Improvements to the aerothermal modelling of …...Numerical Equations Objects Modelling Results Future plans Experimental Facility LC probes TFG probes Sizes Processing Improvements

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Improvements to the aerothermal modelling ofobject-oriented debris re-entry codes

Numerical and experimental progress

Nathan L. Donaldson

Osney Thermofluids LaboratoryUniversity of Oxford

4th International Workshop on Space Debris Re-entryThursday, 1st March 2018

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Contents

1 Numerical modelling of debris aerodynamicsEngineering level modellingCommon debris objectsMultidimensional correlationCorrelation errorsFuture modelling

2 Experimental studies of thermal fluxesExperimental facilityThermochromatic liquid crystal studiesPlatinum thin film gauge heat transfer probesProbe sizes and gauge arrangementsPost processing of thermal flux data

Nathan L. Donaldson 4th International Workshop on Space Debris Re-entry 1 / 19

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Numerical modelling of debris aerodynamicsEngineering level modelling

RAC (Re-entry Aerodynamic Calculator) is used for analysesStandard multi-regime panel method formulation

Continuum: Modified NewtonianFree molecular: Schaaf & ChambreTransition: Wilmoth

Ma

5 10 15 20 25 30 35

Kn1e-04

1e-021e+00

1e+02

CD

1.41.61.82.02.22.4

(a) Unit cylinder, α = 90o

Ma

5 10 15 20 25 30 35

Kn1e-04

1e-021e+00

1e+02

CD

2.0

2.2

2.4

2.6

2.8

(b) Unit cuboid, α = 90o

Figure 1: Mach-Knudsen surfaces for drag coefficient


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Numerical modelling of debris aerodynamicsCommon debris objects

Triangulated surface meshes of a unit cylinder and cuboid

Different aspect ratios are achieved by scaling along thelongitudinal axis

(a) 1:10 (b) 1:1 (c) 10:1

Figure 2: Cylindrical meshes


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Numerical modelling of debris aerodynamicsCommon debris objects

Triangulated surface meshes of a unit cylinder and cuboid

Different aspect ratios are achieved by scaling along thelongitudinal axis

(a) 1:10 (b) 1:1 (c) 10:1

Figure 2: Cuboidal meshes


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Numerical modelling of debris aerodynamicsMultidimensional correlation

Kriging (1), a modified version of a Gaussian radial basisfunction, is utilised for correlative modelling

Models are currently trained with calculations performedusing RAC, but may be trained with data from any source(CFD, DSMC, experiments, etc.)

A single model is used for each aerodynamic coefficient

Prediction time varies depending on the complexity of themodel

Number of training pointsNumber of dimensions

ψ(i) = exp

− k∑j=1

θj |x(i)j − xj |pj

(1)


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Numerical modelling of debris aerodynamicsMultidimensional correlation

Two different types of Kriging models are being explored:

Pure models, wherein a single model with a high numberof training points is used for each aerodynamic coefficientAugmented models, wherein the Mach-Knudsen surface ismodelled for each coefficient using a set of analyticalexpressions. The parameters of these surfaces are thencorrelated using a series of smaller Kriging models.

Augmented models have been shown to have higheraccuracy for a lower training point count

Pure Kriging models are faster to evaluate (very useful ifthey are to be queried as part of a Monte Carlo calculation)

Results presented today are produced using augmentedmodels (pure models are still undergoing training)


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Numerical modelling of debris aerodynamicsCorrelation errors

Cylindrical modelsare trained on 4parameters

Mach, MaKnudsen, KnPitch, αAspect, L

�A vector transformis used to convertEuler angles to asingle equivalentpitch

Absolute errorshave been shownto be < 6%

5101520253035

= 0o = 15o

5101520253035

= 30o = 45o

5101520253035

= 60o = 75o

10 5 10 3 10 1 101 1035

101520253035

= 90o

10 5 10 3 10 1 101 103

Mean

0.0 0.2 0.4 0.6 0.8 1.0Knudsen number Kn

0.0

0.2

0.4

0.6

0.8

1.0

Mac

h nu

mbe

r Ma

0.000

0.123

0.245

0.368

0.491

0.613

0.736

0.859

0.981

1.104

1.227

1.349

1.472

1.595

1.717

1.840

1.963

2.085

2.208

2.331

Erro

r (%

)

Figure 3: CD errors for L� = 1


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5101520253035

= 0o = 15o

5101520253035

= 30o = 45o

5101520253035

= 60o = 75o

10 5 10 3 10 1 101 1035

101520253035

= 90o

10 5 10 3 10 1 101 103

Mean


0.0

0.2

0.4

0.6

0.8

1.0

Mac

h nu

mbe

r Ma

0.000

0.170

0.339

0.509

0.678

0.848

1.017

1.187

1.357

1.526

1.696

1.865

2.035

2.204

2.374

2.543

2.713

2.883

3.052

3.222

Erro

r (%

)



