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Computation of Design Sensitivities in Multi-Species Reacting Flows using the Discrete Adjoint Framework in SU2

September 6^th, 2022

Walter Maier

Advisor: Professor Juan Alonso

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The design of hypersonic vehicles

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Exo-atmospheric

Endo-atmospheric

The design of hypersonic vehicls is difficult, slow and expensive.�Computational tools are often either inadequate in predicting physics or too inefficient for large processes.��This is due to the large expanse hypersonic vehicles operated. �We have slow, manuevable and fast ballistic. �Recenlty there has been a renewed interest.�

Traditional aerospace design is not easy, with new methodologies and frameworks being developed to aid the process.�This problem is compounded when it comes to hypersonic vehicle design.�The hypersonic vehicle design space is arguably the one of the largest regimes. varies from “low speed”, highly maneuverable vehicle, to high-speed reentry capsules.

Much work recently in the airbreathing vehicle and boost glide vehicles -Pose different challenges in the design process

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Thermochemical Nonequilibrium Effects

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Adapted from 6. J. Urzay. Hypersonic Aerothermodynamics, Stanford Course Lecture Slides, 2021.

On top the traditional loads we just talked about, we have the high-temperature effects. These include vibrational excitation, dissociation and ionization. Again, all these effects are highly coupled with each other and can significantly alter the shock structure and temperature field.�To complicated matters, these effects are also intrinsically coupled with shock waves and turbulence.

-Unique to the hypersonic environment, are the so-called high-temperature effects or thermochemical nonequilibrium effects.�-As speed temperature rise, more of the effects are activated due to the molecular collisions in the flow.��-1^st We can see thermal nonequilibrium where the energy states within are no longer in equilibrium. �-2^nd higher/faster we start to the see the gases dissociating (O2->2O).�-3^rd even high we have ionization��These effects are highly-coupled, and can drastically impact the shock structure and temperature field around a body. Which will impact the surface heating.�Now we have our noneqilibrium affected surface heating and we have our typical viscous and shock heating effects. Unfortunately these subsets of heating augmentation are also coupled. We are left with a highly-complex and coupled set of physics we need to account for in the design process.

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Stages of Aircraft Design

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	Conceptual Design	Preliminary Design	Detailed Design
Analysis Types
Analysis Fidelity	Low	Medium	High
Cost	Low	Medium	High
Design freedom	High	Medium	Low

Alkaya, Can, Ashish Alex Sam, and Apostolos Pesyridis. "Conceptual advanced transport aircraft design configuration for sustained hypersonic flight." Aerospace 5.3 (2018): 91.

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Stages of Aircraft Design

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	Conceptual Design	Preliminary Design	Detailed Design
Analysis Types
Analysis Fidelity	Low	Medium-Low Medium	High
Cost	Low	High Medium	Very High High
Design freedom	High	Medium-Low Medium	Low

Alkaya, Can, Ashish Alex Sam, and Apostolos Pesyridis. "Conceptual advanced transport aircraft design configuration for sustained hypersonic flight." Aerospace 5.3 (2018): 91.

That is not necessarily the case for hypersonic design. The premilimary design phase is either hampered by computational expensive cfd analyses and optimization runs, or by lack of fidelity by reverting to low-fidelity correlations. This leads to conservative designs and large factors of safety. Due to the limitations and expense of experimental, not much can be used to supplement the analysis.�

While the conceptual design stage remains the same, things begin to change significantly in the medium and high-fidelity range.
The cost of these mid/high analyses are significantly more expensive:�-Computational fluid mechanic suites are slow, and often require very specific mesh types.�-This often necessities' the uses of lower fidelity correlations to supplement fewer medium fidelity solution.�-The low level correlations lead to large safety factors and uncertainties in design
This would be okay if there experimental/test data to supplement this process.�-Ground test facilities (wind tunnels, arcjets and rocket sleds) cannot mimic the hypersonic flow environment in its totality
-Flight testing is prohibitively expensive, often require multiple test vehicles (X51 -> tB52- Rocket)��Overall the process is slow, expensive and cumbersome.

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SU2-NEMO: A framework for hypersonic flow analysis

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SU2- NonEqulibrium MOdels (NEMO)

Robust and accurate simulation tool for hypersonic flow problems
Including necessary physical models:

Multi-species and chemistry
Thermal nonequilibrium, relaxation and excitation processes
Turbulence models, 1-equation and 2-equations models

Flexible code architecture to include varying gas models, hypersonic convective numerical schemes

Use of Mutation++ and native thermochemical libraries
Appropriate boundary conditions

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Thermochemical nonequilibrium

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¹ Park, C. (1989). Assessment of two-temperature kinetic model for ionizing air. Journal of thermophysics and heat transfer, 3(3), 233-244.

