20

Calculations are performed for a direct oblique-bow shock

interaction. Two examples of these plots are shown in Figure 4 for the M7

2 and the M7

8 test conditions.

Both frozen (Fr.) and equilibrium (Eq.) solutions are presented.

Not surprisingly, the equilibrium calculation and the frozen calculations do not differ significantly at

the 2 MJ/kg enthalpy condition. The equilibrium effects seen in the 8 MJ/kg case influence the polars in

two ways. First, in Figure 4(b), the post shock pressure for the case of strong shocks is reduced for the

equilibrium calculation, when compared with the frozen calculation. Equilibrium chemistry has the effect

of reducing the shear layer angle, compared with the frozen calculations. Calculations like these have been

done for every schlieren data set. Three features calculated are: the bow shock angle, the transmitted shock

angle, and the shear layer angle, and these are compared with experimental measurements.

In general, the best agreement between theory and experiment across all test conditions is with nitrogen

as a test gas. Of all the test conditions the best agreement with shock polar calculations is the M7

2 test

condition. The most disagreement between theory and experiment is the M4

3.6 condition. Error in the

transmitted shock angle is seen up to 50%, while at most for any other test condition they are 15%. This may

be a result of unsteady behavior. This condition also has the largest disagreement in the shear layer angle

as well. Time-resolved schlieren imaging experiments are in process to investigate potential unsteadiness

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(a)

(b)

(c)

(d)

Figure 3. Schlieren images of the double wedge model (flow from left to right) in nitrogen at the (a) M5

4 and (c)

8, and air at the (b) M5

4 and (d) M7

8 test conditions. Bright regions are due to luminescence. All four cases

appear to have type IV interactions.

(a) M7

(b) M7

Figure 4. Polar calculations for the primary triple points. Calculations are performed for air conditions using a direct

oblique-bow shock interaction.

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further.

III.B. Heat Transfer Results

Using the fast response thermocouples discussed in Section II, heat transfer profiles are constructed over the

double wedge model for each of the eight different test conditions. Current capabilities limit data acquisition

to 10 channels. As there are 19 gauges on the model, two shots are required to capture all the points. At

least three full data sets are obtained for each test condition to assess repeatability. In total

∼

60 experiments

were carried out establish working gauges, as well as to profile all of the test conditions. Heat transfer values

are averaged after a steady test time has been established; each transient heat transfer trace is inspected

individually to ensure the useful test time. In addition to averages, the standard deviation of heat flux is

also recorded.

In the following section, each set of heat transfer data are presented along with the schlieren images

shown in Section III.A. The error bars in the heat transfer are

8% of the absolute value. The location of

the hinge is shown by a vertical dashed line, and

location is normalized by the length of the first wedge

face L. (The x axis is in freestream flow direction, thus, the hinge is not located at

x/L

=1). Predictions for

laminar flat plate boundary layer theory are presented for reference. Davis and Sturtevant found reasonable

agreement between flat plate and wedge forebody heat transfer measurements.

III.B.1. M7

2 Test Condition

Heat transfer data for nitrogen and air along with the corresponding schlieren images are shown in Fig-

ures 5(a) and (b). In Figure 5(c) both heat transfer distributions are overlaid. The forward wedge experi-

ences laminar heat transfer behavior on the section upstream of separation. Possibly due to low signal to

noise ratio (nearly an order of magnitude smaller than any other test condition), there is large variability

in the length separation zone. On the aft face there is a sudden increase in heat transfer, and peak values

are

∼

1.3 MW/m

at gauge M. This corresponds roughly with the location of shock impingement on the aft

face. The combined overlay of both data sets in Figure 5(c) shows that, as expected, the heat transfer does

not differ significantly between air and nitrogen flows.

III.B.2. M4

3.6 Test Condition

Heat transfer data for the nitrogen and air along with the corresponding schlieren images are shown in

Figures 6(a) and (b). In Figure 6(c) both heat transfer distributions are overlaid. On the forward wedge,

there is an immediate departure from laminar heating profiles. Additionally, very little difference is observed

between the two test conditions. Data from gauge G is missing due to damage to the gauge. In both Figures,

between gauges F and H, there is a large differential between the heating values (an increase of approximately

a factor of two). This may be due to the the shock interactions that are seen to occur in this area in the

images. Peak heating on the aft wedge is approximately 13 MW/m

for the nitrogen, and approximately

14 MW/m

for air, both occur at gauge M. In general on the aft wedge, the heat transfer rates in air are

slightly higher than those in nitrogen. This is especially true in the area of peak heating.

