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Osney Thermofluids Laboratory Department of Engineering Science

Attitude-Dependent Thermal Flux Estimation in the Slip Regime for Geometric Primitives Towards the Improvement of Destructive Re-entry Simulations Nathan Donaldson, MEng DPhil student, University of Oxford


• Rapid debris demise simulation codes make use of simplified aerothermal models

• Heat flux assessments are often tumble-averaged

• Inaccuracies may manifest in demise estimation as a result

• Also, high fidelity, full trajectory simulations are extremely computationally intensive

Motivation


• Heat flux correlations for common primitives are sometimes used to assess survivability of simplified components during re-entry

• However, a set of correlations for edge heating during stable-attitude descent does not currently exist — random tumbling is favoured

• The application of such correlations would allow attitude dependent temperature history calculations for worst-case heating/stabilisation problems to be performed extremely inexpensively

Motivation


• Rapid assessment codes could hence be updated to produce high resolution results without an appreciable change in simulation duration

• The implementation of dynamic tumbling models could consequently be simplified, such that object stabilisation and tumbling rate could be directly assessed

• A comprehensive series of high fidelity analyses was seen as the first step to developing these correlations.

Motivation


•Geometry definition, meshing and DSMC

•Post-processing and data extraction

•Curve fitting and figure generation

Numerical analysis framework


DSMC


DSMC


DSMC data extraction

Pictured are the data extraction line locations for cuboid and cylinder cases. Side elements are pictured in red, front elements in green.


• Heat flux data were extracted from cells at the four locations shown in the previous slide

• A cubic polynomial surface was fit to the data points using pyeq2, and

coefficients computed • Hence, a relation of the form shown below was found between the

pitch, yaw and incident heat flux of each point analysed

�̇�𝑞 = �̇�𝑞0 𝑎𝑎 + 𝑏𝑏𝛼𝛼 + 𝑐𝑐𝛽𝛽 + 𝑑𝑑𝛼𝛼2 + 𝑓𝑓𝛽𝛽2 + 𝑔𝑔𝛼𝛼3 + ℎ𝛽𝛽3 + 𝑘𝑘𝛽𝛽 + 𝑙𝑙𝛼𝛼2𝛽𝛽 + 𝑚𝑚𝛽𝛽2𝛼𝛼

Cuboid case correlations


Cuboid case correlations

Pictured are the edge data and fitted surfaces for all cuboid cases. Correlations are shown for front and side faces at the edges and corners of

the cuboid.


• Heat flux data were extracted from the ring of cells at the outermost extremity of cylinder’s front face

• An Andrea Prunotto Type A 2D sigmoid surface was fit to the data points

using pyeq2, and coefficients computed • Hence, a relation of the form shown below was found between the pitch

and incident heat flux of each point analysed

�̇�𝑞 = �̇�𝑞0 𝑎𝑎 +𝑏𝑏

1 + 𝑒𝑒𝑐𝑐(𝑑𝑑+ ℎ+𝛼𝛼 +𝑓𝑓 𝑘𝑘+𝜃𝜃 +𝑔𝑔 ℎ+𝛼𝛼 𝑘𝑘+𝜃𝜃 )

Cylinder front face correlation


Cylinder front face correlation

Pictured are the edge data and fitted surfaces for cylinder cases.


• Heat flux data were extracted from the ring of cells at the forwardmost extremity of cylinder’s side face

• A modified 2D sigmoid surface was fit to the data points using pyeq2,

and coefficients computed • Hence, a relation of the form shown below was found between the

pitch, yaw and incident heat flux of each point analysed

�̇�𝑞 = �̇�𝑞0𝑎𝑎

𝑔𝑔 + 𝑏𝑏 𝑐𝑐 − 𝑓𝑓𝛼𝛼 𝑒𝑒 𝑐𝑐−𝑓𝑓𝛼𝛼 𝑛𝑛 + 𝑑𝑑 ℎ − 𝑘𝑘𝜃𝜃 𝑒𝑒 ℎ−𝑘𝑘𝜃𝜃 +𝑙𝑙𝑙𝑙𝜃𝜃𝛼𝛼 + 𝑚𝑚 + 𝑟𝑟

Cylinder side face correlation


Cylinder side face correlation

Pictured are the edge data and fitted surfaces for cylinder cases.


Error relative to local values

Pictured are the relative errors for cylinder correlations. Front and side element correlations are shown from left to right, respectively. The mean

errors for the cuboid and two cylinder correlations were 9.35%, 11.32% and 852.59% respectively (due to small values of normalised heat flux).


Error relative to local maxima

Pictured are the relative errors for cylinder correlations. Front and side element correlations are shown from left to right, respectively. When

normalised to local maxima, mean errors for the cuboid and two cylinder correlations are reduced to 2.08%, 8.58% and 10.80% respectively.


• The correlations may be used trivially as hand calculations in order to make quick, preliminary assessments during a design process

• They are also directly applicable as validation data for aerothermal models

Applying the correlations


• Object-oriented demise codes like DAS, SESAM, and ORSAT can benefit directly from these correlations

• Trends may be applied to primitives, and dimensionalised by multiplying through by the reference heat flux (stagnation at zero incidence)



• Spacecraft-oriented codes such as SCARAB can also benefit

• Computationally inexpensive curvature and shape assessment routines may be utilised to evaluate flat faces, rotational symmetry, and sharp corners

• Correlations may then be applied automatically, and dimensionalised by multiplying through by the reference heat flux (stagnation at zero incidence)



• The reference heat flux may be calculated from freestream conditions using stagnation heat flux correlation such as Detra-Hidalgo, Tauber, or Brandis-Johnston (or indeed the Fay-Riddell expression, which is derived from first principles)

• High resolution heat flux distributions are determined with minimal computational expense – ultimately, only algebraic expressions are employed



• Validation of correlations at different Knudsen numbers

• Modification of correlation equations to reduce peak errors

• Experimental validation using Oxford’s low density wind tunnel (capable of reproducing slip regime flow, Kn ≈ 0.03)

Further work


Questions?

Thank you

[email protected]

Image credit: Thinkstock.com

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