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5101520253035

= 0o = 15o

5101520253035

= 30o = 45o

5101520253035

= 60o = 75o

10 5 10 3 10 1 101 1035

101520253035

= 90o

10 5 10 3 10 1 101 103

Mean


0.0

0.2

0.4

0.6

0.8

1.0

Mac

h nu

mbe

r Ma

0.000

0.308

0.616

0.925

1.233

1.541

1.849

2.158

2.466

2.774

3.082

3.391

3.699

4.007

4.315

4.623

4.932

5.240

5.548

5.856

Erro

r (%

)



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Cuboidal models are the most complex, and are trained on6 parameters:

Mach, MaKnudsen, KnPitch, αYaw, θRoll, βAspect, L

�


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10 5

10 1

103

= 0.00o,= 0.00o

= 7.50o,= 0.00o

= 15.00o,= 0.00o

= 22.50o,= 0.00o

= 30.00o,= 0.00o

= 37.50o,= 0.00o

= 45.00o,= 0.00o

10 5

10 1

103

= 7.50o,= 7.50o

= 15.00o,= 7.50o

= 22.50o,= 7.50o

= 30.00o,= 7.50o

= 37.50o,= 7.50o

= 45.00o,= 7.50o

= 15.00o,= 15.00o

10 5

10 1

103

= 22.50o,= 15.00o

= 30.00o,= 15.00o

= 37.50o,= 15.00o

= 45.00o,= 15.00o

= 22.50o,= 22.50o

= 30.00o,= 22.50o

= 37.50o,= 22.50o

10 20 3010 5

10 1

103

= 45.00o,= 22.50o

10 20 30

= 30.00o,= 30.00o

10 20 30

= 37.50o,= 30.00o

10 20 30

= 45.00o,= 30.00o

10 20 30

= 37.50o,= 37.50o

10 20 30

= 45.00o,= 37.50o

10 20 30

= 45.00o,= 45.00o

0.0 0.2 0.4 0.6 0.8 1.0Mach number Ma

0.0

0.2

0.4

0.6

0.8

1.0Kn

udse

n nu

mbe

r Kn

0.000

0.415

0.829

1.244

1.658

2.073

2.487

2.902

3.317

3.731

4.146

4.560

4.975

5.389

5.804

6.218

6.633

7.047

7.462

7.876

Erro

r (%

)



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10 5

10 1

103

= 0.00o,= 0.00o

= 15.00o,= 0.00o

= 30.00o,= 0.00o

= 45.00o,= 0.00o

= 60.00o,= 0.00o

= 75.00o,= 0.00o

= 90.00o,= 0.00o

10 5

10 1

103

= 15.00o,= 15.00o

= 30.00o,= 15.00o

= 45.00o,= 15.00o

= 60.00o,= 15.00o

= 75.00o,= 15.00o

= 90.00o,= 15.00o

= 30.00o,= 30.00o

10 5

10 1

103

= 45.00o,= 30.00o

= 60.00o,= 30.00o

= 75.00o,= 30.00o

= 90.00o,= 30.00o

= 45.00o,= 45.00o

= 60.00o,= 45.00o

= 75.00o,= 45.00o

10 20 3010 5

10 1

103

= 90.00o,= 45.00o

10 20 30

= 60.00o,= 60.00o

10 20 30

= 75.00o,= 60.00o

10 20 30

= 90.00o,= 60.00o

10 20 30

= 75.00o,= 75.00o

10 20 30

= 90.00o,= 75.00o

10 20 30

= 90.00o,= 90.00o

0.0 0.2 0.4 0.6 0.8 1.0Mach number Ma

0.0

0.2

0.4

0.6

0.8

1.0Kn

udse

n nu

mbe

r Kn

0.000

0.509

1.018

1.527

2.036

2.544

3.053

3.562

4.071

4.580

5.089

5.598

6.107

6.615

7.124

7.633

8.142

8.651

9.160

9.669

Erro

r (%

)



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10 5

10 1

103

= 0.00o,= 0.00o

= 15.00o,= 0.00o

= 30.00o,= 0.00o

= 45.00o,= 0.00o

= 60.00o,= 0.00o

= 75.00o,= 0.00o

= 90.00o,= 0.00o

10 5

10 1

103

= 15.00o,= 15.00o

= 30.00o,= 15.00o

= 45.00o,= 15.00o

= 60.00o,= 15.00o

= 75.00o,= 15.00o

= 90.00o,= 15.00o

= 30.00o,= 30.00o

10 5

10 1

103

= 45.00o,= 30.00o

= 60.00o,= 30.00o

= 75.00o,= 30.00o

= 90.00o,= 30.00o

= 45.00o,= 45.00o

= 60.00o,= 45.00o

= 75.00o,= 45.00o

10 20 3010 5

10 1

103

= 90.00o,= 45.00o

10 20 30

= 60.00o,= 60.00o

10 20 30

= 75.00o,= 60.00o

10 20 30

= 90.00o,= 60.00o

10 20 30

= 75.00o,= 75.00o

10 20 30

= 90.00o,= 75.00o

10 20 30

= 90.00o,= 90.00o

0.0 0.2 0.4 0.6 0.8 1.0Mach number Ma

0.0

0.2

0.4

0.6

0.8

1.0Kn

udse

n nu

mbe

r Kn

0.00

0.61

1.22

1.83

2.43

3.04

3.65

4.26

4.87

5.48

6.09

6.69

7.30

7.91

8.52

9.13

9.74

10.35

10.95

11.56

Erro

r (%

)