III.B.3. M5

4 Test Condition

Figures 7(a) and (b) show the heat transfer for the nitrogen and air along with the corresponding schlieren

images. In Figure 7(c) heat transfer distribution for nitrogen and air are overlaid. On the forward wedge,

laminar heat transfer behavior is observed in both gases. As the boundary layer behavior deviates from

the laminar condition in the images, the heat transfer is seen to increase as expected. As the Reynolds

number is smaller than the M4

3.6 case, the increase occurs further downstream. Interestingly, the nitrogen

experiences a much larger heating value at gauge G, when compared with the air. This may be due to two

things: a lack of gauge resolution may not be detecting the actual peak heat transfer (the location may have

been shifted for air), or some sort of interaction between the shock and boundary layer unique to nitrogen

may be occurring. On the aft end of the wedge, peak heating for the nitrogen is seen to occur at gauge M

and have a value of

∼

10.5 MW/m

, and in air is

∼

13 MW/m

. As in the M4

3.6 case, slighly higher heating

values are seen in the case of the air on the aft cone in the vicinity of shock interaction with the surface.

From the images it is observed that the shock interaction occurs just downstream of gauge L, which is in

agreement with the heat transfer profiles.

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(a) M7

2, N

(b) M7

2, air

Figure 5. Heat transfer profiles for the M7

2 test condition in (a) N

, and (b) air. An overlay of the two profiles is

shown in (c). The green line indicates a laminar flat plate calculation using the work of Simeonides.

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(a) M4

3.6, N

(b) M4

3.6, air

Figure 6. Heat transfer profiles for the M4

3.6 test condition in (a) N

, and (b) air. An overlay of the two profiles is

shown in (c). The green line indicates a laminar flat plate calculation using the work of Simeonides.

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(a) M5

4, N

(b) M5

4, air

Figure 7. Heat transfer profiles for the M5

4 test condition in (a) N

, and (b) air. An overlay of the two profiles is

shown in (c). The green line indicates a laminar flat plate calculation using the work of Simeonides.

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III.B.4. M7

8 Test Condition

Heat transfer data for the nitrogen and air along with the corresponding schlieren images for the highest

Mach number and enthalpy condition are shown in Figures 8(a) and (b). In Figure 8(c) both heat transfer

profiles are overlaid. On the upstream end of the forward wedges, the heat transfer corresponds reasonably

well with laminar predictions. This is the only case where a slight difference is seen with respect to the two

gases for laminar heating rates. The air values are consistently higher than the nitrogen, but are still within

the error bars of the measurements. A distinct separation zone is seen in each plot as a decrease in heat

transfer after

x/L

=0.6. In the nitrogen case, the separation zone appears to begin at gauge F, and in the air

case at gauge G. Perhaps the most noticeable difference between the two cases is the level of peak heating

of the aft wedge. In nitrogen, the peak heating value is 8.5 MW/m

, while in air it is 13.5 MW/m

. In

air, a dip in the heat transfer is observed just prior to the peak heating location. This may be the result

of a secondary separation zone that lies upstream due to shock impingement, although this is difficult to

discern due to the luminescence in the image. There is a considerable amount of variation in the data, not

unexpectedly in the area of shock impingement on the aft wedge.

IV. Conclusions

We investigate the hypersonic flows of nitrogen and air over a double wedge configuration at eight

test conditions with stagnation enthalpies of 2 to 8 MJ/kg. The shock wave-boundary layer interaction is

investigated using single frame schlieren photography and fast response thermocouples to measure surface

heat transfer.

At the 2 MJ/kg enthalpy condition, no appreciable difference between the air and nitrogen heat transfer

distribution is observed over the entire model, as expected. Additionally, in the 3.6 MJ/kg condition, very

little difference between the air and nitrogen conditions is observed. This condition also exhibits a deviation

from the expected laminar heat transfer levels almost immediately on the first wedge surface in both gases.

Distinct differences between the air and nitrogen flows are apparent as low as 4 MJ/kg (M5

4 condition),

indicating that gas thermochemistry plays a role at these enthalpies. For this case, thermochemical effects

seem to be minimal toward the leading edge of the the front wedge where a laminar boundary layer is

observed. As expected, these effects are most prominent in shock wave/boundary layer interaction regions.

Aft wedge heating rates are systematically higher in air than in nitrogen in the region of shock impingement.

We observe that in the case of the nitrogen flow, a departure from laminar boundary layer behavior occurs

slightly upstream in comparison to the air flow.

Lastly, in the 8 MJ/kg test condition significant differences between the air and nitrogen are observed.

Heat transfer levels on the forward wedge are slightly higher in air compared with nitrogen, although still

within error bars. On the aft wedge peak heating is noticeably higher on in the air condition when compared

with the nitrogen condition, again in the region of shock interaction.

Acknowledgments

This work was funded through the U.S. Air Force Office of Scientific Research (award FA 9550-11-1-0129)

with Dr. John Schmisseur as program manager. Invaluable assistance with thermocouple instrumentation

and data processing was provided by William Flaherty at Illinois. We are very grateful to Prof. Hans

Hornung and the Caltech T5 group for the generous sharing of their thermocouple design and expertise.

References

Olejniczak, J., Candler, G. V., Wright, M. J., Hornung, H. G., and Leyva, I., “High enthalpy double-wedge experiments,”

Proceedings of the AIAA Advanced Measurement and Ground Testing Technology Conference

, New Orleans, LA, 1996.