Translation

Rotation

Vibration

Electronic

Energy

Now focus on the non-equilibrium models more specifically.��As I briefly mentioned before the high-enthalpy of hypersonic flows presents challenges at the atomic-level. Energy can be stored in 4 unique modes: translational, rotational, vibration and electronic. At low speeds/temperatures we see most energy being stored in the translational and rotational modes. However, as we raised the speeds and temperatures, we see a significant portion of the energy being stored in the electronic and vibrational modes.��To account for these modes, we use a common model in the hypersonic community, Park’s Two-Temperature model. In this model it is assume that the translational and rotational energy modes are in equilibrium with each other, and the vibrational and electronic modes are in equilibrium. Hence our two temperature (Ttr and Tve).��Additionally, if the energy within the atoms is great enough, we will see the mocules dissociate (like the N2 molecule here.) Now the atomic Nitrogen atoms can react with other gas species or recombine at other points in flow.

�All these effects most be taken into account for the proper simulation of hypersonic flow.

(click) In term of CFD, we generallly

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Thermochemical nonequilibrium

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¹ Park, C. (1989). Assessment of two-temperature kinetic model for ionizing air. Journal of thermophysics and heat transfer, 3(3), 233-244.

Translation

Rotation

Vibration

Electronic

Energy

With the code architecture and extension of SU2 out of the way, ill now focus on the non-equilibrium models more specifically.��As I briefly mentioned before the high-enthalpy of hypersonic flows presents challenges at the atomic-level. Energy can be stored in 4 unique modes: translational, rotational, vibration and electronic. At low speeds/temperatures we see most energy being stored in the translational and rotational modes. However, as we raised the speeds and temperatures, we see a significant portion of the energy being stored in the electronic and vibrational modes.��To account for these modes, we use a common model in the hypersonic community, Park’s Two-Temperature model. In this model it is assume that the translational and rotational energy modes are in equilibrium with each other, and the vibrational and electronic modes are in equilibrium. Hence our two temperature (Ttr and Tve).��Additionally, if the energy within the atoms is great enough, we will see the mocules dissociate (like the N2 molecule here.) Now the atomic Nitrogen atoms can react with other gas species or recombine at other points in flow.

�All these effects most be taken into account for the proper simulation of hypersonic flow.

(click) In term of CFD, we generallly

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Extension of standard Navier-Stokes equations

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Extension of standard hydrocode models

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Dissociation/Multi-species

Electronic and Vibrational Effects

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CFD-based design optimization process

Hypersonic flow simulation take significant computational resources

Low-fidelity models used to avoid overhead

Continuous adjoints for hypersonic flow were implemented in SU2¹

Requires derivation of the governing equations
Cannot easily add additional physics/coupling mechanisms

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Discrete Adjoint

¹Copeland, S. R. (2015). A Continuous Adjoint Formulation for Hypersonic Flows in Thermochemical Nonequilibrium. Stanford University.

With the additional physics needed for hypersonic flow simulations, computational time and cost increases. Unfortunately, the design optimization process requires many simulations…..which means a lot more time and resources. To avoid using lower fidelity models to cut back cost, adjoint methods can be used. In previous work, the continuous adjoint was used to perform sensitivity analysis provided significant improved over a finite difference. however this methodology has a few short comings. Most notably the continuous adjoint requires a derivation and implementation of governing equations. This is subject to errors and requires new derivation every time a new model/boundary condition flux scheme is implemented.��This work aims to improved the flexibility/accuracy of such a framework by using the discrete adjoint the thermochemical reacting flows. �

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HTV-2-like boost glide vehicle

NEMO Air-7 gas model, Inviscid

e-, N2, O2, NO, N, O, NO+

Shape parameterization: 3D FFD (120 control points)

Deformations are performed in the spanwise direction

Comparison between discrete adjoint and finite differences for drag sensitivities

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Computational domain with FFD box (red)

Mach
16.5	246.87	246.87	21.96	30.0

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HTV-2-like boost glide vehicle

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HTV-2-like boost glide vehicle

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Drag surface sensitivity

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Mach 8 Viscous Cylinder

5-Species gas model, WBE transport

(N2, O2, NO, N, O)

Determine sensitivity of total heat-flux along body and maximum heat-flux
Shape parameterization: 2D FFD boxes and Hicks-Henne bump functionals.

Deformation in the y-directions

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Mach
8.0	225.15	225.15	805.0	1.78e+06

Computational Domain with FFD box (red)

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Mach 8 Viscous Cylinder

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Temperature Contours

Mach Contours

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Mach 8 Viscous Cylinder

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Conclusions

The SU2-NEMO code suite has been successfully coupled to the discrete-adjoint in SU2.
The discrete adjoint has been applied to both inviscid and viscous 2D/3D problems with various objective functions (lift, drag, heatflux….).
Further testing is needed for the SU2-NEMO coupling to turbulence and discrete adjoint
Work needed to allow for Mutation++ to be used in gradient computation (currently is incompatible with CoDi/MeDi)
In the process of making a SU2-NEMO tutorial

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