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Numerical modelling of debris aerodynamicsFuture modelling

Both augmented and pure Kriging models of a simplifiedATV geometry are planned

These will be trained on variances in pitch, α and yaw, θ

Y

Z

X

Figure 5: Surface mesh of a simplified ATV geometry


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Experimental studies of thermal fluxesExperimental facility

The experimentalfacility being used isthe Oxford LowDensity Wind Tunnel(LDWT)

3 stage continuousvacuum pumpingsystem (22000 l/s)

Knudsen numbers ofthe order of ∼ 0.001(slip regime)

Mach numbersranging from 3− 10

Figure 6: The low density wind tunnel(LDWT)


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Working gas (air or nitrogen) is heated in an insulatedstagnation chamberThe gas is then expanded through a contoured Mach 6nozzle into the test sectionAutomated traverses control model position, and flowinitialisation

Figure 7: LDWT test section diagram


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The LDWT iscurrentlyundergoingcharacterisa-tion activitiesfollowing anextensiverenovation

These are setto concludewithin thenext fewweeks

Figure 8: Total pressure pitot survey in theMach 6 plume


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Experimental studies of thermal fluxesThermochromatic liquid crystal studies

Thermochromatic liquidcrystal studies have been usedat Osney for decades

Current probes have beenmanufactured from Rohacell

Three crystal solutions havebeen applied, with transitiontemperatures: 25oC , 30oC ,and 35oC

Figure 9: Hemisphere LCprobe undergoing atemperature change


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Experimental studies of thermal fluxesPlatinum thin film gauge heat transfer probes

Thin film gauge probesare manufactured usingMacor glass ceramic

Originally, gauges werepainted onto thesubstrate by hand

This arrangement led totransverse conductionissues inside thesubstrate, skewingthermal readings

Figure 10: Original platinum paintTFG probe


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Experimental studies of thermal fluxesPlatinum thin film gauge heat transfer probes

The new design utilisesprecision printed gauges(details are accuratedown to 5 µm)

Gauges are sputteredusing a vacuumdeposition process

Gauges are double-sidedwith a sheet of kaptonbetween the twoplatinum layers,removing dependenceon the substrateproperties

Figure 10: New sputtered TFG probe


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Experimental studies of thermal fluxesProbe sizes and gauge arrangements

9 LC probes have been manufactured

3 shapes (hemisphere, cylinder, cuboid)3 sizes (�10 mm, �15 mm, �20 mm)

12 TFG probes have been manufactured

2 shapes (cylinder, cuboid)3 sizes (�10 mm, �15 mm, �20 mm)2 probe arrangements (line over corner, line around edges)

Differing sizes allow various Knudsen numbers to beexamined without altering the freestream conditions


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Experimental studies of thermal fluxesPost processing of thermal flux data

Constant current is applied to gauges from an amplifier

Voltage changes are recorded as gauge temperatures change

Calibration curves allow accurate conversion of change involtage to change in temperature

0 2 4 6 8 10 12 14 16 180

1

2

3

4

5

6

7

Tempera

ture

rise,∆T(K

)

T ime, t(s)

Gauge 1Gauge 2Gauge 3

Figure 11: Typical temperature rise profile for thin film gauges


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An impulse response filter is designed based upon thesampling frequency of the gauge dataTemperature profiles are then processed through this filter,producing a heat flux profileDouble-sided gauges remove all dependence on substrateproperties

0 2 4 6 8 10 12 14 16 18−500

0

500

1000

1500

2000

2500

3000

Heatflux,q̇(W m

2)

T ime, t(s)

Gauge 1Gauge 2Gauge 3

Figure 11: Typical heat flux profile for thin film gauges


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Thermochromatic surveys are processed in a similar fashion

Experimental runs are recorded visually using standard CCDor CMOS cameras

An in-house code is used to analyse the colour changesagainst time

A similar impulse response method is then used to convertthese temperature changes into heat flux distributions


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Conclusions

Multidimensional correlative models are being generated forsome common debris shapes

These have been shown to have good accuracy and low runtimes

They may be trained with cheap or expensive data (or anycombination thereof)

Experimental facility characterisation is almost completefollowing an extensive refit

Experimental probes have been manufactured and arecurrently being assembled and tested


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Improvements to the aerothermal modelling of …...Numerical Equations Objects Modelling Results Future plans Experimental Facility LC probes TFG probes Sizes Processing Improvements