Davis, J. and Sturtevant, B., “Separation length in high-enthalpy shock/boundary layer interaction,”

Phys. Fluids

Vol. 12, No. 10, 2000, pp. 2661–87.

Olejniczak, J., Wright, M. J., and Candler, G. V., “Numerical study of shock interactions on double-wedge geometries,”

Proceedings of the 34th AIAA Aerospace Sciences Meeting

, Reno, NV, 1996.

Edney, B. E., “Effects of Shock impingement on the heat transfer around blunt bodies,”

AIAA Journal

, Vol. 6, No. 1,

1968, pp. 15–21.

Olejniczak, J., Candler, G. V., Wright, M. J., Leyva, I., and Hornung, H. G., “Experimental and Computational study

of high enthalpy double-wedge flows,”

J. Thermophys. and Heat Transfer

, Vol. 13, No. 4, 1999, pp. 431–40.

10 of 12

American Institute of Aeronautics and Astronautics

Downloaded by Benjamin Perez on September 25, 2014 | http://arc.aiaa.org | DOI: 10.2514/6.2012-284

(a) M7

8, N

(b) M7

8, air

Figure 8. Heat transfer profiles for the M7

8 test condition in (a) N

, and (b) air. An overlay of the two profiles is

shown in (c). The green line indicates a laminar flat plate calculation using the work of Simeonides.

11 of 12

American Institute of Aeronautics and Astronautics

Downloaded by Benjamin Perez on September 25, 2014 | http://arc.aiaa.org | DOI: 10.2514/6.2012-284

Stewartson, K. and Williams, P. G., “Self-induced separation,”

Proc. R. Soc. London, Ser. A

, Vol. 312, 1969, pp. 181.

Sychev, V. V., “Asymptotic theory of separation flows,”

Fluid Dynamics

, Vol. 17, 1982, pp. 1179.

Roshko, A., “Free shear layers, base pressure and bluff-body drag,”

Symposium on Developments in Fluid Dynamics and

Aerospace Engineering

, Interline, Bangalore, 1995.

Swantek, A. B. and Austin, J. M., “Separation length scaling in hypervelocity double cone air flows,”

Proceedings of the

28th International Symposium on Shock Waves

, Manchester, England, UK, 2011.

Nompelis, I. and Candler, G. V., “Investigation of hypersonic double-cone flow experiments at high enthalpy in the LENS

facility,”

Proceedings of the 45nd AIAA Aerospace Sciences Meeting

, Reno, NV, 2007.

Nompelis, I., Candler, G. V., MacLean, M., Wadhams, T. P., and Holden, M. S., “Numerical investigation of double-cone

flow experiments with high enthalpy effects,”

Proceedings of the 48rd AIAA Aerospace Sciences Meeting

, Orlando, FL, 2010.

Candler, G. V., Doraiswamy, S., and Kelley, J. D., “The potential role of electronically-excited states in recombining

flows,”

Proceedings of the 48th AIAA Aerospace Sciences Meeting

, Orlando, FL, USA, 2010.

Nompelis, I., Candler, G. V., and Holden, M. S., “Effect of vibrational nonequilibrium on hypersonic double-cone exper-

iments,”

AIAA Journal

, Vol. 41, No. 11, 2003, pp. 2162–9.

Parker, T. and Wakemman, T., “Measuring nitric oxide freestream velocity using quantum cascade lasers at CUBRC,”

Proceedings of the 45th AIAA Aerospace Sciences Meeting

, Reno, NV, USA, 2007.

Dufrene, A., Sharma, M., and Austin, J. M., “Design and characterization of a hypervelocity expansion tube facility,”

Journal of Propulsion and Power

, Vol. 23, No. 6, Nov 2007, pp. 1185–1193.

Flaherty, W., Crafton, J., Elliott, G., and Austin, J. M., “Application of fast pressure sensitive paint in hypervelocity

flow,”

Proceedings of the 49th AIAA Aerospace Sciences Meeting

, Orlando, FL, 2011.

Browne, S., Ziegler, J., and Shepherd, J. E., “Numerical solution methods for shock and detonation jump conditions,”

Tech. rep., California Institute of Technology, Pasanda, Ca, August 2008, GALCIT Report FM2006.006.

Goodwin, D., “An open-source, extensible software suite for CVD process simulation,”

Proc. of CVD XVI and EuroCVD

Fourteen

, 2003, pp. 155–162.

Sanderson, S. R., Austin, J. M., Liang, Z., Pintgen, F., Shepherd, J. E., and Hornung, H. G., “Reactant jetting in

unstable detonation,”

Progress in Aerospace Sciences

, Vol. 46, No. 2-3, 2010, pp. 116–131.

Pintgen, F., Eckett, C. A., Austin, J. M., and Shepherd, J. E., “Direct observations of reaction zone structure in

propagating detonations,”

Combustion and Flame

, Vol. 133, No. 3, 2003, pp. 211–229.

Simeonides, G., “Generalized reference enthalpy formulations and simulations of viscous effects,”

Shock Waves

, Vol. 8,

No. 3, 1998, pp. 161–72.

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